### Chocolate

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?

### Doughnut

How can you cut a doughnut into 8 equal pieces with only three cuts of a knife?

### Rectangle Tangle

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?

# Light Blue - Dark Blue

## Light Blue - Dark Blue

Investigate the successive areas of light blue.

What fraction of the total area of the square does the area of light blue take up in each case?

Can you work out what the next two diagrams would look like?

### Why do this problem?

This problem gives children the opportunity to explore fractions in a practical context. They will be identifying and explaining patterns, and justifying their ideas.

### Possible approach

Show the images to the group, perhaps one at a time, inviting them to look carefully at each. Then, hide the images and ask learners to talk to each other about what they saw. After some time, bring them together to discuss as a whole group and at this stage you might encourage them to think about the fractions of each colour if it doesn't come up naturally. It will be necessary to reveal the images again at certain moments, in order to check ideas and facilitate the discussion.

Then ask children to work in pairs to recreate the images and extend the sequence. Squared paper and squares of coloured paper might be useful, but encourage each pair to make their own decisions about the materials they will use. This will be an ideal time for you to wander around the room listening to the conversations. Listen out for those learners who are challenging their partner's assumptions and justifying their answers.

### Key questions

What fractions can you see?
Is there a pattern to the fractions of area in each image?
Can you convince us that your fraction is correct?

### Possible extension

Learners could also make up other patterns of their own for partners to extend.

### Possible support

Some children might benefit from having copies of the images available on a sheet to which they could refer when necessary.