Analysing Alternative Approaches - November 2011, Stage 4&5

This month, we invite you to consider a variety of ways of approaching the tasks, and encourage you to reflect on the merits of different routes to solutions.

Problems

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What's it Worth?

Stage: 3 and 4 Challenge Level: Challenge Level:1

There are lots of different methods to find out what the shapes are worth - how many can you find?

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Steel Cables

Stage: 4 Challenge Level: Challenge Level:1

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

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LCM Sudoku

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

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

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A Long Time at the Till

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

Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?

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A Rational Search

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

Investigate constructible images which contain rational areas.

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Calculating with Cosines

Stage: 5 Challenge Level: Challenge Level:1

If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?

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Dodgy Proofs

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

These proofs are wrong. Can you see why?

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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