# Interpreting Equations

## Mathematical goals

This lesson unit is intended to help students to:

- Connect algebraic equations to real-life situations.
- Uncover and address misconceptions concerning the meaning of variables in equations.

## Introduction

This lesson unit is structured in the following way:

- Before the lesson, students work individually on an assessment task designed to reveal their current understanding. You then review their responses and create questions for students to consider when improving their work.
- In a whole-class discussion, students consider how the meaning of different equations and expressions changes when the definitions of the variables change.
- Students then work in small groups (pairs or threes) on a collaborative discussion task, finding word explanations to go alongside the appropriate expressions and equations. Students are encouraged to challenge one another.
- In a whole-class discussion, students discuss what they have learned.
- Finally, students revisit their initial work on the assessment task and work alone on a task similar to the introductory task.

## Materials required

- Each student will need a copy of the assessment tasks
*Real-life Equations*and*Real-life Equations**(revisited).* - Each small group of students will need some plain paper, cut-up copies of the
*Statements*and*Equations*sheets*,*a large sheet of paper for making a poster, and a glue stick.

## Time needed

15 minutes before the lesson, a 60-minute lesson, and 20 minutes in a follow-up lesson. The timings given are approximate. 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
- 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:*

- 6.EE: Apply and extend previous understandings of arithmetic to algebraic expressions.
- 6.EE: Reason about and solve one-variable equations and inequalities.
- 6.EE: Represent and analyze quantitative relationships between dependent and independent variables.