Read more about the purpose of the MAP Classroom Challenges

Steps to Solving Equations

Mathematical goals

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

  • Form and solve linear equations involving factorizing and using the distributive law.

In particular, this unit aims to help you identify and assist students who have difficulties in:  

  • Using variables to represent quantities in a real-world or mathematical problem.
  • Solving word problems leading to equations of the form px + q = r and p(x + q) = r.


The lesson unit is structured in the following way:

  • Before the lesson, students attempt the assessment task individually. You then review students’ responses and formulate questions that will help them improve their work.
  • During the lesson, students work collaboratively in pairs or threes, matching equations to stories and then ordering the steps used to solve these equations. Throughout their work, students explain their reasoning to their peers.
  • Finally, students again work individually to review their work and attempt a second task, similar to the initial assessment task.

Materials required

  • Each student will need copies of the assessment tasks Express Yourself and Express Yourself (revisited), and Card Set: Stories (not cut up), a mini-whiteboard, a pen, and an eraser.
  • For each small group of students provide cut up copies of Card Set: Stories (cut up), Card Set: Equations, and Card Set: Steps to Solving, a large sheet of paper for making a poster, a marker, and a glue stick.
  • There are also some projector resources to help with whole-class discussion.

Time needed

15 minutes before the lesson for the assessment task, a 1-hour lesson, and 15 minutes in a follow-up lesson (or for homework). All timings are approximate, depending on the needs of your students.

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?