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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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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.

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Is There a Theorem?

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?

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?