Here is a rule: 2n + 3.

If the letter n stands for the number 5, what do you think this whole thing is worth? Hands up with your best answer.

A rule is on the board, shown as a machine. Each machine shows a number put in for the letter and what the rule gives out.

Now two more machines. One multiplies then subtracts (3x − 1). One also multiplies then subtracts, but with the letter y (2y − 3). Same idea: the letter is swapped for the number that goes in.

Notice the order: multiply first, then add or take away.

We do 4n + 1 with n = 3 on the machine together. Before we press the button, predict: what comes out? Remember we multiply 4 × 3 first, then add 1. Say your prediction, then we check.

Then we work two more on the board. For 2x − 5 with x = 7, do the multiply step first: what is 2 × 7? What do we do next? Predict the answer before anyone writes it. Then 5 + 3y with y = 2 looks like it starts with the 5, but we still multiply first. What is 3 × 2? Only then do we add the 5. Predict the final answer.

The output is hidden this time until you check, and you'll be given the rule for each round. We build up round by round on the machine. First 4n + 1 with n = 3. Then 2x − 5 with x = 7. Then 2y + 3 with y = 4. Set the machine and press Check each time.

Last of all we try a two-letter rule on the board, not the machine, because a machine only has one chute. a + b with a = 6 and b = 8. We write 6 in place of a, then 8 in place of b, so a + b becomes 6 + 8 = 14. Both letters get their own number before we add.