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All in the Mind

Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?

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Picture Story

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

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Instant Insanity

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

Picturing Triangular Numbers

Age 11 to 14 Challenge Level:

How could you describe the rectangles that are formed?

Keep a record of your results.

How might square roots help when determining whether or not a number is a triangle number?