Take three or four hands-up answers, not open call-outs, and collect them on the board (1, 2, 3, 4, 6, 12). Don't confirm they've found them all yet — that's the point of the lesson. If a pupil offers 5 or 8, ask does 12 share evenly into fives? and let the class decide.

Factors of 24: shaded are 1, 2, 3, 4, 6, 8, 12, 24. Point to the pairs that multiply to 24 - 1 and 24, 2 and 12, 3 and 8, 4 and 6. Every factor has a partner.

Multiples of 6: 6, 12, 18, 24, 30 and on. Trace how they step across the ten-wide grid in two slanting columns. Ask what comes next after 30 before it shows. Multiples never run out; factors do.

Primes under 30: shaded are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. Key idea - a prime has exactly two factors, itself and 1. More than two makes it composite, e.g. 9 has 1, 3 and 9. Head off the slip that 1 is prime: 1 has only one factor, so neither prime nor composite. Note after 2 none shaded is even, and they spread out through the twenties.

This round is for talking it through together — no marking yet. It runs on the single whole-class board grid, with pupils taking turns to shade while the rest watch and check aloud.

Start with multiples of 4, then switch to multiples of 8 on a fresh grid, and ask why is every multiple of 8 also a multiple of 4? (because 8 is a multiple of 4). Then set it to factors of 36 and count them together (1, 2, 3, 4, 6, 9, 12, 18, 36 — nine factors). Rotate three or four pupils to the board. To keep the watching class with each task, turn-and-name a pupil to say where the next shaded cell will land before it appears.

These are the practice questions — pupils take turns at the board, check each answer, and the class confirms before moving on. Keep the board work brisk rather than over-explaining.

Model the four-factor idea on screen first with 6 (factors 1, 2, 3, 6) so pupils have a method: write the factor list, then count how many there are. Let pupils find the rest by counting factors by hand rather than needing a rule — 6, 8, 10, 14, 15, 21, 22, 26, 27, 33, 34, 35 and so on. If stronger pupils spot the pattern (product of two different primes, or a prime cubed), let them share it, but no pupil needs it to attempt the task. Use the Check button after each of the first three shadings; the class confirms with a yes, that's it. For the stretch, count factors aloud on whatever numbers pupils find and keep the pace moving rather than waiting for a full-grid match.