# Classifying Solutions to Systems of Equations

## Mathematical goals

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

- Classify solutions to a pair of linear equations by considering their graphical representations.
- Use substitution to complete a table of values for a linear equation.
- Identify a linear equation from a given table of values.
- Graph and solve linear equations.

## Introduction

- Before the lesson, students attempt the assessment task individually. You then review students’ solutions and formulate questions that will help them improve their work.
- During the lesson, students work collaboratively in pairs or threes, plotting graphs, completing tables of values and deducing equations. Then, based on the number of common solutions, students link these representations.
- In a follow-up lesson, students receive your comments on the assessment task and use these to attempt the similar task, approaching it with insights gained from the lesson.

## Materials required

- Each student will need a copy of the assessment tasks
*Working with Linear Equations*and*Working with Linear Equations (revisited),*a mini-whiteboard, eraser, and a pen. - Each group of students will need cut up
*Card Set A*:*Equations, Tables & Graphs*,*Card Set B*:*Arrows*, one copy of*Graph Transparency*, copied onto a transparency, a transparency pen, - Provide rulers if requested. There are some projector resources to support whole-class discussion.

## Time needed

15 minutes before the lesson for the assessment task, a 80-minute lesson (or split into two shorter lessons), and 15 minutes in a follow-up lesson (or for homework). All timings are approximate.

## 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.F: Define, evaluate, and compare functions.
- 8.F: Use functions to model relationships between quantities.