{"CFDocument":{"identifier":"5254fd3f-b10b-5aae-95b0-ce4cf3223874","uri":"https://opensalt.net/uri/5254fd3f-b10b-5aae-95b0-ce4cf3223874","creator":"Maryland State Department of Education","title":"Maryland College and Career Ready Standards for Mathematics (2025)","lastChangeDateTime":"2025-07-01T00:00:00+00:00","officialSourceURL":"https://marylandpublicschools.org/about/pages/dcaa/math/revised-standards.aspx","publisher":"Public Consulting Group","subject":["Mathematics"],"language":"en","version":"2025","adoptionStatus":"Adopted"},"CFItems":[{"identifier":"7c23ecff-85fd-5db2-94a2-3beec10a2263","uri":"https://opensalt.net/uri/7c23ecff-85fd-5db2-94a2-3beec10a2263","fullStatement":"Prekindergarten","humanCodingScheme":"PK","language":"en","educationLevel":["PK"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"5493be4f-332f-5c24-bdb8-886ea4b0f62e","uri":"https://opensalt.net/uri/5493be4f-332f-5c24-bdb8-886ea4b0f62e","fullStatement":"Number and Operation Sense","humanCodingScheme":"PK.NOS","language":"en","educationLevel":["PK"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"e892679b-a671-5dfc-9e03-04a7de4e3397","uri":"https://opensalt.net/uri/e892679b-a671-5dfc-9e03-04a7de4e3397","fullStatement":"Know number names and the count sequence","humanCodingScheme":"PK.NOS.A","language":"en","educationLevel":["PK"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"3d6324c1-732d-5dbb-ab9c-eaf22edc246b","uri":"https://opensalt.net/uri/3d6324c1-732d-5dbb-ab9c-eaf22edc246b","fullStatement":"Count to 20 by ones.","humanCodingScheme":"PK.NOS.A.1","language":"en","educationLevel":["PK"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"c5714559-bd07-5a61-8b2a-dbd3335625b3","uri":"https://opensalt.net/uri/c5714559-bd07-5a61-8b2a-dbd3335625b3","fullStatement":"Count backward from 10 by ones.","humanCodingScheme":"PK.NOS.A.2","language":"en","educationLevel":["PK"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"a5af0cdd-e74b-5508-8438-724b8d576e03","uri":"https://opensalt.net/uri/a5af0cdd-e74b-5508-8438-724b8d576e03","fullStatement":"Identify which number comes just after or just before a given number in the counting sequence to 10.","humanCodingScheme":"PK.NOS.A.3","language":"en","educationLevel":["PK"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"91f539f2-ae2a-5c95-93dc-2ee9eb67c722","uri":"https://opensalt.net/uri/91f539f2-ae2a-5c95-93dc-2ee9eb67c722","fullStatement":"Identify written numerals 0-10.","humanCodingScheme":"PK.NOS.A.4","language":"en","educationLevel":["PK"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"677e5716-0261-52e5-8c10-ec4cdc3d629d","uri":"https://opensalt.net/uri/677e5716-0261-52e5-8c10-ec4cdc3d629d","fullStatement":"Count to tell the number of objects","humanCodingScheme":"PK.NOS.B","language":"en","educationLevel":["PK"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"de07a431-8704-5f1e-91ae-2c2af9aee579","uri":"https://opensalt.net/uri/de07a431-8704-5f1e-91ae-2c2af9aee579","fullStatement":"Use the relationship between numbers and quantities within 10 to count objects with one-to-one correspondence and verbalizing the last number stated is the total when asked \"How many\u2026?\u201d (cardinality).","humanCodingScheme":"PK.NOS.B.5","language":"en","educationLevel":["PK"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"3856be37-413b-5fc0-bfb5-8f5e832a94de","uri":"https://opensalt.net/uri/3856be37-413b-5fc0-bfb5-8f5e832a94de","fullStatement":"When counting objects within 10, recognize that each successive number name refers to a quantity that is one larger.","humanCodingScheme":"PK.NOS.B.6","language":"en","educationLevel":["PK"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"48755d74-d40d-5e3c-9e1b-6677c23b7bd4","uri":"https://opensalt.net/uri/48755d74-d40d-5e3c-9e1b-6677c23b7bd4","fullStatement":"Represent a number within 10 by producing a set of objects with concrete materials, drawing pictures, and/or writing numerals. 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100.","humanCodingScheme":"K.NOS.A.2","language":"en","educationLevel":["KG"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"a62e5640-6dc7-5fa3-900e-33100a2fe5d3","uri":"https://opensalt.net/uri/a62e5640-6dc7-5fa3-900e-33100a2fe5d3","fullStatement":"Count backwards from any given number within 20.","humanCodingScheme":"K.NOS.A.3","language":"en","educationLevel":["KG"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"c63a0354-5233-5f32-857d-d49fa81f9387","uri":"https://opensalt.net/uri/c63a0354-5233-5f32-857d-d49fa81f9387","fullStatement":"Write numbers from 0 to 20.","humanCodingScheme":"K.NOS.A.4","language":"en","educationLevel":["KG"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"7f05a47e-4b33-5e04-a7ee-c0ab15dfbacb","uri":"https://opensalt.net/uri/7f05a47e-4b33-5e04-a7ee-c0ab15dfbacb","fullStatement":"Represent a number of objects with a written numeral within 20 (with 0 representing a count of no 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(cardinality).","humanCodingScheme":"K.NOS.B.6","language":"en","educationLevel":["KG"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"bc6cf5d5-fda0-5c54-a6fe-ed3284fc3b4a","uri":"https://opensalt.net/uri/bc6cf5d5-fda0-5c54-a6fe-ed3284fc3b4a","fullStatement":"When counting objects within 20, recognize that each successive number name refers to a quantity that is one larger.","humanCodingScheme":"K.NOS.B.7","language":"en","educationLevel":["KG"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"55c5712a-cf56-583d-a4fa-1c66f553b2a8","uri":"https://opensalt.net/uri/55c5712a-cf56-583d-a4fa-1c66f553b2a8","fullStatement":"Recognize the number of objects in a set without counting (subitizing) with both unfamiliar patterns within 6 and familiar patterns within 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Represent points on a number line with negative numbers.","humanCodingScheme":"6.NOS.C.6","language":"en","educationLevel":["06"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"98a12ca4-0670-5bbd-b40a-2ab9b115cec1","uri":"https://opensalt.net/uri/98a12ca4-0670-5bbd-b40a-2ab9b115cec1","fullStatement":"Estimate quantities by reasoning about their location on a number line, their relationship to benchmark numbers, and by rounding.","humanCodingScheme":"6.NOS.C.6.a","language":"en","educationLevel":["06"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"24411403-ccaa-5970-9fc3-78792894a005","uri":"https://opensalt.net/uri/24411403-ccaa-5970-9fc3-78792894a005","fullStatement":"Locate and interpret the positions of rational numbers on a number line.","humanCodingScheme":"6.NOS.C.6.b","language":"en","educationLevel":["06"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"1083536b-5ff7-52d6-a9ad-c0e2459526c0","uri":"https://opensalt.net/uri/1083536b-5ff7-52d6-a9ad-c0e2459526c0","fullStatement":"Recognize and locate opposite signs of rational numbers as indicating locations on opposite sides of 0 on the number line.","humanCodingScheme":"6.NOS.C.6.c","language":"en","educationLevel":["06"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"f5ddf5d0-3e61-5dd9-a866-4b35b69efd7f","uri":"https://opensalt.net/uri/f5ddf5d0-3e61-5dd9-a866-4b35b69efd7f","fullStatement":"Intersect perpendicular number lines at the point (0,0) as the x-axis and y-axis to introduce the four quadrants of the Coordinate Plane. Represent points on the plane with positive and negative coordinates.","humanCodingScheme":"6.NOS.C.7","language":"en","educationLevel":["06"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"897c7c09-dbdc-53e7-b3ac-3457bc46e5c6","uri":"https://opensalt.net/uri/897c7c09-dbdc-53e7-b3ac-3457bc46e5c6","fullStatement":"Use understanding of the relationship between signs and value of coordinates in ordered pairs to reason about the location of an ordered pair without plotting.","humanCodingScheme":"6.NOS.C.7.a","language":"en","educationLevel":["06"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"95cddb62-65c9-5b41-961a-05a132e0c0e8","uri":"https://opensalt.net/uri/95cddb62-65c9-5b41-961a-05a132e0c0e8","fullStatement":"Locate and interpret the positions of rational numbers on the Coordinate Plane, including how changes in the signs of ordered pairs reflect their location into different 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expressions","humanCodingScheme":"A.SSE","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"0b8bcdd4-71f9-5014-8814-7b95d89c178b","uri":"https://opensalt.net/uri/0b8bcdd4-71f9-5014-8814-7b95d89c178b","fullStatement":"Interpret the structure of expressions","humanCodingScheme":"A.SSE.A","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"79233ea2-527d-5305-aaef-a5e4be4d4682","uri":"https://opensalt.net/uri/79233ea2-527d-5305-aaef-a5e4be4d4682","fullStatement":"Use the structure of an expression to identify ways to rewrite it.\n\n**Clarifications/Examples**\n\n- Use factors of polynomials to simplify/analyze rational expressions and the graphs of the related functions.\n- Factor polynomial expressions, of degree three and higher, completely, over the complex number system (e.g. Factor $x^4 - 3x^2 - 28$ to $(x^2 + 4)(x^2 - 7)$ and then to $(x+2i)(x-2i)(x+\\sqrt{7})(x-\\sqrt{7})$)\n- Rewrite trigonometric expressions based on algebraic structures (e.g. $\\sin^3 x + 1$; $\\frac{\\sin^4 x - \\cos^4 x}{\\sin^2 x - \\cos^2 x}$)\n- Discuss conjugates and how their structure can help when simplifying expressions, verifying identities and solving equations.\n- Factor expressions to include using the sum and difference of cubes (e.g. Factor $x^6 - 27y^3$).\n- Recognize and factor an expression in quadratic form (e.g. $e^{2x} - 9e^x + 14$, $2\\cos^2 x - 3\\cos x + 1$, $x^6 - 9x^3 + 8$).\n\n**Function families to which this standard applies**\n\n- Logarithmic/Exponential Functions\n- Polynomial Functions\n- Radical Power Functions\n- Rational Functions\n- Trigonometric Functions","humanCodingScheme":"A.SSE.A.2","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"944f13fe-a236-5ae7-9b11-8cd382116cee","uri":"https://opensalt.net/uri/944f13fe-a236-5ae7-9b11-8cd382116cee","fullStatement":"Write expressions in equivalent forms to solve problems","humanCodingScheme":"A.SSE.B","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"53d70bee-45bf-588c-87d8-5f2e84740a03","uri":"https://opensalt.net/uri/53d70bee-45bf-588c-87d8-5f2e84740a03","fullStatement":"Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.\n\n**Clarifications/Examples**\n\n- Produce an equivalent form of a rational expression to reveal information about the behavior of the graph of the related function.\n  - number and type of discontinuities\n  - zeros\n  - asymptotes and holes\n- Rewrite complex fractions as rational expressions (e.g. rewrite $\\dfrac{\\frac{1}{x}-\\frac{1}{x^2}}{\\frac{2}{x}+\\frac{1}{x^2}}$ as $\\dfrac{x-1}{2x+1}$)\n\n**Function families to which this standard applies**\n\n- Logarithmic/Exponential Functions\n- Polynomial Functions\n- Radical Power Functions\n- Rational Functions\n- Trigonometric Functions","humanCodingScheme":"A.SSE.B.3","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"1356c3ec-15de-5952-8e6f-f52423f9436d","uri":"https://opensalt.net/uri/1356c3ec-15de-5952-8e6f-f52423f9436d","fullStatement":"Arithmetic with polynomials and rational expressions","humanCodingScheme":"A.APR","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"acc114e2-27b2-5166-985a-945add4558a3","uri":"https://opensalt.net/uri/acc114e2-27b2-5166-985a-945add4558a3","fullStatement":"Understand the relationship between zeroes and factors of polynomials","humanCodingScheme":"A.APR.B","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"bc122a14-eb5e-5f47-802a-9a0673ce37c8","uri":"https://opensalt.net/uri/bc122a14-eb5e-5f47-802a-9a0673ce37c8","fullStatement":"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).\n\n**Clarifications/Examples**\n\n- Factor polynomials to simplify rational expressions.\n- Use the Remainder Theorem to determine zeros (roots) of a polynomial.\n\n**Function families to which this standard applies**\n\n- Polynomial Functions\n- Rational Functions","humanCodingScheme":"A.APR.B.2","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"07d8b978-3704-525d-b999-2a412478661b","uri":"https://opensalt.net/uri/07d8b978-3704-525d-b999-2a412478661b","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- Identify real zeros of polynomials.\n- Understand the relationship between the degree of a polynomial and the number and nature of the zeros of the polynomial.\n\n**Function families to which this standard applies**\n\n- Polynomial Functions","humanCodingScheme":"A.APR.B.3.a","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"b9917f8d-a339-5909-8c79-5c64153ea77c","uri":"https://opensalt.net/uri/b9917f8d-a339-5909-8c79-5c64153ea77c","fullStatement":"Use polynomial identities to solve problems","humanCodingScheme":"A.APR.C","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"27cff432-c093-5935-9d7a-2c5489108e1a","uri":"https://opensalt.net/uri/27cff432-c093-5935-9d7a-2c5489108e1a","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- Limit to n \u2264 5, and binomials with variables coefficient of one, or constants less than four.\n\n**Function families to which this standard applies**\n\n- Polynomial Functions","humanCodingScheme":"A.APR.C.5","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"8e9dcab8-257f-5ed2-a419-7486270f79ec","uri":"https://opensalt.net/uri/8e9dcab8-257f-5ed2-a419-7486270f79ec","fullStatement":"Rewrite rational expressions","humanCodingScheme":"A.APR.D","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"3abd5ccc-344e-57eb-abc3-8690771662bf","uri":"https://opensalt.net/uri/3abd5ccc-344e-57eb-abc3-8690771662bf","fullStatement":"Rewrite simple rational expressions in different forms.\n\n**Clarifications/Examples**\n\n- Rational expressions have no restrictions on degree of the numerator or denominator.\n- Understand the connection between rewriting rational expressions and using long division when factoring polynomials.\n  - Apply the Rational Root Theorem.\n\n**Function families to which this standard applies**\n\n- Polynomial Functions\n- Rational Functions","humanCodingScheme":"A.APR.D.6","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"7377e721-82ce-5738-99ef-704173f6d3bb","uri":"https://opensalt.net/uri/7377e721-82ce-5738-99ef-704173f6d3bb","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- Emphasize operations on rational expressions.\n\n**Function families to which this standard applies**\n\n- Rational Functions","humanCodingScheme":"A.APR.D.7","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"34af7c7a-4039-5994-a7cd-4889c4bb9dbf","uri":"https://opensalt.net/uri/34af7c7a-4039-5994-a7cd-4889c4bb9dbf","fullStatement":"Creating equations","humanCodingScheme":"A.CED","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"76d80dce-734d-5f54-afbe-8d8efd7eba9c","uri":"https://opensalt.net/uri/76d80dce-734d-5f54-afbe-8d8efd7eba9c","fullStatement":"Create equations that describe numbers or relationships","humanCodingScheme":"A.CED.A","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"d7fe5733-74fe-5947-bf35-298721a83d12","uri":"https://opensalt.net/uri/d7fe5733-74fe-5947-bf35-298721a83d12","fullStatement":"Create equations and inequalities in one variable and use them to solve problems.\n\n**Clarifications/Examples**\n\n- Create equations and inequalities in one variable involving all algebraic and transcendental functions and piecewise defined functions that combine different types of functions.\n- Use equations and inequalities that arise from any type of function to solve problems.\n\n**Function families to which this standard applies**\n\n- Logarithmic/Exponential Functions\n- Polynomial Functions\n- Radical Power Functions\n- Rational Functions\n- Trigonometric Functions","humanCodingScheme":"A.CED.A.1.a","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"70cf045e-b652-51ea-b9a5-2d0204cb285d","uri":"https://opensalt.net/uri/70cf045e-b652-51ea-b9a5-2d0204cb285d","fullStatement":"Create polynomial equations given roots.