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

Stage: 1 Challenge Level: Challenge Level:1

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

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

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

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Stage: 2 Challenge Level: Challenge Level:1

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

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Take Three Numbers

Stage: 2 Challenge Level: Challenge Level:1

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

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

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

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Square Subtraction

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

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

Stage: 3 Challenge Level: Challenge Level:1

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

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

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

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Route to Infinity

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Seven Squares

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

Stage: 4 Challenge Level: Challenge Level:1

Simple additions can lead to intriguing results...

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Slick Summing

Stage: 4 Challenge Level: Challenge Level:1

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

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Speedy Summations

Stage: 5 Challenge Level: Challenge Level:1

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

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Polynomial Interpolation

Stage: 5 Challenge Level: Challenge Level:1

Can you fit polynomials through these points?

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Particularly General

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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