Open-ended, release from curriculum - July 2011, Stage 4&5

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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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?

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Weekly Challenge 44: Prime Counter

Stage: 5 Challenge Level: Challenge Level:1

A weekly challenge concerning prime numbers.

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Function Pyramids

Stage: 5 Challenge Level: Challenge Level:1

A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?

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Weekly Challenge 41: Happy Birthday

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

A weekly challenge concerning the interpretation of an algorithm to determine the day on which you were born.

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Mechanical Mindgames

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

A selection of intriguing questions to consider on mechanics, particularly surrounding the ideas concerning impulse and momentum.

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Weekly Challenge 43: A Close Match

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you massage the parameters of these curves to make them match as closely as possible?

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Weekly Challenge 42: What's My Equation?

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you find the differential equations giving rise to these famous solutions?

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Phase Space

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Explore the issues surrounding the concept of Phase Space.