L091 · Allow 10–15 minutes for learners ready to move on. Answers are available after an attempt.
Prove the product of two consecutive integers is even.
n(n+1); one of the consecutive factors is even, so the product is even.
Prove the sum of three consecutive integers is divisible by 3.
(n−1)+n+(n+1)=3n.
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.
I represented the algebraic structure accurately, kept each transformation valid and checked the result by substitution, graph or equivalent reasoning.
I will show the missing inverse operation or algebraic step, keep signs and brackets accurate and test the result in the original relationship.
Stretch: Prove the product of two consecutive integers is even.
Deep challenge: Prove the sum of three consecutive integers is divisible by 3.