Reach for the Star | GCSE Mathematics

L057: Quadratic expressions

Objective

Expand and factorise quadratic expressions using structure.

Calculator: Calculator allowed where labelled; non-calculator reasoning remains required.

Visual model for Quadratic expressions
Points route: Connect 2 · Share 2 · Apply 6 · Review 3 · Stretch 2 · Deep Challenge 3. Record your score honestly after you have checked your answer.

Recall

Retrieve the key fact or method needed for quadratic expressions.

Core practice

Factorise 2x²+7x+3 and check by expansion.

Reasoning

A learner writes (x−4)(x+2)=x²−8. Find the missing terms.

Exam-style

Solve an exam-style problem involving quadratic expressions. Show working, include a check and interpret your answer.

WWW / EBI

Recall & Review: feedback and extension integration

Lesson L057: Quadratic expressions

Objective: Expand and factorise quadratic expressions using structure.

60-minute structure: 0-7 Connect & Check; 7-14 Share; 14-25 Present/model; 25-44 Apply route choice/practice; 44-52 independent exam-style check; 52-60 Recall & Review, WWW/EBI and next step.

What Went Well (WWW)

I represented the algebraic structure accurately, kept each transformation valid and checked the result by substitution, graph or equivalent reasoning.

Even Better If (EBI)

I will show the missing inverse operation or algebraic step, keep signs and brackets accurate and test the result in the original relationship.

Stretch and deep challenge

Stretch: Factorise 2x²+7x+3 and check by expansion.

Deep challenge: A learner writes (x−4)(x+2)=x²−8. Find the missing terms.