Visualising - March 2009, Stage 3&4

This month our problems require you to visualise. We use visualisation almost every time we engage in problem solving, for example to 'step into' a problem, to model a situation, to plan ahead, to support arguments and to communicate ideas.

Problems

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Reflecting Squarely

Age 11 to 14 Challenge Level:

In how many ways can you fit all three pieces together to make shapes with line symmetry?

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Cuboid Challenge

Age 11 to 14 Challenge Level:

What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?

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Pick's Theorem

Age 11 to 14 Challenge Level:

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

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Of All the Areas

Age 14 to 16 Challenge Level:

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?

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Contact

Age 14 to 16 Challenge Level:

A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?

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Cyclic Quad Jigsaw

Age 14 to 16 Challenge Level:

A picture is made by joining five small quadrilaterals together to make a large quadrilateral. Is it possible to draw a similar picture if all the small quadrilaterals are cyclic?