Give five seconds of quiet think-time before any hands go up, then take two or three answers. Hold out for pupils naming what the machine does (adds 3) rather than just the next output.

• +3 machine — send 1, 2, 3, 5 through and read the pairs down the table; ask what stays the same each time?
• ×2 machine — the outputs double; watch for pupils who add instead of multiply.
• −2 machine — the numbers get smaller; a good contrast after the two growing rules.
• ×10 machine — pause before the last input and take a prediction; this is the one that jumps fastest.

Talk this one through together — pupils take turns at the board and the class agrees or corrects out loud.

Set the rule to + 5. Send 3, 6, 9, then 0 — 0 is the one that catches people out: adding 5 to nothing still gives 5. After four rows ask does the same thing happen every time? to name the rule.

Then build the reverse on the board: point to the output 8, ask what went in to make that?, and show that taking 5 away undoes the add. This is the thinking pupils will need in the Class Challenge, so make it visible now.

This is the practice round — 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.

Push pupils to probe a fresh input before guessing the hidden rule, then build it from the operation and number buttons and tap Check. On the last one the machine gives the output and asks for the input — this runs the rule in reverse, just like we undid the + 5 machine earlier: for a times rule you divide the output by the rule number.