NUMBER AND OPERATION



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|NUMBER & OPERATION |

|Whole Number: Counting & Representation |

|Grades K-3 |

|K |1 |2 |3 |

|Understand the relationship between quantities and whole numbers up|Count, compare and represent whole numbers up to 120, with an |Compare and represent whole numbers up to 1000 with an emphasis on |Compare and represent whole numbers up to 100,000 with an emphasis |

|to 31. |emphasis on groups of tens and ones. |place value and equality. |on place value and equality. |

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|NUMBER & OPERATION |

|Whole Number: Operations |

|Grades K-5 |

|K |1 |2 |3 |4 |5 |

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|NUMBER & OPERATION |

|Fractions & Decimals: Representations and Relationships |

|Grades 3-7 |

|3 |4 |5 |6 |7 |

|Understand meanings and uses of fractions in |Represent and compare fractions and decimals in real-world and |Read, write, represent and compare fractions and|Read, write, represent and compare positive rational |Read, write, represent and compare positive and |

|real-world and mathematical situations. |mathematical situations; use place value to understand how |decimals; recognize and write equivalent |numbers expressed as fractions, decimals, percents and|negative rational numbers, expressed as integers, |

| |decimals represent quantities. |fractions; convert between fractions and |ratios; write positive integers as products of |fractions and decimals. |

| | |decimals; use fractions and decimals in |factors; use these representations in real-world and | |

| | |real-world and mathematical situations. |mathematical situations. | |

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|NUMBER & OPERATION |

|Fractions & Decimals: Operations |

|Grades 5-7 |

|5 |6 |7 |

|Add and subtract fractions, mixed numbers and decimals to solve real-world and mathematical |Multiply and divide decimals, fractions and mixed numbers; solve real-world and mathematical|Calculate with positive and negative rational numbers, and rational numbers with whole |

|problems. |problems using arithmetic with positive rational numbers. |number exponents, to solve real-world and mathematical problems. |

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|ALGEBRA |

|Algebra Concepts: Ratios to Proportions to Functions |

|Grades 6-11 |

|6 |7 |8 |9-11 |

|Understand the concept of ratio and its relationship to |Understand the concept of proportionality in real-world and |Understand the concept of function in real-world and mathematical situations,|Understand the concept of function, and identify important features of |

|fractions and to the multiplication and division of whole |mathematical situations, and distinguish between proportional|and distinguish between linear and nonlinear functions. |functions and other relations using symbolic and graphical methods where |

|numbers. Use ratios to solve real-world and mathematical |and other relationships. | |appropriate. |

|problems. | | | |

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|ALGEBRA |

|Algebra: Relationships and Functions |

|Grades K-11 |

|K |1 |2 |3 |4 |5 |

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|ALGEBRA |

|Algebra: Relationships and Functions |

|Grades K-11 |

|6 |7 |8 |9-11 |

|Recognize and represent relationships between |Recognize proportional relationships in real-world |Recognize linear functions in real-world and mathematical situations; represent |Recognize linear, quadratic, exponential and other common functions in real-world and|

|varying quantities; translate from one |and mathematical situations; represent these and |linear functions and other functions with tables, verbal descriptions, symbols and |mathematical situations; represent these functions with tables, verbal descriptions, |

|representation to another; use patterns, tables, |other relationships with tables, verbal |graphs; solve problems involving these functions and explain results in the original |symbols and graphs; solve problems involving these functions, and explain results in |

|graphs and rules to solve real-world and |descriptions, symbols and graphs; solve problems |context. |the original context. |

|mathematical problems. |involving proportional relationships and explain | | |

| |results in the original context. | | |

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|ALGEBRA |

|Algebra: Expressions |

|Grades 5-11 |

|5 |6 |7 |8 |9-11 |

|Use properties of arithmetic to generate |Use properties of arithmetic to generate |Apply understanding of order of operations and |Generate equivalent numerical and algebraic |Generate equivalent algebraic expressions involving polynomials and radicals; |

|equivalent numerical expressions and evaluate |equivalent numerical expressions and evaluate |algebraic properties to generate equivalent |expressions and use algebraic properties to |use algebraic properties to evaluate expressions. |

|expressions involving whole numbers. |expressions involving positive rational numbers. |numerical and algebraic expressions containing |evaluate expressions. | |

| | |positive and negative rational numbers and | | |

| | |grouping symbols; evaluate such expressions. | | |

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|ALGEBRA |

|Algebra: Equations and Inequalities |

|Grades 1-11 |

|1 |2 |3 |4 |5 |

|Use number sentences involving addition and subtraction|Use number sentences involving addition, subtraction |Use number sentences involving multiplication and |Use number sentences involving multiplication, division|Understand and interpret equations and inequalities |

