Experiment-conjecture-prove - February 2008, Stage 2&3

Problems

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Triangle Shapes

Stage: 1 and 2 Challenge Level: Challenge Level:1

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

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Triangle Relations

Stage: 2 Challenge Level: Challenge Level:1

What do these two triangles have in common? How are they related?

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Putting Two and Two Together

Stage: 2 Challenge Level: Challenge Level:1

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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Triangular Faces

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

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Notes on a Triangle

Stage: 3 Challenge Level: Challenge Level:1

Can you describe what happens in this film?

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9 Weights

Stage: 3 Challenge Level: Challenge Level:1

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

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Conway's Chequerboard Army

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Here is a solitaire type environment for you to experiment with. Which targets can you reach?