Representing Inequalities Graphically

Mathematical goals

This lesson unit is intended to help you assess how well students are able to use linear inequalities to create a set of solutions. In particular, the lesson will help you identify and assist students who have difficulties in:

  • Representing a constraint by shading the correct side of the inequality line.
  • Understanding how combining inequalities affects a solution space.


This lesson unit is structured in the following way:

  • Before the lesson, students work individually on an assessment task that is designed to reveal their current levels of understanding and difficulties. You then review their work and create questions for students to answer in order to improve their solutions.
  • After a whole-class introduction students work collaboratively, in pairs, on a game. One student decides on the position of a ‘target point’ on a coordinate grid and gives clues in the form of algebraic inequalities (e.g. 3y + 2x ≤ 12). The other student uses these clues to find the location of the target point. There is a strategic element to the game: what are the best clues to give, so that the target may be found quickly?
  • In a whole-class discussion students review the main math concepts of the lesson.
  • In a follow-up lesson, students try to improve their original responses to the assessment task.

Materials required

  • Each student will need two copies of the assessment task Combining Inequalities, the game sheet Give Us a Clue!, either a mini-whiteboard (preferably with a square grid) or a sheet of squared paper, a pen, and an eraser.
  • There is a projector resource to support whole-class discussions.

Time needed

15 minutes before the lesson, one 70-minute lesson (or two shorter lessons), and 15 minutes in a follow-up lesson. Timings given are approximate.

Lesson Type

Mathematical Practices

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

Mathematical Content Standards

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