\n\n**Clarifications/Examples**\n\n- Use the Factor Theorem.\n- Use the Conjugate Root Theorem as it applies to irrationals.\n\n**Function families to which this standard applies**\n\n- Polynomial Functions","humanCodingScheme":"A.CED.A.1.b","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"9487b754-4bd6-5771-8037-eadbb2bb73f2","uri":"https://opensalt.net/uri/9487b754-4bd6-5771-8037-eadbb2bb73f2","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- Understand why constraints exist for certain equations and inequalities and for systems of equations and inequalities.\n- Represent constraints of equations that contain composite expressions (e.g. $\\sqrt{x^2-4} \\gt 0$)\n\n**Function families to which this standard applies**\n\n- Logarithmic/Exponential Functions\n- Polynomial Functions\n- Radical Power Functions\n- Rational Functions\n- Trigonometric Functions","humanCodingScheme":"A.CED.A.3","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"d9800f72-8c56-523e-9b47-7d0e37fd6841","uri":"https://opensalt.net/uri/d9800f72-8c56-523e-9b47-7d0e37fd6841","fullStatement":"Reasoning with equations and inequalities","humanCodingScheme":"A.REI","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"e75ba6fa-9aa4-571f-8d2e-65de13cd87cc","uri":"https://opensalt.net/uri/e75ba6fa-9aa4-571f-8d2e-65de13cd87cc","fullStatement":"Solve equations and inequalities in one variable","humanCodingScheme":"A.REI.B","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"1ce2a6ac-e95a-5b51-9e9e-602ff4723c64","uri":"https://opensalt.net/uri/1ce2a6ac-e95a-5b51-9e9e-602ff4723c64","fullStatement":"Solve equations and inequalities in one variable.\n\n**Clarifications/Examples**\n\n- Include equations and inequalities that contain combinations of various algebraic and transcendental functions.\n- Include equations that contain composite expressions.\n- Solve equations in one variable algebraically, numerically and/or graphically.\n- Justify solution methods.\n\n**Function families to which this standard applies**\n\n- Logarithmic/Exponential Functions\n- Polynomial Functions\n- Radical Power Functions\n- Rational Functions\n- Trigonometric Functions","humanCodingScheme":"A.REI.B","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"3758a09c-a672-58f8-a732-31df2da2d4cd","uri":"https://opensalt.net/uri/3758a09c-a672-58f8-a732-31df2da2d4cd","fullStatement":"Solve systems of equations","humanCodingScheme":"A.REI.C","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"58ca00e1-3561-56b6-b495-37ff9d9c492c","uri":"https://opensalt.net/uri/58ca00e1-3561-56b6-b495-37ff9d9c492c","fullStatement":"Solve systems of equations comprised of various combinations of all algebraic and transcendental functions in two variables.\n\n**Clarifications/Examples**\n\n- Explore algebraic, numeric and graphical methods for solving systems of equations.\n- Explore systems comprised of functions from two different function families (e.g. Solve the system $y = x^2$ and y = 2 cos x).\n\n**Function families to which this standard applies**\n\n- Logarithmic/Exponential Functions\n- Polynomial Functions\n- Radical Power Functions\n- Rational Functions\n- Trigonometric Functions","humanCodingScheme":"A.REI.C.7.a","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"7abc3823-46c7-5dc1-984a-1a71ea2067fc","uri":"https://opensalt.net/uri/7abc3823-46c7-5dc1-984a-1a71ea2067fc","fullStatement":"Functions","humanCodingScheme":"F","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"9266efa9-5033-5e47-9f2d-6f47838e0703","uri":"https://opensalt.net/uri/9266efa9-5033-5e47-9f2d-6f47838e0703","fullStatement":"Interpret in g functions","humanCodingScheme":"F.IF","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"74316086-e047-5e2d-9b56-fab2c11d1003","uri":"https://opensalt.net/uri/74316086-e047-5e2d-9b56-fab2c11d1003","fullStatement":"Understand the concept of a function and use function notation","humanCodingScheme":"F.IF.A","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"ed89ce97-d58b-5c16-ab3d-e012829a82d7","uri":"https://opensalt.net/uri/ed89ce97-d58b-5c16-ab3d-e012829a82d7","fullStatement":"Extend evaluating functions to include operations with composite functions, e.g. f(x + 2) - f(x).\n\n**Clarifications/Examples**\n\n- Build prerequisite skills needed to simplify difference quotient (e.g. Given f(x) = $x^2 + 3x$ + 1 find f(x + h)).\n\n**Function families to which this standard applies**\n\n- Logarithmic/Exponential Functions\n- Polynomial Functions\n- Radical Power Functions\n- Rational Functions\n- Trigonometric Functions","humanCodingScheme":"F.IF.A.2.a","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"aaca09ea-9efb-509e-a40c-ff1f5dc53c6d","uri":"https://opensalt.net/uri/aaca09ea-9efb-509e-a40c-ff1f5dc53c6d","fullStatement":"Interpret functions that arise in application in terms of context","humanCodingScheme":"F.IF.B","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"6011afe5-b9c4-5a3a-a56e-e0fb79e6a372","uri":"https://opensalt.net/uri/6011afe5-b9c4-5a3a-a56e-e0fb79e6a372","fullStatement":"For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities; sketch graphs showing key features given a verbal description of the relationship.\n\n**Clarifications/Examples**\n\n- Interpret the key features of the graph of any function in terms of context.\n- Explore rate of change over various size intervals.\n- Estimate points of inflection.\n- Describe the concavity on intervals.\n- Explain how to recognize asymptotic behavior given various representations of a function (algebraic, numeric and graphic).\n\n**Function families to which this standard applies**\n\n- Logarithmic/Exponential Functions\n- Polynomial Functions\n- Radical Power Functions\n- Rational Functions\n- Trigonometric Functions","humanCodingScheme":"F.IF.B.4","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"2268ac19-abbd-5331-a6f2-6215027f37f9","uri":"https://opensalt.net/uri/2268ac19-abbd-5331-a6f2-6215027f37f9","fullStatement":"Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.\n\n**Clarifications/Examples**\n\n- Discuss the domain of all function types including composite and inverse functions.\n\n**Function families to which this standard applies**\n\n- Logarithmic/Exponential Functions\n- Polynomial Functions\n- Radical Power Functions\n- Rational Functions\n- Trigonometric Functions","humanCodingScheme":"F.IF.B.5","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"ec72fe45-7cec-5d60-b122-b5584f0e7518","uri":"https://opensalt.net/uri/ec72fe45-7cec-5d60-b122-b5584f0e7518","fullStatement":"Analyze functions using different representations","humanCodingScheme":"F.IF.C","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"4cf85d3c-1ff8-5139-865a-1ccdaef29480","uri":"https://opensalt.net/uri/4cf85d3c-1ff8-5139-865a-1ccdaef29480","fullStatement":"Graph all functions including piecewise-defined functions, step functions and absolute value functions\n\n**Clarifications/Examples**\n\n- Sketch polynomials of higher degree from factored form, using x- and y-intercepts, end behavior and degree.\n- Describe end behavior using appropriate notation, i.e. given an equation, as x \u2192 \u00b1\u221e, f(x) \u2192 \u00b1\u221e.\n- Use information about end behavior of a polynomial to sketch and identify the possible degree of a polynomial.\n- Graph inverse trigonometric functions and identify the related principal values.\n\n**Function families to which this standard applies**\n\n- Logarithmic/Exponential Functions\n- Polynomial Functions\n- Radical Power Functions\n- Rational Functions\n- Trigonometric Functions","humanCodingScheme":"F.IF.C.7.f","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"bf3748b8-cf42-59e0-9f85-8333fb48d23b","uri":"https://opensalt.net/uri/bf3748b8-cf42-59e0-9f85-8333fb48d23b","fullStatement":"Determine the end behavior of the graph of a polynomial function using the degree and leading coefficient.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.\n\n**Function families to which this standard applies**\n\n- Polynomial Functions","humanCodingScheme":"F.IF.C.7.g","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"89ddc2d6-d8ef-578f-b7fa-d325781ab5e4","uri":"https://opensalt.net/uri/89ddc2d6-d8ef-578f-b7fa-d325781ab5e4","fullStatement":"Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.\n\n**Clarifications/Examples**\n\n- Understand why a particular form of an expression would reveal properties such as zeros, extrema, intercepts, etc.\n- Rewrite rational functions to reveal discontinuities.\n\n**Function families to which this standard applies**\n\n- Logarithmic/Exponential Functions\n- Polynomial Functions\n- Radical Power Functions\n- Rational Functions\n- Trigonometric Functions","humanCodingScheme":"F.IF.C.8","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"7360f52d-3550-529c-b18b-a896587473c9","uri":"https://opensalt.net/uri/7360f52d-3550-529c-b18b-a896587473c9","fullStatement":"Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables or by a verbal description).\n\n**Clarifications/Examples**\n\n- Extend student understanding by using more complex situations.\n\n**Function families to which this standard applies**\n\n- Logarithmic/Exponential Functions\n- Polynomial Functions\n- Radical Power Functions\n- Rational Functions\n- Trigonometric Functions","humanCodingScheme":"F.IF.C.9","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"02305db4-143f-50c5-a9a4-1f661c887aab","uri":"https://opensalt.net/uri/02305db4-143f-50c5-a9a4-1f661c887aab","fullStatement":"Building functions","humanCodingScheme":"F.BF","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"bfa5cd59-09d2-5605-8c6e-a7bb4be558f6","uri":"https://opensalt.net/uri/bfa5cd59-09d2-5605-8c6e-a7bb4be558f6","fullStatement":"Build a function that models a relationship between two quantities","humanCodingScheme":"F.BF.A","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"b165e691-9757-51c5-aa5d-278a4fc887d1","uri":"https://opensalt.net/uri/b165e691-9757-51c5-aa5d-278a4fc887d1","fullStatement":"Write a function that describes a relationship between two quantities, including more complex functions.\n\n**Clarifications/Examples**\n\n- Include piecewise defined functions comprised of different types of functions.\n- Include composite functions (e.g. f(x) = sin(2x)).\n\n**Function families to which this standard applies**\n\n- Logarithmic/Exponential Functions\n- Polynomial Functions\n- Radical Power Functions\n- Rational Functions\n- Trigonometric Functions","humanCodingScheme":"F.BF.A.1","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"8ca18015-4ff3-582c-9d66-1fc712e89e7e","uri":"https://opensalt.net/uri/8ca18015-4ff3-582c-9d66-1fc712e89e7e","fullStatement":"Build a function that models a relationship between two quantities","humanCodingScheme":"F.BF.B","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"f0a4836a-a30d-53c8-af06-0d2d17c8ec0f","uri":"https://opensalt.net/uri/f0a4836a-a30d-53c8-af06-0d2d17c8ec0f","fullStatement":"Identify the effect on the graph of replacing $f(x)$ by $f(x) + k$, $kf(x)$, $f(kx)$, 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.\n\n**Clarifications/Examples**\n\n- Identify any function as an even, an odd function or neither given a graphic or algebraic representation.\n- Identify transformations from parent functions.\n\n**Function families to which this standard applies**\n\n- Logarithmic/Exponential Functions\n- Polynomial Functions\n- Trigonometric Functions\n- Radical Power Functions\n- Rational Functions","humanCodingScheme":"F.BF.B.3","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"f01940ca-e9d2-5107-a02f-d72fc3a78c11","uri":"https://opensalt.net/uri/f01940ca-e9d2-5107-a02f-d72fc3a78c11","fullStatement":"Find inverse functions.\n\n**Clarifications/Examples**\n\n- Find inverses of polynomials of the form f(x) = $a(x-h)^n + k$.\n- Note: Read the blog, [Inverse Functions: We're Teaching it all Wrong](https://blogs.ams.org/matheducation/2016/11/28/inverse-functions-were-teaching-it-all-wrong/), before teaching inverses.\n\n**Function families to which this standard applies**\n\n- Logarithmic/Exponential Functions\n- Polynomial Functions\n- Radical Power Functions\n- Rational Functions\n- Trigonometric Functions","humanCodingScheme":"F.BF.B.4","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"ba2e8035-fd95-5282-b1f3-45aa4115cfdf","uri":"https://opensalt.net/uri/ba2e8035-fd95-5282-b1f3-45aa4115cfdf","fullStatement":"Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.\n\n**Clarifications/Examples**\n\n- Solve exponential equations using logarithms.\n- Discuss relationships between domain, range, and asymptotes.\n\n**Function families to which this standard applies**\n\n- Logarithmic/Exponential Functions","humanCodingScheme":"F.BF.B.5","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"d8f72ffe-38e4-5493-b17a-9fe1de274180","uri":"https://opensalt.net/uri/d8f72ffe-38e4-5493-b17a-9fe1de274180","fullStatement":"Linear, quadratic, and exponential models","humanCodingScheme":"F.LE","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"520dcb37-36ef-5c20-b2ae-175772ce9d5c","uri":"https://opensalt.net/uri/520dcb37-36ef-5c20-b2ae-175772ce9d5c","fullStatement":"Construct and compare linear, quadratic, and exponential models and solve problems","humanCodingScheme":"F.LE.A","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"c7eb3181-d9ab-54f4-a896-75063f5dc89e","uri":"https://opensalt.net/uri/c7eb3181-d9ab-54f4-a896-75063f5dc89e","fullStatement":"Use properties of logarithms, including both common and natural logarithms, to rewrite and solve exponential models.\n\n**Clarifications/Examples**\n\n- Write logarithmic functions as inverses of exponential functions, including both common and natural logarithms.\n\n**Function families to which this standard applies**\n\n- Logarithmic/Exponential Functions","humanCodingScheme":"F.LE.A.4.a","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"7572ff21-61bc-533b-8b93-c6cda069c146","uri":"https://opensalt.net/uri/7572ff21-61bc-533b-8b93-c6cda069c146","fullStatement":"Trigonometric functions","humanCodingScheme":"T.TF","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"194b4ac6-f983-50ad-aa1c-3a0e78e25eec","uri":"https://opensalt.net/uri/194b4ac6-f983-50ad-aa1c-3a0e78e25eec","fullStatement":"Extend the domain of trigonometric functions using the unit circle","humanCodingScheme":"F.TF.A","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"c5014329-daea-541d-a07d-157f51a1b130","uri":"https://opensalt.net/uri/c5014329-daea-541d-a07d-157f51a1b130","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- Define the six trigonometric functions in terms of coordinates from the unit circle.\n- Understand the relationship between right triangle trigonometric ratios and trigonometric functions.\n- Evaluate trigonometric functions using reference angles.\n\n**Function families to which this standard applies**\n\n- Trigonometric Functions","humanCodingScheme":"F.TF.A.2","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"6c5f337c-d704-5c87-ae83-7dc8f55ea4dd","uri":"https://opensalt.net/uri/6c5f337c-d704-5c87-ae83-7dc8f55ea4dd","fullStatement":"Use special triangles to determine geometrically the values of sine, cosine, tangent for $\\frac{\\pi}{3}$, $\\frac{\\pi}{4}$, and $\\frac{\\pi}{6}$ and use the unit circle to express the values of sine, cosine, and tangent for $x$, $\\pi + x$, and $2\\pi - x$ in terms of their values for $x$, where $x$ is any real number.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.\n\n**Function families to which this standard applies**\n\n- Trigonometric Functions","humanCodingScheme":"F.TF.A.3","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"ab40afa8-4e4e-55eb-85a6-4692a4da2b9b","uri":"https://opensalt.net/uri/ab40afa8-4e4e-55eb-85a6-4692a4da2b9b","fullStatement":"Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.