r the COR d e s 3 A lg e b r a New York Common Core Pathways
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1 BUI LT fo COM r the MON COR E Gra d e s 3 A lg e b r a New York Common Core Pathways I
2 Grade 3 Number and Operations - Fractions Measurement and Data Geometry Place Value with Whole Numbers Place Value and Rounding Addition and Subtraction Concepts Estimate Sums and Differences Regrouping Concepts Add and Subtract within 1,000 Concept of Multiplication Properties of Addition and Multiplication Concept of Division Relationship Between Multiplication and Division Solve Multiplication and Division Equations Multiplication and Division Word Problems Multiply by Multiples of Ten Solve Two-Step Word Problems Understand Fractions I Unit Fractions on the Number Line Fractions on the Number Line Equivalent Fractions I Whole Numbers as Fractions Compare Fractions I Concept of Area Area of Rectangles Perimeter Classify Quadrilaterals I Describe Patterns
3 Grade 4 Number and Operations - Fractions Measurement and Data Place Value with Whole Numbers Place Value and Rounding Understand and Use Place Value Round Whole Numbers Regrouping Concepts Add and Subtract Whole Numbers Properties of Multiplication and Division Multiply Whole Numbers Divide Whole Numbers Interpret Remainders Relate Factors and Multiples I Relate Factors and Multiples II Equivalent Fractions II Compare Fractions II Decompose Fractions and Mixed Numbers Understand Fractions II Add and Subtract Fractions with Like Denominators Add and Subtract Mixed Numbers with Like Denominators Word Problems with Fractions and Mixed Numbers Multiply Unit Fractions by Whole Numbers Multiply Fractions by Whole Numbers Add Fractions with Denominators of 10 or 100 Compare Decimal Fractions Decimal Notation Decimals to Hundredths Compare Decimals Fraction and Decimal Equivalents Area and Perimeter of Rectangles Angles
4 Grade 4 Geometry Classify Triangles Classify Quadrilaterals II Describe Patterns
5 Grade 5 Number and Operations - Fractions Geometry Measurement and Data Place Value Write and Interpret Simple Expressions Multiply and Divide Whole Numbers Operations with Whole Numbers Relate Factors and Multiples II Equivalent Fractions III Understand Fractions III Compare Rational Numbers Add Fractions Subtract Fractions Multiply Fractions Operations with Fractions I Add and Subtract Fractions Multiply and Divide Fractions I Multiply and Divide Fractions II Decimals to Thousandths Fraction and Decimal Equivalents Round Decimals Add and Subtract Decimals Powers of Ten Multiply and Divide Decimals Operations with Decimals Evaluate Simple Expressions Classify Quadrilaterals II Introduction to the Coordinate Plane Volume of Rectangular Prisms Line Plots Arithmetic Sequences: Closed Form
6 Grade 6 The Number System Number and Operations - Fractions Ratio and Proportion The Number System Geometry Multiply and Divide Whole Numbers Operations with Whole Numbers Add and Subtract Decimals Multiply and Divide Decimals Operations with Decimals Greatest Common Factor Least Common Multiple Compare Rational Numbers Operations with Fractions II Ratios Find Unit Rates Convert of Measure Distance, Rate, and Time Percent Concepts Calculations with Percent Integer Concepts Absolute Value Area of Parallelograms Area of Triangles Area of Trapezoids and Composite Figures Surface Area and Volume of Rectangular Prisms Surface Area of Pyramids Rational Numbers in the Coordinate Plane Integers in the Coordinate Plane Distance on the Coordinate Plane Exponents I Evaluate Simple Expressions Identify One-Step Equations Evaluate Expressions: Two Steps Evaluate Expressions: Distributive Property
7 Grade 6 Statistics and Probability Creating Equations Measures of Center: Median Measures of Center: Mean Measures of Spread: Range Circle Graphs Bar Graphs and Histograms Stem-and-Leaf Plots Quartiles Box Plots Language of Algebra Combine Like Terms Solve Word Problems with Algebra Interpret Graphs of Real-World Situations Sketch Graphs of Real-World Situations Graphs of Real-World Functions Concept of Inequalities Geometric Sequences: Closed Form
8 Grade 7 Ratio and Proportion The Number System Ratio and Proportion Geometry Evaluate Expressions: Two Steps Solve Two-Step Equations Evaluate Expressions: Distributive Property Solve Equations: Distributive Property Interpret Unit Rates on Graphs Proportion Concepts Use Proportions to Solve Problems Similar Figures Fraction, Decimal, and Percent Equivalents Percent and Percent Change Add and Subtract Rational Numbers Multiply and Divide Rational Numbers Operations with Rational Numbers Solve: Simple Interest Literal Formulas Area of Parallelograms Area of Triangles Area of Trapezoids and Composite Figures Circumference Area of Circles Area of Composite Figures Surface Area and Volume of Rectangular Prisms Surface Area of Cylinders Surface Area of Pyramids Surface Area of Cones Surface Area of Spheres Surface Area of Composite Solids Angle Pairs
9 Grade 7 Geometry (continued) Statistics and Probability Seeing Structure in Expressions Creating Equations Reasoning with Equations and Inequalities Angles in a Polygon Simple Probability Compound Probability Making Predictions Language of Algebra Combine Like Terms Simplify Algebraic Expressions Solve Word Problems with Algebra Interpret Graphs of Real-World Situations Sketch Graphs of Real-World Situations Common Factors in Polynomials Factor Expressions Concept of Inequalities Inequalities
