Conjecturing and generalising

There are 405 NRICH Mathematical resources connected to Conjecturing and generalising

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Favourite

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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Favourite

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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Favourite

Fair shares?

Age

14 to 16

Challenge level

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?

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Flashing lights

Age

7 to 11

Challenge level

Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

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Favourite

Shadow play

Age

5 to 7

Challenge level

Here are shadows of some 3D shapes. What shapes could have made them?

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Cubes within cubes revisited

Age

11 to 14

Challenge level

Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?

problem

Favourite

Mirror, mirror...

Age

11 to 14

Challenge level

Explore the effect of reflecting in two parallel mirror lines.

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Conjecturing and generalising

At right angles

Mystic rose

Ip dip

Chocolate

Odd differences

Fair shares?

Flashing lights

Shadow play

Cubes within cubes revisited

Mirror, mirror...