Explaining, convincing and proving

  • Which spinners?
    problem
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    Which Spinners?

    Age
    14 to 18
    Challenge level
    1 out of 3

    Can you work out which spinners were used to generate the frequency charts?

  • Summing geometric progressions
    problem
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    Summing Geometric Progressions

    Age
    14 to 18
    Challenge level
    1 out of 3

    Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

  • Perception versus reality
    problem
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    Perception Versus Reality

    Age
    14 to 18
    Challenge level
    1 out of 3

    Infographics are a powerful way of communicating statistical information. Can you come up with your own?

  • Always Two
    problem
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    Always Two

    Age
    14 to 18
    Challenge level
    2 out of 3

    Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.

  • Trapezium made of wooden tangram pieces, including a square and a parallelogram.
    problem
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    Quad in Quad

    Age
    14 to 18
    Challenge level
    2 out of 3

    Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?

  • Iff
    problem
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    Iff

    Age
    14 to 18
    Challenge level
    2 out of 3

    Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

  • Negative 3 to the power of negative 3.
    problem
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    Negative Powers

    Age
    14 to 18
    Challenge level
    2 out of 3

    What does this number mean? Which order of 1, 2, 3 and 4 makes the highest value? Which makes the lowest?

  • Back fitter
    problem
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    Back Fitter

    Age
    14 to 18
    Challenge level
    2 out of 3

    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?

  • Kite in a Square
    problem
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    Kite in a Square

    Age
    14 to 18
    Challenge level
    2 out of 3

    Can you make sense of the three methods to work out what fraction of the total area is shaded?

  • Curve fitter
    problem
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    Curve Fitter

    Age
    14 to 18
    Challenge level
    2 out of 3

    This problem challenges you to find cubic equations which satisfy different conditions.