Read more about the purpose of the MAP Classroom Challenges

Solving Linear Equations in Two Variables

Mathematical goals

This lesson unit is intended to help you assess how well students are able to formulate and solve problems using algebra and, in particular, to identify and help students who have the following difficulties:

  • Solving a problem using two linear equations with two variables.
  • Interpreting the meaning of algebraic expressions.


This lesson is structured in the following way:

  • Before the lesson, students work individually on the assessment task Notebooks and Pens. You then review their work and create questions for students to answer in order to improve their solutions.
  • During the lesson, students work individually on a task that requires them to interpret and solve two equations in two variables. Students then compare and discuss their solutions in small groups.
  • In the same small groups, students evaluate some sample solutions of the same task.
  • In a whole-class discussion, students explain and compare the alternative solution strategies they have seen and used.
  • Finally, students use what they have learned to revise their work on Notebooks and Pens.

Materials required

  • Each individual student will need two copies of the assessment task Notebooks and Pens and a copy of the lesson task Cash Registers.
  • Each small group of students will need a blank sheet of paper and copies of the four sheets Sample Student Work.
  • Graph paper should be kept in reserve and used only when requested.
  • Projector resources are provided to support the whole-class discussion.

Time needed

15 minutes before the lesson, a 1-hour lesson, and 10 minutes in a follow-up lesson (or for homework). Timings given are only approximate. Exact timings 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

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