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, particular angle measures, and symmetry
Multiplication/Division
Algebraic Foundations & Patterns
Decimal Operations & Application
Fraction Sense
Measurement
Algebraic Applications
Algebraic Applications
Geometry Properties
Geometric Formulas
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)
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
developing understanding of volume
Integers & Rational Numbers
Complex Equations & Inequalities
Ratios & Proportions
Geometry
Percents
Statistical Analysis
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.
Expressions & Equations
Linear Functions
Inequalities
Systems of Linear Equations
Systems of Linear Equations
Transformations
Exponents and Scientific Notation
Real Numbers and the Pythagorean Theorem
Angles and Triangles
Volume and Similar Solids
Probability and StatisticsÂ
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.
Solving Linear Equations/Inequalities
Graphing Linear Equations/Inequalities
Writing Linear Equations/Inequalities
Systems of Linear Equations/Inequalities
Piecewise Functions
Exponential Expressions
Exponential Functions
Arithmetic and Geometric Sequences
Polynomials
Quadratics
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
Logical and Deductive Reasoning
Foundational Geometry
Parallel and Perpendicular Lines
Transformations
Triangle Congruence
Concurrency and Constructions
Circles
Right Triangles
Quadrilaterals
Similarity
2D Figures
3D Figures