## Function Machines

This one is a bit more of a puzzle.

Can you work out what happens in the three circles?

### Why do this problem?

This problem gives a good deal of practice in addition, subtraction, multiplication and division in an interesting and unusual format. The second part of the problem involves much reasoning about numbers.

### Key questions

Would it be a good idea to start with $5$?

What do you do next?

What comes out?

How could you get from $2$ to $22$ ? Will those same operations turn $3$ into $28$?

Would it be a good idea to multiply each number by $2$, then $3$, then $4$, etc until find a pattern?

What do you notice about the numbers going in? What do you notice about the numbers coming out?

### Possible extension

Learners could create their own function machines for friends to complete. Asking them to make examples like the second part of the problem will involve a great deal of mental calculation and reasoning about numbers.

### Possible support

Suggest trying just the first part of the problem which is relatively easy. They could then go on to making their own 'function machine' [as in the second part of the problem] with two, or even just one, circle.