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## 'Think of Two Numbers' printed from http://nrich.maths.org/

### Why do this problem?

This
problem can be solved by both trial and improvement and by
using simple algebra. It is the intriguing kind of "puzzle-game"
that can be taken from the maths classroom into the playground! A
poster of this problem is available

here.

### Possible approach

You could introduce the
problem as it appears on the site as a printed sheet or on a
computer. Learners could first work individually to give them
'thinking time', then work in pairs to support each other and to
give an opportunity for mathematical talk, and finally there could
be a class discussion.

A concluding plenary
could ask them to share any insights and strategies that helped
them succeed at this task.

### Key questions

Have you tried with
several numbers to see what is happening?

What can you say about
the answer and the first number that was chosen?

What can you say about
the answer and the second number that was chosen?

Have you tried doing it
with someone else whose numbers you do not know?

Have you tried using two
letters in place of the two numbers?

### Possible extension

Learners could go on to

Multiply the Addition
Square.

### Possible support

Suggest trying with different numbers, thus practising simple
calculation, even if the generalising is not done.