\n\n**Clarifications/Examples**\n\n- Write the domain of all six trigonometric functions.\n- Write the domain of trigonometric functions under transformations (e.g. y = tan x versus y = tan(2x)).\n\n**Function families to which this standard applies**\n\n- Trigonometric Functions","humanCodingScheme":"F.TF.A.4","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"6de89614-2f45-55c5-811f-a6f084e39e0f","uri":"https://opensalt.net/uri/6de89614-2f45-55c5-811f-a6f084e39e0f","fullStatement":"Model periodic phenomena with trigonometric functions","humanCodingScheme":"F.TF.B","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"35c077cc-0032-5014-b8ae-d7c22e967608","uri":"https://opensalt.net/uri/35c077cc-0032-5014-b8ae-d7c22e967608","fullStatement":"Choose trigonometric functions to model real world phenomena.\n\n**Clarifications/Examples**\n\n- Graph all six trigonometric functions.\n\n**Function families to which this standard applies**\n\n- Trigonometric Functions","humanCodingScheme":"F.TF.B.5","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"df933691-76a3-50ab-8986-827151d33fa8","uri":"https://opensalt.net/uri/df933691-76a3-50ab-8986-827151d33fa8","fullStatement":"Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.\n\n**Function families to which this standard applies**\n\n- Trigonometric Functions","humanCodingScheme":"F.TF.B.6","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"d302eafa-7e8d-5a74-928c-178d3364ff91","uri":"https://opensalt.net/uri/d302eafa-7e8d-5a74-928c-178d3364ff91","fullStatement":"Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology and interpret them in context.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.\n\n**Function families to which this standard applies**\n\n- Trigonometric Functions","humanCodingScheme":"F.TF.B.7","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"94eee27c-cf89-5157-a2a4-3b758c67433d","uri":"https://opensalt.net/uri/94eee27c-cf89-5157-a2a4-3b758c67433d","fullStatement":"Prove and apply trigonometric identities","humanCodingScheme":"F.TF.C","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"d60a3714-b157-5483-b0b4-d921d6608f3d","uri":"https://opensalt.net/uri/d60a3714-b157-5483-b0b4-d921d6608f3d","fullStatement":"Use trigonometric identities to rewrite expressions and as a tool when solving trigonometric equations.\n\n**Clarifications/Examples**\n\n- Use the double angle and half angle identities for trigonometric functions to simplify, verify, and solve expressions and equations involving sine, cosine, and tangent.\n- Emphasize double angle identities are used most frequently in Calculus.\n- Prove trigonometric identities, including Pythagorean identities and even and odd identities, using a variety of strategies. Verify identities graphically.\n- Emphasize Pythagorean identities.\n\n**Function families to which this standard applies**\n\n- Trigonometric Functions","humanCodingScheme":"F.TF.C.9.a","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"7ac43240-e11f-5577-917c-a68c8979171e","uri":"https://opensalt.net/uri/7ac43240-e11f-5577-917c-a68c8979171e","fullStatement":"Geometry","humanCodingScheme":"G","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"88f86526-62a7-57f6-b950-934cd5fc1552","uri":"https://opensalt.net/uri/88f86526-62a7-57f6-b950-934cd5fc1552","fullStatement":"Similarity, right triangles, and trigonometry","humanCodingScheme":"G.SRT","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"bac6978e-83c4-5c8e-a57e-2d600bd084be","uri":"https://opensalt.net/uri/bac6978e-83c4-5c8e-a57e-2d600bd084be","fullStatement":"Apply trigonometry to general triangles","humanCodingScheme":"G.SRT.D","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"430933ee-0f45-5e8d-88d9-843fa2391fa9","uri":"https://opensalt.net/uri/430933ee-0f45-5e8d-88d9-843fa2391fa9","fullStatement":"Prove the Laws of Sines and Cosines and use them to solve problems.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.\n\n**Function families to which this standard applies**\n\n- Trigonometric Functions","humanCodingScheme":"G.SRT.D.10","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"5a7e32bc-0f25-55b4-b89c-9855be51c93d","uri":"https://opensalt.net/uri/5a7e32bc-0f25-55b4-b89c-9855be51c93d","fullStatement":"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, resultant forces).\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.\n\n**Function families to which this standard applies**\n\n- Trigonometric Functions","humanCodingScheme":"G.SRT.D.11","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"58793469-de3a-58a4-ae91-01690afbd535","uri":"https://opensalt.net/uri/58793469-de3a-58a4-ae91-01690afbd535","fullStatement":"Statistics","humanCodingScheme":"S","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"04d04e13-128d-599e-a95d-2d893610f5cc","uri":"https://opensalt.net/uri/04d04e13-128d-599e-a95d-2d893610f5cc","fullStatement":"Interpreting categorical and quantitative data","humanCodingScheme":"S.ID","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"dd619fca-e1c9-5c3d-a09d-b5033fa91303","uri":"https://opensalt.net/uri/dd619fca-e1c9-5c3d-a09d-b5033fa91303","fullStatement":"Summarize, represent, and interpret data on two categorical and quantitative variables","humanCodingScheme":"S.ID.B","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"e51acf39-1f11-5222-9fd3-d7539aaa6c3c","uri":"https://opensalt.net/uri/e51acf39-1f11-5222-9fd3-d7539aaa6c3c","fullStatement":"Fit a function to data represented by a scatterplot; use functions fitted to data to solve problems in the context of the data.\n\n**Clarifications/Examples**\n\n- Determine the best function to represent data on two-quantitative variables by analyzing the context of the data; the behavior of the scatterplot and the fit of the function to the scatterplot.\n\n**Function families to which this standard applies**\n\n- Logarithmic/Exponential Functions\n- Polynomial Functions\n- Radical Power Functions\n- Trigonometric Functions with logistic growth models. Why? What are the similarities and differences between an exponential function and a logistic function? When is it more appropriate to use a logistics model? The answers to these questions are the focus of the standards within this topic.","humanCodingScheme":"S.ID.B.6.d","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"78813eab-b401-56dc-a10c-10557301f89d","uri":"https://opensalt.net/uri/78813eab-b401-56dc-a10c-10557301f89d","fullStatement":"Distinguish between situations that can be modeled with exponential functions and logistic functions.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"F.LE.A.1.d","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"cab969e5-57ad-5522-b74c-55cc3b8ca6ae","uri":"https://opensalt.net/uri/cab969e5-57ad-5522-b74c-55cc3b8ca6ae","fullStatement":"Interpret expressions for functions in terms of the situation they model","humanCodingScheme":"F.LE.B","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"d30d3b06-ef6a-5b36-8acd-4a82cf44e2da","uri":"https://opensalt.net/uri/d30d3b06-ef6a-5b36-8acd-4a82cf44e2da","fullStatement":"Interpret the parameters in a logistic function in terms of a context.\n\n**Clarifications/Examples**\n\n- Interpret the parameters $A$, $B$, and $C$ in expressions of the form $y = \\frac{C}{1 + Ae^{-Bx}}$ in terms of a context.","humanCodingScheme":"F.LE.B.5.a","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"66c10435-a256-5e6c-9b5a-adebaf135bd8","uri":"https://opensalt.net/uri/66c10435-a256-5e6c-9b5a-adebaf135bd8","fullStatement":"Build and interpret logistic functions to model real-world problems.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"F.LE.B.6","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"7dd31926-d107-5c6f-b8d2-cf40c937ddd4","uri":"https://opensalt.net/uri/7dd31926-d107-5c6f-b8d2-cf40c937ddd4","fullStatement":"Precalculus B","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"1f308060-3b45-5515-82d9-cd46d042bb70","uri":"https://opensalt.net/uri/1f308060-3b45-5515-82d9-cd46d042bb70","fullStatement":"Complex Numbers","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"94039493-c2bb-5f12-850b-b6de591a2b35","uri":"https://opensalt.net/uri/94039493-c2bb-5f12-850b-b6de591a2b35","fullStatement":"Number and Quantity","humanCodingScheme":"N","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"27677e4e-29f4-59f2-b8ce-f1a3a80fbce9","uri":"https://opensalt.net/uri/27677e4e-29f4-59f2-b8ce-f1a3a80fbce9","fullStatement":"The complex number system","humanCodingScheme":"N.CN","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"9a882571-dc0f-5d49-97ea-de2debaa1e3f","uri":"https://opensalt.net/uri/9a882571-dc0f-5d49-97ea-de2debaa1e3f","fullStatement":"Perform arithmetic operations with complex numbers","humanCodingScheme":"N.CN.A","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"e37e8189-486d-5b3a-bb11-179540d263eb","uri":"https://opensalt.net/uri/e37e8189-486d-5b3a-bb11-179540d263eb","fullStatement":"Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.\n\n**Clarifications/Examples**\n\n- Understand the connection between modulus of a complex number and the magnitude of a vector.","humanCodingScheme":"N.CN.A.3","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"cf60d08f-6800-5b06-a780-23a6de70d09a","uri":"https://opensalt.net/uri/cf60d08f-6800-5b06-a780-23a6de70d09a","fullStatement":"Represent Complex Numbers and their operations on the complex plane","humanCodingScheme":"N.CN.B","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"e0363778-79e8-55fb-a6dd-be61fc695a69","uri":"https://opensalt.net/uri/e0363778-79e8-55fb-a6dd-be61fc695a69","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"N.CN.B.4","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"7dde1d3c-5d38-5f0c-a7a5-17353ee2e720","uri":"https://opensalt.net/uri/7dde1d3c-5d38-5f0c-a7a5-17353ee2e720","fullStatement":"Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"N.CN.B.5","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"9f084d3c-fd42-5bdd-8518-82b348f939c3","uri":"https://opensalt.net/uri/9f084d3c-fd42-5bdd-8518-82b348f939c3","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- This could be addressed in a unit on vectors or polar coordinates.","humanCodingScheme":"N.CN.B.6","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"43bb75ef-7aa4-5c66-b6e5-313d69952888","uri":"https://opensalt.net/uri/43bb75ef-7aa4-5c66-b6e5-313d69952888","fullStatement":"Vectors and Matrices","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"34d3100b-19fc-5be8-879d-0862202be111","uri":"https://opensalt.net/uri/34d3100b-19fc-5be8-879d-0862202be111","fullStatement":"Number and Quantity","humanCodingScheme":"N","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"54841bff-4cad-505f-b2db-3feca07bf5fd","uri":"https://opensalt.net/uri/54841bff-4cad-505f-b2db-3feca07bf5fd","fullStatement":"Vector and matrix quantities","humanCodingScheme":"N.VM","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"2ec8697b-af2c-57b1-8c13-0e34b9f24a9a","uri":"https://opensalt.net/uri/2ec8697b-af2c-57b1-8c13-0e34b9f24a9a","fullStatement":"Represent and model with vector quantities","humanCodingScheme":"N.VM.A","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"eb7d6192-1e1d-505a-80c6-ab1da22f5ddc","uri":"https://opensalt.net/uri/eb7d6192-1e1d-505a-80c6-ab1da22f5ddc","fullStatement":"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|, \u2016v\u2016, v)\n\n**Clarifications/Examples**\n\n- Understand vocabulary and notation associated with the study of vectors (magnitude, direction, scalar, components, unit vector, resultant force).\n- Write position vectors from initial and terminal points.","humanCodingScheme":"N.VM.A.1","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"c27f2261-26a6-5421-bd57-650778b30d03","uri":"https://opensalt.net/uri/c27f2261-26a6-5421-bd57-650778b30d03","fullStatement":"Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.\n\n**Clarifications/Examples**\n\n- Analyze vectors in terms of their horizontal and vertical components.","humanCodingScheme":"N.VM.A.2","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"3e5a5508-38b9-575f-8842-7a3e3e4b8817","uri":"https://opensalt.net/uri/3e5a5508-38b9-575f-8842-7a3e3e4b8817","fullStatement":"Solve problems involving velocity and other quantities that can be represented by vectors.\n\n**Clarifications/Examples**\n\n- Model situations involving multiple vectors.\n- Determine resultant vectors and interpret them in context.","humanCodingScheme":"N.VM.A.3","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"c867ff4d-a566-5df5-b869-cfe1976a43c4","uri":"https://opensalt.net/uri/c867ff4d-a566-5df5-b869-cfe1976a43c4","fullStatement":"Perform operations on vectors","humanCodingScheme":"N.VM.B","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"f66559de-3a1a-5f5a-8e96-a0d9564ada6f","uri":"https://opensalt.net/uri/f66559de-3a1a-5f5a-8e96-a0d9564ada6f","fullStatement":"Add and subtract vectors.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"N.VM.B.4","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"6f4f4d34-b402-50ea-a301-62b3c0d61f27","uri":"https://opensalt.net/uri/6f4f4d34-b402-50ea-a301-62b3c0d61f27","fullStatement":"Multiply a vector by a scalar.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"N.VM.B.5","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"91ddc36a-aa12-5d7a-bfce-b8899a2e80e4","uri":"https://opensalt.net/uri/91ddc36a-aa12-5d7a-bfce-b8899a2e80e4","fullStatement":"Perform operations on matrices and use matrices in applications","humanCodingScheme":"N.VM.C","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"9a1c0862-fdc3-5476-9e8c-0c10c3457cd8","uri":"https://opensalt.net/uri/9a1c0862-fdc3-5476-9e8c-0c10c3457cd8","fullStatement":"Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"N.VM.C.6","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"9e46def4-22f2-57d9-a3f8-863eee725b25","uri":"https://opensalt.net/uri/9e46def4-22f2-57d9-a3f8-863eee725b25","fullStatement":"Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"N.VM.C.7","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"44e2a5c5-e40d-5b92-a734-1186b00324a0","uri":"https://opensalt.net/uri/44e2a5c5-e40d-5b92-a734-1186b00324a0","fullStatement":"Add, subtract, and multiply matrices of appropriate dimensions.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"N.VM.C.8","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"ee6738ae-1e17-5a8f-954e-5b550e957e9e","uri":"https://opensalt.net/uri/ee6738ae-1e17-5a8f-954e-5b550e957e9e","fullStatement":"Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"N.VM.C.9","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"3dff045a-002d-5e6d-b307-ab712ee67c8a","uri":"https://opensalt.net/uri/3dff045a-002d-5e6d-b307-ab712ee67c8a","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"N.VM.C.10","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"a5876797-d050-5e85-91e3-aa79c8f3bfc1","uri":"https://opensalt.net/uri/a5876797-d050-5e85-91e3-aa79c8f3bfc1","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"N.VM.C.11","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"e5b0b106-b964-58fd-ad24-1dd5d18c748e","uri":"https://opensalt.net/uri/e5b0b106-b964-58fd-ad24-1dd5d18c748e","fullStatement":"Work with 2 \u00d7 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.