types of nouns radian condensation evaporation fractions ecology prehistoric man middle age growth mindset fixed mindset solar system states of matter multiplication world war i world war ii ancient rome earth in the solar system personal budgeting newton's laws of motion ancient greece american revolution human anatomy organ systems indus valley civilization harappan civilization byzantine empire eastern roman empire byzantium composition of earth's moon weather galaxies trigonometry work etiquette interview etiquette force motion velocity acceleration mass gravity asteroids erosion industrial revolution fossils student etiquette decimals latitude longitude bronze age friendship relationships planets conversational etiquette situational etiquette empathy budgeting continents stone age basic cooking book reports types of landforms types of forests research reports food chain components of ecosystem earth's hemispheres comparing fraction equivalent fraction compilers user interface design software development kits biomes adding fractions waves properties of waves wave behavior heat thermometers applications syntax comparing quantities creative arts estimate area algebraic fractions rocks microorganisms multiplication of large numbers addition verbs types of adjectives whole numbers percentage binary operations clouds conservation of energy subtraction integers water cycle minerals exponents climate ratio converting decimals to fractions converting repeating decimals to fractions angle measurement distributivity dividing fractions circle cube square root inverse trigonometric functions embryo convection composition of earth geometric shapes momentum punctuation atmosphere radiation taxonomy sexual reproduction in flowering plants three laws of thermodynamics magnetism electricity fetus internet caves law listening logarithms volume mountains valleys mechanics of plants mindset multiplying fractions narrative natural numbers origin of the universe subtracting large numbers subtracting two digit numbers subtracting three digit numbers practical applications of trigonometry properties of polygons reasoning polar regions desert relevant evidence reproduction sampling speaking middle age great depression algebra stories with characters stories with beginning and end subtracting fractions temperature trust types of numbers scientific method variable manipulation weight writing a summary writing with transitions energy forms of energy standard deviation polar coordinates statistical significance earthquakes matrices leadership accounting scientific notation structure of animals reducing fractions matrix operations volcanoes tectonic structure measurement improper fraction atmospheric pressure division elements reciprocal motivation mixed fraction mixed numbers dividing large numbers human rights political systems muscular system least common multiple lowest common multiple greatest common divisor greatest common measure greatest common factor highest common factor highest common divisor writing genres literary genres storms computers allotropism allotropy periodic table complex fraction compound fractions carbon cycle oxygen cycle nitrogen cycle bullying renaissance cell membranes cytoplasmic membrane plasma membrane cell transport nutrient cycle genetics dna genes metabolism inheritance chromosomes cartesian coordinates enzymatic regulation trade winds machine skeletal system circulatory system chemical reactions chemical equations origin of species isotopes urinary system nose eye tongue ear weather forecasting geochronology skin acid digestive system mineralogy geochemistry meteorites respiratory system endocrine system international relations civil wars terrorism electoral system political parties civil society excretory system osmosis diffusion bases mixture models of democracy realism and neorealism idealism liberalism nationalism anarchism voting behavior expansion of the universe eclipse international law milky way night sky space exploration immune system integumentary system comets e-commerce cell theory coriolis effect probability cell division carbohydrates social cognition depression gender roles artificial intelligence bioinformatics urbanization child abuse statistical regression lipids amino acids iron age nucleic acids cellular organization basic cooking terms enzymes cold war religion slavery carbon-14 dating ideology torque salts derivatives lenses floating sinking archimedes' principle cells and simple circuits cathode rays and cathode ray tubes electrostatics fluid flow equilibrium and center of gravity integrals forestry wildlife tourism fishing land reclamation land rehabilitation vitamins minerals in nutrition trade industry folding faulting proteins structure of plants neuron division of labor french revolution soils glaciation glaciers set theory marxism market equilibrium combustion economic systems social movements venn diagram simple interest shapes human wants production sense organs compound interest home trade entrepreneurship teeth graphical representation of data history prehistory egyptian pyramids business environment algebraic expression pharaohs music business insurance musical instruments business transactions product promotion warehousing inflation global warming business cycle formulae algebraic formulas classical music gas laws sleep psychology insurance compounds molecules theater natural selection and adaptation memory theories animal groups algebraic factorisation liberty pollution memory process agriculture limits continuity factors influencing agriculture soil factors edaphic factors soil constituents land preparation linear equations even numbers odd numbers cardinal numbers ordinal numbers crop propagation photosynthesis types of accounting ratios recombinant proteins anthropology converting degree to radian converting radian to degree planting sentence nursery practices successor predecessor visual arts performing arts trigonometric functions elements of art painting techniques plant nutrients soil fertility organic manures co-operatives health diseases henri fayol’s principles of management concept of financial markets forms of market competition consumer theory parastatals order of operations comparing numbers nouns cost benefit analysis crop pests pest control measures united nations inorganic fertilizers land tenure adjectives length measurement divisibility rules human body basic needs atom sentence structure days of the week weather types time measurement transportation ancient egypt mendelian inheritance antonyms clock seasons doubling numbers halving numbers physical change chemical change language living things non-living things earth adding decimals plants months home habitats counting flowering plants water classification of plant kingdom kingdom plantae classification members of kingdom plantae decimals in expanded form non-flowering plants kinematics one-dimensional kinematics matter roman numerals grammar chemistry properties of matter earth's movements eating habits of animals sources of food geology ecological relationships macromolecules types of plants astronomy time duration civilization human life cycle ancient history pythagoras' theorem food from plants cell blood ancient mesopotamia ancient china reproduction of animals adaptations of animals components of food calendar agricultural economics forage crops neolithic revolution early african civilizations arctic ocean elasticity calendar math nutrients grazing systems subtracting decimals multiplying decimals parts of speech dividing decimals biology factors and multiples ancient greek philosophy atlantic ocean animals emission and transmission of light antarctica organism primary industries rectilinear propagation of light life cycle geography liquid measurement africa secondary industries food plane mirror reflection allergy caspian sea arithmetic progression landforms forests air anesthesia anatomy addiction bacteria air pollution water pollution geometric progression constitution biochemistry algae spherical mirror convex mirror concave mirror economics brain biotechnology alps biomolecules blood disorders angles asthma amazon rainforest permutation archaeology art movements refraction asia climate change calculus nato quadratic equations light graphs of simultaneous linear equation nervous system dispersion of light area perimeter fertilization arc and segment tangent gas macronutrients solids averages insects liquids natural disasters psychology materials family paper ecosystem sound plastic philosophy microeconomics characteristics of sound glass ceramics tertiary industries europe socialism gastronomy politics rubber big bang slope of a straight line section formula intercept form of a straight line environment mythology celestial objects influence oxygen metals substances mental health culture quadrilaterals parallelogram carbon dioxide electrovalent bond covalent bond physics electrical energy chemical properties of metal extraction of metal textile grains sugar viruses time and work vaccines medications diabetes profit and loss stroke heat transfer intelligence obesity nutrition influenza recycling heat expansion poetry pregnancy conduction menstrual cycle menstruation literature triangle antibiotics energy resources cancer oral tradition heat capacity micronutrients social studies similarity in triangles ancient india hydropower solar energy democracy hormones sun congruence of triangles government managing money international monetary fund world health organization change in state of matter capitalism architecture tourism wildlife legal judgment exercise australia hygiene gross domestic product theorems on triangles wood north america fluids south america drama oceania arctic grassland sahara museum judgment maps geographic maps grand canyon rocky mountains fungus anorexia fire vegetable fruit business organizations public corporations spice private limited companies partnerships public companies parasites drug microscope first aid sole proprietorship cardiopulmonary resuscitation malaria fire safety reading comprehension memory human migration pneumonia electromagnetism island globalization infection commutative hospital river associative metallurgy infrastructure smallpox satellite injury orbit colors numbers sanitation monarchy crime media world trade organization civil engineering surgery tuberculosis common cold education rational numbers place value relations infinite series speed parity properties of parallelogram number system abolitionism abiogenesis late modern period social issues art abuse sociology maltreatment linear motion accessories assets achaemenid empire financial assets first civilizations finance chemical bonding arithmetic mathematics large numbers alcoholism smoking words aesthetics financial literacy language arts nile lake victoria scramble for africa afterlife death age of discovery age of enlightenment colonialism early modern period european history philosophical movements agrarian revolution aggression agrarian revolution in britain pests agronomy crop diseases horticulture crop production development of early agriculture agroforestry domestication farm accounts agricultural marketing earth science lungs resources jet engine drink solving for variables organic chemistry bronze political ideology american history political science cardiovascular system lymphatic system liver confucianism western philosophy sumer gupta empire assyria silk road han dynasty mesoamerica andean civilizations roman empire maya civilization andes zoology environmental issues livestock health life sciences dairy products meat hunting eating disorders antioxidants vocabulary synonyms software computer science electrochemistry great wall of china construction sea prehistoric art modernism romanticism technology data ganges asexual reproduction yangtze himalayas association football supernova space science entertainment auroras northern lights universe earth sky cosmology black hole mediterranean sea biosphere snow meteorology latent heat of vaporization pressure relative mass thermal conduction mole nuclear fusion physical chemistry quantitative data aztecs post-classical history oxidation numbers subatomic particle money cooking life skills poverty epistemology tradition scientific theories programming binary and machine language biodiversity species sexual reproduction physiology genetic engineering birth control black death cardiovascular disease epidemic heart body mass index bodies of water nature library comics writing mental disorder broadcasting british empire television management buildings engineering farm structures bulimia self-development discrimination soft skills public limited companies company corporation trade union commerce demand camera game lake display technology magnetic field vacuum types of caves cathode ray tubes electric current energy cycle electric battery chocolate reformation society war conflict clothing vocabulary space race decolonization mail interview conflict resolution web communication programming languages plate tectonics comprehension reading computer networks source code control digital literacy robotics consciousness mathematical constants dictatorship dam contemporary philosophy viking age ottoman empire mongol empire mughal empire soviet union middle east thermal energy etiquette safety crusades social behavior myths folklore ethnic group week day dance suicide forms of government medicine dentistry feelings diet nutritional supplements eating habits numeracy diplomacy social media disability mobile phone malnutrition distance hiv electric potential early african civlizations early agriculture in egypt early agriculture in mesopotamia scientific revolution frigid zones european colonization of the americas history of earth oceanography hydrology species interactions market structure employment macroeconomics investing learning skills women's suffrage mechanical engineering electric motor electromagnetic radiation electric field patterns speed of light electronic medium laser stability of isotopes and elements saturn emotional intelligence empire wind power thermal properties of matter renewable energy human activities martial arts gambling swimming video game olympic games static equilibrium european union indigenous peoples medieval history international organizations existence metaphysics fairy tale exploitation marriage farm tools and equipment fascism parenting personality novel feminism film outdoor activities rain folk music food irradiation food safety organic food weak interaction strong interaction vegetarianism standard model free will peace fortification furniture man woman human sexuality genocide sexual orientation heredity travel polygons ice age global affairs prayer manufacturing pacific ocean theory of relativity great lakes linguistics medical imaging quantity of heat us history holy roman empire puberty people prejudice social equality journalism news international red cross and red crescent movement international politics jazz prose stories mars negative numbers mode variables mathematical formulas meditation mercury military musical movements singing pop music rock music opera national integration navigation number line new religious movement neuroscience printing paleontology social class percentile philosophy of science uranus tang dynasty types of radiation types of radioactivity venus soul science theories world soil conservation tropical cyclone spaceflight year urbanisation water conservation factorial human needs humanitarianism cardinal directions compas time financial markets expenses united states dividing by powers of 10 experiments american colonial period spanish colonial period martial law basic concepts of economics human skeleton subset density h2o australian outback newton's first law gobi southern ocean mojave desert global water cycle baltic sea conservation strategies congo rainforest simple machines taiga geographic information systems compass and navigation caribbean sea sound waves demography soil composition tsunamis cultural landscape cultural geography rock cycle pampas savannas hardware components of computer computer architecture digital communication operating system geological time scale cyber security algorithm server firewalls client server architecture electronic configuration key signatures international trade music theory music history music technology music and culture music and society river system of the world great plains melting software application memory management and storage software methodology central processing unit database management system database system security computer ethics computer malware software engineering political geography downs version control system wi-fi data security acceleration due to gravity classification post war reconstruction and rehabilitation of europe the martial plan the cold war data modeling data encryption adding large numbers data handling ocean copper linear equation in graph financial statements binary population interactions market retail capacitance optics markup languages shares small area estimation digital safety light waves the office modern history degrees human behaviour conic sections statistics geometry abortion reproductive system abstract art business animal husbandry aids violence livestock production ageing clothes farming agrarian revolution in the united states of america fashion farm records sensitive production economics amazon river aluminium revolution tornado carbon alloy vascular system ventilatory system sexually transmitted infection genital system alkynes alcoholic drink pre-columbian era alkanols wine steel respiratory apparatus fluid dynamics space combined gas law buoyancy applications of electrolysis fuel cells fossil fuel structures social science realism astronomical events sport economy milk regions archeology polar lights nitrogen telescope jupiter molecular formula phosphorus cycle iron silver silicon morality chemical compounds electrons detergents god conservatism hunger famine truth biological data analysis economic depression plant processes botany biogeochemical cycle books informatics tree identity elements weight loss radio molecular biology biological processes biological systems supply business administration business units garden plants caffeine cellular biology composition of blood calligraphy bread mass media bridge plant physiology natural resources geographical zones canal classical mechanics mechanics laws of conservation of energy conservation of mass communication explosive conversation photography charle's law cartography coal information internal combustion engine inorganic chemistry circuits stoichiometry electrolytes means of communication molar solutions electrochemical cell eukaryote services goods vacuum tubes coordinate geometry pottery charts telecommunication cryptography card game coffee emotions land power early human migrations knowledge mind gastroenteritis food intolerance festival consumer behavior weeds and weed control stock market dental diseases symmetry popular culture ungrouped data contamination coordinate geometry in 3-dimensions masonry emergency counting forms extinction natural gas latent heat of fusion electric field flood tectonic forces steam engine electric light thermodynamics mains electricity nuclear power gunpowder length tax geophysics tea drawing elements of life documents sexism inca empire rocket racism petroleum food preservation good and evil standard conditions natural environment mensuration genres hurricane gender environmentalism stability music genres fluid mechanics ontology welfare epic poetry fiction jewellery nutrition labeling short story fuel general toy gasoline mississippi river median historical events particle physics mean privacy justice mining police shadows metric space volumetric analysis wheel migration orchestra publishing imperialism great barrier reef sculpture islamic golden age theocracy telephone population neptune solution inertia particles wind energy radar computer languages cellulose ritual lithosphere spirituality dinosaurs raw materials direction national unity heritage multiplying by powers of 10 winds japanese colonial period article climate zones observational astronomy newton's third law friction newton's second law neighborhood geography temperate forest machine learning file extension electric circuit work energy conversion website search engines phishing networking protocols hydrocarbons atomic mass and number respiration concentration of solution plant and animal tissue the particulate nature of matter rhythm time signatures tempo types of chemical reactions nomenclature in organic chemistry ensemble music industry electronic music molecular structure digital art coral sea boiling sublimation freezing software design laboratory safety files and folders flowchart steppes file system management balancing chemical equation ethernet prairies plains avogadro's number stoichiometric calculations carboxylic acids ethers functional groups process of respiration national perspective of different nation process management data structure gas stoichiometry math operations cube root bodmas rule roots radioactivity isomerism radioactive decay differential equations human euclidean vectors boyle's law quantum mechanics alkenes acid-base reaction catalysis alkanes evolution life state culinary theory of demand and supply price currency rotation plane figures solid shapes grouped data vectors natural sciences bank solubility hydrogen interest rounding descriptive statistics displacement inverse elements graham's law prealgebra constants properties of circle chemical symbols parabolas nuclear reactions functions belief solving linear equation with two variables coordinate system science food allergies cathode rays organic substances redox reactions polymers aldehydes current electricity simultaneous equations human evolution stars space station great pyramid of giza organization nation grasslands marketing engine alcohols elasticity power profit and loss reflection bearing and distance hydrogen peroxide linear inequality moon square square equations sequence and series vehicle school indian ocean eastern philosophy gold medieval europe nuclear fission line separation of mixture combination experimental design pronoun adverb voting and majority rule in us ocean current political philosophies and their impact on the united states constitution english role of media in politics civics levels and branches of the us government foundational principles of the us government structure and authority of the us judicial system federalism the us presidency data collection and analysis us constitution individual rights and responsibilities of us citizens the roles of various us governmental departments and agencies figure of speech us state government political parties in the us bill of rights us constitutional amendments civil rights in the united states civil rights movement in the united states contribution of minorities in the united states the women's rights movement in the us the united states in world war ii the united states in world war i government budget and economy game theory monopoly scarcity introduction to index number non-price competition statistical tools and interpretation correlation deflation immigration and emigration inflation types population trends slavery in the united states the mayflower compact nato and us role nation and states historic influence of the magna carta the revolutionary era impact of september 11 on the united states the holocaust us relations with middle east us isolationism and neutrality japanese internment in the us imperialism and nationalism in us history the russian revolution and its impact on the us the treaty of versailles and the us urban and rural societies credit and debt notable historic societies the role of us government in regulating business practices income economics and war supply and demand types of economic systems opportunity cost components of national income fiscal policy keynesian and classical models monetary policy production possibility frontier trade and exchange rates circular flow of income role of economic institutions monetary policy and the federal reserve in us economic relationships and operations production possibilities curve resource allocation surplus and shortage oligopoly price elasticity product differentiation cartels perfect competition labor markets income distribution labor market and wage determination economic indicators types of unemployment balanced surplus and deficit budget foreign exchange rate forms of market and price determination national income economic sectors revenue economic measurements interest rates unemployment 20th-century philosophy primitive and non-primitive control structures functions and modular programming defining functions return values array and linked lists operations on data structure table relational models secure online behavior local area network wide area network internet protocol domain name system web development cascading style sheets application of artificial intelligence ethical considerations in artificial intelligence data privacy intellectual property netiquette software development life cycle software deployment software implementation software testing cloud computing cloud types mobile application development embedded systems internet of things data types parameters microcontrollers software requirements web browser applied ethics bioethics ethical foundations ethics ethics and moral philosophy medical ethics the ethics of artificial intelligence the scientific method and philosophy the philosophy of historical determinism social philosophy political philosophy philosophy of virtual reality and simulation philosophy of technology philosophy of religion philosophy of mind philosophy of language philosophy of history philosophy of art and beauty medieval philosophy history of philosophy environmental philosophy early modern philosophy branches of philosophy applied philosophy ancient philosophy african philosophy and culture 19th-century philosophy logic and critical thinking deductive and inductive reasoning cognitive biases and logical traps logical fallacies syllogisms and propositional logic rationalism and empiricism tension between faith and rationality ethical theories theories of aesthetic judgment theories of consciousness theories of government theories of truth perception and reality personal identity and the self moral relativism and moral absolutism social justice and inequality art and morality freedom and responsibility the mind-body problem political philosophy absurdism and nihilism philosophy of law and justice theories of mind language and reality justice and human rights religious pluralism and tolerance the nature of meaning and reference philosophical inquiry into god’s existence social contract theory lines and planes in 3d skepticism and sources of knowledge translations the role of power and privilege in society argument structure and evaluation the problem of universals free will and determinism the hard problem of consciousness power structures and legitimacy the concept of art science and its philosophical foundations falsifiability and scientific revolutions existentialism and human condition the role of interpretation in history impact of technology on human relationships rights and duties comparing political systems subjective and objective views of beauty distinguishing science from pseudoscience existentialist thinkers non-western philosophical traditions indigenous philosophical perspectives critical thinking and argumentation the nature of historical knowledge structured query language introduction to equation adding single digit numbers adding two digit numbers connecting addition subtraction and properties of operations partitioning shapes into equal parts associative and commutative property of addition comparing whole numbers less than 100 exploring number relationships through addition and subtraction comparing and ordering lengths understanding and solving addition and subtraction statements identifying sides of equations how plants and animals use their body parts signals and responses in animal families patterns in young and parent plants and animals day and night sky patterns movements that create sound effects of materials on light communicating with light and sound matching nouns and verbs in sentences using past present and future words in sentences understanding words with prefixes and suffixes noticing word meanings that are close but not the same patterns of daylight across seasons using common and proper nouns replacing nouns with personal and possessive pronouns types of sentences using clues to understand new words root words and how they change naming and describing with word categories light sources and visibility showing ownership with possessive nouns hypertext markup language mobile frameworks javascript 3-dimensional figures ascii test Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), counterclaims, reasons, and evidence. Develop the topic with relevant facts, definitions, concrete details, quotations, or other information and examples. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. Construct an explanation based on evidence for how geoscience processes have changed Earth's surface at varying time and spatial scales. Develop a model to describe the cycling of Earth's materials and the flow of energy that drives this process. Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary). Rewrite expressions involving radicals and rational exponents using the properties of exponents. Provide a concluding statement or section that follows from and supports the information or explanation presented (e.g., articulating implications or the significance of the topic). Use precise words and phrases, telling details, and sensory language to convey a vivid picture of the experiences, events, setting, and/or characters. The Universe and Its Stars: The star called the sun is changing and will burn out over a life span of approximately 10 billion years. The sun is just one of more than 200 billion stars in the Milky Way galaxy, and the Milky Way is just one of hundreds of billions of galaxies in the universe. The study of stars’ light spectra and brightness is used to identify compositional elements of stars, their movements, and their distances from Earth. The Big Bang theory is supported by observations of distant galaxies receding from our own, of the measured composition of stars and non-stellar gases, and of the maps of spectra of the primordial radiation (cosmic microwave background) that still fills the universe. Other than the hydrogen and helium formed at the time of the Big Bang, nuclear fusion within stars produces all atomic nuclei lighter than and including iron, and the process releases electromagnetic energy. Heavier elements are produced when certain massive stars achieve a supernova stage and explode. Plate tectonics is the unifying theory that explains the past and current movements of the rocks at Earth’s surface and provides a framework for understanding its geologic history. All Earth processes are the result of energy flowing and matter cycling within and among the planet’s systems. This energy is derived from the sun and Earth’s hot interior. The energy that flows and matter that cycles produce chemical and physical changes in Earth’s materials and living organisms. Support claim(s) with logical reasoning and relevant evidence, using accurate, credible sources and demonstrating an understanding of the topic or text. Weather and Climate: The foundation for Earth’s global climate systems is the electromagnetic radiation from the sun, as well as its reflection, absorption, storage, and redistribution among the atmosphere, ocean, and land systems, and this energy’s re-radiation into space. Gradual atmospheric changes were due to plants and other organisms that captured carbon dioxide and released oxygen. Changes in the atmosphere due to human activity have increased carbon dioxide concentrations and thus affect climate. Current models predict that, although future regional climate changes will be complex and varied, average global temperatures will continue to rise. The outcomes predicted by global climate models strongly depend on the amounts of human-generated greenhouse gases added to the atmosphere each year and by the ways in which these gases are absorbed by the ocean and biosphere Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. Human Impacts on Earth’s Systems: The sustainability of human societies and the biodiversity that supports them requires responsible management of natural resources. Scientists and engineers can make major contributions by developing technologies that produce less pollution and waste and that preclude ecosystem degradation. Solve quadratic equations with real coefficients that have complex solutions. Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = - 3, 6 + 6 = . Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. 10 can be thought of as a bundle of ten ones — called a "ten." Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Order three objects by length; compare the lengths of two objects indirectly by using a third object. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. Tell and write time in hours and half-hours using analog and digital clocks. Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. Know there is a complex number i such that i² = -1, and every complex number has the form a + bi with a and b real. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π-x, π+x, and 2π-x in terms of their values for x, where x is any real number. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. Extend polynomial identities to the complex numbers. For example, rewrite x² + 4 as (x + 2i)(x - 2i). Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy). Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Interpret parts of an expression, such as terms, factors, and coefficients. Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle. Rewrite simple rational expressions in different forms; write a(x /b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle. Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. Informally assess the fit of a function by plotting and analyzing residuals. Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model? Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast-food restaurant. Distinguish between correlation and causation. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)³ = 5(1/3)³ to hold, so (51/3)³ must equal 5. Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. Determine an explicit expression, a recursive process, or steps for calculation from a context. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x³ or f(x) = (x+1)/(x-1) for x ≠ 1. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. Mentally add 10 or 100 to a given number 100—900, and mentally subtract 10 or 100 from a given number 100—900. Explain why addition and subtraction strategies work, using place value and the properties of operations. Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, …, and represent whole-number sums and differences within 100 on a number line diagram. Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. Count within 1000; skip-count by 5s, 10s, and 100s. Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. Use place value understanding to round whole numbers to the nearest 10 or 100. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Apply properties of operations as strategies to multiply and divide. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value understanding to round multi-digit whole numbers to any place. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.) Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value understanding to round decimals to any place. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3 °C > -7 °C to express the fact that -3 °C is warmer than -7 °C. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret -3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than -30 dollars represents a debt greater than 30 dollars. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of -30 dollars, write |-30| = 30 to describe the size of the debt in dollars. Write and evaluate numerical expressions involving whole-number exponents. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation "Subtract y from 5" as 5 - y. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students' ages. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Display numerical data in plots on a number line, including dot plots, histograms, and box plots. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes." Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. Apply properties of operations as strategies to add and subtract rational numbers. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event. Explain and use the relationship between the sine and cosine of complementary angles. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2). Lines are taken to lines, and line segments to line segments of the same length. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). The dilation of a line segment is longer or shorter in the ratio given by the scale factor. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Prove that all circles are similar. Construct a tangent line from a point outside a given circle to the circle. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. Use the structure of an expression to identify ways to rewrite it. For example, see x4 — y4 as (x²)² — (y²)², thus recognizing it as a difference of squares that can be factored as (x² — y²)(x² + y²). Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. Understand statistics as a process for making inferences about population parameters based on a random sample from that population. Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ˜ 1.01212t to reveal the approximate equivalent monhly interest rate if the annual rate is 15%. Evaluate reports based on data. Define and explain the meaning of significance, both statistical (using p-values) and practical (using effect size). Count to 100 by ones and by tens. Count forward beginning from a given number within the known sequence (instead of having to begin at 1). Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. Understand that each successive number name refers to a quantity that is one larger. Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1—20, count out that many objects. Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. Compare two numbers between 1 and 10 presented as written numerals. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). Fluently add and subtract within 5. Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. Directly compare two objects with a measurable attribute in common, to see which object has "more of"/"less of" the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. Correctly name shapes regardless of their orientations or overall size. Identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional ("solid"). Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/"corners") and other attributes (e.g., having sides of equal length). Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. Compose simple shapes to form larger shapes. For example, "Can you join these two triangles with full sides touching to make a rectangle?" Identify whether the number of objects in one group is more than, less than or the same as objects in another group for up to at least five objects. Understand that each successive number name refers to a quantity that is one larger. Instantly recognize, without counting, small quantities of up to five objects and say or sign the number. Say or sign the number names in order when counting, pairing one number word that corresponds with one object, up to at least 10. Use the number name of the last object counted to answer “How many?” questions for up to approximately 10 objects. Represent addition and subtraction in different ways, such as with fingers, objects, and drawings. With adult assistance, begin to use counting on (adding 1 or 2, for example) from the larger number for addition. Use comparative language, such as shortest, heavier, biggest, or later. Compare or order up to five objects based on their measurable attributes, such as height or weight. Name and describe shapes in terms of length of sides, number of sides, and number of angles/corners. Understand and use language related to directionality, order, and the position of objects, including up/down and in front/behind. Correctly follow directions involving their own position in space, such as “Stand up” and “Move forward.” Correctly name basic shapes (circle, square, rectangle, triangle) regardless of size and orientation. Analyze, compare, and sort two-and three-dimensional shapes and objects in different sizes. Describe their similarities, differences, and other attributes, such as size and shape. Accurately count as many as five objects in a scattered configuration or out of a collection of more than five objects. Identify and use numbers related to order or position from first to fifth. Associate a number of objects with a written numeral 0–5. Fill in missing elements of simple patterns. Duplicate simple patterns in a different location than demonstrated, such as making the same alternating color pattern with blocks at a table that was demonstrated on the rug. Extend patterns, such as making an eight-block tower of the same pattern that was demonstrated with four blocks. Measure using the same unit, such as putting together snap cubes to see how tall a book is. Identify the core unit of sequentially repeating patterns, such as color in a sequence of alternating red and blue blocks. Compose simple shapes to form larger shapes. Use determiners (e.g., articles, demonstratives). With prompting and support, read informational texts appropriately complex for grade 1. Ask and answer questions to help determine or clarify the meaning of words and phrases in a text. Use the illustrations and details in a text to describe its key ideas. Ask and answer questions about key details in a text. With prompting and support, read prose and poetry of appropriate complexity for grade 1. Use illustrations and details in a story to describe its characters, setting, or events. Describe people, places, things, and events with relevant details, expressing ideas and feelings clearly. Participate in shared research and writing projects (e.g., explore a number of "how-to" books on a given topic and use them to write a sequence of instructions). Know and use various text features (e.g., headings, tables of contents, glossaries, electronic menus, icons) to locate key facts or information in a text. Retell stories, including key details, and demonstrate understanding of their central message or lesson. Explain major differences between books that tell stories and books that give information, drawing on a wide reading of a range of text types. Compare and contrast the adventures and experiences of characters in stories. Ask and answer questions about key details in a text read aloud or information presented orally or through other media. Add drawings or other visual displays to descriptions when appropriate to clarify ideas, thoughts, and feelings. With guidance and support from adults, focus on a topic, respond to questions and suggestions from peers, and add details to strengthen writing as needed. With guidance and support from adults, recall information from experiences or gather information from provided sources to answer a question. Identify the main topic and retell key details of a text. Describe the connection between two individuals, events, ideas, or pieces of information in a text. Use words and phrases acquired through conversations, reading and being read to, and responding to texts, including using frequently occurring conjunctions to signal simple relationships (e.g., because). Distinguish between information provided by pictures or other illustrations and information provided by the words in a text. Identify basic similarities in and differences between two texts on the same topic (e.g., in illustrations, descriptions, or procedures). Describe characters, settings, and major events in a story, using key details. Identify who is telling the story at various points in a text. Produce complete sentences when appropriate to task and situation. With guidance and support from adults, use a variety of digital tools to produce and publish writing, including in collaboration with peers. Print all upper- and lowercase letters. Use common, proper, and possessive nouns. Capitalize dates and names of people. Use sentence-level context as a clue to the meaning of a word or phrase. Recognize the distinguishing features of a sentence (e.g., first word, capitalization, ending punctuation). Distinguish long from short vowel sounds in spoken single-syllable words. Follow agreed-upon rules for discussions (e.g., listening to others with care, speaking one at a time about the topics and texts under discussion). Use singular and plural nouns with matching verbs in basic sentences (e.g., He hops; We hop). Use end punctuation for sentences. Use frequently occurring affixes as a clue to the meaning of a word. Define words by category and by one or more key attributes (e.g., a duck is a bird that swims; a tiger is a large cat with stripes). Orally produce single-syllable words by blending sounds (phonemes), including consonant blends. Read on-level text orally with accuracy, appropriate rate, and expression on successive readings. Build on others' talk in conversations by responding to the comments of others through multiple exchanges. Use personal, possessive, and indefinite pronouns (e.g., I, me, my; they, them, their; anyone, everything). Use commas in dates and to separate single words in a series. Identify real-life connections between words and their use (e.g., note places at home that are cozy). Use context to confirm or self-correct word recognition and understanding, rereading as necessary. Ask questions to clear up any confusion about the topics and texts under discussion. Use verbs to convey a sense of past, present, and future (e.g., Yesterday I walked home; Today I walk home; Tomorrow I will walk home). Use conventional spelling for words with common spelling patterns and for frequently occurring irregular words. Distinguish shades of meaning among verbs differing in manner (e.g., look, peek, glance, stare, glare, scowl) and adjectives differing in intensity (e.g., large, gigantic) by defining or choosing them or by acting out the meanings. Segment spoken single-syllable words into their complete sequence of individual sounds (phonemes). Use frequently occurring adjectives. Spell untaught words phonetically, drawing on phonemic awareness and spelling conventions. Use frequently occurring prepositions (e.g., during, beyond, toward). Produce and expand complete simple and compound declarative, interrogative, imperative, and exclamatory sentences in response to prompts. Supply a reason for the opinion. Name a topic. Supply some facts about the topic. Provide some sense of closure. Recount two or more appropriately sequenced events. Include some details regarding what happened. Sort words into categories (for example: colors, clothing) to gain a sense of the concepts the categories represent. Give and follow simple two-step directions. Make predictions about what will happen in the text and explain whether they were confirmed or not and why, providing evidence from the text. Follow and replicate patterns in predictable poems. Activate schema and background knowledge to construct meaning. Identify and understand compound words. State an opinion. Introduce the topic or name the book they are writing about. Write or dictate questions for inquiry that arise during instruction. With peers, use a variety of resources (for example: direct observation, trade books, texts read aloud or viewed) to answer questions of interest through guided inquiry. Use text features (for example: titles, illustrations, headings, bold type) to locate, interpret, and use information. Identify a clear and significant purpose for research. (for example: Is my purpose for researching frogs clear and is it important to understanding more about mammals?) Propel conversations by posing and responding to questions that probe reasoning and evidence; ensure a hearing for a full range of positions on a topic or issue; clarify, verify, or challenge ideas and conclusions; and promote divergent and creative perspectives. Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text, including determining where the text leaves matters uncertain. Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience. Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the usefulness of each source in answering the research question; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and following a standard format for citation. Identify and correctly use patterns of word changes that indicate different meanings or parts of speech (e.g., conceive, conception, conceivable). Write and edit work so that it conforms to the guidelines in a style manual (e.g., MLA Handbook, Turabian's Manual for Writers) appropriate for the discipline and writing type. Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. Develop the topic thoroughly by selecting the most significant and relevant facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience's knowledge of the topic. Use words, phrases, and clauses as well as varied syntax to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims. Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation. Integrate multiple sources of information presented in diverse formats and media (e.g., visually, quantitatively, orally) in order to make informed decisions and solve problems, evaluating the credibility and accuracy of each source and noting any discrepancies among the data. Acquire and use accurately general academic and domain-specific words and phrases, sufficient for reading, writing, speaking, and listening at the college and career readiness level; demonstrate independence in gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression. Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate. Come to discussions prepared, having read and researched material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, well-reasoned exchange of ideas. Introduce precise, knowledgeable claim(s), establish the significance of the claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that logically sequences claim(s), counterclaims, reasons, and evidence. Use appropriate and varied transitions to link the major sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts. Analyze nuances in the meaning of words with similar denotations. Use narrative techniques, such as dialogue, pacing, description, reflection, and multiple plot lines, to develop experiences, events, and/or characters. Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language of a court opinion differs from that of a newspaper). Determine an author's point of view or purpose in a text and analyze how an author uses rhetoric to advance that point of view or purpose. Use parallel structure. Use a semicolon (and perhaps a conjunctive adverb) to link two or more closely related independent clauses. Use a variety of techniques to sequence events so that they build on one another to create a coherent whole. Use a colon to introduce a list or quotation. Present information, findings, and supporting evidence, conveying a clear and distinct perspective, such that listeners can follow the line of reasoning, alternative or opposing perspectives are addressed, and the organization, development, substance, and style are appropriate to purpose, audience, and a range of formal and informal tasks. Respond thoughtfully to diverse perspectives; synthesize comments, claims, and evidence made on all sides of an issue; resolve contradictions when possible; and determine what additional information or research is required to deepen the investigation or complete the task. Determine two or more central ideas of a text and analyze their development over the course of the text, including how they interact and build on one another to provide a complex analysis; provide an objective summary of the text. Analyze how an author's choices concerning how to structure a text, order events within it (e.g., parallel plots), and manipulate time (e.g., pacing, flashbacks) create such effects as mystery, tension, or surprise. Evaluate a speaker's point of view, reasoning, and use of evidence and rhetoric, identifying any fallacious reasoning or exaggerated or distorted evidence. Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. Analyze how an author draws on and transforms source material in a specific work (e.g., how Shakespeare treats a theme or topic from Ovid or the Bible or how a later author draws on a play by Shakespeare). Provide a concluding statement or section that follows from and supports the argument presented. Use various types of phrases (noun, verb, adjectival, adverbial, participial, prepositional, absolute) and clauses (independent, dependent; noun, relative, adverbial) to convey specific meanings and add variety and interest to writing or presentations. read and comprehend literary nonfiction in the grades 9—10 text complexity band proficiently, with scaffolding as needed at the high end of the range. By the end of grade 10, read and comprehend literary nonfiction at the high end of the grades 9—10 text complexity band independently and proficiently. Analyze various accounts of a subject told in different mediums (e.g., a person's life story in both print and multimedia), determining which details are emphasized in each account. Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and task. Write routinely over extended time frames (time for reflection and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. Analyze in detail how an author's ideas or claims are developed and refined by particular sentences, paragraphs, or larger portions of a text (e.g., a section or chapter). Determine a central idea of a text and analyze its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text. Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is valid and the evidence is relevant and sufficient; identify false statements and fallacious reasoning. Analyze how the author unfolds an analysis or series of ideas or events, including the order in which the points are made, how they are introduced and developed, and the connections that are drawn between them. Analyze a particular point of view or cultural experience reflected in a work of literature from outside the United States, drawing on a wide reading of world literature. Introduce a topic; organize complex ideas, concepts, and information to make important connections and distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension. Apply grades 9—10 Reading standards to literary nonfiction (e.g., "Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is valid and the evidence is relevant and sufficient; identify false statements and fallacious reasoning"). Propel conversations by posing and responding to questions that relate the current discussion to broader themes or larger ideas; actively incorporate others into the discussion; and clarify, verify, or challenge ideas and conclusions. Use words, phrases, and clauses to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims. Respond thoughtfully to diverse perspectives, summarize points of agreement and disagreement, and, when warranted, qualify or justify their own views and understanding and make new connections in light of the evidence and reasoning presented. Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. Spell correctly, consulting reference materials to check as needed. Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the impact of specific word choices on meaning and tone, including words with multiple meanings or language that is particularly fresh, engaging, or beautiful. (Include Shakespeare as well as other authors.) Analyze how an author's choices concerning how to structure specific parts of a text (e.g., the choice of where to begin or end a story, the choice to provide a comedic or tragic resolution) contribute to its overall structure and meaning as well as its aesthetic impact. Use technology, including the Internet, to produce, publish, and update individual or shared writing products in response to ongoing feedback, including new arguments or information. Observe hyphenation conventions. Introduce a topic; organize complex ideas, concepts, and information so that each new element builds on that which precedes it to create a unified whole; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension. Analyze and evaluate the effectiveness of the structure an author uses in his or her exposition or argument, including whether the structure makes points clear, convincing, and engaging. Determine an author's point of view or purpose in a text in which the rhetoric is particularly effective, analyzing how style and content contribute to the power, persuasiveness, or beauty of the text. Apply the understanding that usage is a matter of convention, can change over time, and is sometimes contested. Use a variety of techniques to sequence events so that they build on one another to create a coherent whole and build toward a particular tone and outcome (e.g., a sense of mystery, suspense, growth, or resolution). Use precise language, domain-specific vocabulary, and techniques such as metaphor, simile, and analogy to manage the complexity of the topic. Use narrative techniques, such as dialogue, pacing, description, reflection, and multiple plot lines, to develop experiences, events, and/or characters. Provide a conclusion that follows from and reflects on what is experienced, observed, or resolved over the course of the narrative. Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g., visually, quantitatively, as well as in words) in order to address a question or solve a problem. Delineate and evaluate the reasoning in seminal U.S. texts, including the application of constitutional principles and use of legal reasoning (e.g., in U.S. Supreme Court majority opinions and dissents) and the premises, purposes, and arguments in works of public advocacy (e.g., The Federalist, presidential addresses). Analyze a complex set of ideas or sequence of events and explain how specific individuals, ideas, or events interact and develop over the course of the text. Analyze the impact of the author's choices regarding how to develop and relate elements of a story or drama (e.g., where a story is set, how the action is ordered, how the characters are introduced and developed). Apply grades 11—12 Reading standards to literature (e.g., "Demonstrate knowledge of eighteenth-, nineteenth- and early-twentieth-century foundational works of American literature, including how two or more texts from the same period treat similar themes or topics"). Spell correctly, consulting reference materials to check as needed. By the end of 12th grade, analyze multiple interpretations of a story, drama, or poem (for example: recorded or live production of a play or recorded novel or poetry), evaluating how each version interprets the source text. (for example: a play by Shakespeare and/or a play by an American dramatist.) Analyze 17th-, 18th-, and 19th-century foundational U.S. documents of historical and literary significance (for example: The Declaration of Independence, the Preamble to the Constitution, the Bill of Rights, Lincoln’s Second Inaugural Address) for their themes, purposes, and rhetorical features by the end of 12th grade. Make strategic use of digital media (for example: textual, graphical, audio, visual, and interactive elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add interest. Use context (for example: the overall meaning of a sentence, paragraph, or text; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase. Designate a purpose for reading expository texts and use new learning to complete a specific task (such as convince an audience, shape a personal opinion or decision, or perform an activity). Evaluate quality, accuracy, and completeness of information and the bias, credibility and reliability of the sources. Document sources of quotations, paraphrases, and other information, using a style sheet, such as that of the Modern Language Association (MLA) or the American Psychological Association (APA). Select and use stylistic devices to craft engaging and effective text. Determine the meaning of words and phrases in a text relevant to a grade 2 topic or subject area. Ask and answer such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text. Use information gained from the illustrations and words in a print or digital text to demonstrate understanding of its characters, setting, or plot. Tell a story or recount an experience with appropriate facts and relevant, descriptive details, speaking audibly in coherent sentences. Describe the overall structure of a story, including describing how the beginning introduces the story and the ending concludes the action. Compare and contrast two or more versions of the same story (e.g., Cinderella stories) by different authors or from different cultures. Recount or describe key ideas or details from a text read aloud or information presented orally or through other media. Create audio recordings of stories or poems; add drawings or other visual displays to stories or recounts of experiences when appropriate to clarify ideas, thoughts, and feelings. With guidance and support from adults and peers, focus on a topic and strengthen writing as needed by revising and editing. Recall information from experiences or gather information from provided sources to answer a question. Describe the connection between a series of historical events, scientific ideas or concepts, or steps in technical procedures in a text. Identify the main topic of a multiparagraph text as well as the focus of specific paragraphs within the text. Use words and phrases acquired through conversations, reading and being read to, and responding to texts, including using adjectives and adverbs to describe (e.g., When other kids are happy that makes me happy). Identify the main purpose of a text, including what the author wants to answer, explain, or describe. Compare and contrast the most important points presented by two texts on the same topic. Describe how characters in a story respond to major events and challenges. Acknowledge differences in the points of view of characters, including by speaking in a different voice for each character when reading dialogue aloud. Ask and answer questions about what a speaker says in order to clarify comprehension, gather additional information, or deepen understanding of a topic or issue. Produce complete sentences when appropriate to task and situation in order to provide requested detail or clarification. With guidance and support from adults, use a variety of digital tools to produce and publish writing, including in collaboration with peers. Use collective nouns (e.g., group). Capitalize holidays, product names, and geographic names. Compare formal and informal uses of English. Read on-level text with purpose and understanding. Use sentence-level context as a clue to the meaning of a word or phrase. Follow agreed-upon rules for discussions (e.g., gaining the floor in respectful ways, listening to others with care, speaking one at a time about the topics and texts under discussion). Use adjectives and adverbs, and choose between them depending on what is to be modified. Use commas in greetings and closings of letters. Determine the meaning of the new word formed when a known prefix is added to a known word (e.g., happy/unhappy, tell/retell). Distinguish shades of meaning among closely related verbs (e.g., toss, throw, hurl) and closely related adjectives (e.g., thin, slender, skinny, scrawny). Read on-level text orally with accuracy, appropriate rate, and expression on successive readings. Build on others' talk in conversations by linking their comments to the remarks of others. Use reflexive pronouns (e.g., myself, ourselves). Use a known root word as a clue to the meaning of an unknown word with the same root (e.g., addition, additional). Use context to confirm or self-correct word recognition and understanding, rereading as necessary. Ask for clarification and further explanation as needed about the topics and texts under discussion. Form and use the past tense of frequently occurring irregular verbs (e.g., sat, hid, told). Generalize learned spelling patterns when writing words (e.g., cage → badge; boy → boil). Use knowledge of the meaning of individual words to predict the meaning of compound words (e.g., birdhouse, lighthouse, housefly; bookshelf, notebook, bookmark). Consult reference materials, including beginning dictionaries, as needed to check and correct spellings. Use glossaries and beginning dictionaries, both print and digital, to determine or clarify the meaning of words and phrases. Produce, expand, and rearrange complete simple and compound sentences (e.g., The boy watched the movie; The little boy watched the movie; The action movie was watched by the little boy). Include details to describe actions, thoughts, and feelings. Use temporal words and phrases to signal event order. State an opinion. Supply reasons that support the opinion. Introduce a topic. Provide a sense of closure. Identify a main topic or central idea and retell key details in a text; summarize portions of a text. (RI&RL) Describe how words and phrases (for example: regular beats, alliteration, rhymes, repeated lines) supply rhythm and meaning in a story, poem, or song. Know and use various text features (for example: captions, bold print, subheadings, glossaries, indexes, electronic menus, icons) to locate key facts or information in a text efficiently. Explain how specific images (for example: a diagram showing how a machine works) contribute to and clarify a text. Contribute knowledge to a small group or class discussion to develop a topic. Maintain focus on the topic. Use content-specific vocabulary to ask questions and provide information. Read text to perform a specific task such as follow a recipe or play a game. Adjust reading rate according to type of text and purpose for reading. Read grade-level text accurately and fluently, attending to phrasing, intonation, and punctuation. Determine which strategies should be used to decode multisyllabic words. Use linking words (for example: because, and, also) to connect opinion and reasons. Use facts and definitions to develop points, including relevant details when writing to questions about texts. Write letters and “how-to’s” (for example: procedures, directions, recipes) that follow a logical order and appropriate format. Organize informational texts using main ideas and specific supporting details. Apply appropriate transition words to writing. Writers use technology to support the writing process. Write simple, descriptive poems. Write with precise nouns, active verbs, and descriptive adjectives. Develop characters both internally (thoughts and feelings) and externally (physical features, expressions, clothing). Vary sentence beginnings. Spell high-frequency words correctly. Apply accurate subject-verb agreement while writing. Identify a variety of resources and the information they might contain (for example: dictionary, trade book, library databases, internet web page). Identify a specific question and gather information for purposeful investigation and inquiry. Use text features to locate and interpret information. For example: table of contents, illustrations, diagrams, headings and bold type. Use a variety of multimedia sources to answer questions of interest. Ask primary questions of depth and breadth. Identify how word choice (for example: sensory details, figurative language) enhances meaning in poetry Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers. By the end of the year, read and comprehend informational texts, including history/social studies, science, and technical texts, at the high end of the grades 2—3 text complexity band independently and proficiently. Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 3 topic or subject area. Distinguish the literal and nonliteral meanings of words and phrases in context (e.g., take steps). Explain how specific aspects of a text's illustrations contribute to what is conveyed by the words in a story (e.g., create mood, emphasize aspects of a character or setting). Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. With guidance and support from adults, produce writing in which the development and organization are appropriate to task and purpose. Conduct short research projects that build knowledge about a topic. Determine the main idea of a text; recount the key details and explain how they support the main idea. Recount stories, including fables, folktales, and myths from diverse cultures; determine the central message, lesson, or moral and explain how it is conveyed through key details in the text. Refer to parts of stories, dramas, and poems when writing or speaking about a text, using terms such as chapter, scene, and stanza; describe how each successive part builds on earlier sections. Compare and contrast the themes, settings, and plots of stories written by the same author about the same or similar characters (e.g., in books from a series). Determine the main ideas and supporting details of a text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Create engaging audio recordings of stories or poems that demonstrate fluid reading at an understandable pace; add visual displays when appropriate to emphasize or enhance certain facts or details. With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing. Recall information from experiences or gather information from print and digital sources; take brief notes on sources and sort evidence into provided categories. Acquire and use accurately grade-appropriate conversational, general academic, and domain-specific words and phrases, including those that signal spatial and temporal relationships (e.g., After dinner that night we went looking for them). Describe characters in a story (e.g., their traits, motivations, or feelings) and explain how their actions contribute to the sequence of events. Distinguish their own point of view from that of the narrator or those of the characters. Ask and answer questions about information from a speaker, offering appropriate elaboration and detail. Speak in complete sentences when appropriate to task and situation in order to provide requested detail or clarification. With guidance and support from adults, use technology to produce and publish writing (using keyboarding skills) as well as to interact and collaborate with others. Explain the function of nouns, pronouns, verbs, adjectives, and adverbs in general and their functions in particular sentences. Capitalize appropriate words in titles. Choose words and phrases for effect. Use sentence-level context as a clue to the meaning of a word or phrase. Read on-level text with purpose and understanding. Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. Introduce the topic or text they are writing about, state an opinion, and create an organizational structure that lists reasons. Introduce a topic and group related information together; include illustrations when useful to aiding comprehension. Form and use regular and irregular plural nouns. Ensure subject-verb and pronoun-antecedent agreement. Use commas in addresses. Recognize and observe differences between the conventions of spoken and written standard English. Determine the meaning of the new word formed when a known affix is added to a known word (e.g., agreeable/disagreeable, comfortable/uncomfortable, care/careless, heat/preheat). Identify real-life connections between words and their use (e.g., describe people who are friendly or helpful). Follow agreed-upon rules for discussions (e.g., gaining the floor in respectful ways, listening to others with care, speaking one at a time about the topics and texts under discussion). Provide reasons that support the opinion. Use dialogue and descriptions of actions, thoughts, and feelings to develop experiences and events or show the response of characters to situations. Use abstract nouns (e.g., childhood). Use commas and quotation marks in dialogue. Use a known root word as a clue to the meaning of an unknown word with the same root (e.g., company, companion). Distinguish shades of meaning among related words that describe states of mind or degrees of certainty (e.g., knew, believed, suspected, heard, wondered). Use context to confirm or self-correct word recognition and understanding, rereading as necessary. Ask questions to check understanding of information presented, stay on topic, and link their comments to the remarks of others. Use temporal words and phrases to signal event order. Form and use possessives. Use coordinating and subordinating conjunctions. Use glossaries or beginning dictionaries, both print and digital, to determine or clarify the precise meaning of key words and phrases. Explain their own ideas and understanding in light of the discussion. Provide a concluding statement or section. Provide a sense of closure. Form and use comparative and superlative adjectives and adverbs, and choose between them depending on what is to be modified. Use conventional spelling for high-frequency and other studied words and for adding suffixes to base words (e.g., sitting, smiled, cries, happiness). Use spelling patterns and generalizations (e.g., word families, position-based spellings, syllable patterns, ending rules, meaningful word parts) in writing words. Consult reference materials, including beginning dictionaries, as needed to check and correct spellings. Produce simple, compound, and complex sentences. Use linking words and phrases (for example: also, another, and, more, but) to connect ideas within categories of information. Read grade-level texts fluently with sufficient accuracy, rate and expression to support comprehension. Use text features and search tools (for example: key words, sidebars, hyperlinks) to locate information relevant to a given topic efficiently. Form and use the simple (for example: I walked; I walk; I will walk) verb tenses. Distinguish different levels of formality. Speak clearly, using appropriate volume and pitch for the purpose and audience. Select and organize ideas sequentially or around major points of information that relate to the formality of the audience. Summarize central ideas and important details from a text. Use a variety of comprehension strategies to interpret text (attending, searching, predicting, checking, and self-correcting). Describe and draw inferences about the elements of plot, character, and setting in literary pieces, poems, and plays. Use signal words (such as before, after, next) and text structure (narrative, chronology) to determine the sequence of major events. Identify a main topic of a multi-paragraph text as well as the focus of specific paragraphs within the text. Use semantic cues and signal words (for example: because and although) to identify cause/effect and compare/contrast relationships. Use knowledge of word relationships to identify antonyms or synonyms to clarify meaning. Vary sentence beginnings, and use long and short sentences to create sentence fluency in longer texts. By the end of year, read and comprehend informational texts, including history/social studies, science, and technical texts, in the grades 4—5 text complexity band proficiently, with scaffolding as needed at the high end of the range. Determine the meaning of general academic and domain-specific words or phrases in a text relevant to a grade 4 topic or subject area. Refer to details and examples in a text when explaining what the text says explicitly and when drawing inferences from the text. Determine the meaning of words and phrases as they are used in a text, including those that allude to significant characters found in mythology (e.g., Herculean). Make connections between the text of a story or drama and a visual or oral presentation of the text, identifying where each version reflects specific descriptions and directions in the text. Report on a topic or text, tell a story, or recount an experience in an organized manner, using appropriate facts and relevant, descriptive details to support main ideas or themes; speak clearly at an understandable pace. Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience. Determine the main idea of a text and explain how it is supported by key details; summarize the text. Explain how an author uses reasons and evidence to support particular points in a text. Determine a theme of a story, drama, or poem from details in the text; summarize the text. Explain major differences between poems, drama, and prose, and refer to the structural elements of poems (e.g., verse, rhythm, meter) and drama (e.g., casts of characters, settings, descriptions, dialogue, stage directions) when writing or speaking about a text. Paraphrase portions of a text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Add audio recordings and visual displays to presentations when appropriate to enhance the development of main ideas or themes. With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing. Recall relevant information from experiences or gather relevant information from print and digital sources; take notes and categorize information, and provide a list of sources. Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal precise actions, emotions, or states of being (e.g., quizzed, whined, stammered) and that are basic to a particular topic (e.g., wildlife, conservation, and endangered when discussing animal preservation). Explain events, procedures, ideas, or concepts in a historical, scientific, or technical text, including what happened and why, based on specific information in the text. Compare and contrast a firsthand and secondhand account of the same event or topic; describe the differences in focus and the information provided. Integrate information from two texts on the same topic in order to write or speak about the subject knowledgeably. Describe in depth a character, setting, or event in a story or drama, drawing on specific details in the text (e.g., a character's thoughts, words, or actions). Compare and contrast the point of view from which different stories are narrated, including the difference between first- and third-person narrations. Use relative pronouns (who, whose, whom, which, that) and relative adverbs (where, when, why). With some guidance and support from adults, use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills to type a minimum of one page in a single sitting. Use correct capitalization. Choose words and phrases to convey ideas precisely. Read on-level text with purpose and understanding. Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. Introduce a topic clearly and group related information in paragraphs and sections; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. Orient the reader by establishing a situation and introducing a narrator and/or characters; organize an event sequence that unfolds naturally. Apply grade 4 Reading standards to literature (e.g., "Describe in depth a character, setting, or event in a story or drama, drawing on specific details in the text [e.g., a character's thoughts, words, or actions]."). Form and use the progressive (e.g., I was walking; I am walking; I will be walking) verb tenses. Correctly use frequently confused words (e.g., to, too, two; there, their). Use commas and quotation marks to mark direct speech and quotations from a text. Choose punctuation for effect. Recognize and explain the meaning of common idioms, adages, and proverbs. Follow agreed-upon rules for discussions and carry out assigned roles. Provide reasons that are supported by facts and details. Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. Use dialogue and description to develop experiences and events or show the responses of characters to situations. Use modal auxiliaries (e.g., can, may, must) to convey various conditions. Demonstrate understanding of words by relating them to their opposites (antonyms) and to words with similar but not identical meanings (synonyms). Use context to confirm or self-correct word recognition and understanding, rereading as necessary. Pose and respond to specific questions to clarify or follow up on information, and make comments that contribute to the discussion and link to the remarks of others. Link ideas within categories of information using words and phrases (e.g., another, for example, also, because). Order adjectives within sentences according to conventional patterns (e.g., a small red bag rather than a red small bag). Spell grade-appropriate words correctly, consulting references as needed. Review the key ideas expressed and explain their own ideas and understanding in light of the discussion. Provide a concluding statement or section related to the opinion presented. Use precise language and domain-specific vocabulary to inform about or explain the topic. Use concrete words and phrases and sensory details to convey experiences and events precisely. Form and use prepositional phrases. Differentiate between contexts that call for formal English (for example: presenting ideas) and situations where informal discourse is appropriate (for example: small-group discussion); use formal English when appropriate to task and situation. Compare and contrast the treatment of similar themes and topics (for example: opposition of good and evil) and patterns of events (for example: the quest) in stories, myths, and traditional literature from different cultures. Describe the overall structure (for example, chronology, comparison, cause/effect, problem/solution) of events, ideas, concepts, or information in a text or part of a text. Use context (for example: definitions, examples, or restatements in text) as a clue to the meaning of a word or phrase. Consult reference materials (for example: dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation and determine or clarify the precise meaning of key words and phrases. Recognize and correct inappropriate fragments and run-ons. Describe the development of plot (such as the origin of the central conflict, the action of the plot, and how the conflict is resolved). Read familiar texts orally with fluency, accuracy, and prosody (expression). Read and understand words with common prefixes (for example: un-, re-, dis-) and derivational suffixes ( for example: -ful, -ly, -ness). Read and understand words that change spelling to show past tense (for example: write/wrote, catch/caught, teach/taught). Read multisyllabic words with and without inflectional and derivational suffixes. Infer meaning of words using explanations offered within a text. Identify a text structure appropriate to purpose (sequence, chronology, description, explanation, comparison-and-contrast). Organize relevant ideas and details to convey a central idea or prove a point. Use compound subjects (for example: Tom and Pat went to the store) and compound verbs (for example: Harry thought and worried about the things he said to Jane) to create sentence fluency in writing Produce complete simple, compound, and complex sentences. Identify a topic and formulate open-ended research questions for further inquiry and learning. Present a brief report of the research findings to an audience. Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text. By the end of the year, read and comprehend informational texts, including history/social studies, science, and technical texts, at the high end of the grades 4—5 text complexity band independently and proficiently. Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 5 topic or subject area. Draw on information from multiple print or digital sources, demonstrating the ability to locate an answer to a question quickly or to solve a problem efficiently. Determine the meaning of words and phrases as they are used in a text, including figurative language such as metaphors and similes. Analyze how visual and multimedia elements contribute to the meaning, tone, or beauty of a text (e.g., graphic novel, multimedia presentation of fiction, folktale, myth, poem). Report on a topic or text or present an opinion, sequencing ideas logically and using appropriate facts and relevant, descriptive details to support main ideas or themes; speak clearly at an understandable pace. Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. Orient the reader by establishing a situation and introducing a narrator and/or characters; organize an event sequence that unfolds naturally. Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience. Determine two or more main ideas of a text and explain how they are supported by key details; summarize the text. Determine a theme of a story, drama, or poem from details in the text, including how characters in a story or drama respond to challenges or how the speaker in a poem reflects upon a topic; summarize the text. Explain how a series of chapters, scenes, or stanzas fits together to provide the overall structure of a particular story, drama, or poem. Use narrative techniques, such as dialogue, description, and pacing, to develop experiences and events or show the responses of characters to situations. Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases, including those that signal contrast, addition, and other logical relationships (e.g., however, although, nevertheless, similarly, moreover, in addition). Analyze multiple accounts of the same event or topic, noting important similarities and differences in the point of view they represent. Integrate information from several texts on the same topic in order to write or speak about the subject knowledgeably. Compare and contrast two or more characters, settings, or events in a story or drama, drawing on specific details in the text (e.g., how characters interact). Compare and contrast stories in the same genre (e.g., mysteries and adventure stories) on their approaches to similar themes and topics. Summarize the points a speaker makes and explain how each claim is supported by reasons and evidence. Adapt speech to a variety of contexts and tasks, using formal English when appropriate to task and situation. Use a variety of transitional words, phrases, and clauses to manage the sequence of events. Use concrete words and phrases and sensory details to convey experiences and events precisely. Provide a conclusion that follows from the narrated experiences or events. Explain the function of conjunctions, prepositions, and interjections in general and their function in particular sentences. Use verb tense to convey various times, sequences, states, and conditions. Use punctuation to separate items in a series. Expand, combine, and reduce sentences for meaning, reader/listener interest, and style. Interpret figurative language, including similes and metaphors, in context. Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. Introduce a topic or text clearly, state an opinion, and create an organizational structure in which ideas are logically grouped to support the writer's purpose. Introduce a topic clearly, provide a general observation and focus, and group related information logically; include formatting (e.g., headings), illustrations, and multimedia when useful to aiding comprehension. Apply grade 5 Reading standards to literature (e.g., "Compare and contrast two or more characters, settings, or events in a story or a drama, drawing on specific details in the text [e.g., how characters interact]"). Recognize and correct inappropriate shifts in verb tense. Use a comma to separate an introductory element from the rest of the sentence. Compare and contrast the varieties of English (e.g., dialects, registers) used in stories, dramas, or poems. Recognize and explain the meaning of common idioms, adages, and proverbs. Read on-level prose and poetry orally with accuracy, appropriate rate, and expression on successive readings Follow agreed-upon rules for discussions and carry out assigned roles. Provide logically ordered reasons that are supported by facts and details. Develop the topic with facts, definitions, concrete details, quotations, or other information and examples related to the topic. Use the relationship between particular words (e.g., synonyms, antonyms, homographs) to better understand each of the words. Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others. Use context to confirm or self-correct word recognition and understanding, rereading as necessary. Link ideas within and across categories of information using words, phrases, and clauses (e.g., in contrast, especially). Provide a concluding statement or section related to the opinion presented. Use precise language and domain-specific vocabulary to inform about or explain the topic. Use correlative conjunctions (e.g., either/or, neither/nor). Spell grade-appropriate words correctly, consulting references as needed. With some guidance and support from adults, use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others. Use a comma to set off the words yes and no (for example: Yes, thank you), to set off a tag question from the rest of the sentence (for example: It’s true, isn’t it?), and to indicate direct address (for example: Is that you, Steve?). Compare and contrast the overall structure (for example: chronology, comparison, cause/effect, problem/solution) of events, ideas, concepts, or information in two or more texts. Use context (for example: cause/effect relationships and comparisons in text) as a clue to the meaning of a word or phrase. Consult reference materials (for example, dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation and determine or clarify the precise meaning of key words and phrases. Use appropriate eye contact and speak clearly at an understandable pace. Adapt language as appropriate to purpose: to persuade, explain/provide information, or express an opinion. Use pre-reading strategies, such as identifying a purpose for reading, generating questions to answers while reading, previewing sections of texts and activating prior knowledge. Distinguish between fact and opinion, providing support for judgments made. Use informational text features (such as bold type, headings, graphic organizers, numbering schemes, glossary) and text structures to organize or categorize information, to answer questions, or to perform specific tasks. Apply knowledge of derivational suffixes that change the part of speech of the base word (for example active and activity). Infer meaning of words using structural analysis, context, and knowledge of multiple meanings. Read and identify the meaning of roots and related word families in which the pronunciation of the root does not change. Summarize and support key ideas Develop and present a brief (oral or written) research report with clear focus and supporting detail for an intended audience. Provide documentation of sources used in a grade-appropriate format. Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. Conduct short research projects to answer a question (including a self-generated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration. With some guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on how well purpose and audience have been addressed. Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation. Determine an author's point of view or purpose in a text and explain how it is conveyed in the text. Introduce claim(s) and organize the reasons and evidence clearly. Introduce a topic clearly, previewing what is to follow; organize ideas, concepts, and information into broader categories; include formatting (e.g., headings), graphics (e.g., charts, tables), and multimedia when useful to aiding comprehension. Establish and maintain a formal style. Cite textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings. Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression. Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate. Interpret figures of speech (e.g., personification) in context. Come to discussions prepared, having read or researched material under study; explicitly draw on that preparation by referring to evidence on the topic, text, or issue to probe and reflect on ideas under discussion. Use common, grade-appropriate Greek or Latin affixes and roots as clues to the meaning of a word (e.g., precede, recede, secede). Use the relationship between particular words to better understand each of the words. Follow rules for collegial discussions, set specific goals and deadlines, and define individual roles as needed. Distinguish among the connotations (associations) of words with similar denotations (definitions) (e.g., refined, respectful, polite, diplomatic, condescending). Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary). Analyze the purpose of information presented in diverse media and formats (e.g., visually, quantitatively, orally) and evaluate the motives (e.g., social, commercial, political) behind its presentation. Use punctuation (commas, parentheses, dashes) to set off nonrestrictive/parenthetical elements. Use intensive pronouns (e.g., myself, ourselves). Explain the function of phrases and clauses in general and their function in specific sentences. Maintain consistency in style and tone. Recognize and correct vague pronouns (i.e., ones with unclear or ambiguous antecedents). Use technology, including the Internet, to produce and publish writing and present the relationships between information and ideas efficiently as well as to interact and collaborate with others. Ensure that pronouns are in the proper case (subjective, objective, possessive). Vary sentence patterns for meaning, reader/listener interest, and style. Recognize and correct inappropriate shifts in pronoun number and person. Review the key ideas expressed and demonstrate understanding of multiple perspectives through reflection and paraphrasing. Analyze the structure an author uses to organize a text, including how the major sections contribute to the whole and to the development of the ideas. Recognize variations from standard English in their own and others' writing and speaking, and identify and use strategies to improve expression in conventional language. Present claims and findings, emphasizing salient points in a focused, coherent manner with pertinent descriptions, facts, details, and examples; use appropriate eye contact, adequate volume, and clear pronunciation. Trace and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient to support the claims. Include multimedia components and visual displays in presentations to clarify claims and findings and emphasize salient points. Delineate a speaker's argument and specific claims, evaluating the soundness of the reasoning and the relevance and sufficiency of the evidence. Use a comma to separate coordinate adjectives (e.g., It was a fascinating, enjoyable movie but not He wore an old[,] green shirt). Pose questions that elicit elaboration and respond to others' questions and comments with relevant observations and ideas that bring the discussion back on topic as needed. Acknowledge new information expressed by others and, when warranted, modify their own views. Cite several pieces of textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. Analyze how two or more authors writing about the same topic shape their presentations of key information by emphasizing different evidence or advancing different interpretations of facts. Choose among simple, compound, complex, and compound-complex sentences to signal differing relationships among ideas. Explain the function of verbals (gerunds, participles, infinitives) in general and their function in particular sentences. Use punctuation (comma, ellipsis, dash) to indicate a pause or break. Use an ellipsis to indicate an omission. Use verbs in the active and passive voice and in the conditional and subjunctive mood to achieve particular effects (e.g., emphasizing the actor or the action; expressing uncertainty or describing a state contrary to fact). Form and use verbs in the indicative, imperative, interrogative, conditional, and subjunctive mood. Recognize and correct inappropriate shifts in verb voice and mood. By the end of the year, read and comprehend literary nonfiction in the grades 6—8 text complexity band proficiently, with scaffolding as needed at the high end of the range. Present claims and findings, sequencing ideas logically and using pertinent descriptions, facts, and details to accentuate main ideas or themes; use appropriate eye contact, adequate volume, and clear pronunciation. Determine a central idea of a text and how it is conveyed through particular details; provide a summary of the text distinct from personal opinions or judgments. Analyze how a particular sentence, paragraph, chapter, or section fits into the overall structure of a text and contributes to the development of the ideas. Interpret information presented in diverse media and formats (e.g., visually, quantitatively, orally) and explain how it contributes to a topic, text, or issue under study. Analyze in detail how a key individual, event, or idea is introduced, illustrated, and elaborated in a text (e.g., through examples or anecdotes). Compare and contrast one author's presentation of events with that of another (e.g., a memoir written by and a biography on the same person). Describe how a particular story's or drama's plot unfolds in a series of episodes as well as how the characters respond or change as the plot moves toward a resolution. Explain how an author develops the point of view of the narrator or speaker in a text. Apply grade 6 Reading standards to literary nonfiction (e.g., "Trace and evaluate the argument and specific claims in a text, distinguishing claims that are supported by reasons and evidence from claims that are not"). Use narrative techniques, such as dialogue, pacing, and description, to develop experiences, events, and/or characters. Pose and respond to specific questions with elaboration and detail by making comments that contribute to the topic, text, or issue under discussion. Use a variety of transition words, phrases, and clauses to convey sequence and signal shifts from one time frame or setting to another. Use precise words and phrases, relevant descriptive details, and sensory language to convey experiences and events. Provide a conclusion that follows from the narrated experiences or events. Include multimedia components (for example: graphics, images, music, sound) and visual displays in presentations to clarify information. Consult reference materials (for example: dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning or its part of speech. Correctly spell frequently used words and consult reference materials (for example: dictionaries, both print and digital, spell check, and/or trusted peers and/or adults) to determine the spelling of less frequent vocabulary. Use stylistic techniques (for example: alliteration, onomatopoeia, rhyme scheme); figurative language (for example: simile, metaphor, personification); and graphic elements (for example: capital letters, line length, word position) to express personal or narrative voice. By the end of the year, read and comprehend literary nonfiction in the grades 6–8 text complexity band proficiently, with scaffolding as needed at the high end of the range. Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the impact of a specific word choice on meaning and tone. Compare and contrast a text to an audio, video, or multimedia version of the text, analyzing each medium's portrayal of the subject (e.g., how the delivery of a speech affects the impact of the words). Determine two or more central ideas in a text and analyze their development over the course of the text; provide an objective summary of the text. Compare and contrast a written story, drama, or poem to its audio, filmed, staged, or multimedia version, analyzing the effects of techniques unique to each medium (e.g., lighting, sound, color, or camera focus and angles in a film). Analyze how a drama's or poem's form or structure (e.g., soliloquy, sonnet) contributes to its meaning. Analyze how an author develops and contrasts the points of view of different characters or narrators in a text. Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate. Use technology, including the Internet, to produce and publish writing and link to and cite sources as well as to interact and collaborate with others, including linking to and citing sources. Engage and orient the reader by establishing a context and point of view and introducing a narrator and/or characters; organize an event sequence that unfolds naturally and logically. Apply grade 7 Reading standards to literature (e.g., "Compare and contrast a fictional portrayal of a time, place, or character and a historical account of the same period as a means of understanding how authors of fiction use or alter history"). Use narrative techniques, such as dialogue, pacing, and description, to develop experiences, events, and/or characters. Use a variety of transition words, phrases, and clauses to convey sequence and signal shifts from one time frame or setting to another. Use precise words and phrases, relevant descriptive details, and sensory language to capture the action and convey experiences and events. Provide a conclusion that follows from and reflects on the narrated experiences or events. Use context (for example: the overall meaning of a sentence or paragraph; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase. Correctly spell frequently used words and consult reference materials (for example, dictionaries, both print and digital, spell check, and/or trusted peers and/or adults) to determine the spelling of less frequently used vocabulary. Use stylistic techniques (for example: alliteration, onomatopoeia, rhyme scheme, repetition); figurative language (for example: simile, metaphor, personification); and graphic elements (for example: capital letters, line length, word position) to express personal or narrative voice. Cite the textual evidence that most strongly supports an analysis of what the text says explicitly as well as inferences drawn from the text. Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze the impact of specific word choices on meaning and tone, including analogies or allusions to other texts. Evaluate the advantages and disadvantages of using different mediums (e.g., print or digital text, video, multimedia) to present a particular topic or idea. Present claims and findings, emphasizing salient points in a focused, coherent manner with relevant evidence, sound valid reasoning, and well-chosen details; use appropriate eye contact, adequate volume, and clear pronunciation. Analyze the extent to which a filmed or live production of a story or drama stays faithful to or departs from the text or script, evaluating the choices made by the director or actors. Determine a central idea of a text and analyze its development over the course of the text, including its relationship to supporting ideas; provide an objective summary of the text. Analyze in detail the structure of a specific paragraph in a text, including the role of particular sentences in developing and refining a key concept. Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient; recognize when irrelevant evidence is introduced. Analyze how a text makes connections among and distinctions between individuals, ideas, or events (e.g., through comparisons, analogies, or categories). Determine an author's point of view or purpose in a text and analyze how the author acknowledges and responds to conflicting evidence or viewpoints. Analyze how differences in the points of view of the characters and the audience or reader (e.g., created through the use of dramatic irony) create such effects as suspense or humor. Analyze how particular lines of dialogue or incidents in a story or drama propel the action, reveal aspects of a character, or provoke a decision. Analyze how a modern work of fiction draws on themes, patterns of events, or character types from myths, traditional stories, or religious works such as the Bible, including describing how the material is rendered new. Engage and orient the reader by establishing a context and point of view and introducing a narrator and/or characters; organize an event sequence that unfolds naturally and logically. Apply grade 8 Reading standards to literary nonfiction (e.g., "Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is sound and the evidence is relevant and sufficient; recognize when irrelevant evidence is introduced"). Follow rules for collegial discussions and decision-making, track progress toward specific goals and deadlines, and define individual roles as needed. Use narrative techniques, such as dialogue, pacing, description, and reflection, to develop experiences, events, and/or characters. Pose questions that connect the ideas of several speakers and respond to others' questions and comments with relevant evidence, observations, and ideas. Use a variety of transition words, phrases, and clauses to convey sequence, signal shifts from one time frame or setting to another, and show the relationships among experiences and events. Acknowledge new information expressed by others, and, when warranted, qualify or justify their own views in light of the evidence presented. Use precise words and phrases, relevant descriptive details, and sensory language to capture the action and convey experiences and events. Provide a conclusion that follows from and reflects on the narrated experiences or events. Use context (for example: the overall meaning of a sentence or paragraph; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase. Consult general and specialized reference materials (for example: dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning or its part of speech. Use stylistic techniques (for example: alliteration, onomatopoeia); figurative language (for example: simile, metaphor, personification, hyperbole); and graphic elements (for example: capital letters, line length, word position) to express personal or narrative voice. Analyze how complex characters (for example: those with multiple or conflicting motivations) develop over the course of a text, interact with other characters, and advance the plot or develop the theme. Make strategic use of digital media (for example: textual, graphical, audio, visual, and interactive elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add interest. Use context (for example: the overall meaning of a sentence, paragraph, or text; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase. Interpret figures of speech (for example: euphemism, oxymoron) in context and analyze their role in the text. Use feedback to evaluate and revise the presentation. Analyze the influence of literary and/or historical context on a text and evaluate the contribution to society made by works of literature that deal with similar topics and themes. Determine purpose for writing and use rhetorical appeals (i.e., ethos, pathos, logos) to address audience expectations and needs. Use a range of stylistic devices (for example: poetic techniques, figurative language, imagery, graphic elements) to support the presentation of implicit or explicit themes or to engage and entertain the intended audience. With prompting and support, describe the relationship between illustrations and the text in which they appear (e.g., what person, place, thing, or idea in the text an illustration depicts). With prompting and support, identify basic similarities in and differences between two texts on the same topic (e.g., in illustrations, descriptions, or procedures). With prompting and support, identify the reasons an author gives to support points in a text. With prompting and support, ask and answer questions about key details in a text. Ask and answer questions about unknown words in a text. Describe familiar people, places, things, and events and, with prompting and support, provide additional detail. Use a combination of drawing, dictating, and writing to compose opinion pieces in which they tell a reader the topic or the name of the book they are writing about and state an opinion or preference about the topic or book (e.g., My favorite book is…). With guidance and support from adults, respond to questions and suggestions from peers and add details to strengthen writing as needed. Participate in shared research and writing projects (e.g., explore a number of books by a favorite author and express opinions about them). With prompting and support, identify the main topic and retell key details of a text. Identify the front cover, back cover, and title page of a book. With prompting and support, retell familiar stories, including key details. Recognize common types of texts (e.g., storybooks, poems). Confirm understanding of a text read aloud or information presented orally or through other media by asking and answering questions about key details and requesting clarification if something is not understood. Add drawings or other visual displays to descriptions as desired to provide additional detail. Use a combination of drawing, dictating, and writing to narrate a single event or several loosely linked events, tell about the events in the order in which they occurred, and provide a reaction to what happened. Use a combination of drawing, dictating, and writing to compose informative/explanatory texts in which they name what they are writing about and supply some information about the topic. With guidance and support from adults, explore a variety of digital tools to produce and publish writing, including in collaboration with peers. With guidance and support from adults, recall information from experiences or gather information from provided sources to answer a question. Use words and phrases acquired through conversations, reading and being read to, and responding to texts. Name the author and illustrator of a text and define the role of each in presenting the ideas or information in a text. With prompting and support, describe the connection between two individuals, events, ideas, or pieces of information in a text. With prompting and support, identify characters, settings, and major events in a story. With prompting and support, name the author and illustrator of a story and define the role of each in telling the story. With prompting and support, compare and contrast the adventures and experiences of characters in familiar stories. Ask and answer questions in order to seek help, get information, or clarify something that is not understood. Speak audibly and express thoughts, feelings, and ideas clearly. Read emergent-reader texts with purpose and understanding. Print many upper- and lowercase letters. Use frequently occurring nouns and verbs. Capitalize the first word in a sentence and the pronoun I. Follow words from left to right, top to bottom, and page by page. Identify new meanings for familiar words and apply them accurately (e.g., knowing duck is a bird and learning the verb to duck). Recognize and produce rhyming words. Follow agreed-upon rules for discussions (e.g., listening to others and taking turns speaking about the topics and texts under discussion). Form regular plural nouns orally by adding /s/ or /es/ (e.g., dog, dogs; wish, wishes). Recognize and name end punctuation. Use the most frequently occurring inflections and affixes (e.g., -ed, -s, re-, un-, pre-, -ful, -less) as a clue to the meaning of an unknown word. Demonstrate understanding of frequently occurring verbs and adjectives by relating them to their opposites (antonyms). Recognize that spoken words are represented in written language by specific sequences of letters. Count, pronounce, blend, and segment syllables in spoken words. Continue a conversation through multiple exchanges. Write a letter or letters for most consonant and short-vowel sounds (phonemes). Identify real-life connections between words and their use (e.g., note places at school that are colorful). Understand that words are separated by spaces in print. Understand and use question words (interrogatives) (e.g., who, what, where, when, why, how). Spell simple words phonetically, drawing on knowledge of sound-letter relationships. Distinguish shades of meaning among verbs describing the same general action (e.g., walk, march, strut, prance) by acting out the meanings. Recognize and name all upper- and lowercase letters of the alphabet. Isolate and pronounce the initial, medial vowel, and final sounds (phonemes) in three-phoneme (consonant-vowel-consonant, or CVC) words. (This does not include CVCs ending with /l/, /r/, or /x/.) Use the most frequently occurring prepositions (e.g., to, from, in, out, on, off, for, of, by, with). Produce and expand complete sentences in shared language activities. Add or substitute individual sounds (phonemes) in simple, one-syllable words to make new words. Sort common objects into categories (for example: shapes, foods) to gain a sense of the concepts the categories represent. Identify the initial, final, and medial sounds of spoken words. recognizing spoken alliteration or groups of words that begin with the same onset or initial sound Listen with comprehension to follow two-step directions. Use new vocabulary that is directly taught through reading, speaking, and listening. Relate new vocabulary to prior knowledge. Read text consisting of short sentences comprised of learned sight words and consonant-vowel-consonant (CVC) words. Identify phonemes for letters. Ask a specific question and gather relevant information from various sources related to that question that inform clarity of purpose and conclusions about research. Identify a clear purpose for research or inquiry (for example: If the class is learning about trees, is my need to know more about pets related?). Use a variety of resources to answer questions of interest through guided inquiry (for example: texts read aloud or viewed, direct observation). Gather relevant information and check various information sources for accuracy (for example: In a class discussion focused on butterflies, students ask questions related to a butterfly and the life cycle.). Begin to identify key features of reality versus fantasy in stories, pictures, and events. Use increasingly complex and varied vocabulary. Understand the difference between a question and a statement. Follow two- to three-step directions. Attend to language during conversations, songs, stories or other learning experiences. Use language to express ideas and needs. Participate in conversations of more than three exchanges with peers and adults. Show interest in shared reading experiences and looking at books independently. Identify and discriminate between words in language. Identify and discriminate between separate syllables in words. Recognize how books are read, such as front-to-back and one page at a time, and recognize basic characteristics, such as title, author, and illustrator. Identify and discriminate between sounds and phonemes in language, such as attention to beginning and ending sounds of words and recognition that different words begin or end with the same sound. Ask and answer questions and make comments about print materials. Demonstrate interest in different kinds of literature, such as fiction and nonfiction books and poetry, on a range of topics. Retell stories or information from books through conversation, artistic works, creative movement, or drama. Recognize that writing is a way of communicating for a variety of purposes, such as giving information, sharing stories, or giving an opinion. Use scribbles, shapes, pictures, and letters to represent objects, stories, experiences, or ideas. Copy, trace, or independently write letters or words. Identify problems and search for solutions by asking questions during collaborative explorations of the topic; begin to state facts about the topic. Practice asking questions and making statements. Make predictions based on illustrations. Recognize patterns of sounds in songs, storytelling, and poetry through interactions and meaningful experiences. Recognize that the letters of the alphabet are a special category of visual graphics that can be individually named. Recognize that letters of the alphabet have distinct sound(s) associated with them. Attend to the beginning letters and sounds in familiar words. Identify letters and associate correct sounds with letters, including a minimum of ten letters, preferably including letters in the child’s name. Understand that print conveys meaning. Recognize print in everyday life, such as numbers, letters, one’s name, words, and familiar logos and signs. Understand conventions, such as print moves from left to right and top to bottom of a page. Recognize words as a unit of print and understand that letters are grouped to form words. Recognize the association between spoken or signed and written words. Analyze and interpret primary and secondary sources to ask and research historical questions about the Western Hemisphere (including North America, South America, Central America, and the islands of the Caribbean). Investigate the historical eras, individuals, groups, ideas, and themes within regions of the Western Hemisphere and their relationships with one another. Use geographic tools and sources to research and make geographic inferences and predictions about the Western Hemisphere. Investigate how different economic systems developed based on access to resources, societal values, and human experiences, in order to address the problem of scarcity. Apply an understanding of the historical context of significant current events, individuals, groups, ideas, and themes within regions of the Eastern Hemisphere and their relationships with one another, to draw conclusions, and solve problems. Use geographic tools to research and analyze patterns in human and physical systems in the United States. Apply the historical method of inquiry to formulate compelling questions, evaluate primary and secondary sources, analyze and interpret data, and argue for an interpretation defended by textual evidence. Use geographic tools and resources to analyze Earth's human systems and physical features to investigate and address geographic issues. Make connections among geographic variables that influence the interactions of people, places, and environments. Use observations of the sun, moon, and stars to describe patterns that can be predicted. Sunlight warms Earth’s surface. Plan and conduct investigations to provide evidence that vibrating materials can make sound and that sound can make materials vibrate. Make observations to construct an evidence-based account that objects in darkness can be seen only when illuminated. Plan and conduct investigations to determine the effect of placing objects made with different materials in the path of a beam of light. Use tools and materials to design and build a device that uses light or sound to solve the problem of communicating over a distance. Use materials to design a solution to a human problem by mimicking how plants and/or animals use their external parts to help them survive, grow, and meet their needs. Read texts and use media to determine patterns in behavior of parents and offspring that help offspring survive. Make observations to construct an evidence-based account that young plants and animals are like, but not exactly like, their parents. Make observations at different times of year to relate the amount of daylight to the time of year. Different kinds of matter exist and many of them can be either solid or liquid, depending on temperature. Matter can be described and classified by its observable properties. Heating or cooling a substance may cause changes that can be observed. Sometimes these changes are reversible, and sometimes they are not. There are many different kinds of living things in any area, and they exist in different places on land and in water. Things that people do to live comfortably can affect the world around them. But they can make choices that reduce their impacts on the land, water, air, and other living things. Plan and conduct an investigation to describe and classify different kinds of materials by their observable properties. Analyze data obtained from testing different materials to determine which materials have the properties that are best suited for an intended purpose. Make observations to construct an evidence-based account of how an object made of a small set of pieces can be disassembled and made into a new object. Construct an argument with evidence that some changes caused by heating or cooling can be reversed and some cannot. Develop a simple model that mimics the function of an animal in dispersing seeds or pollinating plants. Make observations of plants and animals to compare the diversity of life in different habitats. Use information from several sources to provide evidence that Earth events can occur quickly or slowly. Compare multiple solutions designed to slow or prevent wind or water from changing the shape of the land. Obtain information to identify where water is found on Earth and that it can be solid or liquid. Interdependent Relationships in Ecosystems: Animals depend on their surroundings to get what they need, including food, water, shelter and a favorable temperature. Animals depend on plants or other animals for food. They use their senses to find food and water, and they use their body parts to gather, catch, eat and chew the food. Plants depend on air, water, minerals (in the soil) and light to grow. Animals can move around, but plants cannot, and they often depend on animals for pollination or to move their seeds around. Different plants survive better in different settings because they have varied needs for water, minerals and sunlight. The History of Planet Earth: Some events on Earth occur in cycles, like day and night, and others have a beginning and an end, like a volcanic eruption. Some events, like an earthquake, happen very quickly; others, such as the formation of the Grand Canyon, occur very slowly over a time period much longer than one can observe. Earth Materials and Systems: Wind and water can change the shape of the land. The resulting landforms, together with the materials on the land, provide homes for living things. Plate Tectonics and Large-Scale System Interactions: Rocks, soils, and sand are present in most areas where plants and animals