Reasoning, convincing and proving

There are 514 NRICH Mathematical resources connected to Reasoning, convincing and proving

problem

Favourite

Number rules - ok

Age

14 to 16

Challenge level

Can you produce convincing arguments that a selection of statements about numbers are true?

problem

Favourite

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?

problem

Favourite

Shadow play

Age

5 to 7

Challenge level

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

problem

Favourite

Growing garlic

Age

5 to 11

Challenge level

Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?

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Favourite

Mechanical integration

Age

16 to 18

Challenge level

To find the integral of a polynomial, evaluate it at some special points and add multiples of these values.

problem

Favourite

American billions

Age

11 to 14

Challenge level

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

problem

Favourite

Marbles in a box

Age

11 to 16

Challenge level

How many winning lines can you make in a three-dimensional version of noughts and crosses?

problem

Favourite

Square corners

Age

7 to 11

Challenge level

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

problem

Favourite

Make 37

Age

5 to 11

Challenge level

Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick any ten numbers from the bags so that their total is 37?

problem

Favourite

The tall tower

Age

5 to 7

Challenge level

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

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Reasoning, convincing and proving

Number rules - ok

Shopping basket

Shadow play

Growing garlic

Mechanical integration

American billions

Marbles in a box

Square corners

Make 37

The tall tower