Picture a machine on a conveyor belt. You drop a number in one end, the machine does the very same thing to it every single time, and a new number rolls out the other end. Today the machine's rule is × 3.

If we drop a 4 into this × 3 machine, what number do you think rolls out the other side?

Each machine takes a number in and follows a rule to give a number out. Watch the four machines in turn and see if you can work out the rule before the output appears.

Today we work through one machine together: the × 3 machine. We will feed it numbers one at a time and write each input-output pair into a table on the board. You call out the output, we check it, and we add the row.

So far we have always known the rule and worked out the output. Now we work the other way. First we build a full table for a two-step machine, the × 2 then + 1 machine, together. Then we play detective: I will show you a pair, like input 3 gives 7, and we will try to find the rule.

Now we work through these rules and complete a full table of four pairs for each one. The last rule is a two-step machine, and one round asks you to work backwards: given an input and its output, find the rule that fits.

What we did today

• We saw a function machine take an input, do the same rule every time, and give an output.
• We built tables of input-output pairs for one-step rules, two-step rules, and a decimal input.
• We learned that one pair is not always enough to be sure of a rule, so we test a second pair.