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.

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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NRICH is part of the family of activities in the Millennium Mathematics Project.