First Semester
Unit 1: Making Relevant Connections within The Number System This unit builds upon the understanding of rational numbers developed in 6th grade, transitioning from exploring to ultimately formalizing rules for basic arithmetic operations (addition, subtraction, multiplication, and division) with rational numbers. Using both contextual and numerical problems, students explore arithmetic combinations of negative numbers and positive numbers. Students will explore the results of adding, subtracting, multiplying, and dividing pairs of numbers in context, leading to the generalization of rules. Rational numbers in different forms (integers, percents, fractions, and decimal numbers) should be used in computations and explorations.
Unit 2: Reasoning with Expressions, Equations, and Inequalities Students build on what was learned in previous grades regarding mathematical properties (such as commutative, associative, and distributive properties) and conventions (such as order of operations), use these conventions and properties of operations to rewrite equivalent expressions, and interpret expressions in context. Students extend properties used with whole numbers to rational numbers in multiple formats (fractions and decimals). Students construct and solve equations and inequalities to solve contextual problems, and interpret solutions based on the context.
Unit 3: Exploring Ratios and Proportional Relationships Building on knowledge and understanding of rate and unit concepts, students use graphs, tables, equations, and diagrams to recognize, represent, explain, and solve proportional relationships. Mathematics should be represented in as many ways as possible in this unit by using graphs, tables, pictures, symbols, and words.