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# Learning to Collaborate

### Seven Squares

### Marbles in a Box

### Steel Cables

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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!

Age 11 to 14

Challenge Level

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

Age 11 to 16

Challenge Level

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

Age 14 to 16

Challenge Level

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