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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Journeys of Discovery

### Triangle Transformation

### Diminishing Returns

### Mixing Paints

### Mixing More Paints

### Squaring the Rectangle

### Vanishing Point

### Related

## You may also like

### Patterns in Number Sequences

### Reasoning Geometrically

### Reasoning with Numbers

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Just because an idea has been around for centuries, it doesn't make it any less exciting when you discover it for yourself. In this feature, we share situations involving maths which may be new to you, to take you on a journey of discovery.

Age 7 to 14

Challenge Level

Start with a triangle. Can you cut it up to make a rectangle?

Age 11 to 14

Challenge Level

How much of the square is coloured blue? How will the pattern continue?

Age 11 to 14

Challenge Level

Can you work out how to produce different shades of pink paint?

Age 14 to 16

Challenge Level

Can you find an efficent way to mix paints in any ratio?

Age 14 to 18

Challenge Level

Can you find a way to turn a rectangle into a square?

Age 14 to 18

Challenge Level

How can visual patterns be used to prove sums of series?

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

These resources are designed to get you thinking about geometrical reasoning.

These resources are designed to get you thinking about reasoning with numbers.