This is an inquiry opener: pose the problem and let pupils genuinely sit with it. Take three or four hands-up ideas, do not reveal a method yet — the whole point is for the class to feel why listing is slow before we hunt for a rule. Listen for anyone who notices the +3 step; revoice it as 'so it grows by the same amount each time' but leave the leap-to-100 question hanging for the next step.

Keep the rules hidden — pupils must deduce them from the numbers, not be told. This is the inquiry beat: the class gathers the evidence, then we name the rule, drawn from what they saw.

• 4, 7, 10 — fully model the bridge on screen: find the +3 step, link it to ×position, then show position 1 × 3 = 3 is one short of 4, so we add 1, giving ×3 then +1. This is the machine where the work-back is demonstrated.
• 2, 4, 6, 8 — the cleaner case: step is +2 and the machine simply doubles, no adjustment needed. Use this to show step and rule are not always the same wording.
• 5, 9, 13, 17 — now pupils apply the modelled work-back: step is +4, position 1 × 4 = 4 is one short of 5, so add 1, rule is ×4 then +1.

Close by naming the big idea: 'the step tells us what to multiply by, then we adjust to fit the first number.'

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

Start with the three preset pairs (1→5, 2→7, 3→9). Ask for the step first (+2), then ask what to do to the input to land on the output: position 1 × 2 = 2, but the output is 5, so we add 3 — the rule is ×2 then +3. Let a pupil feed in a fresh number (say 7) and have the class predict the output before the machine reveals it — that prediction is the test of their rule. Revoice a strong contribution: 'so the step of two told us to multiply by two, then we adjusted by three to fit.'

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.

Work three machines properly with the class: the first two single-step ones (add 4, ×5) to warm up step-spotting, then the headline two-step 6, 11, 16, 21 (step +5; position 1 × 5 = 5 is one short of 6, so add 1 → ×5 then +1). The last two machines (1,4,7,10 and 8,14,20,26) are stretch only — reach them if time allows. For each, get the step first, then the rule, then a prediction on a fresh input before Check.

To close, pose 3, 8, 15, 24 verbally only — it is not in the machine bank. It grows by an increasing step (+5, +7, +9), so it has no single constant-step rule. Ask 'why won't our usual trick work here?' and let pupils notice the step itself is changing.