live. There may also be rivers, streams, lakes and ponds. Maps show where things are located. One can map the shapes and kinds of land and water in any area. The gravitational force of Earth acting on an object near Earth’s surface pulls that object toward the planet’s center. Each force acts on one particular object and has both strength and a direction. An object at rest typically has multiple forces acting on it, but they add to give zero net force on the object. Forces that do not sum to zero can cause changes in the object’s speed or direction of motion. (Boundary: Qualitative and conceptual, but not quantitative addition of forces are used at this level.) Objects in contact exert forces on each other. Electric and magnetic forces between a pair of objects do not require that the objects be in contact. The sizes of the forces in each situation depend on the properties of the objects and their distances apart and, for forces between two magnets, on their orientation relative to each other. Reproduction is essential to the continued existence of every kind of organism. Plants and animals have unique and diverse life cycles. Being part of a group helps animals obtain food, defend themselves, and cope with changes. Groups may serve different functions and vary dramatically in size. Sometimes the differences in characteristics between individuals of the same species provide advantages in surviving, finding mates, and reproducing. Populations live in a variety of habitats, and change in those habitats affects the organisms living there. The locations of mountain ranges, deep ocean trenches, ocean floor structures, earthquakes, and volcanoes occur in patterns. Most earthquakes and volcanoes occur in bands that are often along the boundaries between continents and oceans. Major mountain chains form inside continents or near their edges. Maps can help locate the different land and water features areas of Earth. Energy is present whenever there are moving objects, sound, light, or heat. When objects collide, energy can be transferred from one object to another, thereby changing their motion. In such collisions, some energy is typically also transferred to the surrounding air; as a result, the air gets heated and sound is produced. When objects collide, the contact forces transfer energy so as to change the objects’ motions. Waves, which are regular patterns of motion, can be made in water by disturbing the surface. When waves move across the surface of deep water, the water goes up and down in place; there is no net motion in the direction of the wave except when the water meets a beach. The expression “produce energy” typically refers to the conversion of stored energy into a desired form for practical use. An object can be seen when light reflected from its surface enters the eyes. Digitized information can be transmitted over long distances without significant degradation. High-tech devices, such as computers or cell phones, can receive and decode information—convert it from digitized form to voice—and vice versa. Different sense receptors are specialized for particular kinds of information, which may be then processed by the animal’s brain. Animals are able to use their perceptions and memories to guide their actions. Local, regional, and global patterns of rock formations reveal changes over time due to earth forces, such as earthquakes. The presence and location of certain fossil types indicate the order in which rock layers were formed. Rainfall helps to shape the land and affects the types of living things found in a region. Water, ice, wind, living organisms, and gravity break rocks, soils, and sediments into smaller particles and move them around. Living things affect the physical characteristics of their regions. Energy and fuels that humans use are derived from natural sources, and their use affects the environment in multiple ways. Some resources are renewable over time, and others are not. The energy released [from] food was once energy from the sun that was captured by plants in the chemical process that forms plant matter (from air and water). The food of almost any kind of animal can be traced back to plants. Organisms are related in food webs in which some animals eat plants for food and other animals eat the animals that eat plants. Some organisms, such as fungi and bacteria, break down dead organisms (both plants or plants parts and animals) and therefore operate as “decomposers.” Decomposition eventually restores (recycles) some materials back to the soil. Organisms can survive only in environments in which their particular needs are met. A healthy ecosystem is one in which multiple species of different types are each able to meet their needs in a relatively stable web of life. Newly introduced species can damage the balance of an ecosystem. Matter cycles between the air and soil and among plants, animals, and microbes as these organisms live and die. Organisms obtain gases, and water, from the environment, and release waste matter (gas, liquid, or solid) back into the environment. The sun is a star that appears larger and brighter than other stars because it is closer. Stars range greatly in their distance from Earth. Earth’s major systems are the geosphere (solid and molten rock, soil, and sediments), the hydrosphere (water and ice), the atmosphere (air), and the biosphere (living things, including humans). These systems interact in multiple ways to affect Earth’s surface materials and processes. The ocean supports a variety of ecosystems and organisms, shapes landforms, and influences climate. Winds and clouds in the atmosphere interact with the landforms to determine patterns of weather. Human activities in agriculture, industry, and everyday life have had major effects on the land, vegetation, streams, ocean, air, and even outer space. But individuals and communities are doing things to help protect Earth’s resources and environments. Nearly all of Earth’s available water is in the ocean. Most fresh water is in glaciers or underground; only a tiny fraction is in streams, lakes, wetlands, and the atmosphere. Plan and conduct an investigation to provide evidence of the effects of balanced and unbalanced forces on the motion of an object. Make observations and/or measurements of an object’s motion to provide evidence that a pattern can be used to predict future motion. Ask questions to determine cause and effect relationships of electric or magnetic interactions between two objects not in contact with each other. Construct an argument that some animals form groups that help members survive. Analyze and interpret data to provide evidence that plants and animals have traits inherited from parents and that variation of these traits exists in a group of similar organisms. Develop models to describe that organisms have unique and diverse life cycles but all have in common birth, growth, reproduction, and death. Use evidence to support the explanation that traits can be influenced by the environment. Analyze and interpret data from fossils to provide evidence of the organisms and the environments in which they lived long ago. Use evidence to construct an explanation for how the variations in characteristics among individuals of the same species may provide advantages in surviving, finding mates, and reproducing. Make a claim about the merit of a solution to a problem caused when the environment changes and the types of plants and animals that live there may change. Make a claim about the merit of a design solution that reduces the impacts of a weather-related hazard. Evidence of Common Ancestry and Diversity: Some kinds of plants and animals that once lived on Earth are no longer found anywhere. Fossils provide evidence about the types of organisms that lived long ago and also about the nature of their environments. Weather and Climate: Scientists record patterns of the weather across different times and areas so that they can make predictions about what kind of weather might happen next. Climate describes a range of an area’s typical weather conditions and the extent to which those conditions vary over years. Make observations to provide evidence that energy can be transferred from place to place by sound, light, heat, and electric currents. Use evidence to construct an explanation relating the speed of an object to the energy of that object. Ask questions and predict outcomes about the changes in energy that occur when objects collide. Apply scientific ideas to design, test, and refine a device that converts energy from one form to another. Develop a model of waves to describe patterns in terms of amplitude and wavelength and that waves can cause objects to move. Develop a model to describe that light reflecting from objects and entering the eye allows objects to be seen. Construct an argument that plants and animals have internal and external structures that function to support survival, growth, behavior, and reproduction. Use a model to describe that animals receive different types of information through their senses, process the information in their brain, and respond to the information in different ways. Identify evidence from patterns in rock formations and fossils in rock layers to support an explanation for changes in a landscape over time. Make observations and/or measurements to provide evidence of the effects of weathering or the rate of erosion by water, ice, wind, or vegetation. Obtain and combine information to describe that energy and fuels are derived from natural resources and their uses affect the environment. Generate and compare multiple solutions to reduce the impacts of natural Earth processes on humans. Measure and graph quantities to provide evidence that regardless of the type of change that occurs when heating, cooling, or mixing substances, the total weight of matter is conserved. Support an argument that the gravitational force exerted by Earth on objects is directed down. Use models to describe that energy in animals’ food (used for body repair, growth, and motion and to maintain body warmth) was once energy from the sun. Support an argument that plants get the materials they need for growth chiefly from air and water. Develop a model using an example to describe ways the geosphere, biosphere, hydrosphere, and/or atmosphere interact. Organization for Matter and Energy Flow in Organisms: Plants acquire their material for growth chiefly from air and water. Describe and graph the amounts of salt water and fresh water in various reservoirs to provide evidence about the distribution of water on Earth. Develop models to describe the atomic composition of simple molecules and extended structures. Develop a model that predicts and describes changes in particle motion, temperature, and state of a pure substance when thermal energy is added or removed. Undertake a design project to construct, test, and modify a device that either releases or absorbs thermal energy by chemical processes. Apply Newton’s Third Law to design a solution to a problem involving the motion of two colliding objects. Construct and present arguments using evidence to support the claim that gravitational interactions are attractive and depend on the masses of interacting objects. Use mathematical representations to describe a simple model for waves that includes how the amplitude of a wave is related to the energy in a wave. Develop and use a model to describe that waves are reflected, absorbed, or transmitted through various materials. Integrate qualitative scientific and technical information to support the claim that digitized signals are a more reliable way to encode and transmit information than analog signals. Develop a model to describe how food is rearranged through chemical reactions forming new molecules that support growth and/or release energy as this matter moves through an organism. Construct an argument supported by empirical evidence that changes to physical or biological components of an ecosystem affect populations. Develop a model to describe the cycling of matter and flow of energy among living and nonliving parts of an ecosystem. Evaluate competing design solutions for maintaining biodiversity and ecosystem services. Apply scientific ideas to construct an explanation for the anatomical similarities and differences among modern organisms and between modern and fossil organisms to infer evolutionary relationships. Develop and use a model to describe the role of gravity in the motions within galaxies and the solar system. Construct a scientific explanation based on evidence from rock strata for how the geologic time scale is used to organize Earth's 4.6-billion-year-old history. Analyze and interpret data on the distribution of fossils and rocks, continental shapes, and seafloor structures to provide evidence of the past plate motions. Develop a model to describe the cycling of water through Earth's systems driven by energy from the sun and the force of gravity. Construct a scientific explanation based on evidence for how the uneven distributions of Earth's mineral, energy, and groundwater resources are the result of past and current geoscience processes. Apply scientific principles to design a method for monitoring and minimizing a human impact on the environment. Apply scientific principles to design, construct, and test a device that either minimizes or maximizes thermal energy transfer. Construct, use, and present arguments to support the claim that when the kinetic energy of an object changes, energy is transferred to or from the object. Construct and interpret graphical displays of data to describe the relationships of kinetic energy to the mass of an object and to the speed of an object. Conduct an investigation to provide evidence that living things are made of cells; either one cell or many different numbers and types of cells. Develop and use a model to describe the function of a cell as a whole and ways the parts of cells contribute to the function. Use argument supported by evidence for how the body is a system of interacting subsystems composed of groups of cells. Gather and synthesize information that sensory receptors respond to stimuli by sending messages to the brain for immediate behavior or storage as memories. Construct an explanation that predicts patterns of interactions among organisms across multiple ecosystems. Human activities have significantly altered the biosphere, sometimes damaging or destroying natural habitats and causing the extinction of other species. But changes to Earth’s environments can have different impacts (negative and positive) for different living things. Human activities, such as the release of greenhouse gases from burning fossil fuels, are major factors in the current rise in Earth’s mean surface temperature (global warming). Reducing the level of climate change and reducing human vulnerability to whatever climate changes do occur depend on the understanding of climate science, engineering capabilities, and other kinds of knowledge, such as understanding of human behavior and on applying that knowledge wisely in decisions and activities. Develop and use a model to describe how unequal heating and rotation of the Earth cause patterns of atmospheric and oceanic circulation that determine regional climates. All living things are made up of cells, which is the smallest unit that can be said to be alive. An organism may consist of one single cell (unicellular) or many different numbers and types of cells (multicellular). Each sense receptor responds to different inputs (electromagnetic, mechanical, chemical), transmitting them as signals that travel along nerve cells to the brain. The signals are then processed in the brain, resulting in immediate behaviors or memories. Analyze and interpret data on the properties of substances before and after the substances interact to determine if a chemical reaction has occurred. Gather and make sense of information to describe that synthetic materials come from natural resources and impact society. Plan an investigation to provide evidence that the change in an object’s motion depends on the sum of the forces on the object and the mass of the object. Conduct an investigation and evaluate the experimental design to provide evidence that fields exist between objects exerting forces on each other even though the objects are not in contact. Analyze and interpret data for patterns in the fossil record that document the existence, diversity, extinction, and change of life forms throughout the history of life on Earth under the assumption that natural laws operate today as in the past. Construct an explanation based on evidence that describes how genetic variations of traits in a population increase some individuals’ probability of surviving and reproducing in a specific environment. Gather and synthesize information about technologies that have changed the way humans influence the inheritance of desired traits in organisms. Ecosystems are dynamic in nature; their characteristics can vary over time. Disruptions to any physical or biological component of an ecosystem can lead to shifts in all its populations. Changes in biodiversity can influence humans’ resources, such as food, energy, and medicines, as well as ecosystem services that humans rely on— for example, water purification and recycling. Humans depend on Earth’s land, ocean, atmosphere, and biosphere for many different resources. Minerals, fresh water, and biosphere resources are limited, and many are not renewable or replaceable over human lifetimes. These resources are distributed unevenly around the planet as a result of past geologic processes. Mapping the history of natural hazards in a region, combined with an understanding of related geologic forces can help forecast the locations and likelihoods of future events. Interdependent Relationships in Ecosystems: Organisms, and populations of organisms, are dependent on their environmental interactions both with other living things and with nonliving factors. In any ecosystem, organisms and populations with similar requirements for food, water, oxygen, or other resources may compete with each other for limited resources, access to which consequently constrains their growth and reproduction. Growth of organisms and population increases are limited by access to resources. Electric and magnetic (electromagnetic) forces can be attractive or repulsive, and their sizes depend on the magnitudes of the charges, currents, or magnetic strengths involved and on the distances between the interacting objects. Definitions of Energy: Motion energy is properly called kinetic energy; it is proportional to the mass of the moving object and grows with the square of its speed. A system of objects may also contain stored (potential) energy, depending on their relative positions. Temperature is a measure of the average kinetic energy of particles of matter. The relationships between the temperature and total energy of a system depends on the types, states, and amounts of matter present. Genes are located in the chromosomes of cells, with each chromosome pair containing two variants of each of many distinct genes. Each distinct gene chiefly controls the production of specific proteins, which in turn affects the traits of the individual. Changes (mutations) to genes can result in changes to proteins, which can affect the structures and functions of the organism and thereby change traits. In artificial selection, humans have the capacity to influence certain characteristics of organisms by selective breeding. One can choose desired parental traits determined by genes, which are then passed on to offspring. Adaptation by natural selection acting over generations is one important process by which species change over time in response to changes in environmental conditions. Traits that support successful survival and reproduction in the new environment become more common; those that do not become less common. Thus, the distribution of traits in a population changes. The geologic time scale interpreted from rock strata provides a way to organize Earth’s history. Analyses of rock strata and the fossil record provide only relative dates, not an absolute scale. Forces and Motion: For any pair of interacting objects, the force exerted by the first object on the second object is equal in strength to the force that the second object exerts on the first, but in the opposite direction (Newton’s third law). The motion of an object is determined by the sum of the forces acting on it; if the total force on the object is not zero, its motion will change. The greater the mass of the object, the greater the force needed to achieve the same change in motion. For any given object, a larger force causes a larger change in motion. All positions of objects and the directions of forces and motions must be described in an arbitrarily chosen reference frame and arbitrarily chosen units of size. In order to share information with other people, these choices must also be shared. Relationship Between Energy and Forces: When two objects interact, each one exerts a force on the other that can cause energy to be transferred to or from the object. For example, when energy is transferred to an Earth-object system as an object is raised, the gravitational field energy of the system increases. This energy is released as the object falls; the mechanism of this release is the gravitational force. Likewise, two magnetic and electrically charged objects interacting at a distance exert forces on each other that can transfer energy between the interacting objects. Wave Properties: A simple wave has a repeating pattern with a specific wavelength, frequency, and amplitude. A sound wave needs a medium through which it is transmitted. Geologists use seismic waves and their reflection at interfaces between layers to probe structures deep in the planet. Growth and Development of Organisms: Organisms reproduce, either sexually or asexually, and transfer their genetic information to their offspring. Animals engage in characteristic behaviors that increase the odds of reproduction. Plants reproduce in a variety of ways, sometimes depending on animal behavior and specialized features for reproduction. Genetic factors as well as local conditions affect the growth of the adult plant. The Universe and Its Stars: Patterns of the apparent motion of the sun, the moon, and stars in the sky can be observed, described, predicted, and explained with models. Earth and its solar system are part of the Milky Way galaxy, which is one of many galaxies in the universe. Plate Tectonics and Large-Scale Systems and Interactions: Tectonic processes continually generate new ocean sea floor at ridges and destroy old sea floor at trenches. Maps of ancient land and water patterns, based on investigations of rocks and fossils, make clear how Earth’s plates have moved great distances, collided, and spread apart. The Roles of Water in Earth’s Surface Processes: The planet’s systems interact over scales that range from microscopic to global in size, and they operate over fractions of a second to billions of years. These interactions have shaped Earth’s history and will determine its future. Water’s movements — both on the land and underground — cause weathering and erosion, which change the land’s surface features and create underground formations. Water continually cycles among land, ocean, and atmosphere via transpiration, evaporation, condensation and crystallization, and precipitation, as well as downhill flows on land. Global movements of water and its changes in form are propelled by sunlight and gravity. The complex patterns of the changes and the movement of water in the atmosphere, determined by winds, landforms, and ocean temperatures and currents, are major determinants of local weather patterns. Weather and climate are influenced by interactions involving sunlight, the ocean, the atmosphere, ice, landforms, and living things. These interactions vary with latitude, altitude, and local and regional geography, all of which can affect oceanic and atmospheric flow patterns. Because these patterns are so complex, weather can only be predicted probabilistically. The ocean exerts a major influence on weather and climate by absorbing energy from the sun, releasing it over time, and globally redistributing it through ocean currents. Use the periodic table as a model to predict the relative properties of elements based on the patterns of electrons in the outermost energy level of atoms. Plan and conduct an investigation to gather evidence to compare the structure of substances at the bulk scale to infer the strength of electrical forces between particles. Apply scientific principles and evidence to provide an explanation about the effects of changing the temperature or concentration of the reacting particles on the rate at which a reaction occurs. Apply science and engineering ideas to design, evaluate, and refine a device that minimizes the force on a macroscopic object during a collision. Communicate scientific and technical information about why the molecular-level structure is important in the functioning of designed materials. Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motion of particles (objects) and energy associated with the relative positions of particles (objects). Design, build, and refine a device that works within given constraints to convert one form of energy into another form of energy. Develop and use a model of two objects interacting through electric or magnetic fields to illustrate the forces between objects and the changes in energy of the objects due to the interaction. Evaluate questions about the advantages of using digital transmission and storage of information. Evaluate the claims, evidence, and reasoning behind the idea that electromagnetic radiation can be described either by a wave model or a particle model, and that for some situations one model is more useful than the other. Evaluate the validity and reliability of claims in published materials of the effects that different frequencies of electromagnetic radiation have when absorbed by matter. Communicate technical information about how some technological devices use the principles of wave behavior and wave interactions with matter to transmit and capture information and energy. Develop and use a model to illustrate the hierarchical organization of interacting systems that provide specific functions within multicellular organisms. Use a model to illustrate the role of cellular division (mitosis) and differentiation in producing and maintaining complex organisms. Use mathematical representations to support and revise explanations based on evidence about factors affecting biodiversity and populations in ecosystems of different scales. Develop a model to illustrate the role of photosynthesis and cellular respiration in the cycling of carbon among the biosphere, atmosphere, hydrosphere, and geosphere. Evaluate claims, evidence, and reasoning that the complex interactions in ecosystems maintain relatively consistent numbers and types of organisms in stable conditions, but changing conditions may result in a new ecosystem. Design, evaluate, and refine a solution for reducing the impacts of human activities on the environment and biodiversity. Evaluate evidence for the role of group behavior on individual and species’ chances to survive and reproduce. Ask questions to clarify relationships about the role of DNA and chromosomes in coding the instructions for characteristic traits passed from parents to offspring. Apply concepts of statistics and probability to explain the variation and distribution of expressed traits in a population. Communicate scientific information that common ancestry and biological evolution are supported by multiple lines of empirical evidence. Construct an explanation based on evidence that the process of evolution primarily results from four factors: (1) the potential for a species to increase in number, (2) the heritable genetic variation of individuals in a species due to mutation and sexual reproduction, (3) competition for limited resources, and (4) the proliferation of those organisms that are better able to survive and reproduce in the environment. Construct an explanation based on evidence for how natural selection leads to adaptation of populations. Evaluate the evidence supporting claims that changes in environmental conditions may result in (1) increases in the number of individuals of some species, (2) the emergence of new species over time, and (3) the extinction of other species. Construct an explanation of the Big Bang theory based on astronomical evidence of light spectra, motion of distant galaxies, and composition of matter in the universe. Use mathematical or computational representations to predict the motion of orbiting objects in the solar system. Apply scientific reasoning and evidence from ancient Earth materials, meteorites, and other planetary surfaces to construct an account of Earth’s formation and early history. Develop a model to illustrate how Earth’s internal and surface processes operate at different spatial and temporal scales to form continental and ocean-floor features. Develop a model based on evidence of Earth’s interior to describe the cycling of matter by thermal convection. Analyze geoscience data to make the claim that one change to Earth's surface can create feedbacks that cause changes to other Earth systems. Use a model to describe how variations in the flow of energy into and out of Earth’s systems result in changes in climate. Construct an explanation based on evidence for how the availability of natural resources, occurrence of natural hazards, and changes in climate have influenced human activity. Humans depend on the living world for the resources and other benefits provided by biodiversity. But human activity is also having adverse impacts on biodiversity through overpopulation, overexploitation, habitat destruction, pollution, introduction of invasive species, and climate change. Thus sustaining biodiversity so that ecosystem functioning and productivity are maintained is essential to supporting and enhancing life on Earth. Sustaining biodiversity also aids humanity by preserving landscapes of recreational or inspirational value. Chemical processes, their rates, and whether or not energy is stored or released can be understood in terms of the collisions of molecules and the rearrangements of atoms into new molecules, with consequent changes in the sum of all bond energies in the set of molecules that are matched by changes in kinetic energy. When two objects interacting through a field change relative position, the energy stored in the field is changed. The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing. Multiple technologies based on the understanding of waves and their interactions with matter are part of everyday experiences in the modern world (e.g., medical imaging, communications, scanners) and in scientific research. They are essential tools for producing, transmitting, and capturing signals and for storing and interpreting the information contained in them. Ecosystems have carrying capacities, which are limits to the numbers of organisms and populations they can support. These limits result from such factors as the availability of living and nonliving resources and from such challenges such as predation, competition, and disease. Organisms would have the capacity to produce populations of great size were it not for the fact that environments and resources are finite. This fundamental tension affects the abundance (number of individuals) of species in any given ecosystem. Group behavior has evolved because membership can increase the chances of survival for individuals and their genetic relatives. Each chromosome consists of a single very long DNA molecule, and each gene on the chromosome is a particular segment of that DNA. The instructions for forming species’ characteristics are carried in DNA. All cells in an organism have the same genetic content, but the genes used (expressed) by the cell may be regulated in different ways. Not all DNA codes for a protein; some segments of DNA are involved in regulatory or structural functions, and some have no as-yet known function. Natural selection occurs only if there is both (1) variation in the genetic information between organisms in a population and (2) variation in the expression of that genetic information—that is, trait variation—that leads to differences in performance among individuals. Evolution is a consequence of the interaction of four factors: (1) the potential for a species to increase in number, (2) the genetic variation of individuals in a species due to mutation and sexual reproduction, (3) competition for an environment’s limited supply of the resources that individuals need in order to survive and reproduce, and (4) the ensuing proliferation of those organisms that are better able to survive and reproduce in that environment. Although active geologic processes, such as plate tectonics and erosion, have destroyed or altered most of the very early rock record on Earth, other objects in the solar system, such as lunar rocks, asteroids, and meteorites, have changed little over billions of years. Studying these objects can provide information about Earth’s formation and early history. The abundance of liquid water on Earth’s surface and its unique combination of physical and chemical properties are central to the planet’s dynamics. These properties include water’s exceptional capacity to absorb, store, and release large amounts of energy, transmit sunlight, expand upon freezing, dissolve and transport materials, and lower the viscosities and melting points of rocks. Types of Interactions: Newton’s law of universal gravitation and Coulomb’s law provide the mathematical models to describe and predict the effects of gravitational and electrostatic forces between distant objects. Forces at a distance are explained by fields (gravitational, electric, and magnetic) permeating space that can transfer energy through space. Magnets or electric currents cause magnetic fields; electric charges or changing magnetic fields cause electric fields. Attraction and repulsion between electric charges at the atomic scale explain the structure, properties, and transformations of matter, as well as the contact forces between material objects. Pushing or pulling on an object can change the speed or direction of its motion and can start or stop it. When objects touch or collide, they push on one another and can change motion. All animals need food in order to live and grow. They obtain their food from plants or from other animals. Plants need water and light to live and grow. Weather is the combination of sunlight, wind, snow or rain, and temperature in a particular region at a particular time. People measure these conditions to describe and record the weather and to notice patterns over time. Plants and animals can change their environment. Living things need water, air, and resources from the land, and they live in places that have the things they need. Humans use natural resources for everything they do. Some kinds of severe weather are more likely than others in a given region. Weather scientists forecast severe weather so that the communities can prepare for and respond to these events. Plan and conduct an investigation to compare the effects of different strengths or different directions of pushes and pulls on the motion of an object. Analyze data to determine if a design solution works as intended to change the speed or direction of an object with a push or a pull. Make observations to determine the effect of sunlight on Earth’s surface. Use tools and materials to design and build a structure that will reduce the warming effect of sunlight on an area. Use observations to describe patterns of what plants and animals (including humans) need to survive. Construct an argument supported by evidence for how plants and animals (including humans) can change the environment to meet their needs. Use and share observations of local weather conditions to describe patterns over time. Use a model to represent the relationship between the needs of different plants and animals (including humans) and the places they live. Ask questions to obtain information about the purpose of weather forecasting to prepare for, and respond to, severe weather. Communicate solutions that will reduce the impact of humans on the land, water, air, and/or other living things in the local environment. Relationship Between Energy and Forces: A bigger push or pull makes things speed up or slow down more quickly. By the end of the preschool experience (approximately 60 months/5 years old), students may: Observe, describe, and discuss living things and natural processes. Use senses to explore the properties of objects and materials (e.g., solids, liquids). Collect, describe, predict and record information using words, drawings, maps, graphs and charts. Recognize and investigate cause - and - effect relationships in everyday experiences (pushing, pulling, kicking, rolling or blowing objects). Notice change in matter. Observe, describe and discuss properties of materials and transformation of substances. Seek answers to questions and test predictions using simple experiments. Observe similarities and differences in the needs of living things. Observe and describe how natural habitats provide for the basic needs of plants and animals with respect to shelter, food, water, air and light. Ask and pursue questions through simple investigations and observations of living things. Collect, describe, and record information about living things through discussion, drawings, graphs, technology and charts. Identify differences between living and nonliving things. Identify the common needs such as food, air and water of familiar living things. Predict, explain and infer patterns based on observations and representations of living things, their needs and life cycles. Observe and document changes in living things over time using different modalities such as drawing, dramatization, describing or using technology. Recognize that plants and animals grow and change. Use senses and tools, including technology, to investigate materials, and observe processes and relationships to gather information and explore the environment. Inquire about the natural and physical environment. Observe and discuss common properties, differences and comparisons among objects. Participate in simple investigations to form hypothesis, gather observations, draw conclusions. Record observations using words, drawings, maps, graphs and charts. Predict, explain and infer patterns based on observations and evidence. Recognizes familiar elements of the natural world and demonstrates an understanding that these may change over time (e.g., sun and moon, weather). Articulate findings through a variety of modalities (e.g., drawings, words, dramatizations). Observe and describe patterns observed over the course of a number of days and nights (e.g., differences in the activities or appearance of plants and animals). Computational thinking is used to create algorithmic solutions to real-world problems. Evaluate the ways computing impacts personal, ethical, social, economic, and cultural practices. The creation of a computer program requires a design process. Collaborative tools, methods and strategies can be used to design, develop and update computational artifacts. Client-based design requirements and feedback are essential to a quality computational product or service. Security and software licensing can present constraints and restrictions in computational design and development. Apply effective verbal and nonverbal communication skills to enhance health. Identify valid and reliable resources regarding qualities of healthy family and peer relationships. Evaluate the validity and reliability of information, products, and services to enhance healthy eating behaviors. Comprehend the relationship between feelings and actions during adolescence. Analyze how positive health behaviors can benefit people throughout their lifespan. Describe the interrelationships of emotional, intellectual, physical, and social health. Analyze how family, culture, media, peers, and personal beliefs affect a health-related decision. Support others in making positive and healthful choices about sexual behavior. Use a decision-making process to make healthy decisions about relationships and sexual health. Demonstrate beginning strategies for a variety of activities, games, or sports. Recognize how health-related and skill-related fitness components contribute to a health-enhancing lifestyle that embraces physical fitness. Engage in a variety of lifelong physical activities at a competent level. Recognize how movement concepts affect brain development. Develop, implement and monitor an individual health and fitness plan by establishing goals based on fitness assessment data. Examine resources to maintain lifelong health and wellness. Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Identify real-life connections between words and their use (e.g., describe foods that are spicy or juicy). Explain the relationships or interactions between two or more individuals, events, ideas, or concepts in a historical, scientific, or technical text based on specific information in the text. Form and use verbs in the active and passive voice. Engage and orient the reader by establishing a context and introducing a narrator and/or characters; organize an event sequence that unfolds naturally and logically. Consult general and specialized reference materials (for example: dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning or its part of speech. Correctly spell frequently used words and consult reference materials (for example: dictionaries, both print and digital, spell check, and/or trusted peers and/or adults) to determine the spelling of less frequent vocabulary. Analyze data to support the claim that Newton’s second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration. Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. Solve problems involving velocity and other quantities that can be represented by vectors. Understand vector subtraction v - w as v + (-w), where -w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise. Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Multiply one-digit whole numbers by multiples of 10 in the range 10—90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles. Fluently multiply multi-digit whole numbers using the standard algorithm. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) Classify two-dimensional figures in a hierarchy based on properties. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. Angles are taken to angles of the same measure. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area. Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model. Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes. Identify words and phrases in stories or poems that suggest feelings or appeal to the senses. Identify the reasons an author gives to support points in a text. Ask and answer questions about what a speaker says in order to gather additional information or clarify something that is not understood. Read on-level text with purpose and understanding. Identify frequently occurring root words (e.g., look) and their inflectional forms (e.g., looks, looked, looking). Isolate and pronounce initial, medial vowel, and final sounds (phonemes) in spoken single-syllable words. Write complete simple sentences. Develop claim(s) and counterclaims fairly and thoroughly, supplying the most relevant evidence for each while pointing out the strengths and limitations of both in a manner that anticipates the audience's knowledge level, concerns, values, and possible biases. Use precise language and domain-specific vocabulary to manage the complexity of the topic. Evaluate a speaker's point of view, reasoning, and use of evidence and rhetoric, assessing the stance, premises, links among ideas, word choice, points of emphasis, and tone used. Resolve issues of complex or contested usage, consulting references (e.g., Merriam-Webster's Dictionary of English Usage, Garner's Modern American Usage) as needed. Work with peers to promote civil, democratic discussions and decision-making, set clear goals and deadlines, and establish individual roles as needed. Provide a conclusion that follows from and reflects on what is experienced, observed, or resolved over the course of the narrative. read and comprehend literature, including stories, dramas, and poems, at the high end of the grades 9–10 text complexity band independently and proficiently. Analyze the representation of a subject or a key scene in two different artistic mediums, including what is emphasized or absent in each treatment (e.g., Auden's "Musée des Beaux Arts" and Breughel's Landscape with the Fall of Icarus). Analyze seminal U.S. documents of historical and literary significance (e.g., Washington's Farewell Address, the Gettysburg Address, Roosevelt's Four Freedoms speech, King's "Letter from Birmingham Jail"), including how they address related themes and concepts. Use technology, including the Internet, to produce, publish, and update individual or shared writing products, taking advantage of technology's capacity to link to other information and to display information flexibly and dynamically. Work with peers to set rules for collegial discussions and decision-making (e.g., informal consensus, taking votes on key issues, presentation of alternate views), clear goals and deadlines, and individual roles as needed. Use precise words and phrases, telling details, and sensory language to convey a vivid picture of the experiences, events, setting, and/or characters. Analyze a case in which grasping point of view requires distinguishing what is directly stated in a text from what is really meant (e.g., satire, sarcasm, irony, or understatement). Engage and orient the reader by setting out a problem, situation, or observation and its significance, establishing one or multiple point(s) of view, and introducing a narrator and/or characters; create a smooth progression of experiences or events. Write routinely over extended time frames (time for reflection and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. read and comprehend literary nonfiction in the grades 11—CCR text complexity band proficiently, with scaffolding as needed at the high end of the range. By the end of grade 12, read and comprehend literary nonfiction at the high end of the grades 11—CCR text complexity band independently and proficiently. Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. Consult general and specialized reference materials (for example: dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning, its part of speech, its etymology, or its standard usage. Interpret figures of speech (for example: hyperbole, paradox) in context and analyze their role in the text. By the end of year, read and comprehend informational texts, including history/social studies, science, and technical texts, in the grades 2—3 text complexity band proficiently, with scaffolding as needed at the high end of the range. Participate in shared research and writing projects (e.g., read a number of books on a single topic to produce a report; record science observations). Describe how reasons support specific points the author makes in a text. Recount stories, including fables and folktales from diverse cultures, and determine their central message, lesson, or moral. Use an apostrophe to form contractions and frequently occurring possessives. Provide a concluding statement or section. Demonstrate use of self-monitoring comprehension strategies: rereading, checking context clues, predicting, questioning, clarifying, activating schema/background knowledge to construct meaning and draw inferences. Create new words by combining base words with affixes to connect known words to new words. Apply knowledge about structure and craft gained from mentor text to narrative writing. Report on a topic or text, tell a story, or recount an experience with appropriate facts and relevant, descriptive details, speaking clearly at an understandable pace. Describe the logical connection between particular sentences and paragraphs in a text (e.g., comparison, cause/effect, first/second/third in a sequence). Describe the relationship between a series of historical events, scientific ideas or concepts, or steps in technical procedures in a text, using language that pertains to time, sequence, and cause/effect. Distinguish their own point of view from that of the author of a text. Compare and contrast the most important points and key details presented in two texts on the same topic. Establish a situation and introduce a narrator and/or characters; organize an event sequence that unfolds naturally. Read on-level prose and poetry orally with accuracy, appropriate rate, and expression on successive readings Develop the topic with facts, definitions, and details. Develop supporting visual information (for example: charts, maps, illustrations, models). Present a brief report of the research findings to an audience. Identify the reasons and evidence a speaker provides to support particular points. Introduce a topic or text clearly, state an opinion, and create an organizational structure in which related ideas are grouped to support the writer's purpose. Use common, grade-appropriate Greek and Latin affixes and roots as clues to the meaning of a word (e.g., telegraph, photograph, autograph). Read on-level prose and poetry orally with accuracy, appropriate rate, and expression on successive readings Use a comma before a coordinating conjunction in a compound sentence. Link opinion and reasons using words and phrases (e.g., for instance, in order to, in addition). Use a variety of transitional words and phrases to manage the sequence of events. Provide a conclusion that follows from the narrated experiences or events. Explain how an author uses reasons and evidence to support particular points in a text, identifying which reasons and evidence support which point(s). With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach. Describe how a narrator's or speaker's point of view influences how events are described. Read on-level text with purpose and understanding. Link opinion and reasons using words, phrases, and clauses (e.g., consequently, specifically). Review the key ideas expressed and draw conclusions in light of information and knowledge gained from the discussions. Include multimedia components (for example: graphics, sound) and visual displays in presentations when appropriate to enhance the development of main ideas or themes. Form and use the perfect (for example: I had walked; I have walked; I will have walked) verb tenses. Listen to others’ ideas and form their own opinions. Locate information to support opinions, predictions, inferences, and identification of the author’s message or theme. Develop relevant supporting visual information (for example: charts, maps, graphs, photo evidence, models). Use appropriate and varied transitions to create cohesion and clarify the relationships among ideas and concepts. Provide a concluding statement or section that follows from and supports the argument presented. Place phrases and clauses within a sentence, recognizing and correcting misplaced and dangling modifiers. Choose language that expresses ideas precisely and concisely, recognizing and eliminating wordiness and redundancy. Integrate information presented in different media or formats (e.g., visually, quantitatively) as well as in words to develop a coherent understanding of a topic or issue. Compare and contrast the experience of reading a story, drama, or poem to listening to or viewing an audio, video, or live version of the text, including contrasting what they "see" and "hear" when reading the text to what they perceive when they listen or watch. Compare and contrast texts in different forms or genres (e.g., stories and poems; historical novels and fantasy stories) in terms of their approaches to similar themes and topics. Use context (for example: the overall meaning of a sentence or paragraph; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase. Analyze the interactions between individuals, events, and ideas in a text (e.g., how ideas influence individuals or events, or how individuals influence ideas or events). Analyze how particular elements of a story or drama interact (e.g., how setting shapes the characters or plot). Compare and contrast a fictional portrayal of a time, place, or character and a historical account of the same period as a means of understanding how authors of fiction use or alter history. Follow rules for collegial discussions, track progress toward specific goals and deadlines, and define individual roles as needed. By the end of the year, read and comprehend literary nonfiction at the high end of the grades 6—8 text complexity band independently and proficiently. Compare and contrast the structure of two or more texts and analyze how the differing structure of each text contributes to its meaning and style. Integrate multimedia and visual displays into presentations to clarify information, strengthen claims and evidence, and add interest. Analyze a case in which two or more texts provide conflicting information on the same topic and identify where the texts disagree on matters of fact or interpretation. Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience. Actively engage in group reading activities with purpose and understanding. Blend and segment onsets and rimes of single-syllable spoken words. Experiment with writing tools and materials. Ask primary questions of clarity, significance, relevance, and accuracy to improve quality of thinking. Speak in sentences of five or six words. Describe current forms of government and the specific roles played by citizens in countries of the Western Hemisphere. Evaluate how regional differences and perspectives in the Western Hemisphere impact human and environmental interactions. Investigate the role of consumers and businesses within the Western Hemisphere. Analyze and interpret a variety of primary and secondary sources from multiple perspectives in the Eastern Hemisphere to formulate an appropriate thesis supported by relevant evidence. Develop a contextual understanding of the historical eras, individuals, groups, ideas, and themes from the origins of the American Revolution through Reconstruction. Apply consumer skills to budgeting, spending, saving, and borrowing decisions. Analyze and evaluate key concepts of continuity and change, cause and effect, complexity, unity and diversity, and significant ideas in the United States from Reconstruction to the present. Analyze and evaluate key concepts of continuity and change, cause and effect, complexity, unity and diversity, and significant ideas throughout the world from the Renaissance to the present. Plan and conduct an investigation to determine if plants need sunlight and water to grow. Develop a model to represent the shapes and kinds of land and bodies of water in an area. The Roles of Water in Earth’s Surface Processes: Water is found in the ocean, rivers, lakes and ponds. Water exists as solid ice and in liquid form. It carries soil and rocks from one place to another and determines the variety of life forms that can live in a particular location. Different organisms vary in how they look and function because they have different inherited information. For any particular environment, some kinds of organisms survive well, some survive less well, and some cannot survive at all. Define a simple design problem that can be solved by applying scientific ideas about magnets. Construct an argument with evidence that in a particular habitat some organisms can survive well, some survive less well, and some cannot survive at all. Represent data in tables and graphical displays to describe typical weather conditions expected during a particular season. Obtain and combine information to describe climates in different regions of the world. Ecosystem Dynamics, Functioning, and Resilience: When the environment changes in ways that affect a place’s characteristics, temperature or availability of resources, some organisms survive and reproduce, others move to new locations, yet others move into the transformed environment, and some die. Generate and compare multiple solutions that use patterns to transfer information. Analyze and interpret data from maps to describe patterns of Earth’s features. Definitions of Energy Energy can be moved from place to place by moving objects or through sound, light, or electric currents. Develop a model to describe that matter is made of particles too small to be seen. Conduct an investigation to determine whether the mixing of two or more substances results in new substances. Develop a model to describe the movement of matter among plants, animals, decomposers, and the environment. Represent data in graphical displays to reveal patterns of daily changes in length and direction of shadows, day and night, and the seasonal appearance of some stars in the night sky. Obtain and combine information about ways individual communities use science ideas to protect the Earth’s resources and environment. Chemical Reactions: No matter what reaction or change in properties occurs, the total weight of the substances does not change. (Boundary Statement: Mass and weight are not distinguished at this grade level.) When two or more different substances are mixed, a new substance with different properties may be formed. Analyze and interpret data to determine scale properties of objects in the solar system. Analyze and interpret data on natural hazards to forecast future catastrophic events and inform the development of technologies to mitigate their effects. Ask questions to clarify evidence of the factors that have caused the rise in global temperatures over the past century. Plan an investigation to determine the relationships among the energy transferred, the type of matter, the mass, and the change in the average kinetic energy of the particles as measured by the temperature of the sample. Analyze and interpret data to provide evidence for the effects of resource availability on organisms and populations of organisms in an ecosystem. Collect data to provide evidence for how the motions and complex interactions of air masses result in changes in weather conditions. Weather and climate are influenced by interactions involving sunlight, the ocean, the atmosphere, ice, landforms, and living things. These interactions vary with latitude, altitude, and local and regional geography, all of which can affect oceanic and atmospheric flow patterns. Develop and use a model to describe how the total number of atoms does not change in a chemical reaction and thus mass is conserved. Develop and use a model to describe why structural changes to genes (mutations) located on chromosomes may affect proteins and may result in harmful, beneficial, or neutral effects to the structure and function of the organism. Analyze displays of pictorial data to compare patterns of similarities in the embryological development across multiple species to identify relationships not evident in the fully formed anatomy. Use mathematical representations to support explanations of how natural selection may lead to increases and decreases of specific traits in populations over time. The collection of fossils and their placement in chronological order (e.g., through the location of the sedimentary layers in which they are found or through radioactive dating) is known as the fossil record. It documents the existence, diversity, extinction, and change of many life forms throughout the history of life on Earth. Structure and Properties of Matter: Substances are made from different types of atoms, which combine with one another in various ways. Atoms form molecules that range in size from two to thousands of atoms. Solids may be formed from molecules, or they may be extended structures with repeating sub-units (e.g., crystals). Each pure substance has characteristic physical and chemical properties (for any bulk quantity under given conditions) that can be used to identify it. Gases and liquids are made of molecules or inert atoms that are moving about relative to each other. In a liquid, the molecules are constantly in contact with others; in a gas, they are widely spaced except when they happen to collide. In a solid, atoms are closely spaced and may vibrate in position but do not change relative locations. The changes of state that occur with variations in temperature or pressure can be described and predicted using these models of matter. In a liquid, the molecules are constantly in contact with others; in a gas, they are widely spaced except when they happen to collide. In a solid, atoms are closely spaced and may vibrate in position but do not change relative locations. The changes of state that occur with variations in temperature or pressure can be described and predicted using these models of matter. Use mathematical representations to support the claim that atoms, and therefore mass, are conserved during a chemical reaction. Use mathematical representations of Newton’s Law of Gravitation and Coulomb’s Law to describe and predict the gravitational and electrostatic forces between objects. Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics). Construct an explanation based on evidence for how the structure of DNA determines the structure of proteins, which carry out the essential functions of life through systems of specialized cells. Plan and conduct an investigation to provide evidence that feedback mechanisms maintain homeostasis. Use mathematical and/or computational representations to support explanations of factors that affect carrying capacity of ecosystems at different scales. Develop a model based on evidence to illustrate the life span of the sun and the role of nuclear fusion in the sun’s core to release energy that eventually reaches Earth in the form of radiation. Communicate scientific ideas about the way stars, over their life cycle, produce elements. Construct an argument based on evidence about the simultaneous coevolution of Earth’s systems and life on Earth. Evaluate competing design solutions for developing, managing, and utilizing energy and mineral resources based on cost-benefit ratios. Evaluate or refine a technological solution that reduces impacts of human activities on natural systems. Structure and Function Systems of specialized cells within organisms help them perform the essential functions of life. All cells contain genetic information, in the form of DNA. Genes are specific regions within the extremely large DNA molecules that form the chromosomes. Genes contain the instructions that code for the formation of molecules called proteins, which carry out most of the work of cells to perform the essential functions of life. Proteins provide structural components, serve as signaling devices, regulate cell activities, and determine the performance of cells through their enzymatic actions Conservation of energy means that the total change of energy in any system is always equal to the total energy transferred into or out of the system. Although energy cannot be destroyed, it can be converted to less useful forms—for example, to thermal energy in the surrounding environment. Electromagnetic radiation (e.g., radio, microwaves, light) can be modeled as a wave of changing electric and magnetic fields or as particles called photons. The wave model is useful for explaining many features of electromagnetic radiation, and the particle model explains other features. In multicellular organisms individual cells grow and then divide via a process called mitosis, thereby allowing the organism to grow. The organism begins as a single cell (fertilized egg) that divides successively to produce many cells, with each parent cell passing identical genetic material (two variants of each chromosome pair) to both daughter cells. Cellular division and differentiation produce and maintain a complex organism, composed of systems of tissues and organs that work together to meet the needs of the whole organism. A complex set of interactions within an ecosystem can keep its numbers and types of organisms relatively constant over long periods of time under stable conditions. If a modest biological or physical disturbance to an ecosystem occurs, it may return to its more or less original status (i.e., the ecosystem is resilient), as opposed to becoming a very different ecosystem. Extreme fluctuations in conditions or the size of any population, however, can challenge the functioning of ecosystems in terms of resources and habitat availability. Moreover, anthropogenic changes (induced by human activity) in the environment—including habitat destruction, pollution, introduction of invasive species, overexploitation, and climate change—can disrupt an ecosystem and threaten the survival of some species. Evidence from deep probes and seismic waves, reconstructions of historical changes in Earth’s surface and its magnetic field, and an understanding of physical and chemical processes lead to a model of Earth with a hot but solid inner core, a liquid outer core, a solid mantle and crust. Motions of the mantle and its plates occur primarily through thermal convection, which involves the cycling of matter due to the outward flow of energy from Earth’s interior and gravitational movement of denser materials toward the interior. Definitions of Energy: Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system’s total energy is conserved, even as, within the system, energy is continually transferred from one object to another and between its various possible forms. At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy. These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration (relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space. Forces and Motion: Newton’s second law accurately predicts changes in the motion of macroscopic objects. Momentum is defined for a particular frame of reference; it is the mass times the velocity of the object. If a system interacts with objects outside itself, the total momentum of the system can change; however, any such change is balanced by changes in the momentum of objects outside the system. Make simple observations, predictions, explanations, and generalizations based on real-life experiences. The process of programming involves solving computational problems. Describe how to take more personal responsibility for eating healthy foods. Participate in activities that require problem-solving, cooperation, and team-building. Understand and apply basic principles of training to improving physical fitness. Apply rules, principles, problem-solving skills and concepts to traditional and nontraditional movement settings. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. Use knowledge of literary devices (such as imagery, rhythm, foreshadowing, simple metaphors) to understand and respond to text. Use the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. Compute (using technology) and interpret the correlation coefficient of a linear fit. A square with side length 1 unit, called "a unit square," is said to have "one square unit" of area, and can be used to measure area. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), … Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule "Add 3" and the starting number 0, and given the rule "Add 6" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1—100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not"). Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. Find the point on a directed line segment between two given points that partitions the segment in a given ratio. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. Fit a linear function for a scatter plot that suggests a linear association. Solve addition and subtraction problems set in simple contexts. Add and subtract up to at least five to or from a given number to find a sum or difference up to 10. Demonstrate knowledge of eighteenth-, nineteenth- and early-twentieth-century foundational works of American literature, including how two or more texts from the same period treat similar themes or topics. Use information gained from illustrations (for example: maps, photographs) and the words in a text to demonstrate understanding of the text (for example: where, when, why, and how key events occur). Summarize a written text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. Use precise language and domain-specific vocabulary to inform about or explain the topic. Analyze the main ideas and supporting details presented in diverse media and formats (e.g., visually, quantitatively, orally) and explain how the ideas clarify a topic, text, or issue under study. Choose risk management strategies for protection from the financial risk of lost income, lost or damaged property, health issues, or identity fraud. Electromagnetic Radiation: When light shines on an object, it is reflected, absorbed, or transmitted through the object, depending on the object’s material and the frequency (color) of the light. The path that light travels can be traced as straight lines, except at surfaces between different transparent materials (e.g., air and water, air and glass) where the light path bends. Lenses and prisms are applications of this effect. A wave model of light is useful for explaining brightness, color and the frequency dependent bending of light at a surface between media (prisms). However, because light can travel through space, it cannot be a matter wave, like sound or water waves. Information Technologies and Instrumentation: Appropriately designed technologies (e.g., radio, television, cell-phones, wired and wireless computer networks) make it possible to detect and interpret many types of signals that cannot be sensed directly. Designers of such devices must understand both the signal and its interactions with matter. Many modern communication devices use digitized signals (sent as wave pulses) as a more reliable way to encode and transmit information. Use a model to illustrate how photosynthesis transforms light energy into stored chemical energy. Apply concepts of statistics and probability to support explanations that organisms with an advantageous heritable trait tend to increase in proportion to organisms lacking this trait. Create a computational simulation to illustrate the relationships among the management of natural resources, the sustainability of human populations, and biodiversity. Nuclear processes, including fusion, fission, and radioactive decays of unstable nuclei, involve release or absorption of energy. The total number of neutrons plus protons does not change in any nuclear process. The many dynamic and delicate feedbacks between the biosphere and other Earth systems cause a continual co-evolution of Earth’s surface and the life that exists on it. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)² = q that has the same solutions. Derive the quadratic formula from this form. Consult general and specialized reference materials (for example: dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning, its part of speech, or its etymology. Trace and evaluate the argument and specific claims in a text, distinguishing claims that are supported by reasons and evidence from claims that are not. Make observations and measurements to identify materials based on their properties. Support an argument that the apparent brightness of the sun and stars is due to their relative distances from the Earth. Construct an argument supported by evidence for how increases in human population and per-capita consumption of natural resources impact Earth's systems. Food webs are models that demonstrate how matter and energy is transferred between producers, consumers, and decomposers as the three groups interact within an ecosystem. Transfers of matter into and out of the physical environment occur at every level. Decomposers recycle nutrients from dead plant or animal matter back to the soil in terrestrial environments or to the water in aquatic environments. The atoms that make up the organisms in an ecosystem are cycled repeatedly between the living and nonliving parts of the ecosystem. Construct and revise an explanation for the outcome of a simple chemical reaction based on the outermost electron states of atoms, trends in the periodic table, and knowledge of the patterns of chemical properties. Create or revise a simulation to test a solution to mitigate adverse impacts of human activity on biodiversity. Analyze geoscience data and the results from global climate models to make an evidence-based forecast of the current rate of global or regional climate change and associated future impacts to Earth's systems. Use a computational representation to illustrate the relationships among Earth systems and how those relationships are being modified due to human activity. All forms of energy production and other resource extraction have associated economic, social, environmental, and geopolitical costs and risks as well as benefits. New technologies and social regulations can change the balance of these factors. Apply properties of operations as strategies to add and subtract. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. Graph linear and quadratic functions and show intercepts, maxima, and minima. Demonstrate comprehension of information with supporting logical and valid inferences. Construct a scientific explanation based on evidence for the role of photosynthesis in the cycling of matter and flow of energy into and out of organisms. Develop a model to illustrate that the release or absorption of energy from a chemical reaction system depends upon the changes in total bond energy. Use mathematical representations to support the claim that the total momentum of a system of objects is conserved when there is no net force on the system. Use a model to illustrate that cellular respiration is a chemical process whereby the bonds of food molecules and oxygen molecules are broken and the bonds in new compounds are formed, resulting in a net transfer of energy. Kepler’s laws describe common features of the motions of orbiting objects, including their elliptical paths around the sun. Orbits may change due to the gravitational effects from, or collisions with, other objects in the solar system. Use permutations and combinations to compute probabilities of compound events and solve problems. Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v). Verify by composition that one function is the inverse of another. Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. 100 can be thought of as a bundle of ten tens — called a "hundred." Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4). Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Understand the concept of a unit rate (a/b associated with a ratio a:b with b ≠0, and use rate language in the context of a ratio relationship) and apply it to solve real world problems (e.g., unit pricing, constant speed). For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that "increase by 5%" is the same as "multiply by 1.05." Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. Represent data with plots on the real number line (dot plots, histograms, and box plots). Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x² + y²)2 = (x² — y²)² + (2xy)² can be used to generate Pythagorean triples. Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). Prove theorems about parallelograms. Prove theorems about triangles. Derive the equation of a parabola given a focus and directrix. Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model. Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. Predict the impact an informational text will have on an audience and justify the prediction. Interpret and communicate the information learned by developing a brief summary with supporting details. Use common, grade-appropriate Greek and Latin affixes and roots as clues to the meaning of a word (e.g., photograph, photosynthesis). Use underlining, quotation marks, or italics to indicate titles of works. Read and identify the meaning of words with sophisticated prefixes and suffixes. Plants, algae (including phytoplankton), and many microorganisms use the energy from light to make sugars (food) from carbon dioxide from the atmosphere and water through the process of photosynthesis, which also releases oxygen. These sugars can be used immediately or stored for growth or later use. Interpret the parameters in a linear or exponential function in terms of a context. Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x). Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). Represent a system of linear equations as a single matrix equation in a vector variable. Prove the Laws of Sines and Cosines and use them to solve problems. Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze how an author uses and refines the meaning of a key term or terms over the course of a text (e.g., how Madison defines faction in Federalist No. 10). Interpret information presented visually, orally, or quantitatively (e.g., in charts, graphs, diagrams, time lines, animations, or interactive elements on Web pages) and explain how the information contributes to an understanding of the text in which it appears. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. Parallel lines are taken to parallel lines. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Substances react chemically in characteristic ways. In a chemical process, the atoms that make up the original substances are regrouped into different molecules, and these new substances have different properties from those of the reactants. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ? 0, the direction of cv is either along v (for c > 0) or against v (for c < 0). Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater). Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households? Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?. Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume. Reporting the number of observations. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures. Identify and describe relationships among inscribed angles, radii, and chords. Develop a model to describe that when the arrangement of objects interacting at a distance changes, different amounts of potential energy are stored in the system. Develop models to illustrate the changes in the composition of the nucleus of the atom and the energy released during the processes of fission, fusion, and radioactive decay. Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores? Define appropriate quantities for the purpose of descriptive modeling. Explain the meaning of simple similes and metaphors (e.g., as pretty as a picture) in context. Create a computational model to calculate the change in the energy of one component in a system when the change in energy of the other component(s) and energy flows in and out of the system are known. Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling in various media. Photosynthesis and cellular respiration (including anaerobic processes) provide most of the energy for life processes. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² × 3-5 = 3-3 = 1/3³ = 1/27. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Refine the design of a chemical system by specifying a change in conditions that would produce increased amounts of products at equilibrium. The main way that solar energy is captured and stored on Earth is through the complex chemical process known as photosynthesis. Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Factor a quadratic expression to reveal the zeros of the function it defines. Produce an invertible function from a non-invertible function by restricting the domain. Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. Read values of an inverse function from a graph or a table, given that the function has an inverse. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident. Explain a proof of the Pythagorean Theorem and its converse. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P. Add, subtract, and multiply matrices of appropriate dimensions. