# Comparing Lines and Linear Equations

## Mathematical goals

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

- Interpret speed as the slope of a linear graph.
- Translate between the equation of a line and its graphical representation.

## Introduction

- Before the lesson, students work individually on an assessment task that is designed to reveal their current understanding and difficulties. You then review their work and create questions for students to answer in order to improve their solutions.
- During the lesson, students work in small groups on a collaborative task, matching graphs, equations, and pictures. At the end of the lesson there is a whole-class discussion.
- In a follow-up lesson, students review their initial solutions and then use what they have learned to either revise the same introductory assessment task or complete a different task.

## Materials required

- Each student will need copies of the assessment tasks,
*The Race*and*The Walk-a-thon.*It will help students if the two pages of each task are printed on separate pages. - Each small group of students will need a mini-whiteboard, pen, and eraser, the cut up
*Card Set:**Graphs 1*,*Graphs 2*,*Equations,**Flowing Liquid,*a large sheet of paper for making a poster, and a glue stick. - If possible, a real model of two identical containers connected at the neck to demonstrate the liquid flow. For example, two identical soda bottles, connected at the neck with tape.
- There is a projector resource to support whole-class discussions.

## Time needed

Approximately 20 minutes before the lesson, an 80-minute lesson (or two shorter lessons), and 20 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:*

- 8.EE: Understand the connections between proportional relationships, lines, and linear equations.
- 8.F: Define, evaluate, and compare functions.
- 8.F: Use functions to model relationships between quantities.