Conjecturing and generalising

  • Route to infinity
    problem
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    Route to Infinity

    Age
    11 to 14
    Challenge level
    2 out of 3

    Can you describe this route to infinity? Where will the arrows take you next?

  • Power mad!
    problem
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    Power Mad!

    Age
    11 to 14
    Challenge level
    2 out of 3

    Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

  • Christmas chocolates
    problem
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    Christmas Chocolates

    Age
    11 to 14
    Challenge level
    2 out of 3

    How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?

  • The Tower of Hanoi - three wooden poles, with several coloured rings of decreasing sizes on the middle pole.
    problem
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    Tower of Hanoi

    Age
    11 to 14
    Challenge level
    2 out of 3

    The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

  • Handshakes
    problem
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    Handshakes

    Age
    11 to 14
    Challenge level
    2 out of 3
    Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
  • Opposite vertices
    problem
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    Opposite Vertices

    Age
    11 to 14
    Challenge level
    2 out of 3

    Can you recreate squares and rhombuses if you are only given a side or a diagonal?

  • Seven Squares
    problem
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    Seven Squares

    Age
    11 to 14
    Challenge level
    2 out of 3

    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
    2 out of 3

    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
    2 out of 3

    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
    Favourite

    Estimating Time

    Age
    11 to 14
    Challenge level
    2 out of 3

    How well can you estimate 10 seconds? Investigate with our timing tool.