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# Representing Numbers

## Representing Numbers

Find as many ways as you can of representing the number of dots shown above.

Try to find at least five ways.

Now find ways of representing ten times as many dots. Can you still find at least five different ways?

### Why do this problem?

### Possible approach

Key questions

Possible extension

Possible support

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Age 7 to 11

Challenge Level

- Problem
- Student Solutions
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Find as many ways as you can of representing the number of dots shown above.

Try to find at least five ways.

Now find ways of representing ten times as many dots. Can you still find at least five different ways?

This problem gives an opportunity for children to think about ways in which numbers can be represented and to be creative as they invent original ways of their own. The task may peak individuals' curiosity as they may explore different ways of grouping, lining up or gathering.

Show the image to the group and ask them how many dots there are. Take the image away and ask learners to talk to a partner about how they counted. (See the task How Would We Count?.) Put the image back up and encourage conversation about ways of counting, perhaps sharing some ways with the whole group. Highlight particular strategies that have been used, such as
grouping, seeing lines of dots etc.

You can then set learners off on the challenge itself. You could ask them to record their representations on separate sheets of paper and then at an approprate time, invite everyone to walk around the room looking at the different ways.

A plenary could focus on discussing a few ways in particular, or you could ask if anyone has a question they would like to put to a pair about their representation.

Key questions

Tell me about these.

Will there be more ways?

Would someone else understand what you are representing here?

Possible extension

Replace the "ten times as many" with "nine times as many".

Possible support

It may be helpful to look at the article Children's Mathematical Graphics: Understanding the Key Concept which looks at the different ways children can record their thinking and understanding.

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?