Reasoning, convincing and proving

There are 514 NRICH Mathematical resources connected to Reasoning, convincing and proving
Halving
problem
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Halving

Age
5 to 7
Challenge level
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These pictures show squares split into halves. Can you find other ways?

Break it up!
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Break it up!

Age
5 to 11
Challenge level
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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?

Arithmagons
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Arithmagons

Age
11 to 16
Challenge level
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Can you find the values at the vertices when you know the values on the edges?

Sizing them Up
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Sizing them up

Age
5 to 7
Challenge level
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Can you put these shapes in order of size? Start with the smallest.

Crossed Ends
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Crossed ends

Age
11 to 14
Challenge level
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Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Speeding boats
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Speeding boats

Age
14 to 16
Challenge level
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Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?
Mixing Lemonade
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Mixing lemonade

Age
11 to 14
Challenge level
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Can you work out which drink has the stronger flavour?

Colouring Triangles
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Colouring triangles

Age
5 to 7
Challenge level
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Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

Why 24?
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Why 24?

Age
14 to 16
Challenge level
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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.
Your number is...
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Your number is...

Age
7 to 14
Challenge level
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Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?