Exploring and noticing

There are 412 NRICH Mathematical resources connected to Exploring and noticing

problem

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Fifteen cards

Age

7 to 11

Challenge level

Can you use the information to find out which cards I have used?

problem

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Summing consecutive numbers

Age

11 to 14

Challenge level

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

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All change

Age

5 to 7

Challenge level

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

problem

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Attractive tablecloths

Age

14 to 16

Challenge level

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

problem

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Filling the gaps

Age

14 to 16

Challenge level

Which numbers can we write as a sum of square numbers?

problem

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Jumping

Age

7 to 11

Challenge level

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

problem

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Factor track

Age

7 to 11

Challenge level

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

problem

Favourite

Generating triples

Age

14 to 16

Challenge level

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

problem

Favourite

Sieve of eratosthenes

Age

11 to 14

Challenge level

Follow this recipe for sieving numbers and see what interesting patterns emerge.

problem

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Odds, evens and more evens

Age

11 to 14

Challenge level

Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

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For younger learners

Exploring and noticing

Fifteen cards

Summing consecutive numbers

All change

Attractive tablecloths

Filling the gaps

Jumping

Factor track

Generating triples

Sieve of eratosthenes

Odds, evens and more evens