Exploring and noticing

  • 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!

  • 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?

  • Differences
    problem
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    Differences

    Age
    11 to 14
    Challenge level
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    Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

  • How Many Miles To Go?
    problem
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    How Many Miles to Go?

    Age
    11 to 14
    Challenge level
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    How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

  • Up and across
    problem
    Favourite

    Up and Across

    Age
    11 to 14
    Challenge level
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    Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

  • Litov's Mean Value Theorem
    problem
    Favourite

    Litov's Mean Value Theorem

    Age
    11 to 14
    Challenge level
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    Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

  • A Chance to Win?
    problem
    Favourite

    A Chance to Win?

    Age
    11 to 14
    Challenge level
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    Imagine you were given the chance to win some money... and imagine you had nothing to lose...

  • Going to the cinema
    problem
    Favourite

    Going to the Cinema

    Age
    11 to 16

    A cinema has 100 seats. Is it possible to fill every seat and take exactly £100?

  • Diamond Collector
    game
    Favourite

    Diamond Collector

    Age
    11 to 16
    Challenge level
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    Collect as many diamonds as you can by drawing three straight lines.

  • What's it worth?
    problem
    Favourite

    What's It Worth?

    Age
    11 to 16
    Challenge level
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    There are lots of different methods to find out what the shapes are worth - how many can you find?