Conjecturing and generalising

  • Power mad!
    problem

    Power mad!

    Age
    11 to 14
    Challenge level
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    Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

  • For richer for poorer
    problem

    For richer for poorer

    Age
    14 to 16
    Challenge level
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    Charlie has moved between countries and the average income of both has increased. How can this be so?

  • Cuboid challenge
    problem

    Cuboid challenge

    Age
    11 to 16
    Challenge level
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    What's the largest volume of box you can make from a square of paper?

  • Searching for mean(ing)
    problem

    Searching for mean(ing)

    Age
    11 to 16
    Challenge level
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    If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?

  • problem

    Venn diagrams

    Age
    5 to 11
    Challenge level
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    How will you complete these interactive Venn diagrams?

  • Treasure Hunt
    problem

    Treasure hunt

    Age
    7 to 14
    Challenge level
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    Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

  • Magic Vs
    problem

    Magic Vs

    Age
    7 to 11
    Challenge level
    filled star empty star empty star

    Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

  • Crossed Ends
    problem

    Crossed ends

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

  • tiling
    problem

    Tiling

    Age
    7 to 11
    Challenge level
    filled star empty star empty star
    An investigation that gives you the opportunity to make and justify predictions.
  • Stop the Clock
    problem

    Stop the clock

    Age
    5 to 7
    Challenge level
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    This is a game for two players. Can you find out how to be the first to get to 12 o'clock?