\n\n**Clarifications/Examples**\n\n- Include rotations of 90\u00b0, 180\u00b0, and 270\u00b0, and reflections across x-axis, y-axis, and over the line y = x.","humanCodingScheme":"N.VM.C.12","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"fae8ea53-5175-5ac7-8142-6f7edee94724","uri":"https://opensalt.net/uri/fae8ea53-5175-5ac7-8142-6f7edee94724","fullStatement":"Sequences and Series","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"e119cbc8-598a-5883-aeb8-d69d38835237","uri":"https://opensalt.net/uri/e119cbc8-598a-5883-aeb8-d69d38835237","fullStatement":"Number and Quantity","humanCodingScheme":"N","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"3798c7be-b61c-5585-a356-e1ffc419c3b6","uri":"https://opensalt.net/uri/3798c7be-b61c-5585-a356-e1ffc419c3b6","fullStatement":"Operations and algebraic thinking","humanCodingScheme":"N.OA","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"f14c490c-18cf-563f-9475-db2b4c440eac","uri":"https://opensalt.net/uri/f14c490c-18cf-563f-9475-db2b4c440eac","fullStatement":"Write and interpret numerical expressions","humanCodingScheme":"N.OA.A","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"2f5174f5-eda9-5e74-93c1-9a466eaf2f0d","uri":"https://opensalt.net/uri/2f5174f5-eda9-5e74-93c1-9a466eaf2f0d","fullStatement":"Use the notation for the factorial of a non-negative integer, n!, to evaluate expressions.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"N.OA.A.1","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"8063dc30-8746-510f-b42a-4d2ba18cc7ec","uri":"https://opensalt.net/uri/8063dc30-8746-510f-b42a-4d2ba18cc7ec","fullStatement":"Algebra","humanCodingScheme":"A","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"b5879074-6b55-5d3a-9981-5d4441382790","uri":"https://opensalt.net/uri/b5879074-6b55-5d3a-9981-5d4441382790","fullStatement":"Seeing structure in expressions","humanCodingScheme":"A.SSE","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"bcb29833-f961-5877-b65f-67a6879ba45a","uri":"https://opensalt.net/uri/bcb29833-f961-5877-b65f-67a6879ba45a","fullStatement":"Write expressions in equivalent forms to solve problems","humanCodingScheme":"A.SSE.B","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"07e5e4a3-59cd-5fb2-bca5-35f425ce4e1f","uri":"https://opensalt.net/uri/07e5e4a3-59cd-5fb2-bca5-35f425ce4e1f","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- Connect prior learning from Algebra 2 to the new learning in Precalculus.\n- Solve real world problems that involve finite series.","humanCodingScheme":"A.SSE.B.4","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"0aa22b48-5a3c-5dfc-aabb-653da4ed6034","uri":"https://opensalt.net/uri/0aa22b48-5a3c-5dfc-aabb-653da4ed6034","fullStatement":"Determine the sum, if it exists, of an infinite geometric series.\n\n**Clarifications/Examples**\n\n- Use the sum of an infinite geometric series to express a repeating decimal as a rational number.\n- Solve real world problems that involve infinite series.\n- Use the algebra rules for finite sums to evaluate expressions written using sigma notation (e.g. Evaluate $\\sum_{k=1}^{\\infty} \\frac{1}{k^2}(k-1)$.)\n","humanCodingScheme":"A.SSE.B.5","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"6a2c27ed-7008-5523-821d-686545f93504","uri":"https://opensalt.net/uri/6a2c27ed-7008-5523-821d-686545f93504","fullStatement":"Arithmetic with polynomials and rational expression","humanCodingScheme":"A.APR","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"ebb13ab5-4d49-5cfe-ab7e-81c24f6a8f36","uri":"https://opensalt.net/uri/ebb13ab5-4d49-5cfe-ab7e-81c24f6a8f36","fullStatement":"Use polynomial identities to solve problems","humanCodingScheme":"A.APR.C","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"2e05b5e6-5515-5f57-9612-d3ff048392cb","uri":"https://opensalt.net/uri/2e05b5e6-5515-5f57-9612-d3ff048392cb","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- Limit to n < 6.\n- Limit to binomials with variable coefficient of one or constants less than four.\n- Understand the connection between the Binomial Theorem and an infinite series.","humanCodingScheme":"A.APR.C.5","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"f96aa098-f750-553e-9ecd-212c1d70e5d1","uri":"https://opensalt.net/uri/f96aa098-f750-553e-9ecd-212c1d70e5d1","fullStatement":"Functions","humanCodingScheme":"F","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"284eaafa-2d54-5b03-a68a-9571c5315125","uri":"https://opensalt.net/uri/284eaafa-2d54-5b03-a68a-9571c5315125","fullStatement":"Interpret in g functions","humanCodingScheme":"F.IF","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"10d4f41e-b8e7-5929-9e17-feaa2efd0ea7","uri":"https://opensalt.net/uri/10d4f41e-b8e7-5929-9e17-feaa2efd0ea7","fullStatement":"Understand the concept of function and use function notation","humanCodingScheme":"F.IF.A","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"34e45247-40df-510a-a9ec-7bfb7f8026c2","uri":"https://opensalt.net/uri/34e45247-40df-510a-a9ec-7bfb7f8026c2","fullStatement":"Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.\n\n**Clarifications/Examples**\n\n- Understand the similarities and differences between linear functions and arithmetic sequences.\n- Understand similarities and differences between exponential functions and geometric sequences.\n- Include sequences that do not have a simple defining equation.","humanCodingScheme":"F.IF.A.3","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"ff03e1fc-f112-5f7d-839d-88b921e5036c","uri":"https://opensalt.net/uri/ff03e1fc-f112-5f7d-839d-88b921e5036c","fullStatement":"Analyze functions using different representations","humanCodingScheme":"F.IF.C","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"5f259b86-2739-5694-91ad-1e4d8d9f5b8f","uri":"https://opensalt.net/uri/5f259b86-2739-5694-91ad-1e4d8d9f5b8f","fullStatement":"Describe the behavior of a sequence.\n\n**Clarifications/Examples**\n\n- Generate the terms of a sequence given a formula for the nth term of the sequence.\n- Use the graph of a sequence to intuitively determine if the sequence converges or diverges.\n- Determine if a sequence is increasing, decreasing, or monotonic.","humanCodingScheme":"F.IF.C.10","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"3c267473-9064-5d2d-8f50-11d4cd53f184","uri":"https://opensalt.net/uri/3c267473-9064-5d2d-8f50-11d4cd53f184","fullStatement":"Building functions","humanCodingScheme":"F.BF","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"26265f06-589d-5505-91e0-35e00e15155c","uri":"https://opensalt.net/uri/26265f06-589d-5505-91e0-35e00e15155c","fullStatement":"Build a function that models a relationship between two quantities","humanCodingScheme":"F.BF.A","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"0b9bb2cc-5828-557f-baff-b96482222e6c","uri":"https://opensalt.net/uri/0b9bb2cc-5828-557f-baff-b96482222e6c","fullStatement":"Write a function that describes a relationship between two quantities.\n\n**Clarifications/Examples**\n\n- Understand the connection between the formula for the general term an of a given sequence and the related function that describes the relationship between the term number of the sequence and the value of the term.\n- Graph and analyze the functions that represent a given sequence.","humanCodingScheme":"F.BF.A.1","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"2a6f7a9f-af13-5ce4-a155-307fcaba35df","uri":"https://opensalt.net/uri/2a6f7a9f-af13-5ce4-a155-307fcaba35df","fullStatement":"Write sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.\n\n**Clarifications/Examples**\n\n- Construct a formula for the general term an of a given sequence.","humanCodingScheme":"F.BF.A.2","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"c3547663-118f-5262-9eac-c78cdbca7d6d","uri":"https://opensalt.net/uri/c3547663-118f-5262-9eac-c78cdbca7d6d","fullStatement":"Limits","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"44c0b6f6-c75a-5da0-a1e0-c4bec48b8719","uri":"https://opensalt.net/uri/44c0b6f6-c75a-5da0-a1e0-c4bec48b8719","fullStatement":"Functions","humanCodingScheme":"F","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"5d3fe811-5289-5077-acc1-3a473a8d5f53","uri":"https://opensalt.net/uri/5d3fe811-5289-5077-acc1-3a473a8d5f53","fullStatement":"Interpret in g functions","humanCodingScheme":"F.IF","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"f25824fa-49c4-5f4d-8442-fc1383b2ee56","uri":"https://opensalt.net/uri/f25824fa-49c4-5f4d-8442-fc1383b2ee56","fullStatement":"Understand the concept of function and use function notation","humanCodingScheme":"F.IF.A","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"c4b6789f-50a9-5470-9a70-e090f99b369a","uri":"https://opensalt.net/uri/c4b6789f-50a9-5470-9a70-e090f99b369a","fullStatement":"Understand the concept of limit of a function.\n\n**Clarifications/Examples**\n\n- Understand that the value of a function at a given point may not be the same as the limit as the function approaches the given point.\n- Understand when limits fail to exist.","humanCodingScheme":"F.IF.A.2.a","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"4373c8a4-dcf9-5843-9e10-bd1108162df3","uri":"https://opensalt.net/uri/4373c8a4-dcf9-5843-9e10-bd1108162df3","fullStatement":"Analyze functions using different representations","humanCodingScheme":"F.IF.C","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"33e1198c-f15b-552f-a3d6-d420a8bfb984","uri":"https://opensalt.net/uri/33e1198c-f15b-552f-a3d6-d420a8bfb984","fullStatement":"Interpret the behavior of the graph of a function using the concept of limits.\n\n**Clarifications/Examples**\n\n- Use limits to reveal asymptotic or unbounded behavior.\n- Use limits to analyze functions for intervals of continuity or points of discontinuity.\n- Identify different types of discontinuities.","humanCodingScheme":"F.IF.C.8.c","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"a4fb964f-74b6-5f4e-a59d-c34b0e9415a2","uri":"https://opensalt.net/uri/a4fb964f-74b6-5f4e-a59d-c34b0e9415a2","fullStatement":"Estimate limits algebraically, numerically and graphically.\n\n**Clarifications/Examples**\n\n- Use various algebraic techniques for evaluating limits.\n- Use a table of values to estimate a limit.\n- Use graphs to estimate limits.\n- Find one-sided limits.\n- Understand and use properties of limits.","humanCodingScheme":"F.IF.C.8.d","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"2a3ee6b1-e2e4-5459-8e12-51b3e793df67","uri":"https://opensalt.net/uri/2a3ee6b1-e2e4-5459-8e12-51b3e793df67","fullStatement":"Conic Sections","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"c82daf12-897a-5ec4-b302-7a361bf77fe3","uri":"https://opensalt.net/uri/c82daf12-897a-5ec4-b302-7a361bf77fe3","fullStatement":"Algebra","humanCodingScheme":"A","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"e96c2b17-3e3f-542e-aea9-9b0ff493ca3e","uri":"https://opensalt.net/uri/e96c2b17-3e3f-542e-aea9-9b0ff493ca3e","fullStatement":"Seeing structure in expressions","humanCodingScheme":"A.SSE","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"b3c2bf4b-eacf-5c91-8931-cb16dd2ca395","uri":"https://opensalt.net/uri/b3c2bf4b-eacf-5c91-8931-cb16dd2ca395","fullStatement":"Interpret the structure of expressions","humanCodingScheme":"A.SSE.A","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"0e08c246-be44-5570-8bbb-55a589aa7d4f","uri":"https://opensalt.net/uri/0e08c246-be44-5570-8bbb-55a589aa7d4f","fullStatement":"Analyze the structure of the general form of a second degree equation, $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$, to identify the conic section represented by the equation.\n\n**Clarifications/Examples**\n\n- Evaluate the discriminant, $B^2 - 4AC$, of the general form of a second degree equation, $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$, to determine if the graph of the equation is a circle, an ellipse, a hyperbola or a parabola.","humanCodingScheme":"A.SSE.A.2.a","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"769b1d91-fd91-597e-aa3f-ff5eccd0f74b","uri":"https://opensalt.net/uri/769b1d91-fd91-597e-aa3f-ff5eccd0f74b","fullStatement":"Write expressions in equivalent forms to solve problems","humanCodingScheme":"A.SSE.B","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"7688fb1c-06b3-5b64-9ae2-540347da5c17","uri":"https://opensalt.net/uri/7688fb1c-06b3-5b64-9ae2-540347da5c17","fullStatement":"Choose and produce an equivalent form of a second degree equation, $Ax^2 + Cy^2 + Dx + Ey + F = 0$, to reveal and explain properties of the conic section represented by the equation.\n\n**Clarifications/Examples**\n\n- Produce the standard form of a second degree equation given the general form.\n- Recognize how the coefficients of the terms transform the conic section.","humanCodingScheme":"A.SSE.B.3.d","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"dcdd7763-53a8-5ecf-a10e-937d1f1f0232","uri":"https://opensalt.net/uri/dcdd7763-53a8-5ecf-a10e-937d1f1f0232","fullStatement":"Translate between the standard and general form, $Ax^2 + Cy^2 + Dx + Ey + F = 0$, of a second degree equation.\n\n**Clarifications/Examples**\n\n- Identify key features of a conic section.\n- Recognize how the coefficients of the terms transform the conic section.","humanCodingScheme":"A.SSE.B.3.e","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"9c438930-b099-5269-85f0-073e160c97e6","uri":"https://opensalt.net/uri/9c438930-b099-5269-85f0-073e160c97e6","fullStatement":"Geometry","humanCodingScheme":"G","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"c72257ba-e95d-5877-910d-c7324e6cf804","uri":"https://opensalt.net/uri/c72257ba-e95d-5877-910d-c7324e6cf804","fullStatement":"Geometric measurement and dimension","humanCodingScheme":"G.GMD","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"e5d15d89-fbcf-5182-aa0a-7c00c5f8f81e","uri":"https://opensalt.net/uri/e5d15d89-fbcf-5182-aa0a-7c00c5f8f81e","fullStatement":"Visualize relationships between two-dimensional and three-dimensional objects","humanCodingScheme":"G.GMD.B","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"900274e6-5479-5d0f-af0f-f2a52cff8319","uri":"https://opensalt.net/uri/900274e6-5479-5d0f-af0f-f2a52cff8319","fullStatement":"Identify the shapes of two-dimensional cross-sections of a right double cone.\n\n**Clarifications/Examples**\n\n- Include special cases of plane/cone intersections that result in degenerate conic sections.","humanCodingScheme":"G.GMD.B.4.a","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"9a56b04c-1f21-5ad3-8dcb-30f7fa3a5451","uri":"https://opensalt.net/uri/9a56b04c-1f21-5ad3-8dcb-30f7fa3a5451","fullStatement":"Expressing geometric properties with equations","humanCodingScheme":"G.GPE","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"567549ba-3973-5687-addd-6d98caf636cf","uri":"https://opensalt.net/uri/567549ba-3973-5687-addd-6d98caf636cf","fullStatement":"Translate between the geometric description and the equation for a conic section","humanCodingScheme":"G.GPE.A","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"91f660b7-2b05-5dd0-85ee-b1d2fe00ee95","uri":"https://opensalt.net/uri/91f660b7-2b05-5dd0-85ee-b1d2fe00ee95","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- Understand and apply the locus definition for the circle.\n- Connect the geometric definition of the circle to its algebraic equation.\n- Understand the concept of eccentricity of conic sections, and understand the eccentricity of the circle.\n- Use eccentricity to write equations of circles.","humanCodingScheme":"G.GPE.A.1","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"5aed60fd-51f7-570c-a119-4a777d18b19f","uri":"https://opensalt.net/uri/5aed60fd-51f7-570c-a119-4a777d18b19f","fullStatement":"Derive the equation of a parabola given a focus and directrix.\n\n**Clarifications/Examples**\n\n- Include parabolas that have a horizontal axis of symmetry and parabolas that have a vertical axis of symmetry.\n- Derive the standard form of a parabola, centered at the origin.\n- Understand and apply the locus definition for the parabola.\n- Connect the geometric definition of the parabola to its algebraic equation.\n- Understand the concept of eccentricity of conic sections, and understand the eccentricity of the parabola.