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## 'Two-digit Targets' printed from http://nrich.maths.org/

## Two-digit Targets

You have a set of the digits from $0$ - $9$.

Can you arrange these digits in the five boxes below to make two-digit numbers as close to the targets as possible? You may use each digit once only.

You could use this interactivity.

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This activity has been adapted from one of BEAM's Maths of the Month resources.

### Why do this problem?

This problem would fit in well when pupils in the group are getting to grips with the idea that the position of a digit in a number affects its value, and comparing and ordering numbers, as well as learning or practising the relevant vocabulary. It requires some understanding of how the number system works, and can
help to develop a firm concept of place value.

Possible approach

You could start by having two different digits and asking how the digits could be arranged to make the numbers that are the largest/smallest. Try this several times with different combinations of two digits. Could the digits be arranged to make a multiple of $5$? If not, why not?

Next you could introduce one of the criteria in the problem such as making the largest possible even two-digit number. Alternatively, you could make up your own examples such as the largest even number or the nearest to $70$. You will need to establish whether $0$ can be used at the beginning of a number. This, in itself, can form an interesting discussion point. (The final decision itself
does not matter - it is the reasons that are important, and the fact that the children feel as if it is their decision!)

The best way of continuing on this problem is to use

this sheet and for learners to work in pairs so that they are able to talk through their ideas with a partner. It is ideal if each player can also have a set of digit cards to use to make the numbers. You might suggest
that children could make this problem into a game and play against a friend.
At the end there should be a general discussion on the best strategies and the nearest that anyone got to the target. You could repeat what you did at the start and give children numbers such as $2$, $6$ and ask them how they would arrange these to make the highest/lowest number possible and why this is so. This would be a good assessment opportunity.

### Key questions

Where is the best place to put $1$ when you are aiming for the highest number?

Where is the best place to put $9$ when you are aiming for the lowest number?

Possible extension

Those who find working with two-digit numbers easy could try

this four-digit version.

Possible support

Making the numbers one at a time with set of $0$ - $9$ digit cards should help all children access this problem.