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s³ and A = 6 s² to find the volume and surface area of a cube with sides of length s = 1/2. Develop a self-understanding profile that supports adult transitions and future planning. Assess personal readiness for independent decision-making in adult settings. Analyze how changing roles and expectations affect self-understanding in middle school. Design a self-management plan for adult responsibilities, stress, and independence. Identify values that influence choices about friends, activities, and responsibilities. Analyze emotional triggers that can interfere with judgment and relationships. Evaluate decision-making strategies for risk, responsibility, and long-term impact. Evaluate how boundaries, consent, and accountability strengthen relationships. Develop self-management systems for academic workload, projects, and responsibilities. Apply conflict-resolution strategies in friendships, teams, and online interactions. Evaluate study strategies for attention, retention, and exam readiness. Evaluate digital risks related to identity, scams, and unsafe online interactions. Assess consumer choices using comparison shopping, budgeting, and financial goals. Develop early career planning strategies using interests, goals, and opportunities. Evaluate how self-care choices affect resilience, safety, and long-term wellness. Apply basic first-aid skills and recognize common emergency situations that require adult intervention or calling for help. Analyze how peer pressure, curiosity, and misinformation can influence decisions about alcohol, vaping, and other substances. Analyze the role of consent, respect, and responsibility in relationships. Develop independent living routines for organization, travel, and basic household management. Apply teamwork strategies to complex projects, peer groups, and community action. Evaluate how values and character shape choices in digital, social, and academic settings. Evaluate how civic systems and public issues affect local communities. Apply accountability practices when actions affect other people or shared outcomes. Explain how personal actions online and offline — such as cyberbullying, property damage, or sharing harmful content — can carry legal consequences, and identify how understanding the law supports better decision-making. Develop a readiness plan for the transition to high school and beyond. Create a personal roadmap for near-term goals and longer-term direction. Analyze how values and identity shape decisions about leadership, relationships, and future goals. Analyze strategies for balancing pressure, expectations, and emotional well-being. Develop strategies for processing grief, supporting others through loss, and seeking help during major life transitions. Analyze how empathy and social awareness influence leadership and peer decisions. Evaluate inclusive actions that strengthen school culture and community trust. Develop self-advocacy strategies for relationships, school interactions, and support-seeking. Analyze communication patterns that support trust, consent, and mutual respect. Analyze how values, evidence, and trade-offs shape informed decisions. Develop academic systems for time management, organization, and follow-through in high school. Apply professional habits to communication, reliability, and work-based learning. Assess how banking services, payment methods, and fees affect financial decisions. Explain the purpose of taxes, how income is taxed, and how tax obligations connect to public services and personal financial planning. Analyze how online identity and digital reputation affect opportunities and trust. Apply media-literacy strategies to evaluate news, influencers, and digital persuasion. Apply health and safety knowledge to help-seeking, prevention, and responsible choices. Analyze how consent, communication, and boundaries support relationship safety. Evaluate how to identify and respond to unhealthy relationship patterns, pressure, and boundary violations. Explain how personal values, safety planning, and trusted resources support responsible relationship decisions. Develop practical systems for managing daily responsibilities, belongings, and time. Apply independent living skills to transportation, time management, and household tasks. Analyze ethical responsibilities in leadership, schoolwork, and peer relationships. Assess how trustworthiness, follow-through, and honesty affect adult readiness. Analyze civic rights, responsibilities, and legal awareness in relation to adolescent life. Evaluate how community participation and advocacy can influence public issues. Develop readiness skills for independence, self-advocacy, and future planning. Develop goals that align with values, responsibilities, and future plans. Practice calming and focusing routines to stay ready for learning throughout the day. Recognize how fairness and kindness help everyone feel welcome. Use respectful words and body language to solve everyday social problems. Identify choices that help everyone stay safe and learn together. Use simple questions to think through a problem before acting. Practice focusing attention during teacher directions, activities, and learning tasks. Identify jobs that help a classroom, school, and community work well. Name rules for using devices, websites, and classroom technology safely. Recognize what information should stay private online and on devices. Recognize when the body needs rest, movement, water, or help. Recognize that every person deserves privacy, respect, and safety. Use classroom and home routines for caring for belongings and shared materials. Identify everyday tasks that help keep a home or classroom organized. Practice doing the right thing even when it feels difficult. Identify feelings during play, group time, and classroom routines. Practice starting again after a mistake in play or learning. Recognize when a classmate may need kindness, help, or space. Show respect for people who look, speak, or play in different ways. Practice listening, turn-taking, and kind words in classroom activities. Use simple words to solve small friendship problems. Ask a trusted adult for help when a social situation feels unsafe or unfair. Choose between safe and unsafe options in everyday classroom situations. Practice solving simple problems by trying more than one idea. Practice staying with a task for a short time before switching activities. Identify coins, bills, and simple choices about spending or saving. Recognize that people earn money by working and make choices about how to use it. Identify safe ways to use devices with adult help. Practice kind and careful behavior when using shared technology. Practice safe choices about movement, rest, food, and asking for help. Practice asking for help when touch, words, or behavior feel uncomfortable. Take turns, share roles, and help during classroom activities. Tell the truth, follow rules, and take responsibility for small actions. Show fairness and care when sharing, playing, and working with others. Identify helpers and simple rules that keep the classroom and community safe. Recognize ways people help others in everyday classroom and play situations. Talk about future learning, growing up, and trying new responsibilities. Identify adults and places that help children learn and grow. Notice progress when trying something new or challenging. Identify the organizational components of a calendar. For example: Year, months, weeks, days, and notable events. Use words related to time, sequence, and change. For example: Past, present, future, change, first, next, and last. Determine events from the past, present, and future, using the components of a calendar. Identify information from primary and/or secondary sources that answer questions about patterns and chronological order of events from the past. Identify the unique characteristics of oneself as well as the similarities and differences between themselves and others. For example: Eye color, ability, individuality, family composition, etc. Create simple maps showing both human and natural features. Analyze how weather, climate and environmental characteristics influence individuals and the cultural characteristics of a family. Compare and contrast at least two different communities with respect to schools, neighborhoods, and culture. Describe the characteristics of responsible leaders and how they communicate with others. Describe the qualities of an effective team. For example: Respectful disagreement, advocating for self and others, sharing responsibilities, and including others' perspectives. Identify and explain the relevance of notable civic leaders from different community groups, including African American, Latino, Asian American, Hawaiian/Pacific Islander, Indigenous Peoples, LGBTQ, and religious minorities. Compare and contrast neighborhoods and/or communities, both past and present, through studies of their people and events. For example: The National Western Stock Show, state/county fairs, and community events. Identify local historical primary and secondary sources from multiple diverse perspectives and generate questions about their functions, significance, and perspective. For example: Maps, photographs, letters, etc. Analyze the interactions and contributions of various people and cultures that have lived in or migrated to neighborhoods and/or communities, including African Americans, Latinos, Asian Americans, Hawaiian/Pacific Islander, Indigenous Peoples, LGBTQ, and religious minorities. Identify the purpose of the map being presented. For example: A weather map vs. street map. Identify examples of how culture and lifestyle are impacted by environmental characteristics. Identify possible solutions when there are limited resources and unlimited wants. Compare ways that people may effectively express their ideas and viewpoints while being respectful to others. Describe ways in which you can take an active part in improving your school or community. Describe the characteristics that enable a community member to engage in the community responsibly and effectively. Identify the role(s)of government. For example: Establish order, provide security, and accomplish common goals. Identify qualities of positive leadership and how leaders contribute to a group or community. Identify services provided by the local or state government. For example: police and fire protection, maintenance of roads, and snow removal. Classify financial goals. For example: A need or want, or short-term or long-term goals. Acknowledge that financial priorities vary among people and communities for goods and services. For example: Going to the hairdresser, buying brand name items. Give examples of people, events, and developments that brought important changes to a community or region. Use a variety of primary sources such as artifacts, pictures, oral histories, and documents, to help determine factual information about historical events. Describe the natural and man-made features of a specific area on a map. Observe and describe the physical, cultural, and human-made characteristics of a local region. For example: The Eastern Plains, San Luis Valley, Pikes Peak, Northwest, Front Range, South Central, Southwest, and Western Slope. Identify the factors that make a region unique. For example: Cultural diversity, industry and agriculture, and landforms. Characterize regions using different types of features such as physical, political, cultural, urban, and rural attributes. Describe and give examples of forms of exchange. For example: Monetary exchange and barter. Describe how the exchange of goods and services between businesses and consumers affects all parties. Cite evidence to show how trade benefits individuals, businesses, and communities, and increases interdependency. Identify important personal rights in a democratic society and how they relate to others' rights. Restate the view or opinion of others with their reasoning when it is different from one's own. Give examples of the relationship between rights and responsibilities. Explain the origins and structures of local government. Explain the services local governments provide and how those services are funded. Describe how local government provides opportunities for people to exercise their rights and initiate change. Draw inferences about Colorado history from primary sources such as journals, diaries, maps, treaties, oral histories, etc. Discuss the multiple perspectives of settler colonialism/Westward Expansion and the impact on the political and cultural landscape of the region presently known as Colorado. Describe both past and present interactions among the people and cultures in Colorado. For example: African Americans, Latinos, Asian Americans, Indigenous Peoples, LGBTQ, and religious groups. Create and investigate geographic questions about Colorado in relation to other places. Illustrate, using geographic tools, how places in Colorado have changed and developed over time due to human activity. Analyze how people use geographic factors in creating settlements and have adapted to and modified the local physical environment. Describe how places in Colorado are connected by movement of goods, services, and technology. Define positive and negative economic incentives and describe how people typically respond to those incentives. In a given situation, create a plan of appropriate incentives to achieve a desired result. For example: Offering a prize to the person who picks up the most trash on the playground. Provide supportive arguments for both sides of a current public policy debate involving diverse stakeholders. Identify and use appropriate sources to investigate and analyze issues from multiple diverse perspectives. Explain the historical foundation and events that led to the Colorado Constitution and the formation of the three branches of Colorado government. Describe how the decisions of the state government affect local governments and interact with the federal government and sovereign indigenous nations. Define choice and opportunity cost. Determine the relationship between long-term goals and opportunity cost. Analyze scenarios of choices including opportunity cost. Explain interactions among various groups such as Indigenous Peoples, enslaved individuals (both Indigenous and African), and European colonists. For example: The cultural genocide of Indigenous Peoples, chattel slavery of Africans, the League of the Iroquois, Spanish missions, and trade networks. Identify and describe the contributions of significant individuals and groups of Indigenous Peoples, enslaved individuals, and European colonists through the American Revolution. For example: Crispus Attucks, Sybil Luddington, Benjamin Banneker, Thomas Jefferson, and Patrick Henry. Describe the political, social, and economic reasons for the settlement of the European and American colonies and how it affected Indigenous Peoples and enslaved Africans. Explain migration, trade, and cultural patterns that result from interactions among people, groups, and cultures. Analyze how cooperation and conflict among diverse groups of people contribute(d) to political, economic, and social divisions in the United States. Give examples of the influence of geography on the history of the United States. Identify examples of the productive resources and explain how they are used to produce goods and services. For example: Land, labor, and capital. Compare ways in which people and communities exchanged goods and services. For example: Barter and monetary exchange. Describe how patterns of trade evolved within Early America. Give examples of group and individual actions that illustrate civic ideals in the founding of the United States. For example: Freedom, rule of law, equality, civility, cooperation, respect, responsibility, and civic participation. Describe and explain examples of individual rights as a foundation of citizenship. Describe how the Constitution balances the power of national and state governments. Differentiate between saving and investing. Describe the role of competition and supply and demand in the determination of prices and wages in a market economy. Identify ways different cultures record history in the Western Hemisphere through written and oral sources. Gather, organize, synthesize, and critique information, from multiple and diverse perspectives, to determine if it is sufficient to answer historical questions about the Western Hemisphere. For example: Indigenous People, Latinos, African Americans, Asian Americans, Hawaiian/Pacific Islander, LGBTQ, and religious minorities and differing opinions within such groups. Explain the interdependence and uniqueness among Indigenous Peoples in the Western Hemisphere including the existing conflict and power dynamics between Indigenous Peoples and those in power. Interpret geographic data/evidence to draw conclusions, make predictions, and justify potential solutions to problems at the local, state, national, and global levels. Classify and analyze the types of human and geographic connections between places and regions. Analyze positive and negative interactions of human and physical systems in the Western Hemisphere and give examples of how people have adapted to and modified their physical environment. Explain how different societies view and use money and resources. Examine changes and connections in ideas about citizenship in different times and places in the Western Hemisphere. For example: Indigenous Peoples are either denied citizenship or citizenship is not always desired; immigration and a nation's quota preferences; and the changes in naturalization requirements change over time. Explain how political ideas of significant people and groups interact, are interconnected, and influence nations and regions in the Western Hemisphere, both in the past and today. Identify historical examples illustrating how people from diverse backgrounds such as African American, Latino, Asian American, and Indigenous Peoples in the Western Hemisphere perceived, reacted to, and influenced national and international policies and issues. Analyze political issues from national and global perspectives over time in North America, South America, and the Caribbean. Examine and explain the development of foundational principles of government systems in the Western Hemisphere. Identify how different systems of government relate to their citizens in the Western Hemisphere and how systems of government create advantages for some of their citizens and disadvantages for others. Analyze primary and secondary sources to explain the interdependence and uniqueness among peoples in the Eastern Hemisphere, including their influence on modern society. Summarize how the distribution of resources impacts consumerism. Investigate and evaluate the social, political, cultural, and technological development of regions in the Eastern Hemisphere. For example: The river valley civilizations, Hammurabi's Code, Greek democracy, the Roman Republic, the Chinese inventions of gunpowder and the compass, and the printing press. Explain the interdependence and uniqueness among peoples in the Eastern Hemisphere during significant eras or events, including their influence on modern society. For example: African Empires, the Silk Road and cultural diffusion, and the colonization of Africa, India, and Australia. Describe how the non-violent strategies employed by Dr. King and his followers overcame segregation in the American South. Apply inquiry and research utilizing geographic tools. For example: GPS and satellite imagery. Collect, classify, and analyze data to make geographic inferences and predictions. Assess geographic data to draw conclusions, make predictions, and justify potential solutions to problems in the Eastern Hemisphere at the local, state, national, and global levels using supporting evidence and logical reasoning. Determine how physical and political features impact cultural diffusion and regional differences. For example: Modern environmental issues, cultural patterns, trade barriers, and economic interdependence. Examine the geographic location and distribution of resources within a region to determine the economic and social impact on its people. For example: Middle Eastern water rights, the acceptance of refugees from other countries, and the Salt Trade. Explain how trade supply and demand affects the production of goods and services in different regions. Give examples illustrating the interactions between nations and their citizens. For example: South Africa's system of Apartheid, human rights violations, genocide, Shari'ah law, government sanctioned economic policies, and socialized healthcare and education. Identify international and regional public problems, research ways in which governments address those problems, and make connections to how the United States government addresses issues to protect the public good. Compare and contrast examples of governmental implementation of civic virtues or principles. Evaluate and analyze how various governments and organizations interact, resolve their differences, and cooperate. For example: The African Union (AU), the Association of Southeast Asian Nations (ASEAN), the United Nations, the World Bank, international treaties, and diplomacy. Investigate examples of collaboration and interdependence between international organizations and countries. For example: The protection of human rights; the role of non-governmental organizations (NGOs), the Red Cross, World Health Organization, and United Nations Educational, Scientific, and Cultural Organization (UNESCO). Define resources from an economic and personal finance perspective. Analyze evidence from multiple sources including those with conflicting accounts about specific events in both Colorado and United States history. For example: Indigenous Peoples', Hawaiian/Pacific Islander, and African American perspectives on Western colonization and enslavement; Asian American and Latinos' perspectives on immigration; and the Indian Removal Act, the Buffalo Soldiers, and the Sand Creek Massacre. Critique data for point of view, historical context, distortion, or propaganda and relevance to historical inquiry. Construct a written historical argument supported by relevant evidence and logical reasoning demonstrating the use or understanding of primary and secondary sources. Synthesize data from multiple sources in order to connect those sources to the traditional historical narrative. Determine and explain the historical context of key people and events from the Revolutionary War Era through Reconstruction including the examination of different perspectives. For example: Grievances from the colonists against the British Parliament, the Constitutional Convention, the role of abolitionists, contributions and grievances from Indigenous Peoples and African Americans, and the causes and effects of the Civil War. Place important life events in chronological order on a timeline. Determine whether a source is primary or secondary Assess priorities when making financial decisions. Identify the three branches of the United States government and explain the functions of each. Explain the historical and present-day significance of the Declaration of Independence. Use maps, satellite images, photographs, and other representations to explain the relationships between the locations of places and regions and their political, cultural, and economic dynamics. Generate and compare multiple possible solutions to a problem based on how well each is likely to meet the criteria and constraints of the problem. Substances are made from different types of atoms, which combine with one another in various ways. Atoms form molecules that range in size from two to thousands of atoms. Energy cannot be created or destroyed—it only moves between one place and another place, between objects and/or fields, or between systems. Describe interests and strengths that help with learning and friendships. Recognize proud moments and effort used to finish a task. Describe ways to recover after mistakes, disappointment, or change. Describe how feelings and experiences may be different for different people. Use caring actions that help classmates feel safe, seen, and included. Use clear words, tone, and actions to solve conflict respectfully. Describe how organization helps with materials, homework, and classroom tasks. Use simple planning steps to begin and finish schoolwork on time. Use safe choices when viewing, sharing, or clicking digital content. Describe steps for organizing personal items, school materials, and shared spaces. Show initiative by helping a group without waiting to be asked. Describe how honesty and responsibility build trust with others. Use fair and respectful choices during play, learning, and classroom routines. Identify questions students can ask when learning about future opportunities. Evaluate how confidence, belonging, and feedback affect academic and social growth. Apply resilience strategies during setbacks, heavy workload, and changing goals. Analyze how community needs should influence responsible action and service. Assess how communication choices affect safety, accountability, and healthy relationships. Apply strategies for navigating pressure, disagreement, and boundary violations responsibly. Apply planning and productivity strategies to long-term goals and deadlines. Develop job-readiness skills for applications, interviews, and professional communication. Assess career pathways using interests, labor trends, and education requirements. Apply consumer strategies for comparing financial products and avoiding scams. Develop responsible digital habits for communication, collaboration, and reputation management. Assess how stress, burnout, and risk behaviors affect overall well-being. Demonstrate emergency response skills including CPR, first aid, choking relief, and accident-scene protocols. Assess how coercion, manipulation, and power dynamics affect relationship decisions. Assess practical decisions related to housing, transportation, and service systems. Use forms, schedules, and documents to navigate everyday responsibilities independently. Develop strategies for navigating unfamiliar administrative and service systems by reading instructions, identifying the right contact, asking effective questions, and following through. Apply team-based problem-solving to shared goals, deadlines, and responsibilities. Evaluate character-based choices in complex academic, social, and digital situations. Apply civic responsibility to service, sustainability, and community improvement efforts. Apply planning skills to applications, timelines, and transition decisions. Assess how identity and priorities influence postsecondary, career, and relationship choices. Analyze the role of strengths, limitations, and support systems in long-term planning. Develop a personal resilience system for pressure, deadlines, and competing responsibilities. Develop approaches for contributing to communities with empathy, dignity, and accountability. Evaluate interpersonal skills needed for leadership, collaboration, and responsible relationships. Develop communication approaches for difficult conversations, repair, and accountability. Evaluate complex choices by comparing consequences, opportunity costs, and responsibilities. Apply analytical problem-solving to adult systems, transitions, and competing priorities. Evaluate work-based learning, internships, and other early career opportunities. Develop a career action plan that includes networking, skill-building, and next steps. Apply practical skills to launch and manage a small project or service, including risk assessment, tracking finances, gathering customer feedback, iterating on the product, and adapting to challenges. Evaluate digital ethics related to AI use, content creation, and information sharing. Assess how to fulfill personal tax obligations, track income and expenses, and understand basic tax documents and deadlines. Analyze how digital systems influence civic participation, consumer choices, and privacy. Evaluate health systems, insurance basics, and access to care for young adults. Develop a personal mental health crisis plan including recognizing warning signs, accessing professional support, and navigating the mental healthcare system. Assess how recognizing and responding to relationship risks prepares young adults for healthy, independent decision-making. Assess how daily systems and administrative tasks affect adult readiness. Use basic tools for household repairs and respond to common home emergencies such as leaks, power outages, and appliance issues. Develop a personal system for organizing identity documents, financial records, health records, and important correspondence for adult life. Evaluate leadership responsibilities in service, work, and community roles. Develop strategies for leading with respect, accountability, and shared purpose. Assess ethical decision-making in situations involving pressure, responsibility, and long-term impact. Apply principles of integrity and respect to adult systems and relationships. Evaluate how civic engagement, legal awareness, and advocacy support community change. Analyze the responsibilities of active citizenship including voting, advocacy, and informed participation in public life. Assess when and how to seek legal help, understand the role of lawyers, advocates, and legal aid, and practice exercising basic legal rights in everyday situations such as interactions with authorities, disputes, or unfair treatment. Evaluate how current decisions support postsecondary and adult goals. Develop a long-range action plan with milestones, supports, and contingencies. Assess how empathy and community awareness support ethical action in adult settings. Evaluate ways to build inclusive, respectful communities in work, civic, and social life. Apply relationship and communication skills to adult decisions, boundaries, and consent. Assess how communication habits influence workplace, family, and community relationships. Assess major life decisions using evidence, values, and long-term planning. Design a personal decision-making process for adulthood, independence, and risk management. Design a personal organization system for adult learning, work, and daily responsibilities. Apply career planning strategies to postsecondary choices, employment, and transition goals. Assess workplace expectations related to communication, ethics, and responsibility. Apply knowledge of boundaries, consent, and health resources to adult relationship choices. Assess long-term digital risks and responsibilities in work, education, and community life. Apply health-management skills to adult responsibilities, care access, and independent safety. Apply digital citizenship skills to adult communication, privacy, and professional identity. Develop a personal safety plan for navigating relationships, setting boundaries, and accessing support in adult life. Apply independent living skills to adult routines, housing decisions, and service navigation. Develop a practical plan for managing forms, appointments, bills, and daily logistics. Plan for international travel by understanding travel documents, visa processes, cultural preparation, and how to navigate unfamiliar environments safely. Assess personal leadership strengths and next steps for future roles. Assess how personal action, public systems, and community engagement interact in adult life. Evaluate and interpret common adult contracts including leases, loan agreements, and employment documents. Assess how goals, values, and systems can support long-term success and well-being. Reflect on mistakes, effort, and improvement after feedback. Choose coping strategies that help when school feels stressful or confusing. Explain why listening to others helps build a caring classroom community. Show respect for differences in family life, language, culture, and ability. Explain how kind, honest communication builds trust in friendships and groups. Practice setting simple boundaries and respecting the boundaries of others. Demonstrate how to report bullying, threats, or unsafe peer behavior to a trusted adult. Explain why fair, thoughtful decisions matter in school and community life. Use attention and time strategies during independent and group learning. Practice workplace habits such as punctuality, cooperation, and follow-through in class. Explain why passwords, privacy, and asking an adult matter online. Explain why sleep, nutrition, and movement help the body and brain work well. Explain body autonomy using age-appropriate language about choice and safety. Use daily living routines for chores, cleanup, and care of personal belongings. Explain how planning helps with meals, supplies, and getting ready on time. Use cooperation skills to support fair participation and shared success. Explain why keeping promises and fixing mistakes matters. Demonstrate responsibility for words, actions, and shared tasks. Show initiative by helping others and caring for shared spaces without reminders. Explain how preparation and support help students succeed in new situations. Describe future pathways for learning, work, and service in simple terms. Use a simple plan to work toward a personal or school goal. Describe personal habits that support confidence and responsibility. Apply persistence strategies when tasks feel hard or take longer than expected. Explain how self-control supports respectful choices and problem-solving. Identify healthy ways to cope with loss, change, and difficult life events. Analyze how perspective-taking can prevent hurt and support teamwork. Explain how communication choices affect trust, teamwork, and conflict. Apply a decision-making process to academic, social, and safety-related problems. Use planning tools to manage assignments, materials, and multi-step tasks. Explain how note-taking, review, and practice strengthen learning. Apply responsibility, teamwork, and follow-through to classroom roles and projects. Explain how budgets help people plan for spending, saving, and sharing. Apply money decisions to short-term goals and everyday purchases. Apply media-literacy habits when checking whether information is real or reliable. Explain how healthy choices affect energy, focus, and emotional well-being. Apply basic safety skills for emergencies, injuries, and help-seeking. Use practical skills for packing, organizing, and caring for belongings responsibly. Explain how integrity, fairness, and reliability affect a community. Apply ethical choices to schoolwork, friendships, and shared responsibilities. Describe rights, responsibilities, and age-appropriate civic action in school and community life. Explain how school skills connect to future learning and life roles. Apply steps for setting, tracking, and adjusting a short-term goal. Apply assertive communication during conflict, peer pressure, and group decision-making. Analyze how emotions can influence judgment during conflict or stress. Demonstrate study habits that improve memory, focus, and task completion. Describe how strengths, interests, and habits influence career exploration. Compare financial choices using price, quality, and long-term value. Analyze how messages, images, and media can influence feelings and behavior. Analyze how nutrition, sleep, and exercise affect learning and behavior. Demonstrate age-appropriate first-aid, safety, and prevention habits. Explain how stress can affect the body and how healthy coping supports wellness. Describe physical and emotional changes of growing up in age-appropriate ways. Apply help-seeking strategies for uncomfortable, unsafe, or confusing situations. Apply household routines for food planning, clothing care, and shared responsibilities. Apply teamwork strategies that improve collaboration, communication, and task completion. Compare responsible and irresponsible responses to common school situations. Compare how local community roles and services support safety and daily life. Describe postsecondary pathways such as college, training, and work in age-appropriate ways. Apply planning habits that support readiness for future transitions. Develop action steps and checkpoints for a meaningful goal. Analyze how effort, feedback, and persistence shape self-confidence. Develop a plan for staying organized and regulated during busy school weeks. Explain how stereotypes and assumptions can affect how people are treated. Demonstrate inclusive actions that support dignity and participation for others. Demonstrate boundary-setting, apology, and repair in challenging peer situations. Analyze how communication style affects safety, belonging, and accountability. Use evidence and reasoning to choose among multiple solutions to a problem. Analyze how bias, assumptions, and missing information affect decisions. Analyze how planning, pacing, and reflection improve academic success. Analyze how effort, communication, and responsibility affect work quality. Explore how people create value by identifying needs and developing products, services, or creative projects. Analyze how advertising and influence can affect spending decisions. Develop a simple budget for saving, spending, and planned purchases. Apply strategies for balancing screen time, privacy, and online responsibility. Explain how boundaries, privacy, and respect affect growing relationships. Develop a personal wellness routine that supports physical and emotional health. Use practical living skills to plan ahead, solve household problems, and stay organized. Analyze how effective teams use roles, feedback, and shared accountability. Develop leadership habits that support initiative, fairness, and follow-through. Analyze how rules, rights, and responsibilities work together in communities. Explain how civic participation and service can address community needs. Explain how goals, interests, and responsibilities influence future pathways. Use reflection to revise goals, strategies, and timelines. Distinguish between respectful curiosity and harmful bias in social situations. Analyze how empathy influences conflict resolution, peer support, and belonging. Distinguish among healthy, unhealthy, and unsafe relationship behaviors in middle school. Apply problem-solving steps to school, peer, and online situations. Develop study routines that support independent learning and test preparation. Explore career clusters and personal strengths that may align with future work. Develop workplace habits such as reliability, initiative, and professional communication. Analyze digital choices related to privacy, passwords, and personal information. Use safe reporting and blocking tools in response to cyberbullying or online threats. Analyze how pressure, coercion, and boundary violations can affect safety. Apply refusal, exit, and help-seeking strategies in uncomfortable situations. Develop practical routines for meals, laundry, organization, and daily responsibilities. Read school, transportation, and service forms accurately and ask questions when directions are unclear. Apply collaboration and leadership skills during projects, service, and peer work. Assess how group roles, communication, and accountability affect team success. Assess ethical choices related to honesty, fairness, and peer influence. Apply responsibility and accountability to schoolwork, relationships, and group roles. Analyze how community rules, institutions, and services affect everyday life. Develop readiness habits for new expectations, settings, and responsibilities. Apply planning tools to track progress and adjust next steps. Assess how peer influence can shape self-image and decision-making. Reflect on how strengths and limits affect participation in school and community roles. Assess how habits, sleep, and workload affect mood, focus, and self-control. Develop routines that support persistence during conflict, setbacks, and responsibility. Assess how social pressure can affect fairness, inclusion, and community behavior. Develop community-minded actions that support respect across differences. Assess how tone, timing, and digital communication affect trust and misunderstanding. Assess how incomplete information and emotions can affect decision quality. Distinguish between impulsive reactions and informed choices in complex situations. Assess how distraction, procrastination, and digital habits affect performance. Use planning tools to manage long-term assignments and competing deadlines. Analyze how interests, values, and skills influence career pathways. Apply employability skills during collaborative projects and service activities. Analyze the steps of planning a small project or service, including identifying a target audience, testing an idea on a small scale, managing resources, and measuring results. Analyze spending choices, opportunity cost, and financial trade-offs. Develop financial habits that support saving, planning, and responsible spending. Assess how algorithms, social media, and digital habits influence attention and mood. Distinguish between credible information and manipulated online content. Develop responsible practices for online communication, privacy, and digital reputation. Assess health habits that influence concentration, energy, and emotional regulation. Explain how alcohol, tobacco, vaping, and other substances affect the developing brain, body, and decision-making. Distinguish among healthy, unhealthy, and unsafe relationship behaviors. Evaluate digital boundaries and privacy in relation to messages, images, and online pressure. Apply practical life skills for shopping, meal planning, and managing personal belongings. Complete applications, permission forms, and basic service paperwork on time. Develop leadership behaviors that support inclusion, responsibility, and shared goals. Analyze how integrity affects trust, reputation, and leadership. Develop responses to ethical dilemmas involving rules, pressure, and responsibility. Assess how laws, rights, and responsibilities shape community life for young people. Develop community participation strategies that support fairness, sustainability, and shared responsibility. Assess interests, goals, and supports that influence future educational choices. Apply transition skills such as help-seeking, planning, and self-advocacy. Assess how motivation, habits, and time use affect goal achievement. Develop a strategy for balancing