Factorising Quadratics | I Do, We Do, You Do | Year 10 Maths Foundation | Print Free

Teach pupils to factorise quadratic expressions of the form x² + bx + c with this editable Year 10 Maths Foundation lesson. Pupils choose two integers using their sum and product, manage positive and negative signs, and check their factors by expanding. Later tasks require simplification before factorising and reasoning about missing coefficients.

WHAT IS INCLUDED
• One editable 65-slide PowerPoint with answers.
• Six retrieval questions and six prerequisite questions, each with grouped answers.
• Key vocabulary and the connection between expansion and factorisation.
• Six I Do / We Do examples in three matched pairs, with different questions and worked answers.
• Twenty individual AFL questions, each followed by its answer.
• Thirty-six whole-class practice questions on one slide, with all answers on one slide.
• One differentiated page with 14 Developing, 14 Secure and five Greater Depth questions, plus one Super Challenge.
• All 33 differentiated answers together, followed by a complete challenge explanation.
• Three misconception checks with explained answers.
• An original six-mark exam-style task with suggested marking points.
• Three exit questions, each followed by its answer.

MODELLING AND PRACTICE
The paired models establish how to use both a sum and a product, choose signs when the constant is negative, and collect like terms before factorising. Every worked model checks the result by expanding the brackets.

Three practice columns explore different factor pairs for the same product, opposite-sign constants with sums of 1 or −1, and expressions that need simplifying first. Answers follow the same numbering and column order for checking.

DIFFERENTIATION WITH DEPTH
Developing covers mixed signs and repeated factors. Secure requires pupils to collect like terms, combine constants or expand an existing bracket before factorising the resulting quadratic. Greater Depth asks pupils to recover a missing coefficient from a known factor, identify squared brackets, find a rectangle’s length and perimeter from its area, justify why integer factors are impossible and connect two related factorisations.

ONE SUPER CHALLENGE
Two quadratic expressions have the same constant term but consecutive coefficients of x. Pupils find every value that allows both expressions to factorise using positive whole-number bracket constants. They give both factorisations and explain why no other value works.

PRINT FREE AND PRACTICAL
Project the slides while pupils work in exercise books or on mini whiteboards. No printed worksheets are required. The whole class can use the same differentiated slide, with the Super Challenge clearly separated beneath the other questions.

Misconceptions address using only the product, choosing the wrong signs and reversing the signs for a negative constant. Exit checks revisit factorising, simplifying first and finding a missing coefficient.

Year 10 Unit 20, U178. Original questions from Beyond Printables.