Visualising and representing

  • Filling the gaps
    problem

    Filling the gaps

    Age
    14 to 16
    Challenge level
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    Which numbers can we write as a sum of square numbers?

  • Sieve of Eratosthenes
    problem

    Sieve of Eratosthenes

    Age
    11 to 14
    Challenge level
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    Follow this recipe for sieving numbers and see what interesting patterns emerge.

  • Number Pyramids
    problem

    Number pyramids

    Age
    11 to 14
    Challenge level
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    Try entering different sets of numbers in the number pyramids. How does the total at the top change?

  • Odds, Evens and More Evens
    problem

    Odds, evens and more evens

    Age
    11 to 14
    Challenge level
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    Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

  • problem

    Track design

    Age
    14 to 16
    Challenge level
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    Where should runners start the 200m race so that they have all run the same distance by the finish?

  • Fill Me Up Too
    problem

    Fill me up too

    Age
    14 to 16
    Challenge level
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    In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

  • What's that graph?
    problem

    What's that graph?

    Age
    14 to 18
    Challenge level
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    Can you work out which processes are represented by the graphs?

  • Alison's quilt
    problem

    Alison's quilt

    Age
    11 to 14
    Challenge level
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    Nine squares are fitted together to form a rectangle. Can you find its dimensions?

  • Fractions Rectangle
    problem

    Fractions rectangle

    Age
    11 to 14
    Challenge level
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    The large rectangle is divided into quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?

  • Seven Squares
    problem

    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?