## Six Is the Sum

What do the digits in the number fifteen add up to?

How many other numbers have digits with the same total if we only include numbers without zeros?

### Why do this problem?

This

activity allows pupils to explore numbers in what might be a new and unusual way. It encourages them to work systematically, and different approaches can then be discussed.

### Possible approach

You could introduce this challenge simply by asking children to write down a number whose digits add to six, perhaps on a mini-whiteboard. Tell them to keep their number hidden from everyone else and then ask them to consider whether there might be any other numbers whose digits add to six. Give them time to think and write down any others that come to mind.

You can then set up the task and you could start by inviting children to compare their numbers with a neighbour. At this stage you may need to clarify whether numbers with a zero in can be included or not. Encourage the children themselves to justify why we should leave out numbers with a zero. Pairs could then work together to find other numbers.

After some time, stop the group and ask how they will know when they have found all the possibilities. Draw on suggestions that focus on finding numbers in a particular order or by using a particular system, and then give more time for paired work.

You could encourage pairs to record each number they find on a strip of paper. Then, in the plenary you could attach strips to the board, each displaying a different number. By ordering the numbers the group can then work out whether any are missing. Different pupils will have different ways of doing this ordering, so encourage pairs to explain their own way rather than only focusing on one
approach.

### Key questions

What numbers have you found?

How did you find these answers?

How do you know that you have found all the numbers?

### Possible extension

Pupils could use a similar systematic approach to try other numbers whose digits have a different sum.

### Possible support

By writing each number on a different piece of paper, children are not expected to be systematic straight away. Having digit cards might help some learners.