Prove facts about consecutive, odd and even numbers and n² patterns, show identities, and explain why checking examples is not a proof.
What you will learn
- Write consecutive, odd and even numbers with one letter
- Expand, simplify and factorise to show a result
- Finish a proof with a sentence that says why
- Explain why examples are not a proof and find a counterexample
The building blocks
A proof must work for every whole number, so use a letter:
- even: 2n; odd: 2n + 1
- consecutive numbers: n, n + 1, n + 2
- consecutive even numbers: 2n, 2n + 2, 2n + 4; consecutive odd numbers: 2n + 1, 2n + 3
- a multiple of k: kn
The rest of this lesson and its 9 practice questions are locked.
In this lesson
- The building blocks
- Expand, simplify, factorise, conclude
- Squares and n² patterns
- Examples are not a proof
- Try it: An easy one first
9 practice questions, marked as you go; about 30 minutes in all.
In this unit: Problem solving and proof
Reasoning and problem solving: multi-step money problems, angle chains with reasons, interpreting and justifying with statistics, algebraic proof, and mixed problems across topics.