Conjecturing and generalising

There are 405 NRICH Mathematical resources connected to Conjecturing and generalising

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Consecutive numbers

Age

7 to 14

Challenge level

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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Of all the areas

Age

14 to 16

Challenge level

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?

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Abundant numbers

Age

7 to 11

Challenge level

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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Which is quicker?

Age

7 to 11

Challenge level

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

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Partitioning revisited

Age

11 to 14

Challenge level

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

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At right angles

Age

14 to 16

Challenge level

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

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Mystic rose

Age

14 to 16

Challenge level

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

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Ip dip

Age

5 to 11

Challenge level

"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 ...?

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Chocolate

Age

7 to 14

Challenge level

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

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Odd differences

Age

14 to 16

Challenge level

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = nÂ² Use the diagram to show that any odd number is the difference of two squares.

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For younger learners

Conjecturing and generalising

Consecutive numbers

Of all the areas

Abundant numbers

Which is quicker?

Partitioning revisited

At right angles

Mystic rose

Ip dip

Chocolate

Odd differences