Geometry and Algebra - October 2006, Stage 2&3

Problems

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Coordinate Challenge

Stage: 2 Challenge Level: Challenge Level:1

Use the clues about the symmetrical properties of these letters to place them on the grid.

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Tubular Path

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

Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?

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A Maze of Directions

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

Use the blue spot to help you move the yellow spot from one star to the other. How are the trails of the blue and yellow spots related?

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Escher Tessellations

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

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

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Decoding Transformations

Stage: 3 Challenge Level: Challenge Level:1

See the effects of some combined transformations on a shape. Can you describe what the individual transformations do?

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Combining Transformations

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

Does changing the order of transformations always/sometimes/never produce the same transformation?

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Simplifying Transformations

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

How many different transformations can you find made up from combinations of R, S and their inverses? Can you be sure that you have found them all?