• ## Module 3: Reasoning Algebraically

In this module, students build on their experiences with algebraic expressions and one-step equations in grade 6. The expressions, equations, and inequalities they encounter will involve a wide range of rational numbers and require two steps rather than one. Students will write equations and inequalities for problem situations, interpret the meanings of quantities in the problems, create tables of values, graph problem situations, and make connections across the representations.

• This topic builds on students' prior work with numeric and algebraic expressions with positive rational coefficients to explore algebraic expressions with any rational coefficients.
• MATHia Workspaces (6)
• Factoring Linear Expressions
• Rewriting Simple Algebraic Expressions Involving Integer Coefficients
• Rewriting Algebraic Expressions Involving Integer Coefficients with Four Operations
• Rewriting Algebraic Expressions Involving Integer Coefficients with Parentheses and Exponents
• Rewriting Complex Algebraic Expressions Involving Integer Coefficients
• Rewriting Algebraic Expressions Involving Integer Coefficients

Topic 2: Two-Step Equations & Inequalities

• This topic continues to develop students’ understanding of a solution to an equation or the solution set of an inequality. Throughout a variety of reasoning exercises, the meaning of a solution to an equation is reinforced: students check their solutions with substitution and write equations from solutions.
• MATHia Workspaces (13)
• Using Picture Algebra with Equations
• Identifying Attributes of Linear Relationships
• Analyzing Models of Two-Step Linear Relationships
• Modeling Two-Step Expressions
• Checking Solutions to Linear Equations
• Solving with Multiplication (No Type In)
• Solving with Multiplication (Type In)
• Solving with Division (No Type In)
• Solving with Division (Type In)
• Solving Two-Step Equations
• Graphing Inequalities with Rational Numbers
• Solving One-Step Linear Inequalities
• Solving Two-Step Linear Inequalities

Topic 3: Multiple Representations of Equations

• This topic broadens students’ perspective on solving and interpreting linear equations and inequalities through the use of tables and graphs. Students write, analyze, and solve two-step equations using positive and negative numbers on four-quadrant graphs. In the process of problem solving, students identify independent and dependent variables and interpret negative solutions to problem situations.
• MATHia Workspaces (6)
• Determining the Value of an Independent Variable
• Using Linear Equations and Inequalities
• Solving Problems with Integers
• Solving Problems with Decimals and Fractions
• Graphs of Equations
• Using Graphs to Solve Equations