Give five seconds of quiet think-time before any hands go up. Take two or three hands-up answers, not open call-outs.

If a pupil says 12, ask how they got it before confirming. The point is the machine does the same rule every time, so the number changes but the rule does not.

Walk each machine aloud, one at a time. The first two are familiar ground, so move briskly; slow right down on the last two, because the two-step rule and the decimal input are both new ideas.

• × 3 — pause on the 0 row. Ask 'what comes out when nothing goes in?' Three lots of nothing is still nothing, so 0 → 0.
• + 5 — point out the output is always 5 bigger; the gap never changes.
• × 2 then + 1 — give this longer dwell time. Show the middle value: 3 doubles to 6, then 6 + 1 = 7. Have the class name both steps aloud, in order, before you reveal the output.
• × 10 — give this longer dwell time too. Ask the class to say what 0.5 ten times makes before you reveal it: half, ten times, is a whole 5. Decimals go through the same machine as whole numbers.

This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud.

Keep the rule visible at × 3. Slide an input in, ask the class to predict the output before pressing send, then add the pair to the table. Bring a few pupils up in turn to drive the machine. Watch for pupils who add 3 instead of multiplying by 3 — head it off by asking 'three lots of this number, or three more than this number?'

This round is guided — you drive the machine on the board and model the thinking aloud while pupils watch and answer.

Build the × 2 then + 1 table first: name both steps each time (double, then add 1). Then run the detective move on screen. Show input 3 gives 7 and ask the class for a rule that fits — collect both + 4 and × 2 then + 1. Now make the key point visible: one pair can fool us, so we send a second number to be sure. Send 5 through each rule on the board and let the class see them part company (9 versus 11). Finish with the stretch pair (input 6 gives 25): try × 4 then + 1, then test a second pair to confirm.

This round is the practice bank — 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.

Rounds rise in difficulty: a × 4 table, a + 7 table, a × 10 table with a decimal input, then a two-step × 2 then + 1 table, then the work-backwards stretch (input 6, output 25 — try × 4 then + 1, just as we modelled). On the stretch, hold the class to testing a second pair before committing to a rule.

Keep this brisk. Recap the three table types (one-step, two-step, decimal input) so the class hears the pattern named one more time before they move to the activity book.