Exploring and noticing

There are 412 NRICH Mathematical resources connected to Exploring and noticing

problem

Favourite

Differences

Age

11 to 14

Challenge level

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

problem

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Prison cells

Age

7 to 11

Challenge level

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?

problem

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Numerically equal

Age

7 to 11

Challenge level

Can you draw a square in which the perimeter is numerically equal to the area?

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Shopping basket

Age

11 to 16

Challenge level

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

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Favourite

Pick's theorem

Age

14 to 16

Challenge level

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.

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Special numbers

Age

11 to 14

Challenge level

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?

problem

Favourite

Mixing paints

Age

11 to 14

Challenge level

Can you work out how to produce different shades of pink paint?

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Sort the street

Age

5 to 7

Challenge level

Sort the houses in my street into different groups. Can you do it in any other ways?

problem

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A chance to win?

Age

11 to 14

Challenge level

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

problem

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In the bag

Age

11 to 14

Challenge level

Can you guess the colours of the 10 marbles in the bag? Can you develop an effective strategy for reaching 1000 points in the least number of rounds?

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Exploring and noticing

Differences

Prison cells

Numerically equal

Shopping basket

Pick's theorem

Special numbers

Mixing paints

Sort the street

A chance to win?

In the bag