Reach for the Star | GCSE Mathematics

L091: Proof and algebraic structure

Objective

Explain algebraic structure and build a logical argument.

Calculator: Non-calculator core; calculator optional only for checking where labelled.

Visual model for Proof and algebraic structure
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 proof and algebraic structure.

Core practice

Prove the product of two consecutive integers is even.

Reasoning

Prove the sum of three consecutive integers is divisible by 3.

Exam-style

Solve an exam-style problem involving proof and algebraic structure. Show working, include a check and interpret your answer.

WWW / EBI

Recall & Review: feedback and extension integration

Lesson L091: Proof and algebraic structure

Objective: Explain algebraic structure and build a logical argument.

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: Prove the product of two consecutive integers is even.

Deep challenge: Prove the sum of three consecutive integers is divisible by 3.