Conjecturing and generalising

  • Seven Squares
    problem
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    Seven Squares

    Age
    11 to 14
    Challenge level
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    Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

  • Changing areas, changing volumes
    problem
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    Changing Areas, Changing Volumes

    Age
    11 to 14
    Challenge level
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    How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?

  • Non-Transitive Dice
    problem
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    Non-transitive Dice

    Age
    11 to 14
    Challenge level
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    Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?

  • Hourglass with blue sand.
    problem
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    Estimating Time

    Age
    11 to 14
    Challenge level
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    How well can you estimate 10 seconds? Investigate with our timing tool.

  • Garden Shed
    problem
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    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?

  • Unequal Averages
    problem
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    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...

  • Fibonacci Surprises
    problem
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    Fibonacci Surprises

    Age
    11 to 14
    Challenge level
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    Play around with the Fibonacci sequence and discover some surprising results!

  • Maxagon
    problem

    Maxagon

    Age
    11 to 14
    Challenge level
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    What's the greatest number of sides a polygon on a dotty grid could have?

  • Terminating or not
    problem
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    Terminating or Not

    Age
    11 to 14
    Challenge level
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    Is there a quick way to work out whether a fraction terminates or recurs when you write it as a decimal?

  • What numbers can we make now?
    problem
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    What Numbers Can We Make Now?

    Age
    11 to 14
    Challenge level
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    Imagine we have four bags containing numbers from a sequence. What numbers can we make now?