Visualising and representing

  • Ford Circles
    problem

    Ford circles

    Age
    16 to 18
    Challenge level
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    Can you find the link between these beautiful circle patterns and Farey Sequences?

  • Classical Means
    problem

    Classical means

    Age
    16 to 18
    Challenge level
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    Use the diagram to investigate the classical Pythagorean means.
  • Summing squares
    problem

    Summing squares

    Age
    14 to 16
    Challenge level
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    Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?
  • Coordinated crystals
    problem

    Coordinated crystals

    Age
    16 to 18
    Challenge level
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    Explore the lattice and vector structure of this crystal.
  • Vector walk
    problem

    Vector walk

    Age
    14 to 18
    Challenge level
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    Starting with two basic vector steps, which destinations can you reach on a vector walk?

  • Coded hundred square
    problem

    Coded hundred square

    Age
    7 to 11
    Challenge level
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    This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

  • Surprising Transformations
    problem

    Surprising transformations

    Age
    14 to 16
    Challenge level
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    I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

  • Translating Lines
    problem

    Translating lines

    Age
    11 to 14
    Challenge level
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    Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.

  • HexPentas
    problem

    HexPentas

    Age
    5 to 11
    Challenge level
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    How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

  • Back fitter
    problem

    Back fitter

    Age
    14 to 18
    Challenge level
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    10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?