Reasoning, convincing and proving

  • Square subtraction
    problem

    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?

  • Take three numbers
    problem

    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?

  • Odd times Even
    problem

    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.

  • problem

    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.

  • Particularly general
    problem

    Particularly general

    Age
    16 to 18
    Challenge level
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    By proving these particular identities, prove the existence of general cases.
  • Take one example
    article

    Take one example

    This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.
  • What's happening?
    problem

    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?
    problem

    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.

  • Going for Gold
    problem

    Going for gold

    Age
    7 to 11
    Challenge level
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    Looking at the Olympic Medal table, can you see how the data is organised? Could the results be presented differently to give another nation the top place?