Visualising and representing

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

A 1x2x3 block is placed on an 8x8 board and rolled several times.... How many squares has it occupied altogether?

If a sum invested gains 10% each year how long before it has doubled its value?

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?

A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?

What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

Can you work out what kind of rotation produced this pattern of pegs in our pegboard?

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?