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From isolation to collaboration

Students often think of mathematics as a solitary pursuit. By offering students opportunities to collaborate mathematically, they can develop a positive mindset through sharing ideas and strategies, and working together to overcome obstacles that they might not be able to tackle alone.

Seven Squares and Marbles in a Box include solutions that have previously been submitted to NRICH, so students may wish to try these problems first and then compare their own approaches with the published ones. Then they could go on to try Mixing Lemonade and Steel Cables, which are open for them to submit their own solutions.

Seven Squares
problem
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Seven squares

Age
11 to 14
Challenge level
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Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
Marbles in a box
problem
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Marbles in a box

Age
11 to 16
Challenge level
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How many winning lines can you make in a three-dimensional version of noughts and crosses?
Mixing Lemonade
problem
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Mixing lemonade

Age
11 to 14
Challenge level
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Can you work out which drink has the stronger flavour?

Steel Cables
problem
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Steel cables

Age
14 to 16
Challenge level
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Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?