Problem Teachers' Notes Hint Solution

# What Was in the Box?

### Why do this problem?

Of course this problem is rather like a function machine, but it can be more interesting and is easily extended to challenge a wide range of pupils. It could even be used to introduce children to the idea of addition and subtraction.

### Possible approach

Introduce the class to just one number going in and to give them one outcome to start with so that they understand the process. Then, gradually increase the number of numbers going in until you reach four, as in the problem. Your own examples can be adjusted in complexity according to the level of your pupils.

Once learners have had some time to work on the first part of the problem in pairs, ask them to share their ways of working with the whole group. Look out for those who give good reasons for choosing particular methods.

### Key questions

What might have gone on in the box to get this number answer?
Could that have produced the other answers too?

### Possible extension

Pupils who have gone onto multiplication and division and are doing well may be moved onto further thinking by going to What's in the Box.

### Possible support

For just one number going in you can use counters and a cloth. Show the counters and then cover them with the cloth. Secretly add the required extra number of counters under the cover before revealing them to the pupil. Then a number of probing questions can be asked: How many counters now? What must have happened under the cover?