\n- Use eccentricity to write equations of parabolas.","humanCodingScheme":"G.GPE.A.2","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"69b8b1bd-7ced-50e0-95c9-070856620ca1","uri":"https://opensalt.net/uri/69b8b1bd-7ced-50e0-95c9-070856620ca1","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- Derive the standard form of an ellipse and a hyperbola, centered at the origin.\n- Understand and apply the locus definitions of the ellipse and the hyperbola.\n- Connect the geometric definitions of the ellipse and hyperbola to their algebraic equations.\n- Understand the concept of eccentricity of conic sections, and understand the eccentricity of the ellipse and the hyperbola.\n- Use eccentricity to write equations of ellipses and hyperbolas.","humanCodingScheme":"G.GPE.A.3","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"3cad7f65-edc6-5957-a056-b413355129cb","uri":"https://opensalt.net/uri/3cad7f65-edc6-5957-a056-b413355129cb","fullStatement":"Parametric Equations","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"bbb26b3f-1737-599d-8a88-c84980478b7c","uri":"https://opensalt.net/uri/bbb26b3f-1737-599d-8a88-c84980478b7c","fullStatement":"Parametric Equations","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"4d7944cd-4939-58c2-9800-2dde882c65c1","uri":"https://opensalt.net/uri/4d7944cd-4939-58c2-9800-2dde882c65c1","fullStatement":"Interpreting parametric equations","humanCodingScheme":"P.IPE","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"0f88ba34-e93c-52d3-85d7-4a88b3cc9c30","uri":"https://opensalt.net/uri/0f88ba34-e93c-52d3-85d7-4a88b3cc9c30","fullStatement":"Analyze parametric equations","humanCodingScheme":"P.IPE.A","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"7342d4f4-83ed-5b52-b39b-9aa3512eb5a9","uri":"https://opensalt.net/uri/7342d4f4-83ed-5b52-b39b-9aa3512eb5a9","fullStatement":"Sketch the curve defined by parametric equations.\n\n**Clarifications/Examples**\n\n- Indicate with an arrow on the curve the direction in which the curve is traced as t increases.\n- Describe the motion of a particle with position ( x, y ) as t varies in a given interval.","humanCodingScheme":"P.IPE.A.1","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"632b03e1-84e7-5645-9881-f0318e0b5b8d","uri":"https://opensalt.net/uri/632b03e1-84e7-5645-9881-f0318e0b5b8d","fullStatement":"Use parametric equations to model and solve motion problems.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"P.IPE.A.2","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"c84d5fea-b140-53ae-99a3-395094a0e90d","uri":"https://opensalt.net/uri/c84d5fea-b140-53ae-99a3-395094a0e90d","fullStatement":"Creating equations","humanCodingScheme":"P.CED","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"45602580-328d-5674-b06c-7c4265344037","uri":"https://opensalt.net/uri/45602580-328d-5674-b06c-7c4265344037","fullStatement":"Creating equations that describe numbers or relationships","humanCodingScheme":"P.CED.A","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"9db80334-6d67-5d7c-9abd-e42aab13c215","uri":"https://opensalt.net/uri/9db80334-6d67-5d7c-9abd-e42aab13c215","fullStatement":"Create a single equation, using rectangular coordinates, that is equivalent to a pair of parametric equations.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"P.CED.A.1","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"13cdbc8e-43d6-592b-9727-e5df6a9dc5a5","uri":"https://opensalt.net/uri/13cdbc8e-43d6-592b-9727-e5df6a9dc5a5","fullStatement":"Given a data set, create a parametric equation and a single equation using rectangular coordinates to fit the data.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"P.CED.A.2","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"eb19a0b8-3db7-5120-ab4f-937cbef5f0df","uri":"https://opensalt.net/uri/eb19a0b8-3db7-5120-ab4f-937cbef5f0df","fullStatement":"Polar Coordinate System and Polar Equations","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"bdf22fbe-3573-580d-a988-49a94956d477","uri":"https://opensalt.net/uri/bdf22fbe-3573-580d-a988-49a94956d477","fullStatement":"Geometry","humanCodingScheme":"G","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"8cdcec38-c0d3-5470-b9a2-85ddc8b382fa","uri":"https://opensalt.net/uri/8cdcec38-c0d3-5470-b9a2-85ddc8b382fa","fullStatement":"Expressing geometric properties with equations","humanCodingScheme":"G.GPE","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"cc96a809-40c6-5ea0-9eb5-0bae1c3d1552","uri":"https://opensalt.net/uri/cc96a809-40c6-5ea0-9eb5-0bae1c3d1552","fullStatement":"Polar Coordinates","humanCodingScheme":"G.GPE.C","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"c406ad59-72a0-520f-84bf-a0653d644ac8","uri":"https://opensalt.net/uri/c406ad59-72a0-520f-84bf-a0653d644ac8","fullStatement":"Understand the relationship between polar coordinates and Cartesian coordinates.\n\n**Clarifications/Examples**\n\n- Understand that a single point on the polar coordinate plane has more than one set of polar coordinates that can be used to identify the location of the point.","humanCodingScheme":"G.GPE.C.8","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"b5a6ffef-6918-5b51-9cb6-c80c1b129240","uri":"https://opensalt.net/uri/b5a6ffef-6918-5b51-9cb6-c80c1b129240","fullStatement":"Convert between polar and rectangular coordinates.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"G.GPE.C.9","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"ddeef123-dc48-5c5d-b811-8faf276c8814","uri":"https://opensalt.net/uri/ddeef123-dc48-5c5d-b811-8faf276c8814","fullStatement":"Plot points on a polar coordinate grid.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"G.GPE.C.10","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"86d9b680-1bdd-51e3-82ff-e19fbf4838dc","uri":"https://opensalt.net/uri/86d9b680-1bdd-51e3-82ff-e19fbf4838dc","fullStatement":"Polar Equations","humanCodingScheme":"G.GPE.D","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"2165549d-33ca-525a-af86-c9c0a8a4b153","uri":"https://opensalt.net/uri/2165549d-33ca-525a-af86-c9c0a8a4b153","fullStatement":"Convert equations between polar and rectangular forms.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"G.GPE.D.11","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"09ea7c13-0bab-5d13-8831-d37dee981ca2","uri":"https://opensalt.net/uri/09ea7c13-0bab-5d13-8831-d37dee981ca2","fullStatement":"Graph polar equations by hand and using technology.\n\n**Clarifications/Examples**\n\n- Make connections between the structure of a polar equation and the shape of the corresponding graph.\n- Graphs could include circles, lines, rose curves, cardioids, lemniscates, lima\u00e7ons and spirals.","humanCodingScheme":"G.GPE.D.12","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"c3ae348b-fe51-52bc-b122-13e4a0d2c20c","uri":"https://opensalt.net/uri/c3ae348b-fe51-52bc-b122-13e4a0d2c20c","fullStatement":"Solve systems of polar equations.\n\n**Clarifications/Examples**\n\n- Restrict solutions to $[0, 2\\pi)$.","humanCodingScheme":"G.GPE.D.13","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"445ad34c-549a-5654-b893-38ff7a776aba","uri":"https://opensalt.net/uri/445ad34c-549a-5654-b893-38ff7a776aba","fullStatement":"Use the properties of exponents to transform expressions for exponential functions. For example, the expression $1.15^t$ can be rewritten as $(1.15^{1/12})^{12t} \\approx 1.012^{12t}$ to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.\n\n**Clarifications/Examples**\n\n- Model in context.\n\n**Function families to which this standard applies**\n\n- Logarithmic/Exponential Functions","humanCodingScheme":"A.SSE.B.3.c","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"0750d25c-f266-5de5-bdf4-39864eed533e","uri":"https://opensalt.net/uri/0750d25c-f266-5de5-bdf4-39864eed533e","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- Identify the domain and range of a composite function.\n- Recognize when a function is the composition of two simpler functions (e.g. $f(x) = e^{\\sin x}$).\n\n**Function families to which this standard applies**\n\n- Logarithmic/Exponential Functions\n- Polynomial Functions\n- Radical Power Functions\n- Rational Functions\n- Trigonometric Functions","humanCodingScheme":"F.BF.A.1.c","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"aeaaff63-acff-50e5-ac19-d5502557634d","uri":"https://opensalt.net/uri/aeaaff63-acff-50e5-ac19-d5502557634d","fullStatement":"Verify by composition that one function is the inverse of another.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.\n\n**Function families to which this standard applies**\n\n- Polynomial Functions\n- Radical Power Functions\n- Rational Functions","humanCodingScheme":"F.BF.B.4.b","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"859a13ee-b287-50ec-98b0-b1ef826d9d99","uri":"https://opensalt.net/uri/859a13ee-b287-50ec-98b0-b1ef826d9d99","fullStatement":"Read values of an inverse function from a graph or a table, given that the function has an inverse.\n\n**Clarifications/Examples**\n\n- Given the numeric or graphic representation of an invertible function, produce the graphic and numeric representation of the inverse.\n- Interpret the reflection of a function over the line y = x as a representation of the inverse of a function.\n\n**Function families to which this standard applies**\n\n- Logarithmic/Exponential Functions\n- Polynomial Functions\n- Radical Power Functions\n- Rational Functions\n- Trigonometric Functions","humanCodingScheme":"F.BF.B.4.c","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"db4c2201-588b-5aed-9707-4f82bbf843ef","uri":"https://opensalt.net/uri/db4c2201-588b-5aed-9707-4f82bbf843ef","fullStatement":"Produce an invertible function from a non-invertible function by restricting the domain.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.\n\n**Function families to which this standard applies**\n\n- Polynomial Functions\n- Radical Power Functions\n- Trigonometric Functions","humanCodingScheme":"F.BF.B.4.d","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"5ce3f5f1-0127-58f4-834d-14f1966077e4","uri":"https://opensalt.net/uri/5ce3f5f1-0127-58f4-834d-14f1966077e4","fullStatement":"Build inverse trigonometric functions.\n\n**Clarifications/Examples**\n\n- Build from unit circle.\n\n**Function families to which this standard applies**\n\n- Trigonometric Functions","humanCodingScheme":"F.BF.B.4.e","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"8a022c8b-775d-5e73-8998-cb86e3f268ef","uri":"https://opensalt.net/uri/8a022c8b-775d-5e73-8998-cb86e3f268ef","fullStatement":"Sketch and analyze the graphs of logistic functions.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"F.LE.B.6.a","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"15537204-2e8e-5258-8bd4-2467ff65e5f0","uri":"https://opensalt.net/uri/15537204-2e8e-5258-8bd4-2467ff65e5f0","fullStatement":"Compare and contrast the exponential, logarithmic, and logistic models.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"F.LE.B.6.b","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"2e486cba-15b4-553e-86eb-494998a8cfe4","uri":"https://opensalt.net/uri/2e486cba-15b4-553e-86eb-494998a8cfe4","fullStatement":"Apply understanding of logarithmic and logistic functions to solve real-world problems.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"F.LE.B.6.c","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"57589e9a-69a5-5486-9445-23a4630fcad5","uri":"https://opensalt.net/uri/57589e9a-69a5-5486-9445-23a4630fcad5","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- Add vectors symbolically and graphically.","humanCodingScheme":"N.VM.B.4.a","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"c817f8cd-f8c0-55ae-aa0f-cc65429a7923","uri":"https://opensalt.net/uri/c817f8cd-f8c0-55ae-aa0f-cc65429a7923","fullStatement":"Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.\n\n**Clarifications/Examples**\n\n- Use right triangles to derive formulas for the direction and magnitude of a vector.\n- Determine whether a system is in equilibrium.","humanCodingScheme":"N.VM.B.4.b","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"00c1680d-1d58-5c8f-af37-de83273c50e2","uri":"https://opensalt.net/uri/00c1680d-1d58-5c8f-af37-de83273c50e2","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"N.VM.B.4.c","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"da302f67-94ab-57cf-b5e9-028db5377749","uri":"https://opensalt.net/uri/da302f67-94ab-57cf-b5e9-028db5377749","fullStatement":"Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as $c(v_x, v_y) = (cv_x, cv_y)$ .\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"N.VM.B.5.a","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"32616662-23c5-5405-8342-c374dde34ac6","uri":"https://opensalt.net/uri/32616662-23c5-5405-8342-c374dde34ac6","fullStatement":"Compute the magnitude of a scalar multiple cv using \u2016cv\u2016 = |c|v. Compute the direction of cv knowing that when |c|v \u2260 0, the direction of cv is either along v (for c > 0) or against v (for c > 0).\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"N.VM.B.5.b","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"3edddeff-697c-5ecd-b122-29f5f87ce1eb","uri":"https://opensalt.net/uri/3edddeff-697c-5ecd-b122-29f5f87ce1eb","fullStatement":"Determine the dot product of two vectors.\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.","humanCodingScheme":"N.VM.B.5.c","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"a9b6a5b2-33f5-543a-9745-dea9fdc566de","uri":"https://opensalt.net/uri/a9b6a5b2-33f5-543a-9745-dea9fdc566de","fullStatement":"Express the sums in a series using sigma notation.\n\n**Clarifications/Examples**\n\n- Use the algebra rules for finite sums to evaluate expressions written using sigma notation (e.g. Evaluate $\\sum_{k=1}^{5} k(k-1)$.)\n- Find the partial sums of a series defined using sigma notation.\n","humanCodingScheme":"A.SSE.B.4.a","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"9e03f33e-916d-5f36-81f8-8d422160e470","uri":"https://opensalt.net/uri/9e03f33e-916d-5f36-81f8-8d422160e470","fullStatement":"Determine an explicit expression, a recursive process, or steps for calculation from a context.\n\n**Clarifications/Examples**\n\n- Include a variety of sequences that are neither arithmetic nor geometric.","humanCodingScheme":"F.BF.A.1.a","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"a81f6a1b-b2eb-5d3c-89cf-3acab3c0bee5","uri":"https://opensalt.net/uri/a81f6a1b-b2eb-5d3c-89cf-3acab3c0bee5","fullStatement":"Statistics","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"b11d7c6a-bbca-5014-9863-d86e212415e7","uri":"https://opensalt.net/uri/b11d7c6a-bbca-5014-9863-d86e212415e7","fullStatement":"Interpreting Categorical and Quantitative Data","humanCodingScheme":"S.ID","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"9178ac9b-2388-5b90-bc97-33a56335a746","uri":"https://opensalt.net/uri/9178ac9b-2388-5b90-bc97-33a56335a746","fullStatement":"Summarize, represent, and interpret data on a single count or measurement variable","humanCodingScheme":"S.ID.A","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"8db282b3-8015-54a0-ab3f-cc89a698760d","uri":"https://opensalt.net/uri/8db282b3-8015-54a0-ab3f-cc89a698760d","fullStatement":"Represent data with plots on the real number line (dot plots, histograms and box plots).\n\n**Clarifications/Examples**\n\n- Represent a data set using multiple plots. Identify key statistical information each plot provides.\n- Informally discuss shape, center, and spread of data using appropriate data displays.\n- Emphasize which displays to use for discrete versus continuous data.\n\n**Coherence**\n\n- Where students are coming from:\n  - 6.SP.B.4: Display numerical data in plots on a number line, including dot plots, histograms, and box plots.\n- Where students are going:\n  - S.ID.A.2: 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.\n  - S.ID.A.