2, 4, 6, 8

Why do this problem?

This problem gives children the opportunity to create their own number sentences. The discussion it provokes will give them the opportunity to use vocabulary related to addition and subtraction, and to begin to develop ways of working systematically.

Possible approach

Having the digits and operation signs on the interactive whiteboard will allow you flexibility to be led by the children as they tackle this task. This very simple interactivity could be useful. You could begin by dragging some of the numbers and operations to make an incorrect number sentence. Invite children to talk in pairs about what is on the board. Ask learners to share their thoughts with everyone which will no doubt mean that your error is pointed out. How could they make the sum correct? Invite a pair to do this alongside the incorrect number sentence so that the original version can still be seen. Ask if another pair can make it right in a different way. Collect some other suggestions and then set up the first task. Working with these number and operation cards, pairs can try out their ideas.

Gather the class together to talk about this first challenge and then introduce the second one so that this time they don't have to use all the cards, but must make as many true number statements as they can. As they work, encourage them to record what they have done, and look out of those that have a system of some description, for example finding all the sentences with $8$ to being with, then with $6$ etc.

Key questions

Possible extension

Children could be encouraged to consider a similar problem using the odd digits less than ten. Does this create difficulties? If so, why?
The set of numbers being considered can be extended in various ways. The children can be encouraged to think about extensions which generate interesting results and those that do not do so.
A similar idea could be introduced using multiplication and division as well as addition and subtraction.

Possible support

Some children may need the support of concrete apparatus such as counters or Multilink cubes to make the calculations. Trying out some one step calculations using these digits would be a good introductory task.
You could break the task down a bit for some children, for example, by asking them to find all the number sentences which use the $2$ first, then the $4$ etc. Having the number and operation cards to manipulate will mean that children will find it easier to change their minds rather than feeling pressured to have a correct calculation immediately.