# Classifying Equations of Parallel and Perpendicular Lines

## Mathematical goals

This lesson unit is intended to help you assess how well students understand the relationship between the slopes of parallel and perpendicular lines and in particular, to help identify students who find it difficult to:

- Find, from their equations, lines that are parallel and perpendicular.
- Identify and use intercepts.

It also aims to encourage discussion on some common misconceptions about equations of lines.

## Introduction

The lesson unit is structured in the following way:

- Before the lesson, students work individually on a task designed to reveal their current level of understanding and their 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 related task, justifying and explaining their decisions to each other. They then re-group to critique each other’s work. Finally, in a whole-class discussion, students explain and extend their methods and solutions.
- In a follow-up lesson, students work alone to improve their solutions to the assessment task.

## Materials required

- Each student will need two copies of
*Parallel and Perpendicular Lines,*a mini-whiteboard, pen, and eraser. - Each small group of students will need the
*Card Set: Equations*(already cut up into cards)*,*two copies of the*Properties*table*,*and a glue stick. - Graph paper should be kept in reserve and only used when requested.
- There is a projector resource to help introduce activities and support the whole-class discussion.

## Time needed

Approximately 15 minutes before the lesson, a 1-hour lesson, and 15 minutes in a follow-up lesson.

## 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:*

- H.F-IF: Analyze functions using different representations
- H.G-GPE: Use coordinates to prove simple geometric theorems algebraically