Conjecturing and generalising

  • The square top of a red gift box with a bow.
    problem
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    Square Number Surprises

    Age
    14 to 16
    Challenge level
    2 out of 3

    There are unexpected discoveries to be made about square numbers...

  • Harmonic Triangle
    problem
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    Harmonic Triangle

    Age
    14 to 16
    Challenge level
    3 out of 3

    Can you see how to build a harmonic triangle? Can you work out the next two rows?

  • Mixing More Paints
    problem
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    Mixing More Paints

    Age
    14 to 16
    Challenge level
    3 out of 3

    Can you find an efficent way to mix paints in any ratio?

  • Parabolic Patterns
    problem
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    Parabolic Patterns

    Age
    14 to 18
    Challenge level
    1 out of 3

    The illustration shows the graphs of fifteen functions. Two of them have equations $y=x^2$ and $y=-(x-4)^2$. Find the equations of all the other graphs.

  • Vector walk
    problem
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    Vector Walk

    Age
    14 to 18
    Challenge level
    1 out of 3

    Starting with two basic vector steps, which destinations can you reach on a vector walk?

  • Vector journeys
    problem
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    Vector Journeys

    Age
    14 to 18
    Challenge level
    1 out of 3

    Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

  • 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?

  • 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?

  • Tangled Trig Graphs
    problem
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    Tangled Trig Graphs

    Age
    16 to 18
    Challenge level
    1 out of 3

    Can you work out the equations of the trig graphs I used to make my pattern?