Read more about the purpose of the MAP Classroom Challenges

Finding Equations of Parallel and Perpendicular Lines

Mathematical goals

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


The lesson unit is structured in the following way:

  • Before the lesson, students work individually on a task designed to reveal their current levels 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 task related to the assessment task. Next, they re-group to critique each other’s work. Throughout this work they justify and explain their decisions to each other.
  • In a whole-class discussion, students explain and extend their methods and solutions.
  • Finally, students again work individually to improve their solutions to the assessment task.

Materials required

  • Each student will need two copies of the assessment task Parallel and Perpendicular Lines, a mini-whiteboard, pen, and eraser.
  • Each small group of students will need a copy of Card Set: Equations (already cut up into cards), two copies of the table Properties, and a glue stick.
  • Graph paper should be kept in reserve, and only used when requested.
  • There is a projector resource Lines and Rectangles for use during the plenary discussion.

Time needed

15 minutes before the lesson, a 1-hour lesson, and 10 minutes in the next lesson (or for homework). Timings are approximate and will depend on the needs of the class. 

Mathematical Practices

This lesson involves a range of mathematical practices from the standards, with emphasis on:

Mathematical Content

This lesson asks students to select and apply mathematical content from across the grades, including the content standards:


Lesson (complete)

Projector Resources

A draft Brief Guide for teachers and administrators (PDF) is now available, and is recommended for anybody using the MAP Classroom Challenges for the first time.

We have assigned lessons to grades based on the Common Core State Standards for Mathematical Content. During this transition period, you should use your judgement as to where they fit in your current course.

The Beta versions of the MAP Lesson Units may be distributed, unmodified, under the Creative Commons Attribution, Non-commercial, No Derivatives License 3.0. All other rights reserved. Please send any enquiries about commercial use or derived works to

Can you help us by sending samples of students' work on the Classroom Challenges?