# Solving Linear Equations in Two Variables

## Mathematical goals

This lesson unit is intended to help you assess how well students are able to formulate and solve problems using algebra and in particular, to identify and help students who have the following difficulties:

- Solving a problem using two linear equations with two variables.
- Interpreting the meaning of algebraic expressions.

## Introduction

This lesson is structured in the following way:

- Before the lesson, students work individually on the
*Notebooks and Pens*task. You then review their work and create questions for students to answer in order to improve their solutions. - During the lesson, students work alone on a new task involving interpreting and solving two equations in two variables. They discuss their solutions in small groups before producing a joint solution. In the same small groups students evaluate some sample solutions to the task.
- In a whole-class discussion, students explain and compare the alternative solution strategies they have seen and used.
- Finally, in a follow-up lesson, students use what they have learned to revise their work on
*Notebooks and Pens*.

## Materials required

- Each individual student will need two copies of
*Notebooks and Pens*and a copy of*School Fair.* - Each small group of students will need a large sheet of poster paper and an enlarged copy of the
*Sample Responses to Discuss.* - Graph paper should be kept in reserve and used only when requested.
- A projector resource is provided to support whole-class discussions.

## Time needed

15 minutes before the lesson, a 75-minute lesson (or two 40 minute lessons), and 15 minutes in a follow-up lesson. Exact timings will depend on the needs of the class.

## 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
- MP5: Use appropriate tools strategically
- 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:*