Look at this list of numbers on the board: 2, 5, 8, 11, ...

What number do you think comes next? And the one after that? How are you working it out?

Watch four function machines on the IWB. A number goes in the top, the rule changes it, a new number comes out the bottom. The output of one then feeds back in to make the next term of the sequence.

Add 3

Watch the first one — two in gives five, then five in gives eight, then eight in gives eleven. Each number that comes out is the next term in the sequence, and it becomes the next input.

Multiply by 2

A sequence that grows fast: 1, 2, 4, 8. Notice how the jumps get bigger each time.

Subtract 5

A sequence that shrinks: 50, 45, 40, 35. The rule still applies every step.

Double then add 1

A trickier two-step rule: 1 becomes 3, then 7, then 15. Two things happen each time — first double, then add one.

Now we drive the machine ourselves. The rule on screen is +3, and we're starting from 2.

When we've finished that sequence, we'll try a new starting input — 7 — and build a fresh sequence with the same +3 rule.