Exploring and noticing

There are 412 NRICH Mathematical resources connected to Exploring and noticing
Fair Shares?
problem
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Fair shares?

Age
14 to 16
Challenge level
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A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?
Mystery Matrix
problem
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Mystery matrix

Age
7 to 11
Challenge level
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Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Skeleton Shapes
problem
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Skeleton shapes

Age
5 to 7
Challenge level
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How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

Stars
problem
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Stars

Age
11 to 14
Challenge level
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Can you work out what step size to take to ensure you visit all the dots on the circle?
Up and across
problem
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Up and across

Age
11 to 14
Challenge level
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Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

Route to infinity
problem
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Route to infinity

Age
11 to 14
Challenge level
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Can you describe this route to infinity? Where will the arrows take you next?
Matchless
problem
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Matchless

Age
14 to 16
Challenge level
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There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?
Strike it out
problem
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Strike it out

Age
5 to 11
Challenge level
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Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Counting Cogs
problem
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Counting cogs

Age
7 to 14
Challenge level
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Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
Area and perimeter
problem
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Area and perimeter

Age
7 to 11
Challenge level
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What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.