Reasoning, convincing and proving

There are 458 NRICH Mathematical resources connected to Reasoning, convincing and proving
Adding odd numbers
problem

Adding odd numbers

Age
11 to 16
Challenge level
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Is there a quick and easy way to calculate the sum of the first 100 odd numbers?
Three consecutive odd numbers
problem

Three consecutive odd numbers

Age
11 to 16
Challenge level
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How many sets of three consecutive odd numbers can you find, in which all three numbers are prime?
Where are the primes?
problem

Where are the primes?

Age
11 to 16
Challenge level
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What can we say about all the primes which are greater than 3?
Three neighbours
problem

Three neighbours

Age
7 to 14
Challenge level
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Take three consecutive numbers and add them together. What do you notice?
Network Trees
problem

Network Trees

Age
14 to 18
Challenge level
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Explore some of the different types of network, and prove a result about network trees.
Always Perfect
problem

Always Perfect

Age
14 to 18
Challenge level
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Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
Equivalent Pairs
problem

Equivalent Pairs

Age
5 to 7
Challenge level
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Can you match pairs of cards which show the same amount?
Interactive Balance
interactivity

Interactive Balance

In this simulation of a balance, you can drag numbers and parts of number sentences on to the trays. Have a play!
True or False?
problem

True or False?

Age
7 to 11
Challenge level
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Without doing lots of calculations, can you decide which of these number sentences are true? How do you know?