academic, personal, and social goals. Evaluate how identity, belonging, and confidence influence personal choices. Develop a personal regulation plan for school stress and social pressure. Evaluate how coping choices affect resilience, safety, and decision-making. Evaluate how perspective-taking improves collaboration in diverse groups. Analyze how exclusion, bias, and stereotypes affect individual and group well-being. Explain how fraud, scams, and misinformation can affect financial safety. Develop a personal digital safety plan for middle school and beyond. Assess education and training options connected to different careers. Interpret everyday forms, appointment details, and service information independently. Identify the types of personal documents needed for education, employment, and official purposes, and practice organizing them. Analyze how responsible participation can improve school, community, and civic outcomes. Evaluate how choices today affect future options and opportunities. Develop a high school career-readiness plan that aligns courses, goals, and opportunities. Analyze how lifestyle habits influence health, performance, and personal safety. Assess the health risks of alcohol, drugs, and vaping, and apply refusal and help-seeking strategies in social situations. Develop collaboration habits for school, work-based learning, and community settings. Name personal strengths shown in classroom roles, activities, and play. Use self-control strategies while waiting, sharing, and following directions. Identify ways to include others in games, activities, and classroom groups. Name classroom and community roles that help shared spaces run well. Follow routines for caring for shared materials, spaces, and learning resources safely. Recognize that different people learn, work, and help in different settings. Use simple calming tools when feelings become big during the school day. Follow routines for putting away materials and caring for shared spaces. Practice simple self-care tasks such as washing hands, dressing, and cleaning up. Show leadership by helping others and joining group work kindly. Discuss common and unique characteristics of different cultures, including African American, Latino, Asian American, Hawaiian/Pacific Islanders, Indigenous Peoples, LGBTQ, and religious minorities, using multiple sources of information. Distinguish between land and water on a map and globe. Provide examples of how individuals and families interact with their environment. Listen and consider the ideas of others in order to make decisions as a group. Identify and explain the meaning of various civic symbols important to diverse community groups. For example: The American flag, the National Anthem, Statue of Liberty, Mount Rushmore, Crazy Horse Memorial, Liberty Bell, Emancipation Proclamation, a yellow sash (i.e., for women's rights), tribal flags of Native Nations whose ancestral homelands include present-day Colorado, LGBTQ Pride Flag, and the Colorado Flag. Explain the significance of major civic holidays. For example: Veterans Day, Martin Luther King Day, Independence Day, Presidents' Day, Memorial Day, Juneteenth, Labor Day, Indigenous Peoples Day, and César Chávez Day. Explain that the nature of history involves stories of the past preserved in various primary and secondary sources. For example: Images, oral and written accounts, etc. Describe the changes within one neighborhood and/or community over time. Organize historical events by creating timelines and explaining the information conveyed by them. Explain how communities manage and use nonrenewable and renewable resources. Explain scarcity of goods and resources. Recognize that different goods and services have different monetary values. Solve simple financial word problems to aid in making financial decisions. For example: A video game costs $20. If I earn $5 per week in allowance, I will need to save for ____ weeks to earn enough money. Compare information from multiple sources recounting the same event. Describe the history, interaction, and contribution of various peoples and cultures, including African American, Latino, Asian American, Hawaiian/Pacific Islander, Indigenous Peoples, LGBTQ, and religious minorities that have lived in or migrated to a community or region and how that migration has influenced change and development. Identify and explain a variety of roles leaders, citizens, and others play in local government. Explain, through multiple perspectives, the human interactions among people and cultures that are indigenous to or migrated to present-day Colorado. Including but not limited to: historic tribes of Colorado, the Ute Mountain Ute, Southern Ute, Spanish explorers, trappers, and traders. Identify and describe how political and cultural groups have affected the development of the region. Including but not limited to: African American, Latino, Asian American, Indigenous Peoples, religious groups, and European settlers. Describe the impact of various technological developments. For example: Changes in mining technologies, agricultural technology (center pivot irrigation), transportation, early 20th century industrial developments, and 20th century nuclear and computer technologies. Describe similarities and differences between the physical geography of Colorado and its neighboring states. Describe how the physical environment provides opportunities for and places constraints on human activities. Explain how physical environments influence immigration into the state. Discuss how various individuals and groups influence the way an issue affecting the state is viewed and resolved. Including but not limited to the contributions of African Americans, Latinos, Japanese Americans, Indigenous Peoples, LGBTQ, and religious groups. Identify and explain a variety of roles leaders, citizens, and others play in state government. Describe how a citizen might engage in local and state government to demonstrate their rights or initiate change. Describe and analyze how specific physical and political features influenced historical events, movements, and adaptation to the environment. Analyze important political, social, economic, and military developments leading to and during the American Revolution. Describe the influence of accessible resources on the development of local and regional communities throughout North America and the United States. Identify variables associated with discovery, exploration, and migration. Explain some of the challenges that American colonists faced that would eventually lead them to the creation of commercial banks. Establish the function of banking. Analyze multiple primary and secondary sources while formulating historical questions about the Western Hemisphere. For example: Oral histories, art, artifacts, eyewitness accounts, letters, and diaries, real or simulated historical sites, charts, graphs, diagrams, and written texts. Examine geographic sources to formulate and investigate inquiry questions to understand the past, analyze the present, or plan for the future. Describe how current economic systems in the Western Hemisphere (such as traditional, command, market, and mixed) developed. Use economic reasoning to explain how specialization of production in a country can result in more interdependence. For example: International trade patterns. Explore how consumer spending decisions and demand impact market economies. Investigate the historical, social, and cultural influences of minorities on civil governments of the United States, and the rest of the Western Hemisphere. Examine primary and secondary sources from multiple and diverse perspectives to identify point of view using art, eyewitness accounts, letters and diaries, artifacts, historical sites, charts, graphs, diagrams, and written texts. Describe the interactions, conflicts, and contributions of various peoples and cultures that have lived in or migrated within/to the Eastern Hemisphere. For example: Conflicts over land and resources between countries, the foundations of eastern world religions, the historical roots of current issues, East/West contact, settlement patterns, the Korean War, the war in Vietnam, the Chinese Cultural Revolution, the Khmer Rouge in Cambodia, including acts of violence towards groups of people, and the discriminatory policies and events preceding those acts. Investigate geographic sources to formulate inquiry questions to understand the past, analyze the present, or plan for the future. Describe how economic systems in the Eastern Hemisphere (such as traditional, command, market, and mixed) were developed. Describe civic virtues and principles that guide governments and societies. For example: Citizenship, civic participation, and rule of law. Explain the origins, functions, and structure of different governments. For example: Dictatorship, totalitarianism, authoritarian, monarchy, democracy, constitutional republic, socialism, fascism, and communism. Compare and contrast goods and services available to consumers within different cultures as they developed in the Eastern Hemisphere throughout history. Evaluate continuity and change over the course of United States history by examining various eras and determining major sources of conflict and compromise both in Colorado and across the nation. Including but not limited to: the Indian Removal Act, the Buffalo Soldiers, and the Sand Creek Massacre. Compare how differing geographic perspectives apply to a historic issue. Give examples of regional, national, and international differences in resources, productivity, and costs that provide a basis for trade. Explain why nations sometimes restrict trade by using quotas, tariffs, and nontariff barriers. Describe major political and/or social changes that affected the definition of citizenship, expanded or restricted the rights of citizens, and how those changes impacted women, Indigenous Peoples, African Americans, Latinos, Asian Americans, LGBTQ, religious minorities, and people living in annexed territories. Evaluate the results of various strategies used to enact political change over time. Analyze primary sources supporting democratic freedoms and the founding of our government and explain how they provide for both continuity and change. Including but not limited to: the Declaration of Independence, the Constitution, Bill of Rights, and the Declaration of Sentiments. Examine ways members of society may effectively and civilly voice opinions, monitor government, and bring about change on a local, state, and national level, and which could have global implications. Explain the role and importance of the Constitution and the strength of amendments made during this time period. Including but not limited to: the Bill of Rights, and the 13th, 14th, and 15th Amendments. Apply knowledge about the three branches of government and how they interact with one another to historical and contemporary problems. Discuss the tensions between individual rights and liberties with state, tribal, and national laws. Use a variety of resources, including Supreme Court decisions, to identify and evaluate issues that involve civic responsibility, individual rights, and the common good. Explain factors that have impacted borrowing and investing over time. For example: Currency stability, stocks, and banking practices. Analyze the changes in the development of human capital over time. For example: Gaining knowledge and skill through education, apprenticeship, entrepreneurship, and work experience. Analyze the impact of taxes on the people of the United States over time. Analyze variations in spatial patterns of cultural and environmental characteristics at multiple scales while gathering geographic data from a variety of valid sources. For example: Maps, Geographic Information Systems (GIS), graphs, and charts. Explain how migration of people and movement of goods and ideas can contribute to and enrich cultures, but also create tensions. Formulate compelling and supporting questions after evaluating primary sources for point of view and historical context. Construct and defend a historical argument that evaluates interpretations by analyzing, critiquing, and synthesizing evidence from a wide range of relevant historical sources. Analyze continuity and change over the course of United States history. Including but not limited to: The expansion and limitations of rights, the balance between liberty and security, shifts in internationalist and isolationist policies, debates over the role of government, and the impacts of expansionist policies. Investigate the historical development and impact of major scientific and technological innovations in the Industrial Age, the Space Age, and the Digital Age. For example: Scientific innovations by diverse individuals, creation of mass production/assembly line process, creation of the atomic bomb, NASA, and the introduction of mass media and the Internet. Analyze and evaluate ideas critical to the understanding of American history. Including but not limited to: populism, progressivism, isolationism, imperialism, capitalism, racism, extremism, nationalism, patriotism, anti-communism, environmentalism, liberalism, fundamentalism, and conservatism. Describe and analyze the historical development and impact of the arts and literature on the culture of the United States. Including but not limited to: the writings of the Muckrakers, political cartoons, Americana, the Harlem Renaissance, the Lost Generation, Jazz, Rock and Roll, protest songs and American literature. Investigate the historical development and impact of major scientific and technological innovations. For example: The Industrial Age (e.g., the British factory system), the Space Age (e.g., Sputnik), and scientific advancements such as the printing press, vaccinations, nuclear power, and the Internet. Describe and analyze the historical development and impact of the arts and literature on the cultures of the world. For example: The Renaissance, Modernism, and the use of art and literature as a form of both social progress and resistance. Examine patterns of distribution and arrangements of settlements and the processes of the diffusion of human activities. For example: Urban/rural, regional, and transportation patterns. Research and interpret viewpoints from diverse groups. Including but not limited to: African Americans, Latinos, Asian Americans, Hawaiian/Pacific Islander, Indigenous Peoples, LGBTQ, and religious minorities' perspectives on issues that shape policies and programs for resource use and sustainability. For example: Immigration, resource distribution, universal human rights and the UN Sustainable Development Goals. Make predictions and draw conclusions about the positive and negative global impact of cultural diffusion and assimilation. For example: Human rights, language, religion, and ethnicity. Examine geographic concepts through the lens of multiple diverse perspectives from various regions of the world and with consideration for indigenous, dominant, and marginalized populations. Including but not limited to: Indigenous Peoples in Colorado, Christians in the Middle East, the Uyghurs in China, and tribal groups in Afghanistan. Analyze how the principles of economic thinking influence the choices made by individuals, households, businesses, and governments. Including but not limited to: cost vs. benefits, thinking at the margin, incentives matter, trade makes people better off, and future consequences count. Compare and contrast economic systems in terms of their ability to achieve or impede economic goals. For example: Traditional, command, market, and modern mixed economies. Explore how economic crises create an environment where genocide is allowed to occur. For example: Rationing, scapegoating, including the incremental dehumanization of minority groups, and mitigating conflict over resources. Explore how all policies have costs and benefits that impact participants of an economic system in different ways. Explain how trade policies affect international trade and domestic markets. Including but not limited to: free trade, tariffs, quotas, subsidies, and current policies. Explore the effects of current globalization trends and policies. For example: Economic growth, labor markets, the rights of citizens, and the environment in different nations. Research and discuss current issues to participate in civil discourse. Describe and evaluate the effectiveness and acceptability of a variety of methods of civic participation that individuals and groups may use to shape policy at various levels of government. Evaluate traditional and non-traditional types of media (both historic and modern), including social media for reliability, credibility, and how they may influence government policy and public opinion. Engage as active community members with local, state, tribal, or federal levels of government on policy issues or for individual or group rights. Describe the origins, purposes, and limitations of government, and include the contribution of key philosophers and American historical figures of diverse backgrounds. Identify the structure, function, and roles of current members of local, state, and national governments. Including but not limited to: understanding the three branches of government at each level of government. Analyze the processes for amending the Constitutions of Colorado and the United States and the significant changes that have occurred to those documents including both the Colorado and the United States' Bills of Rights. Evaluate the role of the judicial system in protecting life, liberty, and property for all persons in the United States. Understand the structure of the American judicial system, the process of judicial appointments and key court decisions, in both Colorado and the United States, that affect the system of checks and balances and interactions of the local, state, tribal, and federal systems. Including but not limited to: significant Colorado court decisions such as Francisco Maestas et al. v. George H. Shone (1914), U.S. Term Limits, Inc. v. Thornton (1995), Romer v. Evans (1996), Colorado Union of Taxpayers Found. v. City of Aspen (2018); and landmark U.S. Supreme Court Cases such as Korematsu v. United States (1944), Tinker v. Des Moines Independent Community School District (1969). Describe the role and development of the founding documents of Colorado and the United States from their inception to modern day. Including but not limited to: the Great Law of Peace, the Declaration of Independence, the Constitutions of the United States and Colorado, the Federalist Papers, and the Bill of Rights. Analyze how current global issues impact American policy. Compare and contrast how other systems of government function. For example: Authoritarian regimes, parliamentary, and other systems. Describe the relationship of tribal governments with state and federal governments. Including but not limited to: The Ute Mountain Ute and Southern Ute tribal governments and the State of Colorado. Evaluate opportunities for people to participate in and influence government through interest groups and social movements. For example: The tactics and strategies of nonviolent resistance championed by Dr. Martin Luther King in response to the Jim Crow laws of that era, or the Indigenous land rights movement. Examine how people in other systems of government exercise their civic rights and responsibilities. Use reliable information resources when making financial decisions. Formulate strategies to protect personal and financial information. Compare financial institutions and products. Analyze the impact of economic conditions and cost of living factors on income and purchasing power. Investigate the total cost, affordability, and payment options associated with postsecondary options, degrees, and credentials, including personal savings, scholarships, grants, employer tuition programs, work study, and public and private loans. Explain the types and purpose of insurance products. For example: Automotive, identity theft, health, disability, long-term care, life insurance, renters/homeowners' insurance, and professional liability. Outline steps to monitor and safeguard personal financial data to minimize, avoid and/or resolve identity theft or fraud issues. Analyze consumer and financial information for relevance, credibility, and accuracy. Ask questions about the past using question starters. For example: What did? Where did? When did? Which did? Who did? Why did? How did? From whose perspective? Explore differences and similarities in the lives of children and families from different time periods by using a variety of sources. For example: Personal artifacts and stories, texts, pictures, and videos from different societies. Explain why knowing the order of events is important. Recognize and engage in ways to use another individual's items. For example: Asking for permission to share and taking turns. Practice citizenship skills when working with others including courtesy, honesty, and fairness. Identify the difference between fact and opinion. Create and follow classroom rules. Identify the difference between a want and a need and how that impacts purchasing decisions when resources are limited. For example: Buying a healthy snack vs. a candy bar, new shoes vs. a new toy, or a coat vs. a new game. Explain how money gives people the ability to buy goods and services. Begin to understand concepts of the past, present, and future. Develop an awareness of their own home, classroom, school, neighborhood, and community. Develop an awareness of basic, developmentally appropriate spatial concepts such as near and far. Identify choices that individuals can make to get their needs and wants met. Understand similarities and respect differences among people of diverse backgrounds within their classroom and community. Utilize positive social skill methods such as communication, trade-offs, common goals, kind actions, etc. to get positive results for obtaining needs and wants from other individuals, classmates, friends, and adults to empathize with others and begin to solve problems. Understand how similarities and differences can make a family, classroom, and community stronger. Identify emotions using age-appropriate vocabulary and correlate cause and effect to those emotions. Understand how rules in the classroom, home, and community keep us safe. Show interest in interacting with and developing relationships with others, including those who are African American, Latino, Asian American, Hawaiian/Pacific Islander, Indigenous Peoples, LGBTQ, and religious minorities. Demonstrate self-regulated behaviors and problem-solving skills when resolving conflicts. Identify different forms of money and their different values. Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate. Systems in the natural and designed world have parts that work together. The shape and stability of structures of natural and designed objects are related to their function(s). Make observations (firsthand or from media) to collect data that can be used to make comparisons. Construct an argument with evidence to support a claim. Read grade-appropriate texts and/or use media to obtain scientific and/or technical information to determine patterns in and/or evidence about the natural and designed world(s). Things may change slowly or rapidly. Obtain information using various texts, text features (e.g., headings, tables of contents, glossaries, electronic menus, icons), and other media that will be useful in answering a scientific question and/or supporting a scientific claim. Generate and/or compare multiple solutions to a problem. Events have causes that generate observable patterns. Make observations from several sources to construct an evidence-based account for natural phenomena onstructing Explanations and Designing Solutions) A system can be described in terms of its components and their interactions. Identify the evidence that supports particular points in an explanation. Obtain and combine information from books and other reliable media to explain phenomena. Make a claim about the merit of a solution to a problem by citing relevant evidence about how it meets the criteria and constraints of the problem. Natural objects and/or observable phenomena exist from the very small to the immensely large or from very short to very long time periods. Energy can be transferred in various ways and between objects. Develop a model using an analogy, example, or abstract representation to describe a scientific principle or design solution. Patterns can be used as evidence to support an explanation. Apply scientific ideas to solve design problems. Use a model to test cause and effect relationships or interactions concerning the functioning of a natural or designed system. Matter of any type can be subdivided into particles that are too small to see, but even then the matter still exists and can be detected by other means. A model showing that gases are made from matter particles that are too small to see and are moving freely around in space can explain many observations, including the inflation and shape of a balloon; the effects of air on larger particles or objects Obtain and combine information from books and/or other reliable media to explain phenomena or solutions to a design problem. Define a simple problem that can be solved through the development of a new or improved object or tool. Similarities and differences in patterns can be used to sort and classify natural phenomena. Use evidence (e.g., observations, patterns) to construct an explanation. Inheritance of Traits: Many characteristics of organisms are inherited from their parents. Other characteristics result from individuals’ interactions with the environment, which can range from diet to learning. Many characteristics involve both inheritance and environment. Constructing Explanations and Designing Solutions Use evidence (e.g. observations, patterns) to construct an explanation. Critiquing the scientific explanations or solutions proposed by peers by citing relevant evidence about the natural and designed world(s). Use evidence (e.g., measurements, observations, patterns) to construct an explanation. Measure and graph quantities such as weight to address scientific and engineering questions and problems. Develop a model using an example to describe a scientific principle. Gather, read and synthesize information from multiple appropriate sources and assess the credibility, accuracy and possible bias of each publication and methods used, and describe how they are support or not supported by evidence Develop a model to describe unobservable mechanisms. Use mathematical representations to describe and/or support scientific conclusions and design solutions. Cause and effect relationships may be used to predict phenomena in natural or designed systems. Relationships can be classified as causal or correlational, and correlation does not necessarily imply causation. Stability might be disturbed either by sudden events or gradual changes that accumulate over time. Structures can be designed to serve particular functions by taking into account properties of different materials, and how materials can be shaped and used. Phenomena may have more than one cause, and some cause and effect relationships in systems can only be described using probability. Phenomena that can be observed at one scale may not be observable at another scale. Design, evaluate, and/or refine a solution to a complex real-world problem, based on scientific knowledge, student-generated sources of evidence, prioritized criteria, and tradeoff considerations. When investigating or describing a system, the boundaries and initial conditions of the system need to be defined and their inputs and outputs analyzed and described using models. Models (e.g., physical, mathematical, computer models) can be used to simulate systems and interactions—including energy, matter, and information flows—within and between systems at different scales. Plan and conduct an investigation individually and collaboratively to produce data to serve as the basis for evidence, and in the design: decide on types, how much, and accuracy of data needed to produce reliable measurements and consider limitations on the precision of the data (e.g., number of trials, cost, risk, time), and refine the design accordingly. Use mathematical and/or computational representations of phenomena or design solutions to support explanations. Analyze data using tools, technologies, and/or models (e.g., computational, mathematical) in order to make valid and reliable scientific claims or determine an optimal design solution. Ask and/or evaluate questions that challenge the premise(s) of an argument, the interpretation of a data set, or the suitability of the design. Apply scientific reasoning, theory, and/or models to link evidence to the claims to assess the extent to which the reasoning and data support the explanation or conclusion. Feedback (negative or positive) can stabilize or destabilize a system. Much of science deals with constructing explanations of how things change and how they remain stable. Use a model to represent relationships in the natural world. Identify the goods and/or services that different types of businesses produce in the local community. Identify and categorize goods and services and provide examples of each. Explain the roles of buyers and sellers in product, labor, and financial markets. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Explain how the uneven distribution of resources in the world can lead to conflict, competition, or cooperation among nations, regions, and cultural groups. Identify safe ways to ask for help when a relationship problem feels too big to solve alone. Describe how online actions can affect other people. Describe how healthy habits support learning, energy, and mood. Develop a personal growth strategy based on reflection, goals, and support systems. Recognize signs of severe mental health distress in self and peers and identify appropriate help-seeking responses. Assess how cultural awareness and respect shape collaboration in diverse settings. Develop decision tools for complex academic, digital, and social situations. Evaluate how organization systems affect stress, performance, and balance. Assess how privacy settings, data sharing, and platform design affect online safety. Explain how recognizing personal rights, accessing support systems, and making informed choices contribute to safety in relationships. Assess how initiative, planning, and communication affect leadership effectiveness. Develop a balanced plan for school, work, wellness, and future preparation. Evaluate how bias, assumptions, and perspective affect participation in communities. Assess how executive functioning skills support work, school, and independent responsibilities. Analyze safety decisions related to substances, emergencies, and serious health risks. Analyze support systems for situations involving coercive pressure, unsafe relationships, or health concerns. Evaluate relationship decisions using consent, responsibility, safety, and health information. Develop independent living strategies for housing, time, logistics, and personal upkeep. Develop a postsecondary action plan that includes deadlines, supports, and next steps. Assess long-term habits that support well-being, persistence, and responsible choices. Apply executive functioning strategies to manage independence, deadlines, and self-direction. Evaluate personal readiness for self-employment or entrepreneurship by assessing skills, market opportunity, competition, financial sustainability, legal basics, and risk management. Assess borrowing, repayment, and opportunity costs when making postsecondary decisions. Evaluate how maintaining personal boundaries, mutual accountability, and open communication support long-term relationship well-being. Evaluate how personal character influences adult choices, trust, and responsibility. Apply postsecondary readiness skills to applications, decisions, and transition planning. Compare possible solutions when a problem affects more than one person. Apply routines for planning, organizing, and checking work for completeness. Describe how interests and strengths can connect to different kinds of work. Explain why saving helps people prepare for future needs. Recognize when to ask a trusted adult for health or safety help. Identify trusted supports for questions about body changes, privacy, and safety. Distinguish facts, feelings, and guesses when solving a problem. Describe healthy routines for sleep, food, movement, and stress management. Explain how respect, privacy, and boundaries support healthy relationships. Explain how home routines, chores, and planning support independence. Explain how communities use rules, services, and participation to meet shared needs. Compare personal strengths, challenges, and supports across school responsibilities. Use reflection to identify areas for growth in academic and social situations. Describe habits that help maintain effort across longer assignments and goals. Compare how different people may respond to the same situation or challenge. Apply empathy and fairness in group decisions and shared responsibilities. Present ideas clearly and confidently to a group using organized thoughts, eye contact, and appropriate voice and pacing. Apply prioritization and organization strategies during longer projects. Apply critical thinking to messages, claims, and everyday choices. Demonstrate work-readiness habits during projects, service, and group tasks. Demonstrate accountability by correcting mistakes and following through on commitments. Apply civic responsibility through service, stewardship, and respect for shared resources. Explore pathways from school skills to future careers and community roles. Analyze how habits, obstacles, and supports influence goal progress. Use grounding and coping strategies during stress, frustration, or pressure. Apply communication strategies that reduce conflict and build mutual respect. Apply media-literacy strategies to evaluate online claims, creators, and sources. Apply personal safety strategies in school, community, and online situations. Use transportation, scheduling, and planning skills to manage increasing independence. Apply age-appropriate civic action through service, advocacy, and respectful participation. Develop personal goals that connect effort, priorities, and responsibility. Develop help-seeking and documentation skills for bullying, coercion, or unsafe peer situations. Develop help-seeking strategies for physical, emotional, and safety concerns. Explain how household systems, schedules, and responsibilities support independence. Develop problem-solving approaches for conflict, pressure, and uncertainty. Assess how myths, media, and peer messages can affect beliefs about relationships and personal safety. Analyze postsecondary pathways using interests, goals, and adult responsibilities. Name body boundaries and safe ways to respond when a boundary is not respected. Practice teamwork by listening, cooperating, and finishing shared tasks. Explain that maps and globes are different representations of Earth. Describe locations using terms related to direction and distance. For example: Forward and backward, left and right, near and far, is next to, and close. Identify the attributes of a responsible team member and how they communicate with others. Demonstrate the ability to be both a leader and team member. Identify and explain the relevance of significant civic places. For example: The state and national Capitol, the White House, and sites within the local community. Explain how the environment influences why people settle in certain areas. Analyze how community members, including African American, Latino, Asian American, Hawaiian/Pacific Islander, Indigenous Peoples, LGBTQ, and religious minorities advocate for their interests and responsibly influence decisions in their community. Identify the roles and characteristics of various leaders at the local, state, and national levels. For example: The President of the United States, the Governor of Colorado, and the city mayor. Compare primary sources with works of fiction about the same topic. Identify geography-based problems and examine the ways that people have tried to solve them. Describe the difference between producers and consumers and explain how they need each other. Identify and apply the elements of civil discourse. For example: Listening with respect, speaking in a respectful manner, and restating an opposing viewpoint or opinion. Identify activities that individuals can do to earn money to reach personal financial goals. Identify cause-and-effect relationships using primary sources to understand the history of Colorado's development. Recognize how historical context can affect the perspective of historical sources. Examine significant historical documents. For example: The Proclamation of 1763, the Stamp Act, the Declaration of Independence, the Constitution, and treaties with Indigenous Nations such as the Two Row Wampum Treaty. Interpret timelines of eras and themes in North America from early Indigenous Peoples through the European Age of Exploration/post-Columbian colonization and the establishment of the United States Government. Identify the goods and services that were traded among different cultures and regions. Discuss how the concept of citizenship changed over time in the early American colonies. Explain the foundational documents and significance of the events that led to the establishment of the United States government. Including but not limited to the Philadelphia Convention, the Declaration of Independence, the Articles of Confederation, the Iroquois Confederacy, the Constitution, and the Bill of Rights. Identify political principles of American democracy and how the Constitution and Bill of Rights reflect and preserve these principles. Determine and explain the historical context of key people, events, cause and effect relationships, and ideas over time including the examination of different perspectives from people involved. For example: The complex interactions between majority and minority groups and individuals involved in European colonization in the Western hemisphere. Identify examples of the social, political, cultural, and economic development in the Western Hemisphere. For example: The extension of networks of communication, colonial empires, patterns of migration over time, and international trade. Explain the value each nation and/or culture places on economic prosperity, individual liberty, human rights, freedom of the press, freedom of religion, equal rights, and respect for neighbors. Analyze the opportunities and limitations of civic participation in societies in the Eastern Hemisphere. Recognize patterns of land acquisition and apply to events of the past. Compare the relationship between human settlement and the environment to recognize important regional connections to early U.S. historical events. Interpret geographic and environmental data to understand how competition over land and resources shaped the development of the early United States. For example: Establishing the Mason/Dixon line, development of railroads, the Louisiana Purchase, and the Treaty of Guadalupe Hidalgo. Explain the effects of domestic policies on international trade. Compare how the leadership of various individuals has influenced the United States government and politics. For example: Women, American Indians, African Americans, and people in the unsettled territories. Explain how the state and federal courts' power of judicial review is reflected in the United States' form of constitutional government. For example: Marbury v. Madison. Evaluate the historical development and impact of political thought, theory, and actions. For example: Shifts in the platforms of political parties, expansion and limitations of suffrage, and the impact of various reform and socio-cultural movements. Examine and evaluate how the United States was involved in and responded to international events over the course of history. Including but not limited to: the World Wars, the Holocaust, the Nuremburg trials, Cold War policies, Berlin Airlift, Korean War, Vietnam War, and the genocides in Bosnia and Darfur. Investigate causes and effects of significant events from the Renaissance to the present. Including but not limited to: the Renaissance, the Protestant Reformation, the Industrial Revolution, the French, Russian, Chinese, and Latin American Revolutions, the World Wars, and the Arab Spring movement. Examine and evaluate issues of unity and diversity in world history from the Renaissance to the present. For example: Migration and immigration (e.g., rapid global population growth), colonialism and the resulting changes in political geography, anti-colonial and nationalist movements, imperialism, world conferences and international agreements (e.g., Berlin Conference, United Nations, and Bandung Conference), and human rights issues. Identify, evaluate, and communicate strategies to respond to constraints placed on human systems by the physical environment. Compare and contrast the market outcomes created by various market structures including monopolistic competition, oligopoly, and monopoly. Explain the principles of a democracy and analyze how competing democratic values are balanced. For example: Freedom and security, individual rights and common good, general welfare, and rights and responsibilities. Analyze how individual rights have been affected over time by court decisions, legislative debates at various levels of government, or by the advocacy of individuals and groups. Compare different sources of personal income and compensation. Including but not limited to: earned income, profit income, interest income, dividend income, rental income, capital gains, and royalties. Analyze the monetary and non-monetary value of employee benefits in addition to pay. For example: Benefits, flexible work options, and retirement plans. Summarize factors to consider when selecting borrowing options, including costs, relevance, payoffs, and tradeoffs. For example: Comparing student, auto, home, and payday loans. Distinguish between a map and a globe as ways to show places people live. Explain how a class rule may promote fairness and resolve conflict and compare against a rule that may not. Contribute to making and maintaining class community decisions. Recognize choices people make with their money and explain how financial decisions are made. Begin to recall family traditions or personal events that happened in the past (this can include immediate past events from that day or week, or longer) and the present, especially as it pertains to diverse backgrounds, such as race, and individual family traditions. Begin to understand that previous, current, and future events can have an impact on our daily, weekly, or monthly lives. Identify aspects of their immediate environment, such as areas of their preschool classroom, their own room or house, and/or building and roads, trees, gardens, bodies of water, and land formations. Recognize membership in family, neighborhood, school, team, and various other groups and organizations. Recognize that everyone has rights and responsibilities within a group. Recognize coins and currency as money. