Reasoning, convincing and proving
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Break it up!
In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?
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Arithmagons
Can you find the values at the vertices when you know the values on the edges?
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Sizing them up
Can you put these shapes in order of size? Start with the smallest.
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Crossed ends
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
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Speeding boats
Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?
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Colouring triangles
Explore ways of colouring this set of triangles. Can you make symmetrical patterns?
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Why 24?
Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.
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Your number is...
Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?