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### Number and algebra

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### Working mathematically

### For younger learners

### Advanced mathematics

# Look Again

### Gibraltar Geometry

### Pocket Money

### Farey Sequences

### Same Answer

### Mediant Madness

### Farey Neighbours

### Ford Circles

### Polar Coordinates

## You may also like

### Patterns in Number Sequences

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Just because a mathematical situation is familiar doesn't mean it has to be dull! Looking at a familiar context through a new lens can generate new insights and understanding. These problems invite you to look again at ideas you may think you know inside-out, and see what new discoveries you can make.

Age 11 to 14

Challenge Level

Take a look at the photos of tiles at a school in Gibraltar. What questions can you ask about them?

Age 11 to 14

Challenge Level

Which of these pocket money systems would you rather have?

Age 11 to 14

Challenge Level

There are lots of ideas to explore in these sequences of ordered fractions.

Age 11 to 14

Challenge Level

Aisha's division and subtraction calculations both gave the same answer! Can you find some more examples?

Age 14 to 16

Challenge Level

Kyle and his teacher disagree about his test score - who is right?

Age 16 to 18

Challenge Level

Farey sequences are lists of fractions in ascending order of magnitude. Can you prove that in every Farey sequence there is a special relationship between Farey neighbours?

Age 16 to 18

Challenge Level

Can you find the link between these beautiful circle patterns and Farey Sequences?

Age 14 to 18

Cartesian Coordinates are not the only way!

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