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Light Blue - Dark Blue

Age 7 to 11
Challenge Level

Light Blue - Dark Blue

Look at each of these five squares.

What is the pattern?

How much of the second square is light blue? Can you write this as a fraction?

For each of the five squares, write the area of the square that is light blue as a fraction.

Can you work out what the next two diagrams would look like? What fraction of these squares will be light blue?

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.