Reasoning, convincing and proving

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

problem

Different products

Age

14 to 16

Challenge level

Take four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

problem

What does it all add up to?

Age

11 to 18

Challenge level

If you take four consecutive numbers and add them together, the answer will always be even. What else do you notice?

problem

Adding odd numbers

Age

11 to 16

Challenge level

Is there a quick and easy way to calculate the sum of the first 100 odd numbers?

problem

Three consecutive odd numbers

Age

11 to 16

Challenge level

How many sets of three consecutive odd numbers can you find, in which all three numbers are prime?

problem

Where are the primes?

Age

11 to 16

Challenge level

What can we say about all the primes which are greater than 3?

problem

Euler meets schlegel

Age

16 to 18

Challenge level

Discover how networks can be used to prove Euler's Polyhedron formula.

problem

Network trees

Age

14 to 18

Challenge level

Explore some of the different types of network, and prove a result about network trees.

problem

Common divisor

Age

14 to 18

Challenge level

Can you find out what numbers divide these expressions? Can you prove that they are always divisors?

problem

True or false?

Age

7 to 11

Challenge level

Without doing lots of calculations, can you decide which of these number sentences are true? How do you know?

problem

Sweetie box

Age

5 to 11

Challenge level

Max and Bryony both have a box of sweets. What do you know about the number of sweets they each have?

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Reasoning, convincing and proving

Different products

What does it all add up to?

Adding odd numbers

Three consecutive odd numbers

Where are the primes?

Euler meets schlegel

Network trees

Common divisor

True or false?

Sweetie box