Students learn how to represent inequalities on a number line and solve an inequation using the balance method.

This unit takes place in Term 6 of Year 10 and follows on from solving equations.

Inequalities Lessons
Revision Lessons

Prerequisite Knowledge
  • order positive and negative integers
  • apply the four operations, including formal written methods, to integers, both positive and negative;
  • solve linear equations in one unknown algebraically (including those with the unknown on both sides of the equation)

Success Criteria
  • solve linear inequalities in one variable;
  • represent the solution set on a number line;
  • understand and use the concepts and vocabulary of expressions, equations, formulae, identities and inequalities

Key Concepts
  • Knowledge of <,>, ≤ & ≥ notation is critical to this topic. Numbers which are less or greater than but not equal to are represented on a number line with a hollow circle. Full circles are used when an inequality can be equal to a number.
  • Inequations have a set of solutions whereas equations have distinct solutions.
  • Inequations can be solved using the balance method.
  • When dividing or multiplying both sides of an inequality by a negative number the sign is reversed.

Common Misconceptions
  • Students are often confused with the direction of the inequality sign. Use the number line to show < represents less than and > means greater than.
  • Inequalities such as 5 < x ≤ 10 represents x as any value greater than 5 and less than or equal to 10. Encourage students to read such inequalities in two directions i.e., 5 < x and x ≤ 10.

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes:

<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Mr Mathematics Blog

Solving Inequalities using a Number Line

Students should be able to represent the solutions to an inequality on a number line, using set notation or as a list of integer values.  Here’s how I teach using the balance method for solving inequalities using a number line. Matching inequalities, Number sets and Number Lines At the start of the lesson students recap […]

Practical Tips for Using Mini-Whiteboards in a Mathematics Lesson

In this blog I will share some practical tips for using mini-whiteboards in a mathematics lesson.  I use mini-whiteboards nearly every lesson because they help the students show me the progress they are making.  When I understand what the misconceptions are I am able to address them in subsequent examples as part of my feedback.  […]

Showing Progress during a Mathematics Lesson

Demonstrating student progression during a mathematics lesson is about understanding the learning objective and breaking that down into explicit success criteria. Using Success Criteria Take, for example, a lesson on calculating the area of compound rectilinear shapes. The intended learning objective was written on the main whiteboard. Success criteria were used to break down the individual […]