In this lesson, students learn to solve quadratic equations by factorising. They start with simpler equations such as x² + 9 = 90, rearranging and square-rooting to find both the positive and negative solutions. Students then learn the key idea behind solving by factorising: if two numbers multiply to give 0, at least one of them must be 0. They practise a clear method:

Rearrange the equation so it equals 0.
Factorise it into two brackets.
Set each bracket equal to 0.
Check the answers by substituting them back in.

The lesson finishes with problem-solving questions. Students form their own quadratic equations from shapes (rectangles, squares, triangles, trapeziums and a parallelogram exam question) and from age puzzles. They then decide which solution makes sense, rejecting negative lengths and ages.

Success criteria

Grade 4: I can solve equations like x² + 9 = 90, giving the positive and negative solutions.
Grade 6: I can rearrange a quadratic equation so it equals 0, then factorise and solve it.
Extend: I can form and solve quadratic equations to solve problems.