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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Around and Around

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Divisibility Tests

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Clock Arithmetic

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Stars

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Clock Squares

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More Adventures with Modular Arithmetic

## You may also like

### Patterns in Number Sequences

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The problems in this feature will give you the chance to investigate the properties of numbers in a variety of contexts. We hope that this will give you the opportunity to explore, conjecture and develop convincing arguments for any general results that you discover.

Age 11 to 16

This article explains various divisibility rules and why they work. An article to read with pencil and paper handy.

Age 11 to 18

Challenge Level

What happens if we change the rules and make the usual straight number line into a circle?

Age 11 to 14

Challenge Level

Can you work out what step size to take to ensure you visit all the dots on the circle?

Age 14 to 18

Challenge Level

Can you find a way of predicting the value of large square numbers with the help of our power modulo calculator?

Age 14 to 18

Challenge Level

Investigate what happens when we add or multiply numbers using modular arithmetic.

*We are very grateful to the Heilbronn Institute for Mathematical Research for their generous support for the development of these resources.*

These resources are designed to get you thinking about number sequences and patterns.