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These two group activities use mathematical reasoning - one is numerical, one geometric.

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Round and Round the Circle

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

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Tom's Number

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

Penta Primes

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Here are ten cards numbered 0 to 9:

cards numbered 0-9

Using all ten cards, rearrange them to make five prime numbers.

Can you find a way of doing it with five two-digit numbers?

How about using one one-digit number, one three-digit number and three two-digit numbers? ...

This problem is based on an idea from Mathematical Challenges for Able Pupils Key Stages 1 and 2, published by DfES.


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. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.