Actions on objects - March 2011, Stage 3&4

In preparation for this month we worked with Professor John Mason exploring 'actions on mathematical objects'. All the tasks involve appreciating mathematical structure, whether this is through recognising relationships or perceiving properties.

Problems

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Missing Multipliers

Stage: 3 Challenge Level: Challenge Level:1

What is the smallest number of answers you need to reveal in order to work out the missing headers?

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Arithmagons

Stage: 3 Challenge Level: Challenge Level:1

Can you find the values at the vertices when you know the values on the edges?

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Opposite Vertices

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Can you recreate squares and rhombuses if you are only given a side or a diagonal?

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Finding Factors

Stage: 4 Challenge Level: Challenge Level:1

Can you find the hidden factors which multiply together to produce each quadratic expression?

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Multiplication Arithmagons

Stage: 4 Challenge Level: Challenge Level:1

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

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Vector Journeys

Stage: 4 Challenge Level: Challenge Level:1

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

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Poison, Antidote, Water

Stage: 4 and 5 Challenge Level: Challenge Level:1

Play the game of Poison, Antidote, Water to start to understand the mathematics of associativity and groups.