Why do 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.
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.
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?
Those who find working with two-digit numbers easy could try this
Making the numbers one at a time with set of $0$ - $9$ digit cards should help all children access this problem.