Here is a small table. When 1 goes in, 4 comes out. When 2 goes in, 5 comes out. What do you think the machine is doing to each number? And if we put 3 in, what would come out?

Four machines on the board, each with its rule showing. The number that goes in is the input, and the number that comes out is the output. Watch a number go in one side and see what comes out the other. For the last machine, look at the table before I send the number through and be ready to say what will come out.

Today we work an 'add 5' machine together. We'll send these numbers through in turn: 3, then 6, then 9, then 0. Before each one lands in the table, say what will come out. Then we'll check the rule held for every row.

Now let's go the other way. We know the output 8 sits in one row. What input made it? The machine added 5, so to get back we take 5 away: 8 take away 5 gives the input 3.

Some of these rules are hidden. We'll do four in order:

• finish a machine where the rule is shown
• work out a hidden add rule from the pairs
• work out a hidden times rule
• work backwards to find the input for a known output under a 'times 5' rule