# Solving Linear Equations

## Mathematical goals

This lesson unit is intended to help you assess how well students are able to:

- Form and solve linear equations involving factorizing and using the distributive law.

In particular, this unit aims to help you identify and assist students who have difficulties in:

- Using variables to represent quantities in a real-world or mathematical problem.
- Solving word problems leading to equations of the form p
*x*+ q = r and p(*x*+ q) = r.

## Introduction

The lesson unit is structured in the following way:

- Before the lesson, students attempt the assessment task individually. You then review students’ responses and formulate questions that will help them improve their work.
- During the lesson, students work collaboratively in pairs or threes, matching equations to stories and then ordering the steps used to solve these equations. Throughout their work, students explain their reasoning to their peers.
- Finally, students again work individually to review their work and attempt a second task, similar to the initial assessment task.

## Materials required

- Each student will need copies of the assessment tasks
*Express Yourself*and*Express Yourself*(*revisited*) and*Card Set: Stories*(not cut up), a mini-whiteboard, a pen, and an eraser. - For each small group of students provide cut-up copies of
*Card Set: Stories*,*Card Set: Equations*, and*Card Set: Steps to Solving*,

## Time needed

15 minutes before the lesson, a 90-minute lesson (or two 50-minute lessons), and 15 minutes in a follow-up lesson. Exact timings will depend on the needs of your students.

## Lesson Type

## Mathematical Practices

This lesson involves a range of *mathematical practices* from the standards, with emphasis on:

- MP1: Make sense of problems and persevere in solving them
- MP2: Reason abstractly and quantitatively
- MP3: Construct viable arguments and critique the reasoning of others
- MP4: Model with mathematics
- MP6: Attend to precision
- MP7: Look for and make use of structure
- MP8: Look for and express regularity in repeated reasoning

## Mathematical Content Standards

This lesson asks students to select and apply mathematical content from across the grades, including the *content standards:*

- 7.EE: Use properties of operations to generate equivalent expressions.
- 7.EE: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.