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).","humanCodingScheme":"S.ID.A.1","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"fa8dba8e-5689-5f6f-9d7f-960c9fe3a936","uri":"https://opensalt.net/uri/fa8dba8e-5689-5f6f-9d7f-960c9fe3a936","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- Focus on interpretation of data and decision- making based on analysis of data.\n- Note: Standard deviation is the new learning in this standard.\n\n**Coherence**\n\n- Where students are coming from:\n  - 6.SP.B.5c: Use measures of center (mean, median) and variability (IQR, MAD) to describe data.\n  - 7.SP.B.3: Measure difference between centers of data sets by expressing it as a multiple of the measure of variability.\n- Where students are going:\n  - S.ID.A.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).","humanCodingScheme":"S.ID.A.2","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"bbcc1ee0-ef65-5bb5-9f9e-ea6b8afba054","uri":"https://opensalt.net/uri/bbcc1ee0-ef65-5bb5-9f9e-ea6b8afba054","fullStatement":"Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).\n\n**Clarifications/Examples**\n\n- Focus on interpretations in terms of real-world context.\n- Emphasize which measures of center are resistant to extreme values.\n- Differentiate between extreme values and outliers (i.e. how far out does an extreme value have to be in order to be considered an outlier?).\n- Introduce the 1.5(IQR) rule for determining outliers.\n\n**Coherence**\n\n- Where students are coming from:\n  - 6.SP.A: Develop an understanding of statistical variability.\n  - 6.SP.B: Summarize and describe distributions.\n  - 7.SP.B.3: Measure difference between centers of data sets by expressing it as a multiple of the measure of variability.\n- Where students are going:\n  - S.ID.A.4: 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.","humanCodingScheme":"S.ID.A.3","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"c3bb199a-ba99-5ddb-a588-d61f73172e86","uri":"https://opensalt.net/uri/c3bb199a-ba99-5ddb-a588-d61f73172e86","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- Focus on analysis and application, and not on tedious calculations.\n- Introduce the Empirical Rule (68%-95%-99.7% Rule) and percentiles.\n- Introduce z-scores as the number of standard deviations a data value is from the mean. Compare the extremity of data values from competing data sets using z-score values.\n- Allow access to statistical software and technology, which are tools that students should use strategically. Include reading statistical summaries from various statistical software outputs.\n- Recognize data sets for which procedures are not appropriate and normal distribution calculations and processes will not work (e.g., skewed distributions, non-normal, uniform, etc.).\n\n**Coherence**\n\n- Where students are coming from:\n  - 6.SP.B: Summarize and describe distributions.\n  - 7.SP.A: Use random sampling to draw inferences about a population.\n  - 7.SP.B: Draw informal comparative inferences about two populations.\n  - S.ID.A.2: 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.\n- Where students are going:\n  - S.IC.A: Understand and evaluate random processes underlying statistical experiments.\n  - S.IC.B: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.","humanCodingScheme":"S.ID.A.4","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"6f5be198-a9c2-5e4b-8123-ea313afdf820","uri":"https://opensalt.net/uri/6f5be198-a9c2-5e4b-8123-ea313afdf820","fullStatement":"Summarize, represent, and interpret data on two categorical and quantitative variables","humanCodingScheme":"S.ID.B","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"f6752851-ad25-5e21-9d6d-e1593291dddf","uri":"https://opensalt.net/uri/f6752851-ad25-5e21-9d6d-e1593291dddf","fullStatement":"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).\n\n**Clarifications/Examples**\n\n- Refer to the wording of the standard.\n\n**Coherence**\n\n- Where students are coming from:\n  - 8.SP.A.4: 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.\n- Where students are going:\n  - S.IC.A.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.\n  - S.CP.A.4: 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.","humanCodingScheme":"S.ID.B.5","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"5d1c1595-b638-500b-8919-28d57560735e","uri":"https://opensalt.net/uri/5d1c1595-b638-500b-8919-28d57560735e","fullStatement":"Represent data on two quantitative variables on a scatter plot and describe how the variables are related.\n\n**Clarifications/Examples**\n\n- Describe the trend and pattern (linear, quadratic or exponential) of data.\n\n**Coherence**\n\n- Where students are coming from:\n  - 8.SP.A.1: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities.\n  - HSS.ID.B.6: (Algebra I and Algebra II) Summarize, represent, and interpret data on two categorical and quantitative variables.\n- Where students are going:\n  - S.ID.B.6.a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context.","humanCodingScheme":"S.ID.B.6","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"e2aa9b82-f610-5fa9-99d9-4538a26fb33e","uri":"https://opensalt.net/uri/e2aa9b82-f610-5fa9-99d9-4538a26fb33e","fullStatement":"Interpret linear models","humanCodingScheme":"S.ID.C","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"e2457c66-9050-5bf6-98db-c00b56afd77e","uri":"https://opensalt.net/uri/e2457c66-9050-5bf6-98db-c00b56afd77e","fullStatement":"Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.\n\n**Clarifications/Examples**\n\n- Analyze the reasonableness of the y-intercept in the context of the situation.\n- Interpret slope in the context of the situation.\n\n**Coherence**\n\n- Where students are coming from:\n  - 8.SP.A.3: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.\n  - S.ID.B.6.c: Fit a linear function for a scatter plot that suggests a linear association.\n- Where students are going:\n  - S.ID.C.8: Compute (using technology) and interpret the correlation coefficient of a linear fit.","humanCodingScheme":"S.ID.C.7","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"95676ea4-2c46-5291-858d-af028c31fd1e","uri":"https://opensalt.net/uri/95676ea4-2c46-5291-858d-af028c31fd1e","fullStatement":"Compute (using technology) and interpret the correlation coefficient of a linear fit.\n\n**Clarifications/Examples**\n\n- Identify and interpret the correlation coefficient as a measure of how well the data fits the relationship.\n- Comment on the strength and direction of the association in context of the variables.\n- Include analyzing residual plots, correlation coefficients, and coefficient of determination.\n\n**Coherence**\n\n- Where students are coming from:\n  - 8.SP.A.2: Know straight lines are used to model relationships between two quantitative variables.\n  - S.ID.B.6.b: Informally assess the fit of a function by plotting and analyzing residuals.\n- Where students are going:\n  - S.ID.9: Distinguish between a statistical relationship and a cause-and-effect relationship.\n  - S.IC.B: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.","humanCodingScheme":"S.ID.C.8","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"55407bb8-b23d-511a-9d9e-f2496acb841f","uri":"https://opensalt.net/uri/55407bb8-b23d-511a-9d9e-f2496acb841f","fullStatement":"Distinguish between correlation and causation.\n\n**Clarifications/Examples**\n\n- Recognize a strong correlation does not indicate causation.\n\n**Coherence**\n\n- Where students are coming from:\n  - S.ID.B.5: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data. Recognize possible associations/trends in the data.\n  - S.ID.B.6: Represent data on two quantitative variables on a scatter plot and describe how the variables are related.\n- Where students are going:\n  - S.IC.B.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.","humanCodingScheme":"S.ID.C.9","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"e66b6aad-37a6-50cf-b962-15d827417551","uri":"https://opensalt.net/uri/e66b6aad-37a6-50cf-b962-15d827417551","fullStatement":"Making Inferences and Justifying Conclusions","humanCodingScheme":"S.IC","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"aecf6dfe-d216-5d68-83d1-6517120e21d4","uri":"https://opensalt.net/uri/aecf6dfe-d216-5d68-83d1-6517120e21d4","fullStatement":"Understand and evaluate random processes underlying statistical experiments","humanCodingScheme":"S.IC.A","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"3b32ce31-d03d-5183-8840-aad757013227","uri":"https://opensalt.net/uri/3b32ce31-d03d-5183-8840-aad757013227","fullStatement":"Understand statistics as a process for making inferences about population parameters based on a random sample from that population.\n\n**Clarifications/Examples**\n\n- Emphasize the importance of randomization in selecting samples from a population, understanding that randomization guarantees that a process is unbiased.\n- Understand the goal of randomization is to obtain a sample that is representative of the population.\n- Understand the use of a sample statistic to measure a population parameter.\n\n**Coherence**\n\n- Where students are coming from:\n  - 7.SP.A.1: Understand that statistics can be used to gain information about a population by examining a representative sample of the population.\n  - 7.SP.A.2: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.\n- Where students are going:\n  - S.IC.B.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.\n  - S.IC.B.4: 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.","humanCodingScheme":"S.IC.A.1","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"b6b78224-9200-598b-ac24-3d79fdfcb286","uri":"https://opensalt.net/uri/b6b78224-9200-598b-ac24-3d79fdfcb286","fullStatement":"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?\n\n**Clarifications/Examples**\n\n- Allow time for students to concretely simulate meaningful events in real life before moving to computer simulations.\n- Use technology to help make connections between experimental and theoretical probability (i.e., the law of large numbers says that experimental probability will approach theoretical probability over a sufficiently large number of trials).\n- Emphasize that the variability around the expected value is diminished when based on larger sample sizes.\n- Establish connections to the ideas of independence of events and simulations.\n\n**Coherence**\n\n- Where students are coming from:\n  - 7.SP.C.7: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.\n  - 7.SP.C.8.c: Design and use a simulation to generate frequencies for compound events.\n- Where students are going:\n  - S.IC.B.4: 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.\n  - S.IC.B.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.","humanCodingScheme":"S.IC.A.2","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"438e190b-0486-502f-8b38-72f0bdf33e91","uri":"https://opensalt.net/uri/438e190b-0486-502f-8b38-72f0bdf33e91","fullStatement":"Make inferences and justify conclusions from sample surveys, experiments and observational studies","humanCodingScheme":"S.IC.B","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"dae12311-90e7-5f76-9b3d-fdf70d941660","uri":"https://opensalt.net/uri/dae12311-90e7-5f76-9b3d-fdf70d941660","fullStatement":"Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.\n\n**Clarifications/Examples**\n\n- Develop procedures for random selection and assignment that extend further than a classroom census either with simulation or within larger populations to make appropriate inferences.\n- Determine the impact of how questions are asked and how accurately responses are recorded on sample surveys.\n- Identify types of bias and emphasize their impact on the conclusion made.\n- Recognize how aspects in the design of an experiment or observational study influence the conclusions that can be drawn.\n- Develop understanding of sampling techniques including but not limited to convenience sampling, voluntary response sampling, simple random sampling, stratified random sampling, and cluster sampling.\n\n**Coherence**\n\n- Where students are coming from:\n  - 7.SP.A: Use random sampling to draw inferences about a population.\n  - S.IC.A.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.\n- Where students are going:\n  - S.IC.B.4: 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.\n  - S.IC.B.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.","humanCodingScheme":"S.IC.B.3","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"ece528ac-c5fa-5282-8e77-17024639b745","uri":"https://opensalt.net/uri/ece528ac-c5fa-5282-8e77-17024639b745","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- Create sampling distributions through simulation with technology or in-class experiments.\n- Use technology to provide opportunities for students to explore multiple situations.\n- Emphasize the factors that influence the margin of error, such as sample size and confidence levels.\n- Establish a clear distinction between estimates for means and proportions.\n- Explore confidence levels and confidence intervals.\n- Explore random sampling with replacement, also known as bootstrapping, to develop the margin of error.\n\n**Coherence**\n\n- Where students are coming from:\n- S.IC.A.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.\n- S.IC.A.2: Decide if a specified model is consistent with results from a given data- generating process.\n- S.IC.B.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.\n- Where students are going:\n- S.IC.B.6: Evaluate reports based on data.","humanCodingScheme":"S.IC.B.4","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"6fbac655-6622-50ee-bdcf-7e6f635137a1","uri":"https://opensalt.net/uri/6fbac655-6622-50ee-bdcf-7e6f635137a1","fullStatement":"Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.\n\n**Clarifications/Examples**\n\n- Use data from well-designed experiments (treatments, control groups, experimental units, random assignments, and replications) to conduct informal hypothesis tests.\n- Compare two or more samples of data to infer whether there is a real difference between the populations from which they were sampled.\n- Make generalizations that go beyond describing the given data, using given data as evidence.\n- Form conclusions, recognizing and expressing degrees of uncertainty.\n- Judge two competing models or statements to informally determine which is more likely to be true.\n\n**Coherence**\n\n- Where students are coming from:\n  - 7.SP.B.4: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.\n  - S.IC.A.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.\n  - S.IC.A.2: Decide if a specified model is consistent with results from a given data-generating process.\n  - S.IC.B.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.\n- Where students are going:\n  - S.IC.B.6: Evaluate reports based on data.","humanCodingScheme":"S.IC.B.5","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"2fd3e86b-aab5-5f0e-9e81-c19e48a5f879","uri":"https://opensalt.net/uri/2fd3e86b-aab5-5f0e-9e81-c19e48a5f879","fullStatement":"Evaluate reports based on data.\n\n**Clarifications/Examples**\n\n- Use and evaluate statistical language appropriately. For example, avoid using absolute language, such as \"will happen.\u201d\n- Evaluate graphs, tables, and reports to identify possibly misleading characteristics.\n- Evaluate how randomness is applied in real world articles and studies.\n- Interpret and critically evaluate statistical information and data-based arguments from a diverse range of sources.\n\n**Coherence**\n\n- Where students are coming from:\n  - 6.SP.B.5: Summarize numerical data sets in relation to their context.\n  - S.IC.B.4: 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.\n  - S.IC.B.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.\n- Where students are going:\n  - IHE: Formally conduct hypothesis tests and formally establish confidence intervals.","humanCodingScheme":"S.IC.B.6","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"9c8c031d-6afc-5fc4-b167-9b8c199a23ab","uri":"https://opensalt.net/uri/9c8c031d-6afc-5fc4-b167-9b8c199a23ab","fullStatement":"Conduct statistical investigations.