Reasoning, convincing and proving

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

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Painted cube

Age

14 to 16

Challenge level

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

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Contrary logic

Age

16 to 18

Challenge level

Can you invert the logic to prove these statements?

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The greedy algorithm

Age

11 to 14

Challenge level

The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.

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Finding factors

Age

14 to 16

Challenge level

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

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Terminology

Age

14 to 16

Challenge level

Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?

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Children at large

Age

11 to 14

Challenge level

There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?

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Cuisenaire counting

Age

5 to 7

Challenge level

Here are some rods that are different colours. How could I make a yellow rod using white and red rods?

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Stringy quads

Age

7 to 11

Challenge level

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

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Direct logic

Age

16 to 18

Challenge level

Can you work through these direct proofs, using our interactive proof sorters?

Strike it out

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Favourite

Strike it out

Age

5 to 11

Challenge level

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.