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For younger learners

  • Early Years Foundation Stage

Learning to Collaborate

You might think of mathematics as a solitary pursuit, but in fact, many mathematical breakthroughs have been made by people working together to solve problems that they couldn't tackle alone. The problems in this collection include suggestions of multiple ways to think about the mathematics, so why not try an approach that you might not usually think of? If you have someone else to work with on the problems, even better!

Seven Squares and Marbles in a Box include solutions that have previously been submitted to NRICH, so you may wish to try these problems first and then compare your approach with the published ones. Then try Mixing Lemonade and Steel Cables, and send us your solutions!

Seven Squares

Age 11 to 14
Challenge Level Yellow starYellow star

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

Marbles in a Box

Age 11 to 16
Challenge Level Yellow starYellow star

How many winning lines can you make in a three-dimensional version of noughts and crosses?

Mixing Lemonade

Age 11 to 14
Challenge Level Yellow star

Can you work out which drink has the stronger flavour?

Steel Cables

Age 14 to 16
Challenge Level Yellow star

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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