This is another opportunity for the children to work and record results logically. This problem lends itself to using a table to organise possible solutions.

It is likely that the children will start with any random five number combination to make 44.

The question again is: How can they be sure that they have all possible combinations?

Encourage pupils to record their combinations in a way that makes it easy to check if they are repeating themselves e.g. highest number first. Increasing one number while decreasing another is a good way to trawl through all the possibilities.

The problem states 'At least one number has to be different for each score of 44.' Is it, in fact, possible to only change one number?

The final prompt for the children is to create their own set of numbers for the dart board. It is a good idea to have them choose a new set for the target score of 44 in the first instance, as this idea has already been modelled for them. Then the target number can be changes. Depending on the skill level of the children, the number set can be limited to one digit numbers or, for children needing a greater challenge, two digit numbers with a target score of 100 or more.