Exploring and noticing

There are 412 NRICH Mathematical resources connected to Exploring and noticing
Sizing them Up
problem
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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.

Factor-Multiple Chains
problem
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Factor-multiple chains

Age
7 to 11
Challenge level
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Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
The Legacy
problem
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The legacy

Age
14 to 16
Challenge level
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Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?
Two-digit targets
problem
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Two-digit targets

Age
5 to 7
Challenge level
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You have a set of the digits from 0 to 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?

Follow the numbers
problem
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Follow the numbers

Age
7 to 11
Challenge level
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What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

Cubes
problem
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Cubes

Age
7 to 11
Challenge level
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How many faces can you see when you arrange these three cubes in different ways?
Tree tops
problem
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Tree tops

Age
14 to 16
Challenge level
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Can you make sense of information about trees in order to maximise the profits of a forestry company?
Make 100
problem
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Make 100

Age
7 to 11
Challenge level
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Find at least one way to put in some operation signs to make these digits come to 100.
One Wasn't Square
problem
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One wasn't square

Age
7 to 11
Challenge level
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Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.
Tiny Nines
problem
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Tiny nines

Age
14 to 16
Challenge level
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What do you notice about these families of recurring decimals?