Reasoning, convincing and proving

  • Multiplication arithmagons
    problem

    Multiplication arithmagons

    Age
    14 to 16
    Challenge level
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    Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

  • Reversals
    problem

    Reversals

    Age
    11 to 14
    Challenge level
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    Where should you start, if you want to finish back where you started?

  • Unequal Averages
    problem

    Unequal averages

    Age
    11 to 14
    Challenge level
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    Play around with sets of five numbers and see what you can discover about different types of average...

  • Box plot match
    problem

    Box plot match

    Age
    14 to 16
    Challenge level
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    Match the cumulative frequency curves with their corresponding box plots.

  • Pythagoras Perimeters
    problem

    Pythagoras perimeters

    Age
    14 to 16
    Challenge level
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    If you know the perimeter of a right angled triangle, what can you say about the area?

  • Difference of Two Squares
    problem

    Difference of two squares

    Age
    14 to 16
    Challenge level
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    What is special about the difference between squares of numbers adjacent to multiples of three?

  • Impossibilities
    problem

    Impossibilities

    Age
    11 to 14
    Challenge level
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    Just because a problem is impossible doesn't mean it's difficult...

  • Garden Shed
    problem

    Garden shed

    Age
    11 to 14
    Challenge level
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    Can you minimise the amount of wood needed to build the roof of my garden shed?

  • Perimeter Challenge
    problem

    Perimeter challenge

    Age
    11 to 14
    Challenge level
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    Can you deduce the perimeters of the shapes from the information given?