Session 1 · SOLVE: See the Pattern
The rectangle test
- 10 minHook: a mystery envelope holds a padlock and the clue 'the smallest number bigger than 20 that can only make one rectangle'. What could that mean?
- 20 minIn pairs, use tiles to make every possible rectangle for each number from 1 to 30. Record the dimensions in a table (for example 12: 1×12, 2×6, 3×4).
- 10 minSort the numbers: only one rectangle, more than one, and the odd one out (1). Name them: prime, composite, neither.
- 10 minEvidence wall: write one conjecture about prime numbers. Open the padlock with the answer to the hook clue (23).
Session 2 · SOLVE: See the Pattern
The sieve and the cicadas
- 10 minRead 'Prime numbers: the atoms of maths'. Why is 1 not a prime?
- 20 minSieve of Eratosthenes: on a hundreds board, cross out 1, then every multiple of 2 after 2, of 3 after 3, of 5 after 5 and of 7 after 7. Circle what is left. Count the primes to 100.
- 10 minPattern hunt: which columns have no primes at all? Why? Test the divisibility rules for 3 and 9 on some crossed-out numbers.
- 10 minCicada puzzle: some cicadas come out every 13 or 17 years. Why might a prime cycle help them avoid predators that come every 2, 3, 4 or 6 years?
Getting started
Work with numbers 1–20 and use tiles for every number before trying the sieve.
Stretch
Twin primes are pairs like 11 and 13 that are two apart. List all the twin primes under 100. Do you think they ever run out?
Checkpoint
Everyone can say whether a number under 100 is prime and explain how they know using factors or rectangles.
Activities for this week
- The rectangle test: Why can some numbers make lots of rectangles and others only one?
- Sieve of Eratosthenes: Can we find every prime number up to 100 without testing each one?
Useful this week
- Prime numbers chart and calculator ↗ A clear chart of primes and a checker to test your own conjectures.