|basic facts to represent and solve real-world and |and unknowns to represent and solve real-world and |division basic facts and unknowns to represent and |and unknowns to represent and solve real-world and |involving variables and whole numbers, and use them to |

|mathematical problems; create real-world situations |mathematical problems; create real-world situations |solve real-world and mathematical problems; create |mathematical problems; create real-world situations |represent and solve real-world and mathematical |

|corresponding to number sentences. |corresponding to number sentences. |real-world situations corresponding to number |corresponding to number sentences. |problems. |

| | |sentences. | | |

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|ALGEBRA |

|Algebra: Equations and Inequalities |

|Grades 1-11 |

|Grade 6 |Grade 7 |Grade 8 |Grades 9-11 |

|Understand and interpret equations and |Represent real-world and mathematical situations|Represent real-world and mathematical situations using equations and inequalities |Represent real-world and mathematical situations using equations and inequalities involving |

|inequalities involving variables and positive |using equations with variables. Solve equations |involving linear expressions. Solve equations and inequalities symbolically and |linear, quadratic, exponential and nth root functions. Solve equations and inequalities |

|rational numbers. Use equations and inequalities|symbolically, using the properties of equality. |graphically. Interpret solutions in the original context. |symbolically and graphically. Interpret solutions in the original context. |

|to represent real-world and mathematical |Also solve equations graphically and | | |

|problems; use the idea of maintaining equality |numerically. Interpret solutions in the original| | |

|to solve equations. Interpret solutions in the |context. | | |

|original context. | | | |

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|GEOMETRY & MEASUREMENT |

|Geometry: Shapes |

|Grades K-5 |

|K |1 |2 |3 |4 |5 |

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|GEOMETRY & MEASUREMENT |

|Geometry: Measurement |

|Grades K-11 |

|K |1 |2 |3 |4 |5 |

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| | | |Use time, money and temperature to solve | | |

| | | |real-world and mathematical problems. | | |

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|GEOMETRY & MEASUREMENT |

|Geometry: Measurement |

|Grades K-11 |

|Grade 6 |Grade 7 |Grade 8 |Grades 9-11 |

|Calculate perimeter, area, surface area and volume of two- and |Use reasoning with proportions and ratios to determine measurements, |Solve problems involving right triangles using the Pythagorean |Calculate measurements of plane and solid geometric figures; know |

|three-dimensional figures to solve real-world and mathematical |justify formulas and solve real-world and mathematical problems |Theorem and its converse. |that physical measurements depend on the choice of a unit and that |

|problems. |involving circles and related geometric figures. | |they are approximations. |

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|GEOMETRY & MEASUREMENT |

|Algebra in Geometry |

|Grades 6-11 |

|Grade 6 |Grade 7 |Grade 8 |Grades 9-11 |

|Choose appropriate units of measurement and use |Analyze the effect of change of scale, translations |Solve problems involving parallel and perpendicular |Solve real-world and mathematical geometric problems using algebraic methods. |

|ratios to convert within measurement systems to |and reflections on the attributes of two-dimensional|lines on a coordinate system. | |

|solve real-world and mathematical problems. |figures. | | |

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|GEOMETRY & MEASUREMENT |

|Euclidean Geometry and Reasoning |

|Grades 4-11 |

|Grade 4 |Grade 6 |Grade 7 |Grade 8 |Grades 9-11 |

|Use translations, reflections and|Understand and use |Analyze the effect of change of scale, |Solve problems involving right |Construct logical arguments, based on axioms, definitions and theorems, to prove theorems and other results in geometry. |

|rotations to establish congruency|relationships between angles in|translations and reflections on the attributes of |triangles using the Pythagorean | |

|and understand symmetries. |geometric figures |two-dimensional figures. |Theorem and its converse. | |

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| | | | |Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results |

| | | | |in geometry. |

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|DATA ANALYSIS |

|Grades 3-11 |

|3 |4 |5 |7 |8 |9-11 |

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| | | |Display and interpret data in a variety| |Explain the uses of data and statistical thinking to draw inferences, make|

| | | |of ways, including circle graphs and | |predictions and justify conclusions. |

| | | |histograms. | | |

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|PROBABILITY |

|Grades 6-11 |

|Grade 6 |Grade 7 |Grades 9-11 |

|Use probabilities to solve real-world and mathematical problems; represent probabilities |Calculate probabilities and reason about probabilities using proportions to solve real-world|Calculate probabilities and apply probability concepts to solve real-world and mathematical |

|using fractions, decimals and percents. |and mathematical problems. |problems. |

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