Conjecturing and generalising

There are 405 NRICH Mathematical resources connected to Conjecturing and generalising

problem

Favourite

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

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Mirror, mirror...

Age

11 to 14

Challenge level

Explore the effect of reflecting in two parallel mirror lines.

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Consecutive negative numbers

Age

11 to 14

Challenge level

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

problem

Favourite

Handshakes

Age

11 to 14

Challenge level

Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?

problem

Favourite

How odd

Age

5 to 7

Challenge level

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

problem

Favourite

What was in the box?

Age

5 to 7

Challenge level

This big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?

problem

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Pebbles

Age

7 to 11

Challenge level

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?

problem

Favourite

Dozens

Age

7 to 14

Challenge level

Can you select the missing digit(s) to find the largest multiple?

problem

Favourite

1 step 2 step

Age

11 to 14

Challenge level

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

problem

Favourite

Picturing triangular numbers

Age

11 to 14

Challenge level

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

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For younger learners

Conjecturing and generalising

Cubes within cubes revisited

Mirror, mirror...

Consecutive negative numbers

Handshakes

How odd

What was in the box?

Pebbles

Dozens

1 step 2 step

Picturing triangular numbers