Reasoning, convincing and proving

There are 514 NRICH Mathematical resources connected to Reasoning, convincing and proving
What numbers can we make now?
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What numbers can we make now?

Age
11 to 14
Challenge level
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Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

More Less is More
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More less is more

Age
7 to 14
Challenge level
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In each of these games, you will need a little bit of luck, and your knowledge of place value to develop a winning strategy.
5 by 5 Mathdokus
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5 by 5 mathdokus

Age
7 to 16
Challenge level
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Can you use the clues to complete these 5 by 5 Mathematical Sudokus?
4 by 4 Mathdokus
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4 by 4 mathdokus

Age
7 to 14
Challenge level
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Can you use the clues to complete these 4 by 4 Mathematical Sudokus?
Pythagoras Proofs
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Pythagoras proofs

Age
11 to 16
Challenge level
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Can you make sense of these three proofs of Pythagoras' Theorem?

An Easy Way to Multiply by 10?
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An easy way to multiply by 10?

Age
7 to 11
Challenge level
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Do you agree with Badger's statements? Is Badger's reasoning 'watertight'? Why or why not?
Three neighbours
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Three neighbours

Age
7 to 14
Challenge level
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Take three consecutive numbers and add them together. What do you notice?
Always Perfect
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Always perfect

Age
14 to 18
Challenge level
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Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
Equivalent Pairs
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Equivalent pairs

Age
5 to 7
Challenge level
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Can you match pairs of cards which show the same amount?
Curve fitter
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Curve fitter

Age
14 to 18
Challenge level
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This problem challenges you to find cubic equations which satisfy different conditions.