10 Grade 8 Seeing Structure in Expressions Geometry Functions Language of Algebra Evaluate Expressions: Two Steps Solve Two-Step Equations Solve Equations: Distributive Property Simplify Algebraic Expressions Factor Expressions Solve Equations with the Variable on Both Sides Exponents II Square and Cube Roots Scientific Notation Angles in a Polygon Volume of Cylinders Volume of Pyramids and Cones Volume of Spheres Volume of Composite Solids Parallel Lines and Transversals Pythagorean Theorem: Hypotenuse Pythagorean Theorem: Legs Pythagorean Theorem: Mixed Problems Pythagorean Theorem: Distance Formula Translations Reflections Rotations Composition of Transformations Interpret Graphs of Real-World Situations Sketch Graphs of Real-World Situations Graphs of Real-World Functions Slope and Rate of Change Slope Slope-Intercept Form
11 Grade 8 Building Functions Functions Reasoning with Equations and Inequalities Creating Equations Reasoning with Equations and Inequalities Equations in Slope Form Direct Variation Point-Slope Form Concept of Inequalitites Inequalities Solve Word Problems with Algebra Solve a System of Linear Equations Graphically Solve Systems of Equations Solve a System of Linear Equations Algebraically Arithmetic Sequences: Recursive Form Geometric Sequences: Recursive Form
12 Algebra Readiness Seeing Structure in Expressions Geometry Functions Language of Algebra Evaluate Expressions: Two Steps Solve Two-Step Equations Solve Equations: Distributive Property Simplify Algebraic Expressions Factor Expressions Solve Equations with the Variable on Both Sides Exponents II Square and Cube Roots Scientific Notation Angles in a Polygon Volume of Cylinders Volume of Pyramids and Cones Volume of Spheres Volume of Composite Solids Parallel Lines and Transversals Pythagorean Theorem: Hypotenuse Pythagorean Theorem: Legs Pythagorean Theorem: Mixed Problems Pythagorean Theorem: Distance Formula Translations Reflections Rotations Composition of Transformations Interpret Graphs of Real-World Situations Sketch Graphs of Real-World Situations Graphs of Real-World Functions Slope and Rate of Change Slope Slope-Intercept Form
13 Algebra Readiness Building Functions Functions Reasoning with Equations and Inequalities Creating Equations Reasoning with Equations and Inequalities Equations in Slope Form Direct Variation Point-Slope Form Concept of Inequalitites Inequalities Solve Word Problems with Algebra Solve a System of Linear Equations Graphically Solve Systems of Equations Solve a System of Linear Equations Algebraically Arithmetic Sequences: Recursive Form Geometric Sequences: Recursive Form
14 Algebra I Seeing Structure in Expressions Creating Equations Reasoning with Equations and Inequalities Creating Equations Building Functions Reasoning with Equations and Inequalities Arithmetic with Polynomials and Rational Expressions Arithmetic with Polynomials and Rational Expressions Seeing Structure in Expressions Linear, Quadratic, and Exponential Models Language of Algebra Interpret Graphs of Real-World Situations Sketch Graphs of Real-World Situations Graphs of Real-World Functions Evaluate Expressions with Real Numbers Simplify Algebraic Expressions Write Equations in One Variable Solve Equations: One Variable Solve One-Step Equations Solve Multistep Equations Write Equations: Two or More Variables Solve Word Problems with Algebra Solve Literal Equations Graph Linear Equations Slope and Rate of Change Direct Variation Equations in Slope Form Concept of Inequalities Inequalities Graph Inequalities Solve Systems of Equations Factor Expressions Add and Subtract Polynomials Simplify Monomials Multiply and Divide Monomials Multiply Polynomials Factor Polynomials Common Factors in Polynomials Graphs of Quadratic Functions
15 Algebra I Reasoning with Equations and Inequalities Linear, Quadratic, and Exponential Models Use the Quadratic Formula Problem Solving with Quadratic Functions Graphs of Exponential Functions Radical Functions and Their Graphs Rational Functions and Their Graphs Function Notation
16 Geometry Foundations Ratio and Proportion Geometry Ratios Find Unit Rates Convert of Measure Interpret Unit Rates on Graphs Use Proportions to Solve Problems Similar Figures Square and Cube Roots Circumference Area of Parallelograms Area of Triangles Area of Trapezoids and Composite Figures Area of Circles Area of Composite Figures Rational Numbers in the Coordinate Plane Distance on the Coordinate Plane Classify Triangles Classify Quadrilaterals II Angles in a Polygon Parallel Lines and Transversals Translations Reflections Rotations Composition of Transformations Pythagorean Theorem: Mixed Problems Pythagorean Theorem: Distance Formula Surface Area and Volume of Rectangular Prisms Surface Area of Cylinders Surface Area of Pyramids
17 Geometry Foundations Geometry (continued) Surface Area of Cones Surface Area of Spheres Volume of Cylinders Volume of Pyramids and Cones Volume of Spheres Volume of Composite Solids
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