Reasoning, convincing and proving

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

problem

Favourite

Triangle numbers

Age

11 to 14

Challenge level

Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?

problem

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What do you need?

Age

7 to 11

Challenge level

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

problem

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Two-digit targets

Age

5 to 7

Challenge level

You have a set of the digits from 0 to 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?

problem

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Cyclic quadrilaterals

Age

11 to 16

Challenge level

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

problem

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Common divisor

Age

14 to 16

Challenge level

Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.

problem

Favourite

Iff

Age

14 to 18

Challenge level

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

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?

problem

Favourite

Quad in quad

Age

14 to 18

Challenge level

Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?

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?

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Reasoning, convincing and proving

Triangle numbers

What do you need?

Two-digit targets

Cyclic quadrilaterals

Common divisor

Iff

Shadow play

Growing garlic

Quad in quad

Number rules - ok