Explaining, convincing and proving

  • 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?
  • Unravelling Sequences
    problem

    Unravelling sequences

    Age
    7 to 11
    Challenge level
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    Can you describe what is happening as this program runs? Can you unpick the steps in the process?
  • An Easy Way to Multiply by 10?
    problem

    An easy way to multiply by 10?

    Age
    7 to 11
    Challenge level
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    Do you agree with Badger's statements? Is Badger's reasoning 'watertight'? Why or why not?

  • Mathdoku
    problem

    Mathdoku

    Age
    7 to 11
    Challenge level
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    Complete the Mathdoku grid using the clues. Can you convince us that the number you have chosen for each square has to be correct?
  • Diagonally Square
    problem

    Diagonally square

    Age
    7 to 11
    Challenge level
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    Ayah conjectures that the diagonals of a square meet at right angles. Do you agree? How could you find out?

  • Triangle in a Square
    problem

    Triangle in a square

    Age
    7 to 11
    Challenge level
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    Do you agree with Badger's statements? Is Badger's reasoning watertight? Why or why not?
  • Digit Discovery
    problem

    Digit discovery

    Age
    7 to 11
    Challenge level
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    Here is an interesting property about two sets of digits. Can you work out what the digits might be?

  • problem

    Reach 100

    Age
    7 to 11
    Challenge level
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    Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

  • Stringy Quads
    problem

    Stringy quads

    Age
    7 to 11
    Challenge level
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    This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

  • Route Product
    problem

    Route product

    Age
    7 to 11
    Challenge level
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    Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?