Exploring and noticing

There are 412 NRICH Mathematical resources connected to Exploring and noticing
Order, Order!
problem
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Order, order!

Age
5 to 11
Challenge level
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Can you place these quantities in order from smallest to largest?

Discuss and Choose
problem
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Discuss and choose

Age
5 to 11
Challenge level
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This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.

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?

Shopping Basket
problem
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Shopping basket

Age
11 to 16
Challenge level
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The items in the shopping basket add and multiply to give the same amount. What could their prices be?
Pick's Theorem
problem
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Pick's theorem

Age
14 to 16
Challenge level
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Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
Special Numbers
problem
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Special numbers

Age
11 to 14
Challenge level
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My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?