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?

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.