Take two or three hands-up answers for the 100th term before revealing anything. Some pupils will want to count on in threes; hold out for the idea that finding a rule beats continuing the list. Do not confirm the rule yet, that is the job of Watch and Notice.

Let n stand for the position: 1st term n=1, 2nd n=2, and so on.

Before the arrow lands, ask why the multiplier is 3, not another number — the pattern steps up by 3, so 3 lots of the position build the value, then a fixed +1. Rule: 3n + 1. Name it: an expression.

Test it against the fourth term: 3 × 4 = 12, plus 1 is 13 — matches.

Second machine is the pivot: the rule that generated the pattern becomes the equation that solves for a term. Say it plainly — forwards we put a position in and get a value; backwards we know the value and find the position.

Take a term of 34: write 3n + 1 = 34. Name it: an equation. Undo in reverse — take away 1 to get 3n = 33, then share by 3 to get n = 11.

Walk the reverse working slowly, pointing at each step; ask why we take away the 1 before we share by 3.

Talk this one through together — pupils take turns at the board and the class agrees or corrects out loud. The explore machine covers the pattern-and-rule stage; the expression and equation stages are board-and-talk, so keep the pen moving as you build them.

Feed positions 1, 2, 3 through the machine so the class sees the step is 4 each time and the start is 5. Draw out the rule: times four, then add one, so the expression is 4n + 1. Then flip it: to reach 61, write 4n + 1 = 61, undo the +1 to get 4n = 60, share by 4 to get n = 15. Check by feeding 15 back through the machine.

Watch for the classic slip of undoing the ×4 before the +1 — head it off by asking which did the machine do last?

This is the practice round. Run it one way: each pupil works the five stages in their maths copy, and after each stage the class confirms the answer aloud before moving to the next. The 'unlocks' framing is just a narrative device to describe the order — there is no on-screen gate.

The stages rise in difficulty — stage 1 is a plain pattern step, stage 5 is a two-step equation, so every pupil can enter and the strongest stretch to the end.

Stretch prompt for fast finishers: write your own five-stage mystery, starting from a pattern of your choice. They wait quietly or draft this — no separate device work.