Copyright © University of Cambridge. All rights reserved.

'What Was in the Box?' printed from http://nrich.maths.org/

Show menu

What Was in the Box?


A number in a little box is put into a wonderful big box that adds something to the number and then a new number comes out at the end:




The first time this happens, 10 is put into the little box, so what happened in the big box to get the answer in the picture above?

Now three more boxes with new numbers in, go into the wonderful box one at a time. It still does the same as before.

 

 

So, what were these three new numbers that went in and do you have a better idea of what  has been going on - remember it was the same for all four numbers that went in.

 

-----------

 

Imagine four new boxes now (with new numbers in) and the wonderful box does a new and different add or take away this time. For one of these boxes the number 10 was put in. The numbers that come out are these:

 

 



What could have happened? How did you work these out?
Discuss with others and see if there were different ways that you found the answers.

 

 

 


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 be used to introduce children to the idea of addition and subtraction, and offers great opportunities for learners to record in different ways.


Possible approach

Introduce the class to just one number going in and 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. 

You may also like to draw attention to different methods of recording that you observe.  Some children may have drawn pictures whereas others may have created calculations.

 

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 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?