TES Maths: Inspect the spec - inequalities

Support pupils as they learn to solve linear and quadratic inequalities with these tips and resources, tailored to the new GCSE specification

Craig Barton

TES Maths, Inspect The Spec, GCSE, New Specification, Linear, Quadratic, Inequalities, Set Notation, Secondary, KS4, Year 10, Year 11

Get to grips with the changes to the teaching of inequalities as part of the new GCSE specification

Everyone is talking about functions and frequency trees, but what else has changed with the advent of the new specification? And what resources are available to help? Throughout this series, TES Maths aims to find out.

What does the specification say?

The expectation is that:

  • All students will develop confidence and competence with the content identified by standard type
  • All students will be assessed on the content identified by the standard and the underlined type; more highly attaining students will develop confidence and competence with all of this content
  • Only the more highly attaining students will be assessed on the content identified by bold type. The highest attaining students will develop confidence and competence with the bold content.

A22: Solve linear inequalities in one or two variables and quadratic inequalities in one variable; represent the solution set on a number line, using set notation and on a graph

What's the same?

All of the requirements from the previous specification still exist. So, both foundation and higher students will need to understand inequality notation in terms of the relative sizes of positive and negative numbers, and represent these inequalities on number lines with the classic hollow or filled-in circles. They will also need to be able to solve linear inequalities and represent the solution on a number line in a similar way. Only higher tier students need to be able to represent several linear inequalities on a graph and shade the region that satisfies them all.

What has changed?

There have been two major changes, both of which only affect higher tier students.

The first is a classic C1 A-level topic: quadratic inequalities. GCSE students sitting the higher tier paper will be expected to solve quadratic inequalities and represent their solution on a graph. Now, the good news for all A-level teachers out there is that the content appears to be exactly the same as in C1, and the advice I will be giving to my GCSE students will be the same as I have always given my sixth formers – “draw the flipping graph!”

The second thing to have changed is the use of set notation. This is completely new to me, but it is just a different way of representing a set of solutions. So, for example, if the solution to your quadratic inequality is  x < -3 or x > 5, students would be expected to write it as {x: x < -3} ∪ {x: x > 5}.

How can TES Maths can help?

As ever, the wonderfully talented authors of the TES Maths community have stepped up to the mark to lend a hand. Here is a selection of my favourite resources to help support the teaching of this topic:

  1. Inequalities lessons
    Once again, TES Author, Pixi_17, has this covered with two differentiated lessons, packed with engaging activities on both linear and quadratic inequalities.
  2. Introduction to inequalities
    Designed for the old specification, this well-structured presentation still has plenty to offer in terms of providing a useful introduction.
  3. Set notation practice
    Get pupils using number lines and set notation interchangeably with this straightforward worksheet, including answers.
  4. Quadratic inequalities match-up
    In this unique activity, which can be simply differentiated, learners must match up quadratic inequalities to their graphical representations.
  5. Spot the mistake
    Use this well-presented exercise to highlight common misconceptions pupils have about solving quadratic inequalities.
  6. Quadratic inequalities questions
    Scaffold students' understanding of solving and drawing graphs for quadratic inequalities by completing this simple worksheet.
  7. C1 worksheet pack
    Originally created for C1 pupils, this comprehensive pack is ideal for revising all aspects of inequalities, including quadratics.

Craig Barton, TES Maths adviser

Craig is a secondary maths teacher in the North of England.

Find more resources to support the changes to the GCSE maths specification by taking a look at the rest of the series.