Actions on objects - March 2011, Stage 2&3

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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Beads and Bags

Stage: 1 and 2 Challenge Level: Challenge Level:1

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

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Count the Digits

Stage: 1 and 2 Challenge Level: Challenge Level:1

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

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The Numbers Give the Design

Stage: 2 Challenge Level: Challenge Level:1

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

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Journeys in Numberland

Stage: 2 Challenge Level: Challenge Level:1

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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Area and Perimeter

Stage: 2 Challenge Level: Challenge Level:1

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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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?