Open-ended, release from curriculum - July 2011, Stage 3&4

This month we have chosen a selection of activities, both for use in the classroom and for working on during the holidays.

Problems

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Sieve of Eratosthenes

Stage: 3 Challenge Level: Challenge Level:1

Follow this recipe for sieving numbers and see what interesting patterns emerge.

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Can They Be Equal?

Stage: 3 Challenge Level: Challenge Level:1

Can you find rectangles where the value of the area is the same as the value of the perimeter?

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Number Pyramids

Stage: 3 Challenge Level: Challenge Level:1

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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More Number Pyramids

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

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

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Generating Triples

Stage: 4 Challenge Level: Challenge Level:1

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

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Filling the Gaps

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Which numbers can we write as a sum of square numbers?

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The Best Square

Stage: 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

How would you judge a competition to draw a freehand square?