# Matching Situations, Graphs and Linear Equations

## Mathematical goals

This lesson unit is intended to help you assess how well students use algebra to:

- Explore relationships between variables in everyday situations.
- Find unknown values from known values.
- Find relationships between pairs of unknowns and express these as tables and graphs.
- Find general relationships between several variables and express these in different ways by rearranging formulas.

## Introduction

This activity links several aspects of algebra.

- Before the lesson, students work individually on the assessment task
*The Guitar Class*. You then review their work and create questions for students to answer, to help them improve their solutions. - During the lesson, students translate between words, algebraic formulas, tables, and graphs in an interactive whole-class discussion. The intention is that you focus students on making sense of the context using algebra, rather than just the routine use of techniques and skills. Students then work in pairs to graph the relationship between two of the variables. In a final whole-class discussion, students identify general formulas showing the relationships between all the variables.
- In a follow-up lesson, students receive your comments on the assessment task and use these to attempt a similar task, approaching it with insights gained from the lesson.

## Materials required

- Each student will need two copies of the assessment task
*The Guitar Class*, either the*Making and Selling Candles*lesson task sheet*,*or the*Rescue Helicopter*lesson task sheet, depending on the outcome of the assessment task, a mini-whiteboard, pen, and eraser. - Each pair of students will need a sheet of graph paper.
- There is a projector resource to support whole-class discussion.

## Time needed

15 minutes before the lesson, a one-hour lesson, and 10 minutes in a follow-up lesson. All timings are approximate. 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

*content standards:*