\n\n**Clarifications/Examples**\n\n- Apply the Statistical Problem-Solving Process (i.e. formulate statistical questions, collect and consider the data, analyze the data, and interpret the results).\n- Distinguish between random assignment and random selection and their implications on the conclusions that can be drawn.\n\n**Coherence**\n\n- Where students are coming from:\n  - 7.SP.A: Use random sampling to draw inferences about a population.\n  - S.IC.A.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.\n- Where students are going:\n  - S.IC.B.4: 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.\n  - S.IC.B.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.","humanCodingScheme":"S.IC.B.7","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"d775bb61-ed2e-5300-b09b-4ab8942c0a67","uri":"https://opensalt.net/uri/d775bb61-ed2e-5300-b09b-4ab8942c0a67","fullStatement":"Conditional Probability and the Rules of Probability","humanCodingScheme":"S.CP","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"fec8ef7b-0650-5c3b-9f46-47825974ca7e","uri":"https://opensalt.net/uri/fec8ef7b-0650-5c3b-9f46-47825974ca7e","fullStatement":"Understand independence and conditional probability and use them to interpret data","humanCodingScheme":"S.CP.A","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"98dcab7a-9077-54e2-b5e6-f5021d5c5731","uri":"https://opensalt.net/uri/98dcab7a-9077-54e2-b5e6-f5021d5c5731","fullStatement":"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\").\n\n**Clarifications/Examples**\n\n- Explore sample spaces and probability models using various displays (i.e., tree diagrams, Venn diagrams and two-way tables).\n- Represent events using appropriate notation (e.g., $\\cap, \\cup, \\sim, \\in, c$ ).\n\n**Coherence**\n\n- Where students are coming from:\n  - 7.SP.C.8: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulations.\n- Where students are going:\n  - S.CP.A.2: 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.\n  - S.CP.A.3: Understand the conditional probability of A given B as $P(A \\text{ and } B)/P(B)$, 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.","humanCodingScheme":"S.CP.A.1","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"7d3e46f1-3ddd-5755-91bb-c355538782e9","uri":"https://opensalt.net/uri/7d3e46f1-3ddd-5755-91bb-c355538782e9","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- Build understanding through real world contexts and experiments before advancing to theoretical and formulaic approaches (e.g., experiment with flipping a coin or playing egg roulette).\n- Develop an understanding of the formula for determining if events are independent.\n\n**Coherence**\n\n- Where students are coming from:\n  - 7.SP.C.7: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.\n  - 7.SP.C.8: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.\n- Where students are going:\n  - S.CP.A.3: Understand the conditional probability of A given B as $P(A \\text{ and } B)/P(B)$, 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.\n  - S.CP.B.8: Apply the general Multiplication Rule in a uniform probability model and interpret the answer in terms of the model.","humanCodingScheme":"S.CP.A.2","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"cf19029a-6ecc-556b-a9c5-ac966615c91c","uri":"https://opensalt.net/uri/cf19029a-6ecc-556b-a9c5-ac966615c91c","fullStatement":"Understand the conditional probability of A given B as $P(A \\text{ and } B)/P(B)$, 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.\n\n**Clarifications/Examples**\n\n- This standard should be taught in conjunction with S.CP.A.4 and S.CP.A.5 to build coherence and understanding of conditional and independent probabilities.\n- Attention should be paid to the coherence of the standards for the cluster S.CP.A.\n- Use the formula, Venn Diagrams, and properties for conditional probability to determine if two events are independent or dependent.\n\n**Coherence**\n\n- Where students are coming from:\n  - 7.SP.C: Investigate chance processes and develop, use, and evaluate probability models.\n  - S.CP.A: Understand independence and conditional probability and use them to interpret data.\n- Where students are going:\n  - S.CP.A.1: 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\").\n  - S.CP.A.2: 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.\n  - S.CP.B.8: Apply the general Multiplication Rule in a uniform probability model and interpret the answer in terms of the model.","humanCodingScheme":"S.CP.A.3","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"45223809-3d3e-5c33-a54f-3373bedfabb4","uri":"https://opensalt.net/uri/45223809-3d3e-5c33-a54f-3373bedfabb4","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- This standard should be taught in conjunction with S.CP.A.3 and S.CP.A.5 to build coherence and understanding of conditional and independent probabilities.\n- Attention should be paid to the coherence of the standards for the cluster S.CP.A.\n- Analyze a table to calculate and interpret marginal and conditional probabilities and any association or independence that may exist.\n\n**Coherence**\n\n- Where students are coming from:\n  - 7.SP.C: Investigate chance processes and develop, use, and evaluate probability models.\n  - 8.SP.A.4: 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.\n  - S.CP.A: Understand independence and conditional probability and use them to interpret data.\n- Where students are going:\n  - S.CP.A.1: 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\").\n  - S.CP.A.2: 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.","humanCodingScheme":"S.CP.A.4","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"9b406d4c-8e5c-5809-8d4e-8978166c795c","uri":"https://opensalt.net/uri/9b406d4c-8e5c-5809-8d4e-8978166c795c","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- This standard should be taught in conjunction with S.CP.A.3 and S.CP.A.4 to build coherence and understanding of conditional and independent probabilities.\n- Make connections between the wording in the scenario and the formula $P(A|B) \\neq P(B|A)$.\n\n**Coherence**\n\n- Where students are coming from:\n  - 7.SP.C: Investigate chance processes and develop, use, and evaluate probability models.\n  - S.CP.A: Understand independence and conditional probability and use them to interpret data.\n- Where students are going:\n  - S.CP.A.1: 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\").\n  - S.CP.A.2: 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.","humanCodingScheme":"S.CP.A.5","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"d40d3632-fe37-57ec-8e06-c9ef16e90e23","uri":"https://opensalt.net/uri/d40d3632-fe37-57ec-8e06-c9ef16e90e23","fullStatement":"Use the rules of probability to compute probabilities of compound events","humanCodingScheme":"S.CP.B","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"ebbd614e-ec11-5137-8ebc-ca2c08871a55","uri":"https://opensalt.net/uri/ebbd614e-ec11-5137-8ebc-ca2c08871a55","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- Connect addition and multiplication rules with counting outcomes.\n- Present data in multiple representations (i.e., tables, tree diagrams, Venn Diagrams, and lists).\n\n**Coherence**\n\n- Where students are coming from:\n  - S.CP.A: Understand independence and conditional probability and use them to interpret data.\n- Where students are going:\n  - S.CP.B.7: Apply the Addition Rule and interpret the answer in terms of the model.\n  - S.CP.B.8: Apply the Multiplication Rule in a uniform probability model and interpret the answer in terms of the model.","humanCodingScheme":"S.CP.B.6","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"feb848dd-7cbf-5bca-9a40-c19cfc9c8b0e","uri":"https://opensalt.net/uri/feb848dd-7cbf-5bca-9a40-c19cfc9c8b0e","fullStatement":"Apply the Addition Rule, $P(A \\text{ or } B) = P(A) + P(B) - P(A \\text{ and } B)$, and interpret the answer in terms of the model.\n\n**Clarifications/Examples**\n\n- Connect addition and multiplication rules with counting outcomes.\n- Present data in multiple representations (i.e., two- way tables, Venn Diagrams, and lists).\n- Develop conceptual understanding of the addition rule before introducing the formula.\n- Distinguish between mutually exclusive events, disjoint events, and independent events.\n- Show how the addition rule can be applied when events are mutually exclusive.\n\n**Coherence**\n\n- Where students are coming from:\n  - S.CP.B.6: 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.\n- Where students are going:\n  - S.CP.B.8: Apply the Multiplication Rule in a uniform probability model and interpret the answer in terms of the model.","humanCodingScheme":"S.CP.B.7","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"fa93fa57-8349-5f2a-96cf-349aa676702d","uri":"https://opensalt.net/uri/fa93fa57-8349-5f2a-96cf-349aa676702d","fullStatement":"Apply the general Multiplication Rule in a uniform probability model, $P(A \\text{ and } B) = P(A)P(B|A) = P(B)P(A|B)$, and interpret the answer in terms of the model.\n\n**Clarifications/Examples**\n\n- Connect addition and multiplication rules with counting outcomes.\n- Present data in multiple representations (i.e., tables, Venn Diagrams and lists).\n- Explore false positives and false negatives that arise from multiple contexts using conditional probability.\n- Show how the multiplication rule can be applied when events are independent.\n\n**Coherence**\n\n- Where students are coming from:\n  - S.CP.A.3: Understand the conditional probability of A given B as $P(A \\text{ and } B)/P(B)$, 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.\n  - S.CP.A.5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.\n  - S.CP.B.6: 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.\n  - S.CP.B.7: Apply the Addition Rule and interpret the answer in terms of the model.\n- Where students are going:\n  - S.MD: Apply probability models and formulas to make decisions.","humanCodingScheme":"S.CP.B.8","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"9f3b4e26-4314-58f9-bd54-7fd37f0d6171","uri":"https://opensalt.net/uri/9f3b4e26-4314-58f9-bd54-7fd37f0d6171","fullStatement":"Use permutations and combinations to compute probabilities of compound events and solve problems.\n\n**Clarifications/Examples**\n\n- Perform simple calculations by hand to develop understanding of permutations and combinations.\n- Use technology to perform calculations when computing permutations and combinations to solve more complex problems.\n- Connect to the fundamental counting principle.\n\n**Coherence**\n\n- Where students are coming from:\n  - S.CP.A: Understand independence and conditional probability and use them to interpret data.\n- Where students are going:\n  - S.MD: Apply probability models and formulas to make decisions.","humanCodingScheme":"S.CP.B.9","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"e3f05cf1-42d8-5bf6-b995-c4d087941276","uri":"https://opensalt.net/uri/e3f05cf1-42d8-5bf6-b995-c4d087941276","fullStatement":"Using Probability to Make Decisions","humanCodingScheme":"S.MD","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"9d13756c-7e0f-5d38-a609-d6ca12b71246","uri":"https://opensalt.net/uri/9d13756c-7e0f-5d38-a609-d6ca12b71246","fullStatement":"Calculate expected values and use them to solve problems","humanCodingScheme":"S.MD.A","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"f7e05102-4636-5644-bb84-e28b7a4f8730","uri":"https://opensalt.net/uri/f7e05102-4636-5644-bb84-e28b7a4f8730","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- Construct probability distributions as dot plots, stacked bar graphs, frequency line graphs, mosaic plots and box plots for categorical data.\n- Use simulations and real-world data to build sample spaces.\n- Distinguish between discrete and continuous random variables.\n\n**Coherence**\n\n- Where students are coming from:\n  - S.IC.B.6: Evaluate reports based on data.\n  - S.ID.A.1: Represent data with plots on the real number line (dot plots, histograms, and box plots).\n- Where students are going:\n  - S.IC.A: Understand and evaluate random processes underlying statistical experiments.\n  - S.IC.B: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.","humanCodingScheme":"S.MD.A.1","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"398d69a1-f1eb-5f5f-b060-42cfbd20c120","uri":"https://opensalt.net/uri/398d69a1-f1eb-5f5f-b060-42cfbd20c120","fullStatement":"Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.\n\n**Clarifications/Examples**\n\n- Relate expected value to distributions of samples and confidence intervals.\n- Use experiments, patterns, and theoretical probability distributions to develop and interpret the formula for expected value.\n- Apply the expected value to real world situations that require finding the mean of the distribution.\n- Distinguish between binomial and geometric random variables.\n\n**Coherence**\n\n- Where students are coming from:\n  - S.ID.A.2: 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.\n  - S.MD.A.1: 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.\n- Where students are going:\n  - S.MD.A.3: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.\n  - S.MD.B.5.b: Evaluate and compare strategies based on expected values.","humanCodingScheme":"S.MD.A.2","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"d07fae5a-8576-5d7e-a184-5e1202c10a24","uri":"https://opensalt.net/uri/d07fae5a-8576-5d7e-a184-5e1202c10a24","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- Experiment with common real-world probabilities (e.g., playing cards) to calculate and apply expected value.\n- Explore different approaches to find probabilities of events (short term vs. long term).\n\n**Coherence**\n\n- Where students are coming from:\n  - S.MD.A.1: 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.\n- Where students are going:\n  - S.MD.A.4: Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.","humanCodingScheme":"S.MD.A.3","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"4d1023ad-05ef-575b-9f8e-a3ea97f2109c","uri":"https://opensalt.net/uri/4d1023ad-05ef-575b-9f8e-a3ea97f2109c","fullStatement":"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?\n\n**Clarifications/Examples**\n\n- Apply the Data Science Process to:\n  - formulate informed questions.\n  - collect, analyze, and report out on data.\n  - make informed decisions based on probability models.\n\n**Coherence**\n\n- Where students are coming from:\n  - S.MD.A.3: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.\n- Where students are going:\n  - S.MD.B: Use probability to evaluate outcomes of decisions.","humanCodingScheme":"S.MD.A.4","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"d5b93621-a1b3-5583-8095-1e53e7b00cb5","uri":"https://opensalt.net/uri/d5b93621-a1b3-5583-8095-1e53e7b00cb5","fullStatement":"Use probability to evaluate outcomes of decisions","humanCodingScheme":"S.MD.B","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"e471d6fb-4603-58f0-90af-f918c18cd1e5","uri":"https://opensalt.net/uri/e471d6fb-4603-58f0-90af-f918c18cd1e5","fullStatement":"Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.\n\n**Clarifications/Examples**\n\n- See S.MD.B.5.a and S.MD.B.5.b.\n\n**Coherence**\n\n- Where students are coming from:\n  - 7.SP.C: Investigate chance processes and develop, use, and evaluate probability models.\n- Where students are going:\n  - S.MD.B: Use probability to evaluate outcomes of decisions.","humanCodingScheme":"S.MD.B.5","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"bda7042a-31f0-5166-b449-126a10632bee","uri":"https://opensalt.net/uri/bda7042a-31f0-5166-b449-126a10632bee","fullStatement":"Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).