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'Light Blue - Dark Blue' printed from http://nrich.maths.org/
Why do this problem?
gives children the opportunity to explore fractions in a practical context. They will be identifying and explaining patterns, and justifying their ideas.
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.
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?
Learners could also make up other patterns of their own for partners to extend.
Some children might benefit from having copies of the images available on a sheet to which they could refer when necessary.