Exploring and noticing

There are 412 NRICH Mathematical resources connected to Exploring and noticing
Repeating Patterns
problem
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Repeating patterns

Age
5 to 7
Challenge level
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Try continuing these patterns made from triangles. Can you create your own repeating pattern?
Back fitter
problem
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Back fitter

Age
14 to 18
Challenge level
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10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

Partly Painted Cube
problem
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Partly painted cube

Age
14 to 16
Challenge level
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Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
Ip Dip
problem
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Ip dip

Age
5 to 11
Challenge level
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"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

Number Families
problem
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Number families

Age
11 to 14
Challenge level
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How many different number families can you find?
Pebbles
problem
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Pebbles

Age
7 to 11
Challenge level
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Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Round and round the circle
problem
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Round and round the circle

Age
7 to 11
Challenge level
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What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

Differences
problem
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Differences

Age
11 to 14
Challenge level
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Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
Prison Cells
problem
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Prison cells

Age
7 to 11
Challenge level
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There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
Numerically Equal
problem
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Numerically equal

Age
7 to 11
Challenge level
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Can you draw a square in which the perimeter is numerically equal to the area?