Generic examples - March 2012, All Stages

Sometimes it is possible to state what is general by perceiving the structure in just one example. Vivid proofs of generalisations can be located in a particular, well-chosen example. This month we invite you to explore and notice what is generalisable in carefully chosen generic examples.

Problems

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Walking Round a Triangle

Age 5 to 7 Challenge Level:

This ladybird is taking a walk round a triangle. Can you see how much he has turned when he gets back to where he started?

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Two Numbers Under the Microscope

Age 5 to 7 Challenge Level:

This investigates one particular property of number by looking closely at an example of adding two odd numbers together.

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Odd Times Even

Age 5 to 7 Challenge Level:

This problem looks at how one example of your choice can show something about the general structure of multiplication.

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Round a Hexagon

Age 7 to 11 Challenge Level:

This problem shows that the external angles of an irregular hexagon add to a circle.

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Take Three Numbers

Age 7 to 11 Challenge Level:

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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Three Neighbours

Age 7 to 11 Challenge Level:

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

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Square Subtraction

Age 7 to 11 Challenge Level:

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

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Magic Letters

Age 11 to 14 Challenge Level:

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

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Coordinate Patterns

Age 11 to 14 Challenge Level:

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

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Route to Infinity

Age 11 to 14 Challenge Level:

Can you describe this route to infinity? Where will the arrows take you next?

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Seven Squares

Age 11 to 14 Challenge Level:

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

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Double Trouble

Age 14 to 16 Challenge Level:

Simple additions can lead to intriguing results...

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Slick Summing

Age 14 to 16 Challenge Level:

Watch the video to see how Charlie works out the sum. Can you adapt his method?

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Speedy Summations

Age 16 to 18 Challenge Level:

Watch the video to see how to add together an arithmetic sequence of numbers efficiently.

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Polynomial Interpolation

Age 16 to 18 Challenge Level:

Can you fit polynomials through these points?

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Particularly General

Age 16 to 18 Challenge Level:

By proving these particular identities, prove the existence of general cases.