Representing - May 2009, Stage 4&5

Representations play a key role in problem-solving. When confronted by a mathematical situation, we often need to represent it in some way (for example pictures, diagrams and symbols) to help us make sense of it and move on. We also use representations to analyse and share outcomes. Often we need to make sense of other people’s representations, such as their use of tables, diagrams or symbols.

Problems

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Rectangle Outline Sudoku

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

Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.

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Building Gnomons

Stage: 4 Challenge Level: Challenge Level:1

Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible.

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Gnomon Dimensions

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

These gnomons appear to have more than a passing connection with the Fibonacci sequence. This problem ask you to investigate some of these connections.

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Galley Division

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you explain how Galley Division works?

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What's Your Mean?

Stage: 5 Challenge Level: Challenge Level:1

Can you work out the means of these distributions using numerical methods?

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Shuffles

Stage: 5 Challenge Level: Challenge Level:1

An environment for exploring the properties of small groups.

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Into the Exponential Distribution

Stage: 5 Challenge Level: Challenge Level:1

Get into the exponential distribution through an exploration of its pdf.

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Into the Normal Distribution

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

Investigate the normal distribution

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Time to Evolve 2

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

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?