Give five seconds of quiet think-time before any hands go up. Take two or three answers, not open call-outs. Don't confirm yet, the point of the model step is to show how we get there, so hold the reveal. Listen for the trap answer where a pupil adds first (5 + 3 = 8, then × 2 = 16); note it silently and let the model beat correct it.

Point at the first machine: replace the letter with the number that goes in, then follow the rule. For 2n + 3 with n = 5, say the two moves aloud, multiply first (2 × 5 = 10), then add (10 + 3 = 13).

Head off the add-first slip from the hook: ask why 5 + 3 first would be wrong, and revoice we multiply before we add.

• Machine 1, the make-or-break: order matters (× before +).
• Machine 2, 3x − 1, now with subtraction at the end.
• Machine 3, 2y − 3: the value of y goes straight in, multiply by 2 first, then take away 3. Ask what the output would be if y were 2.

Talk this one through together. Pupils take turns at the board and the class agrees or corrects out loud. Hold the reveal until pupils have predicted.

The machine shows 4n + 1 only; feed the input 3 and read the output 13. For 2x − 5 with x = 7, the working is 2 × 7 = 14, then − 5 = 9. For 5 + 3y with y = 2, the addition is written first but the multiply (3 × 2 = 6) still happens first, then 5 + 6 = 11 — a deliberate wrinkle. Ask a pupil to explain why we don't do 5 + 3 first. Only reveal each answer after the class has predicted it.

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.

The three machine rounds rise in difficulty: a two-step rule, then a subtraction, then another two-step rule. The two-letter a + b is done on the board because one machine chute cannot take two separate inputs. Point to both letters in turn: write 6 for a, then 8 for b, then add to reach 14. Insist both letters are replaced before the adding starts. Fast finishers watch the board and predict the next output.