Read more about the purpose of the MAP Classroom Challenges

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.

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

  • Using substitution to complete a table of values for a linear equation.
  • Identifying a linear equation from a given table of values.
  • Graphing and solving linear equations.


The lesson unit is structured in the following way:

  • 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.
  • After a final whole-class discussion, students work individually on a new assessment task.

Materials required

  • Each individual student will need a copy of the assessment task Working with Linear Equations, a copy of the assessment task Working with Linear Equations (revisited), a mini-whiteboard, eraser, and a pen.
  • For each small group of students provide a cut up copy of Card Set A: Equations, Tables & Graphs, two cut up copies of Card Set B: Arrows, one copy of Graph Transparency, copied onto a transparency, a transparency pen, a large sheet of paper for making a poster, some plain paper, and a glue stick.
  • Provide rulers if requested.
  • There are some projector resources to help with whole-class discussion.

Time needed

15 minutes before the lesson for the assessment task, a 75-minute 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

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