Factorising quadratic expressions – Unpick what’s going on

What's included?

PDF lesson plan and worksheet

Key Stage



Years 10-11


Students sometimes carry out factorising quadratic expressions by applying poorly-understood procedures that make little mathematical sense to them. This can be especially so when it comes to non-monic quadratics (those where the coefficient of x2 is not 1).

In this lesson, students approach factorising non-monic quadratics by trying to find factorisations which will expand and simplify to produce a quadratic expression of a specified form.

This entails lots of useful practice at expanding pairs of brackets and collecting like terms. It also gives students the opportunity to unpick what is going on. This way they gain insight into how the inverse process of factorising works.

By working backwards in this way to obtain the necessary factors, students build a deeper understanding of factorising quadratic.

Factorising quadratic expressions download

  • Making quadratics KS4 lesson plan PDF
  • Making quadratics task sheet

Colin Foster is a Senior Research Fellow in the School of Education at the University of Nottingham, and writes books for mathematics teachers. Browse more factoring quadratics worksheets and more KS4 maths lesson plans from Colin Foster.

Factorising quadratic expressions
Factorising quadratic expressions – Unpick what’s going on

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