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### Number and algebra

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### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Tales of the Unexpected

### Subtraction Surprise

### Legs Eleven

### Angles Inside

### Triangle in a Triangle

### Areas and Ratios

### Another Triangle in a Triangle

### Utter Chaos!

### Related

## You may also like

### Patterns in Number Sequences

### Reasoning Geometrically

### Reasoning with Numbers

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When working on mathematical tasks, you may sometimes discover unexpected results that take you by surprise. In this feature, we have chosen some problems that we hope will astonish and amaze you.

Age 7 to 14

Challenge Level

Try out some calculations. Are you surprised by the results?

Age 11 to 14

Challenge Level

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

Age 11 to 14

Challenge Level

Draw some angles inside a rectangle. What do you notice? Can you prove it?

Age 14 to 16

Challenge Level

Can you work out the fraction of the original triangle that is covered by the inner triangle?

Age 16 to 18

Challenge Level

Do you have enough information to work out the area of the shaded quadrilateral?

Age 16 to 18

Challenge Level

Can you work out the fraction of the original triangle that is covered by the green triangle?

Age 14 to 18

A small change can have a big effect! Read all about Chaos Theory in this short article.

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.