\n\n**Clarifications/Examples**\n\n- Explore the use of different tools to generate random samples and explore the fairness of random selection processes.\n- Students should be required to simulate events. Focus student attention towards the context of the situation and how this is represented with the chosen tool or simulation.\n\n**Coherence**\n\n- Where students are coming from:\n  - S.MD.B.5: Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.","humanCodingScheme":"S.MD.B.6","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"ae726e69-6252-52dc-bab2-3cf0b0db83a6","uri":"https://opensalt.net/uri/ae726e69-6252-52dc-bab2-3cf0b0db83a6","fullStatement":"Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).\n\n**Clarifications/Examples**\n\n- Analyze both cost and benefits in different contextual situations.\n- Explore negative values occurring when the cost outweighs the benefit in certain situations.\n\n**Coherence**\n\n- Where students are coming from:\n  - S.MD.B.5: Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.","humanCodingScheme":"S.MD.B.7","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"661c8420-f3c8-5b32-a98a-d8190a01e049","uri":"https://opensalt.net/uri/661c8420-f3c8-5b32-a98a-d8190a01e049","fullStatement":"Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.\n\n**Clarifications/Examples**\n\n- Standard S.ID.B.6.a focuses on using information such as a given function or the context of the problem to solve problems compared to standard S.ID.B.6.c that more specifically asks to fit a linear function to a scatter plot.\n- Explore the uses and limitations of interpolation and extrapolation.\n- Explore the connections between the population sampled and more generalized populations.\n\n**Coherence**\n\n- Where students are coming from:\n  - Fitting functions to data included linear, quadratic, and exponential models, as these are the function families studied in Algebra I and Algebra II.\n  - 8.SP.A.2: Informally fit a straight line to data that suggests a linear association.\n- Where students are going:\n  - S.ID.B.6.b: Informally assess the fit of a function by plotting and analyzing residuals.","humanCodingScheme":"S.ID.B.6.a","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"95fa8804-5430-5686-b5c9-5e3b75836137","uri":"https://opensalt.net/uri/95fa8804-5430-5686-b5c9-5e3b75836137","fullStatement":"Informally assess the fit of a function by plotting and analyzing residuals.\n\n**Clarifications/Examples**\n\n- Formally assess the fit of a function, including analyzing residual plots, correlation coefficients, and coefficient of determination by utilizing appropriate technology and statistical programs.\n- Recognize and explore linear, quadratic, and exponential patterns in data and notice such patterns in residual plots.\n- Recognize that a relatively high correlation coefficient is no guarantee that the model is appropriate.\n\n**Coherence**\n\n- Where students are coming from:\n  - S.ID.B.6.a: Fit a function to the data. Use functions fitted to data to solve problems in the context of the data.\n- Where students are going:\n  - S.ID.C.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.","humanCodingScheme":"S.ID.B.6.b","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"8950843a-6667-56fc-b008-72015b2c578f","uri":"https://opensalt.net/uri/8950843a-6667-56fc-b008-72015b2c578f","fullStatement":"Fit a linear function for a scatter plot that suggests a linear association.\n\n**Clarifications/Examples**\n\n- Recognize a linear relationship displayed in a scatter plot.\n- Determine an equation for the line of best fit for a set of data points.\n\n**Coherence**\n\n- Where students are coming from:\n  - S.ID.B.6.a: Fit a function to the data. Use functions fitted to data to solve problems in the context of the data.\n  - S.ID.B.6.b: Informally assess the fit of a function by plotting and analyzing residuals.\n- Where students are going:\n  - S.ID.C.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.\n  - S.ID.C.8: Compute (using technology) and interpret the correlation coefficient of a linear fit.","humanCodingScheme":"S.ID.B.6.c","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"912364b8-695c-521f-97ec-c28b5feb5754","uri":"https://opensalt.net/uri/912364b8-695c-521f-97ec-c28b5feb5754","fullStatement":"Introduce sampling distributions as a means to explore variability in sample statistics and ultimately evaluate a claim about a population.\n\n**Clarifications/Examples**\n\n- Distinguish between a parameter and a statistic.\n- Distinguish among the distribution of a population, the distribution of a sample, and the sampling distribution of a statistic.\n- Use the sampling distribution of a statistic to evaluate a claim about a parameter.\n- Describe the relationship between sample size and the variability of a statistic.\n- Determine whether a statistic is an unbiased estimator of a population parameter.\n\n**Coherence**\n\n- Where students are coming from:\n- 7.SP.A.1: Understand that statistics can be used to gain information about a population by examining a representative sample of the population.\n- 7.SP.A.2: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.\n- Where students are going:\n- S.IC.B.4: 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.","humanCodingScheme":"S.IC.A.1.a","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"728c58c9-b916-526e-9336-2068c3014fc2","uri":"https://opensalt.net/uri/728c58c9-b916-526e-9336-2068c3014fc2","fullStatement":"Conduct observational studies.\n\n**Clarifications/Examples**\n\n- Plan and conduct well-designed observational studies by applying methods of random selection and limiting bias when possible.\n\n**Coherence**\n\n- Where students are coming from:\n  - 7.SP.A: Use random sampling to draw inferences about a population.\n  - S.IC.A.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.\n- Where students are going:\n  - S.IC.B.4: 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.\n  - S.IC.B.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.","humanCodingScheme":"S.IC.B.7.a","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"c7ea36a5-b572-5ecc-97fc-72cd51afe93b","uri":"https://opensalt.net/uri/c7ea36a5-b572-5ecc-97fc-72cd51afe93b","fullStatement":"Conduct statistical experiments.\n\n**Clarifications/Examples**\n\n- Plan and conduct well-designed experiments (i.e. random assignment to treatment and control group, etc.).\n\n**Coherence**\n\n- Where students are coming from:\n  - 7.SP.A: Use random sampling to draw inferences about a population.\n  - S.IC.A.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.\n- Where students are going:\n  - S.IC.B.4: 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.\n  - S.IC.B.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.","humanCodingScheme":"S.IC.B.7.b","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"b98bd467-11a6-5dec-a41d-77bda8d11b92","uri":"https://opensalt.net/uri/b98bd467-11a6-5dec-a41d-77bda8d11b92","fullStatement":"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.\n\n**Clarifications/Examples**\n\n- Analyze the benefits or drawbacks when weighing a decision based on money or another valuable item that can be numerically quantified.\n- Interpret expected value as the long-run expected outcome of the variable, considering the probability of each possible outcome.\n\n**Coherence**\n\n- Where students are coming from:\n  - 7.SP.C: Investigate chance processes and develop, use, and evaluate probability models.\n- Where students are going:\n  - S.MD.B: Use probability to evaluate outcomes of decisions.","humanCodingScheme":"S.MD.B.5.a","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"1e6e45b9-ab06-59ce-8a36-727107fce198","uri":"https://opensalt.net/uri/1e6e45b9-ab06-59ce-8a36-727107fce198","fullStatement":"Evaluate and compare strategies based on 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.\n\n**Clarifications/Examples**\n\n- Interpretations of expected value should be thought of as what is expected in the long run.\n- Explore the notion of \u2018Monte Carlo Fallacy\u2019 (the mistaken belief that if something happens less frequently than normal, it will happen more often in the future).\n- Work with various simulation tools such as dice, coins, roulette wheels, spinners, and other simulation tools to assign particular payoffs and costs for play.\n\n**Coherence**\n\n- Where students are coming from:\n  - 7.SP.C: Investigate chance processes and develop, use, and evaluate probability models.\n- Where students are going:\n  - S.MD.B: Use probability to evaluate outcomes of decisions.","humanCodingScheme":"S.MD.B.5.b","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"d6ac2b75-4abc-5ada-aaa9-ba8fef0f7d74","uri":"https://opensalt.net/uri/d6ac2b75-4abc-5ada-aaa9-ba8fef0f7d74","fullStatement":"Integrated Algebra 1","humanCodingScheme":"IA1","notes":"For Implementation in Future School Years","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"7e4be5e3-3ee1-5696-b249-05950d3c4dc7","uri":"https://opensalt.net/uri/7e4be5e3-3ee1-5696-b249-05950d3c4dc7","fullStatement":"Algebraic Thinking","humanCodingScheme":"IA1.AT","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"3e96536f-fd45-5629-a5c0-f3bbc59ef406","uri":"https://opensalt.net/uri/3e96536f-fd45-5629-a5c0-f3bbc59ef406","fullStatement":"Look for and make use of structure to rewrite expressions in equivalent 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Justify the solution process using logical steps and explanations. Interpret the meaning of the solution in context.","humanCodingScheme":"IA1.AT.B.2.b","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"ce8f4324-adc5-5925-91d3-70359a953baf","uri":"https://opensalt.net/uri/ce8f4324-adc5-5925-91d3-70359a953baf","fullStatement":"Solve absolute value equations in one variable where the absolute value expression is isolated on one side of the equation. Justify the solution process and interpret the solution(s) in context.","humanCodingScheme":"IA1.AT.B.2.c","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"8196a680-6570-58af-8ef7-e431e2d90413","uri":"https://opensalt.net/uri/8196a680-6570-58af-8ef7-e431e2d90413","fullStatement":"Solve exponential equations where both sides have comparable exponential expressions, requiring at most two steps to rewrite expressions to the same base, and explain the reasoning using properties of exponents.","humanCodingScheme":"IA1.AT.B.2.d","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"0223e8a8-46b1-5172-8c51-c2a6a2357b66","uri":"https://opensalt.net/uri/0223e8a8-46b1-5172-8c51-c2a6a2357b66","fullStatement":"Create and solve one-variable inequalities, justify the solution process, and interpret the solutions in context.","humanCodingScheme":"IA1.AT.B.3","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"86f4f5bc-55dc-5ca5-83ae-70763b413e4c","uri":"https://opensalt.net/uri/86f4f5bc-55dc-5ca5-83ae-70763b413e4c","fullStatement":"Create inequalities in one variable to represent constraints or conditions.","humanCodingScheme":"IA1.AT.B.3.a","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"8feeb1b6-24f9-5779-abac-9480b9a77edf","uri":"https://opensalt.net/uri/8feeb1b6-24f9-5779-abac-9480b9a77edf","fullStatement":"Solve linear inequalities in one variable, including those with variables on both sides, using flexible and efficient strategies. Represent the solution set using a number line and inequality notation.","humanCodingScheme":"IA1.AT.B.3.b","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"d5cfba3a-a7d6-5a67-8ebb-f9bbfcfb991e","uri":"https://opensalt.net/uri/d5cfba3a-a7d6-5a67-8ebb-f9bbfcfb991e","fullStatement":"Solve absolute value inequalities in one variable where the absolute value expression is isolated on one side of the inequality. Represent the solution set using compound inequalities and a number line.","humanCodingScheme":"IA1.AT.B.3.c","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"bc3e5d87-b7a9-5b3c-b344-5e75632194d8","uri":"https://opensalt.net/uri/bc3e5d87-b7a9-5b3c-b344-5e75632194d8","fullStatement":"Interpret the meaning of the solution set in the context of the problem, including what values are reasonable within the given situation.","humanCodingScheme":"IA1.AT.B.3.d","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"c4e45652-159f-5c8c-b622-241643222d8d","uri":"https://opensalt.net/uri/c4e45652-159f-5c8c-b622-241643222d8d","fullStatement":"Create linear and exponential equations in two variables, graph them, and use those graphs to represent and solve problems in context.","humanCodingScheme":"IA1.AT.B.4","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"e4f4d21f-bb82-55f7-81b3-eb67ca511b9b","uri":"https://opensalt.net/uri/e4f4d21f-bb82-55f7-81b3-eb67ca511b9b","fullStatement":"Create linear and exponential equations in two variables to model relationships, and graph them on the coordinate plane.","humanCodingScheme":"IA1.AT.B.4.a","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"542d9394-30a7-5449-a5ad-74c59ed01a7c","uri":"https://opensalt.net/uri/542d9394-30a7-5449-a5ad-74c59ed01a7c","fullStatement":"Use the understanding that the graph of an equation represents the set of all its solutions to identify solutions, describe patterns, and interpret the relationship between variables.","humanCodingScheme":"IA1.AT.B.4.b","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"bee51c92-0a91-5e5f-a1ac-58920c68d0ae","uri":"https://opensalt.net/uri/bee51c92-0a91-5e5f-a1ac-58920c68d0ae","fullStatement":"Create, solve, and analyze systems of two linear equations in two variables in context.","humanCodingScheme":"IA1.AT.B.5","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"384a0743-9aa9-5b8e-bf5e-f6b2549bf5eb","uri":"https://opensalt.net/uri/384a0743-9aa9-5b8e-bf5e-f6b2549bf5eb","fullStatement":"Create systems of linear equations to represent relationships.","humanCodingScheme":"IA1.AT.B.5.a","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"97bc6e82-263a-5993-a631-5fb320ac34cb","uri":"https://opensalt.net/uri/97bc6e82-263a-5993-a631-5fb320ac34cb","fullStatement":"Solve systems of linear equations using algebraic methods (i.e., substitution and linear combination).","humanCodingScheme":"IA1.AT.B.5.b","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"d5fc61b7-4414-5e5e-af30-633a4ff00640","uri":"https://opensalt.net/uri/d5fc61b7-4414-5e5e-af30-633a4ff00640","fullStatement":"Approximate or verify solutions to systems of equations by graphing and identifying the point of intersection.","humanCodingScheme":"IA1.AT.B.5.c","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"e4fa684d-a50c-5252-8d1a-7f592afe2062","uri":"https://opensalt.net/uri/e4fa684d-a50c-5252-8d1a-7f592afe2062","fullStatement":"Interpret the meaning of the solution in context.","humanCodingScheme":"IA1.AT.B.5.d","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"2253e4db-133b-56fd-9beb-73249f0eb6d9","uri":"https://opensalt.net/uri/2253e4db-133b-56fd-9beb-73249f0eb6d9","fullStatement":"Create linear inequalities in two variables to represent constraints in context and graph the solution set as a half-plane within the coordinate plane.","humanCodingScheme":"IA1.AT.B.6","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"d125b230-987b-5c48-b137-e11dc9594159","uri":"https://opensalt.net/uri/d125b230-987b-5c48-b137-e11dc9594159","fullStatement":"Represent and analyze systems of two linear inequalities in two variables in context.","humanCodingScheme":"IA1.AT.B.7","language":"en","educationLevel":["09","10","11","12"],"lastChangeDateTime":"2025-07-01T00:00:00+00:00"},{"identifier":"4f7e8574-5ac4-5c6c-98e9-b95cfef49094","uri":"https://opensalt.net/uri/4f7e8574-5ac4-5c6c-98e9-b95cfef49094","fullStatement":"Create systems of linear inequalities in two variables to represent constraints and 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