Reasoning, convincing and proving

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

Age
14 to 16
Challenge level
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Simple additions can lead to intriguing results...
Two numbers under the microscope
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Two numbers under the microscope

Age
5 to 7
Challenge level
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This investigates one particular property of number by looking closely at an example of adding two odd numbers together.
Odd times Even
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Odd times even

Age
5 to 7
Challenge level
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This problem looks at how one example of your choice can show something about the general structure of multiplication.
Take three numbers
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Take three numbers

Age
7 to 11
Challenge level
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What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Square subtraction
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Square subtraction

Age
7 to 11
Challenge level
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Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
What's happening?
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What's happening?

Age
5 to 7
Challenge level
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Shapes are added to other shapes. Can you see what is happening? What is the rule?

What's in a name?
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What's in a name?

Age
5 to 7
Challenge level
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Here's a very elementary code that requires young children to read a table, and look for similarities and differences.

The animals' sports day
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The animals' sports day

Age
5 to 7
Challenge level
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One day five small animals in my garden were going to have a sports day. They decided to have a swimming race, a running race, a high jump and a long jump.

So it's times!
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So it's times!

Age
7 to 14
Challenge level
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How will you decide which way of flipping over and/or turning the grid will give you the highest total?

The Domesday Project
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The domesday project

Age
7 to 11
Challenge level
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Take a look at these data collected by children in 1986 as part of the Domesday Project. What do they tell you? What do you think about the way they are presented?