#### Algebra 1

Relationships Between Quantities and Reasoning with Equations Reason quantitatively and use units to solve problems. Interpret the structure of expressions. Create equations that describe numbers or relationships. Understand solving equations as a process of reasoning and explain the reasoning. Solve equations and inequalities in one variable. Linear and Exponential Relationships Extend the properties of exponents to rational exponents. Solve systems of equations. Represent and solve equations and inequalities graphically. Understand the concept of a function and use function notation. Interpret functions that arise in applications in terms of a context. Analyze functions using different representations. Build a function that models ...

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#### Grade 3

In Grade 3, instructional time focuses on four critical areas: developing understanding of multiplication and division and strategies for multiplication and division within 100; developing understanding of fractions, especially unit fractions (fractions with numerator 1); developing understanding of the structure of rectangular arrays and of area; and describing and analyzing two-dimensional shapes ...

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#### Grade 4

In Grade 4, instructional time focuses on three critical areas: developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particularangle measures, and symmetry ...

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#### Grade 5

In Grade 5, instructional time should focus on three critical areas: (1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions) (2) extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; (3) developing understanding of volume ...

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#### Grade 6

In Grade 6, instructional time focuses on four critical areas: connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; writing, interpreting, and using expressions and equations; and developing understanding of statistical thinking ...

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#### Grade 7

In Grade 7, instructional time focuses on four critical areas: developing understanding of and applying proportional relationships; developing understanding of operations with rational numbers and working with expressions and linear equations; solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and drawing inferences about populations based on samples ...

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#### Grade 8

In Grade 8, instructional time focuses on three critical areas: formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; grasping the concept of a function and using functions to describe quantitative relationships; analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem ...

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#### High School: Algebra 2

Polynomial, Rational, and Radical Relationships Perform arithmetic operations with complex numbers. Use complex numbers in polynomial identities and equations. Interpret the structure of expressions. Write expressions in equivalent forms to solve
problems. Perform arithmetic operations on polynomials. Understand the relationship between zeros and factors of polynomials. Use polynomial identities to solve problems. Rewrite rational expressions. Understand solving equations as a process of reasoning and explain the reasoning. Represent and solve equations and inequalities graphically. Analyze functions using different representations. Trigonometric Functions Extend the domain of trigonometric functions using the unit circle. Model periodic phenomena with trigonometric function. Prove and apply ...

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#### High School: Geometry

Congruence, Proof, and Constructions Experiment with transformations in the plane. Understand congruence in terms of rigid motions. Prove geometric theorems. Make geometric constructions. Similarity, Proof, and Trigonometry Understand similarity in terms of similarity transformations. Prove theorems involving similarity. Define trigonometric ratios and solve problems involving right triangles. Apply geometric concepts in modeling situations. Apply trigonometry to general triangles. Extending to Three Dimensions Explain volume formulas and use them to solve problems. Visualize the relation between two-dimensional and three-dimensional objects. Apply geometric concepts in modeling situations. Connecting Algebra and Geometry through Coordinates Use coordinates to prove simple geometric theorems algebraically. Translate between ...

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#### High School: Statistics & Probability

Statistics & Probability Overview Interpreting Categorical and Quantitative Data Summarize, represent, and interpret data on a single count or measurement variable Summarize, represent, and interpret data on two categorical and quantitative variables Interpret linear models Making Inferences and Justifying Conclusions Understand and evaluate random processes underlying statistical experiments Make inferences and justify conclusions from sample surveys, experiments and observational studies Conditional Probability and the Rules of Probability Understand independence and conditional probability and use them to interpret data Use the rules of probability to compute probabilities of compound events in a uniform probability model Using Probability to Make Decisions Calculate ...

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