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate. Simple tests can be designed to gather evidence to support or refute student ideas about causes. Plan and conduct an investigation collaboratively to produce data to serve as the basis for evidence to answer a question. Use tools and/or materials to design and/or build a device that solves a specific problem or a solution to a specific problem. Ask questions based on observations to find more information about the natural and/or designed world(s). Patterns in the natural world can be observed. Events have causes that generate observable patterns. Simple tests can be designed to gather evidence to support or refute student ideas about causes. Cause and effect relationships are routinely identified, tested, and used to explain change. Make observations and/or measurements to produce data to serve as the basis for evidence for an explanation of a phenomenon or test a design solution. A variety of hazards result from natural processes (e.g., earthquakes, tsunamis, volcanic eruptions). Humans cannot eliminate the hazards but can take steps to reduce their impacts Constructing Explanations and Designing Solutions Generate and compare multiple solutions to a problem based on how well they meet the criteria and constraints of the design solution. Ask questions that can be investigated within the scope of the classroom, outdoor environment, and museums and other public facilities with available resources and when appropriate, frame a hypothesis based on observations and scientific principles. Natural objects exist from the very small to the immensely large. Describe and graph quantities such as area and volume to address scientific questions. Construct and present oral and written arguments supported by empirical evidence and scientific reasoning to support or refute an explanation or a model for a phenomenon or a solution to a problem. Develop a model to predict and/or describe phenomena. Develop and use a model to describe phenomena and unobservable mechanisms. Integrate qualitative scientific and technical information in written text with that contained in media and visual displays to clarify claims and findings. Graphs, charts, and images can be used to identify patterns in data. Cause and effect relationships can be suggested and predicted for complex natural and human designed systems by examining what is known about smaller scale mechanisms within the system. Models can be used to predict the behavior of a system, but these predictions have limited precision and reliability due to the assumptions and approximations inherent in models. Much of science deals with constructing explanations of how things change and how they remain stable. Change and rates of change can be quantified and modeled over very short or very long periods of time. Some system changes are irreversible. Feedback (negative or positive) can stabilize or destabilize a system. Ask questions that arise from examining models or a theory, to clarify and/or seek additional information and relationships. Natural hazards and other geologic events have shaped the course of human history; [they] have significantly altered the sizes of human populations and have driven human migrations. (HS-ESS3-1) Apply scientific ideas to solve a design problem, taking into account possible unanticipated effects. Identify and describe how the physical and human characteristics of places and regions connect to human identities and cultures in the Western Hemisphere. (Geography) Give examples of choices that are made because of scarcity. Describe the difference between needs, wants, and choices. Describe how students share responsibility for cleanup, materials, and group spaces. Assess how stress responses can affect health, relationships, and school performance. Develop strategies for responding safely to online coercive pressure or image-based harm. Develop negotiation skills for practical adult situations such as salary discussions, service agreements, and financial decisions, including preparation techniques, anchoring, knowing when to walk away, and advocating for fair terms. Evaluate when self-management challenges require support from trusted adults or professionals. Develop advanced study and planning systems for postsecondary readiness. Assess how investing, compound growth, and risk affect future planning. Apply negotiation and de-escalation strategies in high-pressure or adversarial situations, including staying composed under emotional manipulation, handling power imbalances, recognizing bad-faith tactics, protecting personal interests with an uncooperative counterpart, and knowing when and how to involve a third party. Assess long-term wellness choices related to work, relationships, and independent living. Apply basic automotive maintenance skills including tire changes, jumpstarting, and vehicle safety checks for independent transportation. Apply leadership and teamwork skills to adult responsibilities and collaborative settings. Apply civic knowledge and legal awareness to adult responsibilities and community participation. Explain personal strengths that support learning new skills. Recognize unkind or unsafe online behavior and report it to a trusted adult. Explain why goals work better when they are clear and specific. Explain how rules and helpers support fairness and teamwork at school. Use feedback and respectful disagreement to strengthen group work. Explain how consequences can differ in the short term and long term. Explain how a digital footprint is created through online choices. Recognize pressure, manipulation, or unsafe behavior in age-appropriate situations. Demonstrate initiative in projects, service, and collaborative learning. Apply emotional regulation strategies during conflict, change, and disappointment. Compare safe and unsafe ways to communicate, share, and search online. Compare short-term and long-term goals in school and life. Analyze how perseverance and recovery after setbacks contribute to resilience. Develop systems for tracking deadlines, materials, and progress across subjects. Explain how misinformation, advertising, and online influence can shape decisions. Explain how budgeting time, materials, and tasks supports independence at home and school. Develop habits of responsibility that support school, home, and community life. Apply budgeting strategies to allowance, purchases, and personal goals. Analyze how sleep, stress, nutrition, and activity affect middle school functioning. Develop a self-advocacy plan based on needs, strengths, and goals. Analyze the complexity of events throughout United States history. For example: The Civil Rights Movement (e.g., Double V Campaign, the Voting Rights Act of 1965, and the Stonewall Riots); migration, immigration, and displacement (e.g., immigration and citizenship legislation, Japanese American incarceration, and debates over tribal sovereignty); landmark court cases (e.g., Keyes v. School District #1 Denver, Brown v. Board of Education, and Obergefell v. Hodges), and the war on terror (e.g., 9/11, Afghanistan and Iraq wars, Middle Eastern discrimination, and the evolution of U.S. counterterrorism efforts). Investigate causes and effects of significant events throughout United States history. For example: World and national conflicts (e.g., Spanish American War, the continued conflict over Indigenous lands, and the Tulsa Massacre), urbanization and suburbanization (e.g., Great Migration and Levittown), economic cycles (e.g., The Great Depression and the 2008 Great Recession), and both popular and counterculture movements. Examine and evaluate issues of unity and diversity from Reconstruction to present. For example: The systemic impact of racism and nativism (e.g., Jim Crow, affirmative action, and mass incarceration), the definition and role of patriotism, expansion and limitations of rights, and the role of religion. Analyze how opposing perspectives, compromise, and cooperation have shaped national unity and diversity. For example: The rights and contributions of diverse groups and individuals, including African Americans, Latinos, Asian Americans, Indigenous Peoples, LGBTQ individuals, women, immigrants, individuals with disabilities, and ethnic and religious minorities, and the role of organizations and government in advancing these rights (e.g., NAACP, American Indian Movement, and United Farm Workers). Use supply and demand analysis to explain how competitive markets efficiently allocate scarce resources. Explain the roles and influence of individuals, groups, and the press, as checks on governmental practices. For example: Direct contact with elected officials, participation in civic organizations, use of social media, and attendance at local governance meetings. Analyze student loan repayment options, terms, requirements, and state and federal repayment programs and their impact on a student's financial future. Explain the qualities of an informed and engaged citizen. Explain why rules are needed. Follow classroom routines, rules, and expectations. Discuss why we need money. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Analyze data from tests of an object or tool to determine if it works as intended. Patterns of change can be used to make predictions. Standard units are used to measure and describe physical quantities such as weight, time, temperature, and volume. Similarities and differences in patterns can be used to sort and classify designed products. Identifying patterns in large data sets and using mathematical concepts to support explanations and arguments. Use mathematical representations to support scientific conclusions and design solutions. Time, space, and energy phenomena can be observed at various scales using models to study systems that are too large or too small. Systems may interact with other systems; they may have sub-systems and be a part of larger complex systems. Explanations of stability and change in natural or designed systems can be constructed by examining the changes over time and processes at different scales, including the atomic scale. Different patterns may be observed at each of the scales at which a system is studied and can provide evidence for causality in explanations of phenomena. Systems can be designed to cause a desired effect. Global Climate Change: Though the magnitudes of humans’ impacts are greater than they have ever been, so too are humans’ abilities to model, predict, and manage current and future impacts. Through computer simulations and other studies, important discoveries are still being made about how the ocean, the atmosphere, and the biosphere interact and are modified in response to human activities, as well as to changes in human activities. Use observations (firsthand or from media) to describe patterns in the natural world in order to answer scientific questions. Analyze the role of comparative advantage in international trade of goods and services. Explain when to ask for help and what kind of support is needed. Use words, breathing, or movement to manage frustration during learning. Use a step-by-step process to solve everyday classroom problems. Use simple money decisions in pretend shopping and saving activities. Describe how teamwork helps people solve problems and complete tasks. Develop accountability habits that support work, community, and independent decision-making. Apply sustainable household practices including recycling, energy efficiency, and environmentally responsible consumer choices. Assess how laws, institutions, and civic processes affect personal and community decisions. Assess the requirements, benefits, and costs of different postsecondary options. Develop a financial plan for short-term needs and long-term goals. Apply future-planning skills to adult decisions, transitions, and responsibilities. Set a simple goal based on a personal interest or area for growth. Explain how routines and habits support focus, calm, and follow-through. Explain how interests and strengths connect to learning choices. Describe how inclusion strengthens classroom and community belonging. Identify choices that help students prepare for future opportunities. Describe roles that help teams stay organized, respectful, and productive. Describe how planning and reflection help people reach goals. Describe how earning, saving, and spending choices affect financial goals. Explain how leadership can involve service, responsibility, and encouragement. Develop a personal profile of strengths, needs, and learning preferences. Apply health and safety habits to busy schedules, changing routines, and growing independence. Identify reliable sources of information about personal development, safety, and health. Develop questions to ask when exploring schools, careers, and adult roles. Apply respectful negotiation strategies to resolve disagreements and reach fair outcomes, including understanding the other side's perspective, proposing alternatives, and finding compromises. Analyze choices by considering consequences, values, and social pressure. Deliver a structured presentation with organized ideas, supporting evidence, visual aids, and engaging delivery, applying practical techniques used by effective speakers. Analyze personal and community safety responses in urgent or risky situations. Evaluate postsecondary options using strengths, goals, and requirements. Explain how credit, debt, and borrowing can affect future financial stability. Describe choices that show growing independence at school. Follow speaking and listening routines during partner, group, and class discussions. Use classroom routines for organizing materials and following directions. Name ways people use money for needs, wants, and shared responsibilities. Practice simple saving and spending choices in classroom activities. Name trusted adults who can help when something feels hard or confusing. Follow simple routines that help start, finish, and clean up activities. Set a simple goal for play, learning, or daily routines. Give examples of different types of jobs held by family members and/or individuals in the local community. Find the value of a collection of a variety of coins. Identify examples of how human activity influences environmental characteristics of a place over time. Identify and compare examples of civic responsibilities, such as volunteering in the community, that are important to privileged and marginalized individuals, families, and communities. Give examples of places that are similar and different from a local region. Recognize that different currencies exist and explain the functions of money. For example: Medium of exchange, store of value, and measure of value. Model strategies to achieve a personal financial goal using arithmetic operations. Explain how productive resources (natural, human, and capital) have influenced the types of goods produced and services provided in Colorado. Analyze how external factors might influence spending decisions for different individuals. Examine the causes and effects of the territorial, political, and economic expansion of the United States. Analyze patterns of conflict and cooperation that resulted from human migration and the economic, political, ethnic, and social implications of those interactions. Explain the economic way of thinking: The condition of scarcity requires choice and choice has a cost (opportunity cost). Describe how members of a civil society can impact public policy on local, state, national, or international issues by exercising their civic rights and responsibilities. For example: Participation in primaries and general elections, contact with elected officials, petitions, protesting, attending public forums, or through initiatives and referenda. Analyze how financial markets react to changes in market conditions, monetary policy, fiscal policy, and information. For example: The business cycle. Evaluate strategies for consumers to avoid financial risk, reduce risk, accept risk, or transfer risk to others through insurance. Provide rationale about something from the past using statements. For example: Because, as a result, I know ___. Identify information from primary and/or secondary sources that answer questions about the past and contribute to the collective memory. Identify the costs and benefits of a choice an individual makes when acquiring an item. Explain how individuals earn money and use it to make choices among their various wants. Patterns in the natural and human designed world can be observed, used to describe phenomena, and used as evidence. Comprehend increasingly complex and varied vocabulary. Plan and conduct an investigation collaboratively to produce data to serve as the basis for evidence, using fair tests in which variables are controlled and the number of trials considered. Ask questions that can be investigated and predict reasonable outcomes based on patterns such as cause and effect relationships. Analyze and interpret data to make sense of phenomena, using logical reasoning, mathematics, and/or computation. Develop a model to describe phenomena. Develop a model to describe phenomena. The transfer of energy can be tracked as energy flows through a natural system. Patterns can be used to identify cause-and-effect relationships. Empirical evidence is required to differentiate between cause and correlation and make claims about specific causes and effects. Empirical evidence is needed to identify patterns. Construct, use, and/or present an oral and written argument or counter-arguments based on data and evidence. Create a plan with specific steps to reach a short-term financial goal. Explain how different choices can lead to different outcomes. Participate in simple community actions that help others feel safe and included. Describe short-term goals for learning, behavior, or responsibility. Develop a plan for an online project or digital venture, including market research, audience building, content strategy, monetization, and evaluating demand before scaling. Analyze how taxes, paychecks, and deductions influence personal income. Develop a personal health plan that includes prevention, care, and help-seeking. Compare simple spending choices based on value and purpose. Explain how communities depend on many kinds of work and service. Develop strategies for solving problems that involve competing needs or priorities. Apply problem-solving to common daily-life logistics such as timing, supplies, and transportation. Apply critical thinking to real-life choices involving health, money, and relationships. Analyze leadership choices that influence trust, participation, and accountability. Apply safe food handling, basic cooking techniques, and budget-friendly meal preparation. Tell a trusted adult when teasing, exclusion, or unsafe behavior happens. Describe work habits like listening, trying, and finishing tasks. Compare past and present situations and events. Give examples of short-term spending and savings goals. Give examples of the kinds of goods and services produced in Colorado, in different historical periods, and their connection to economic incentives. Use geographic tools to identify, locate, and describe places and regions in the Western Hemisphere to investigate and solve geographic problems. For example: Farming practices in a dry climate, implications of building a dam, and deforestation. Recognize the alternatives, consequences, and responsibilities associated with personal financial decisions. Describe how to use and manage different types of accounts and payment methods. Select financial investments that align with financial goals, risk tolerance, and personal and retirement options for different life stages. Introduce precise claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that establishes clear relationships among claim(s), counterclaims, reasons, and evidence. Construct and/or support an argument with evidence, data, and/or a model. Analyze and interpret data to make sense of phenomena using logical reasoning. Support an argument with evidence, data, or a model. Use an oral and written argument supported by evidence to support or refute an explanation or a model for a phenomenon. Algebraic thinking is used to examine scientific data and predict the effect of a change in one variable on another (e.g., linear growth vs. exponential growth). Evaluate competing design solutions to a real-world problem based on scientific ideas and principles, empirical evidence, and logical arguments regarding relevant factors (e.g. economic, societal, environmental, ethical considerations). Evaluate the validity and reliability of and/or synthesize multiple claims, methods, and/or designs that appear in scientific and technical texts or media reports, verifying the data when possible. Communicate information or design ideas and/or solutions with others in oral and/or written forms using models, drawings, writing, or numbers that provide detail about scientific ideas, practices, and/or design ideas. Create maps to display and explain the spatial patterns of culture and environment. Recognize classroom jobs that build responsibility and teamwork. Describe how listening carefully helps people understand one another. Assess strategies for supporting peers in mental health crises and navigating community mental health resources as a responsible adult. Compare decision options by weighing fairness, risk, and responsibility. Describe transportation, schedules, and planning skills used in everyday life. Analyze how media, peers, and habits influence health choices. Explore pathways after high school, including college, training, and work. Analyze how media and online communities shape beliefs, bias, and behavior. Use map keys, legends, symbols, intermediate directions, and a compass rose to locate and describe spaces and places. Identify the hemispheres, Equator/Prime Meridian, and the North/South poles. Identify and locate cultural, human, political, and natural features using map keys and legends. Use maps and geographic tools to find patterns in human systems and/or physical features to investigate and propose a solution to geographic problems. Analyze how factors of production (land, labor, capital) are brought together to produce goods and services in an economic system. Compare and contrast different types of taxing. For example: Progressive, regressive, proportional, and marginal vs. average tax rates. Explore the multiple roles governments can play dealing with economic crises, including monetary and fiscal policy changes, and reallocation of resources and redistribution of wealth. Describe how fiscal and monetary policy are used to manipulate the economy including their potential lasting consequences. Simulate a sustainable household budget based on future personal and career goals. Use geographic tools to describe places. For example: Globes, maps, and GPS. Ask questions to identify and clarify evidence of an argument Analyzing data progresses to extending quantitative analysis to investigations, distinguishing between correlation and causation, and basic statistical techniques of data and error analysis and analyze and interpret data to determine similarities and differences in findings. Within a natural system, the transfer of energy drives the motion and/or cycling of matter. Energy drives the cycling of matter within and between systems. Explain how responsibility and effort connect to doing a job well. Practice simple routines for food, clothing, and daily care. Describe what it means to be ready for new learning and responsibilities. Assess how risk, ethics, and consequences affect major decisions. Evaluate college, career, and training pathways using personal priorities and evidence. Explain how leaders and teammates share responsibility in group work. Distinguish between healthy friendship behaviors and harmful relationship patterns. Evaluate leadership styles and when each may be effective in group situations. Assess personal strengths that support success in high school responsibilities. Recognize how effort helps people make progress over time. Recognize different jobs people do at school and in the community. Recite an address including city, state, and country, and explain how those labels help find places on a map. Discuss ways to earn or receive money. Identify types of currency and how currency is used. For example: Cash, coins, credit card, and debit card. Locate oceans and continents, major countries, bodies of water, mountains, urban areas, the state of Colorado, and neighboring states on maps. Discuss the role of elections in choosing specific candidates to represent the public interest in local government. Identify and explain the services the state government provides and how those services are funded. Analyze the push and pull factors that shaped immigration to and migration within the early United States. For example: Economic opportunities, religious refuge, and forced migration. Calculate how the value of money has changed over time impacting earning, spending, borrowing, and investing. For example: Inflation and recession. Explain how shifts in the world's population are connected to and dependent upon other people for both human and natural resources. Summarize the advantages and disadvantages of leasing versus purchasing automobiles, homes, and other large purchases. Identify how the environment, geographic features, and climate impact lifestyles. For example: Food, sports, shelter, transportation, school, etc. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 10^8 and the population of the world as 7 × 10^9, and determine that the world population is more than 20 times larger. Apply scientific ideas or principles to design an object, tool, process, or system. Construct an explanation that includes qualitative or quantitative relationships between variables that predict phenomena. Models can be used to represent systems and their interactions—such as inputs, processes and outputs—and energy and matter flows within systems. Energy cannot be created or destroyed — only moved between one place and another place, between objects and/or fields, or between systems. In nuclear processes, atoms are not conserved, but the total number of protons plus neutrons is conserved. Analyze basic labor rights, employment protections, and the role of contracts in workplace and housing settings. Assess personal readiness for life after high school in academic, work, and living contexts. Analyze how initiative and reliability influence teamwork outcomes. Name a goal and one or two steps for reaching it. Recognize favorite activities and simple preferences at school. Understand that the United States is made up of the diverse perspectives and traditions of many cultures. For example: The diversity of foods available in the local community. Read and interpret information from geographic tools and formulate geographic questions. Give examples of issues faced by the state of Colorado and develop possible solutions. Investigate causes and effects of significant events in early United States history. For example: The establishment of Jamestown, George Washington's crossing of the Delaware River, the French and Indian War, and the Constitutional Convention. Evaluate the strengths of rule of law. Explore the role of government in addressing market failures. For example: Monopoly power/antitrust legislation, public goods, negative/positive externalities, the environment, property rights, regulation, access to essential goods and services, and income distribution. Identify the cost and benefits of purchasing insurance. For example: Insured profile, number and size of claims, frequency, and costs of natural disasters. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01 12t, y = (1.2)t/10, and classify them as representing exponential growth or decay. Matter is transported into, out of, and within systems. Use mathematical, computational, and/or algorithmic representations of phenomena or design solutions to describe and/or support claims and/or explanations. Explain the relationship among credit scores, borrowing, and financial opportunity. Assess how planning, reflection, and revision improve long-term goal progress. Evaluate financial decisions related to savings, loans, and postsecondary costs. Analyze how honesty, fairness, and respect shape trust and reputation. Tell what helps the body and mind feel ready to learn. Recognize ways a class leader can help a group succeed. Construct a timeline of the major events in Colorado history. Sequence information using words. For example: Present, future, days, weeks, months, years, first, next, last, before, and after. Construct a scientific explanation based on valid and reliable evidence obtained from sources (including the students’ own experiments) and the assumption that theories and laws that describe the natural world operate today as they did in the past and will continue to do so in the future. Patterns in rates of change and other numerical relationships can provide information about natural systems. Conservation of Energy and Energy Transfer: When the motion energy of an object changes, there is inevitably some other change in energy at the same time. The amount of energy transfer needed to change the temperature of a matter sample by a given amount depends on the nature of the matter, the size of the sample, and the environment. Energy is spontaneously transferred out of hotter regions or objects and into colder ones. Apply concepts of statistics and probability (including determining function fits to data, slope, intercept, and correlation coefficient for linear fits) to scientific and engineering questions and problems, using digital tools when feasible. In nuclear processes, atoms are not conserved, but the total number of protons plus neutrons is conserved. Present arguments persuasively by analyzing what makes real-world speakers effective, adapting structure and tone to the audience, using storytelling and evidence, and handling questions with confidence. Develop an ethical framework for independent living, work, and community participation. Recognize honest, respectful, and responsible behavior in the classroom. Name goals for learning, growing, and being ready for the next school year. Compare at least two different job choices that individuals have with respect to the benefits and costs of each job. Define types of transactions such as deposit, purchase, borrow, donate, and barter. Understand how basic budgeting, investing, saving, and personal behavior with money affects the economic system as a consumer and/or producer. Explain how people, cultures, and ideas interact and are interconnected in the Western Hemisphere and how they have impacted modern times. For example: The "Great Dying" of Indigenous Peoples in the Americas and its consequences; rapid deforestation of the Amazon; anti-colonial and nationalist movements, the Columbian Exchange, and revolutions in energy. Evaluate the historical development and impact of philosophical and political movements and belief systems. Including but not limited to: the Enlightenment, humanism, communism, socialism, and the development and expansion of Judaism, Christianity, Islam, Hinduism, Buddhism, Sikhism, and Taoism. Examine the advantages and disadvantages of a two-party system or a multiparty system within a democratic government. Identify ways students' lives are similar and different from those in other communities. Identify how money is obtained (e.g., through work or gifts) and how it is used. Complex and microscopic structures and systems can be visualized, modeled, and used to describe how their function depends on the shapes, composition, and relationships among its parts, therefore complex natural structures/systems can be analyzed to determine how they function. Small changes in one part of a system might cause large changes in another part. Develop a basic plan for a small offline project or service, including audience analysis, a minimum viable product, budgeting, pricing, and marketing strategies. Develop a personal budget that includes income, expenses, and savings goals. Talk about ways children can help as responsible classroom helpers. Predict positive and negative consequences when making financial decisions. For example: If… Then... decision making. Develop a model to represent patterns in the natural world. Analyze and interpret data to determine similarities and differences in findings. Plan an investigation individually and collaboratively, and in the design: identify independent and dependent variables and controls, what tools are needed to do the gathering, how measurements will be recorded, and how many data are needed to support a claim. Construct and interpret graphical displays of data to identify linear and nonlinear relationships. Matter is conserved because atoms are conserved in physical and chemical processes. Structures can be designed to serve particular functions. Analyze data using computational models in order to make valid and reliable scientific claims. Track simple progress toward a goal and celebrate growth. Develop a responsible money-management plan for work, housing, and future goals. Interpret maps to make inferences and predictions. Describe how economic indicators provide various perspectives of the health of the economy and vary with the business cycle. Including but not limited to: Gross Domestic Product (GDP), inflation, unemployment, and other non-traditional indicators. Predict the potential impact of education and skill development choices on career earnings, including starting salary by field and level of degree or credential. Compare the advantages and disadvantages of various types of credit. Explain the difference between democratic decision-making and decisions made by authorities. For example: A parent, teacher, principal, and a police officer. Develop a simple model based on evidence to represent a proposed object or tool. Evaluate the influence of long-term climate variability on human migration and settlement patterns, resource use, and land uses at local-to-global scales. Apply financial planning skills to adult responsibilities, bills, and independent living. Explain how banking tools support saving, security, and financial responsibility. Explain the relationship between major events in Colorado history and events in United States history during the same era. Including but not limited to: Colorado statehood, the Ludlow and Sand Creek Massacres, creation of national parks in Colorado, the Great Depression, the Dust Bowl, Amaché, Chicano movement, and busing in Denver. Identify consumer responsibilities, rights, and consumer protection laws that regulate contracts and financial transactions. Develop and/or use models to describe and/or predict phenomena. The total amount of energy and matter in closed systems is conserved. Distinguish between different types of financial institutions such as banks and credit unions, and the services provided. For example: Checking accounts, savings accounts, investments, and loans. Review the purpose and the process of accessing state and federal financial aid. Including but not limited to: the Colorado Application for State Financial Aid (CASFA), the Free Application for Federal Student Aid (FAFSA) application for financial aid. Evaluate the claims, evidence, and/or reasoning behind currently accepted explanations or solutions to determine the merits of arguments. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Name habits that support sleep, hygiene, and healthy eating. Develop a system for keeping and using financial records. Design a household budget (using gross and net income) that addresses financial obligations and integrates saving for future goals and retirement based on your values and goals. Communicate scientific and/or technical information or ideas (e.g. about phenomena and/or the process of development and the design and performance of a proposed process or system) in multiple formats (including orally, graphically, textually, and mathematically). Explain how altering the environment has brought prosperity to some places and created environmental dilemmas for others. Use a model based on evidence to illustrate the relationships between systems or between components of a system. Differentiate the role of income and expenses when creating a budget. Explain how an individual's credit history can affect borrowing power. Represent data in tables and/or various graphical displays (bar graphs, pictographs, and/or pie charts) to reveal patterns that indicate relationships. Use safe routines for hygiene, illness prevention, and daily well-being. Analyze and interpret data to provide evidence for phenomena. Differentiate among examples of civic participation. For example: Describe personal connections to community events, such as voting, debating, running for office, advocating, fundraising, and volunteering. Conduct an investigation to produce data to serve as the basis for evidence that meet the goals of an investigation. With guidance, plan and conduct an investigation in collaboration with peers. Proportional relationships (e.g. speed as the ratio of distance traveled to time taken) among different types of quantities provide information about the magnitude of properties and processes. Communicate technical information or ideas (e.g., about phenomena and/or the process of development and the design and performance of a proposed process or system) in multiple formats (including orally, graphically, textually, and mathematically). Create and/or revise a computational model or simulation of a phenomenon, designed device, process, or system. Evaluate the different economic systems in the Eastern Hemisphere, utilizing economic data. For example: Economic growth, per capita income, and standard of living. Conduct an investigation and evaluate the experimental design to produce data to serve as the basis for evidence that can meet the goals of the investigation. The significance of a phenomenon is dependent on the scale, proportion, and quantity at which it occurs. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Create a way to keep track of money spent and money saved. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? Analyze how inflation and cost of living impact consumer purchasing and saving power. Plan and conduct an investigation that control variables and provide evidence to support explanations or design solutions. Solve real-world and mathematical problems involving the four operations with rational numbers.