Visualising and representing

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Favourite

Is There a Theorem?

Age

11 to 14

Challenge level

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?
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Favourite

One and Three

Age

14 to 16

Challenge level

Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400 metres from B. How long is the lake?
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Favourite

Hamiltonian Cube

Age

11 to 16

Challenge level

Weekly Problem 36 - 2007
Find the length along the shortest path passing through certain points on the cube.
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Favourite

John's Train Is on Time

Age

11 to 14

Challenge level

A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?
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Favourite

Cubes Within Cubes Revisited

Age

11 to 14

Challenge level

Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?
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Favourite

Seesaw Shenanigans

Age

3 to 7

Challenge level

A group of animals has made a seesaw in the woods. How can you make the seesaw balance?
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Favourite

Always, Sometimes or Never? KS1

Age

5 to 7

Challenge level

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?
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Favourite

Eightness of Eight

Age

5 to 7

Challenge level

What do you see as you watch this video? Can you create a similar video for the number 12?
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Favourite

Biscuit Decorations

Age

5 to 7

Challenge level

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?
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Favourite

Writing Digits

Age

5 to 7

Challenge level

Lee was writing all the counting numbers from 1 to 20. She stopped for a rest after writing seventeen digits. What was the last number she wrote?