Conjecturing and generalising

  • Beelines
    problem

    Beelines

    Age
    14 to 16
    Challenge level
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    Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

  • Odds and Evens made fair
    problem

    Odds and evens made fair

    Age
    14 to 16
    Challenge level
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    In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.

  • Train Spotters' Paradise
    article

    Train spotters' paradise

    Dave Hewitt suggests that there might be more to mathematics than looking at numerical results, finding patterns and generalising.
  • Summing geometric progressions
    problem

    Summing geometric progressions

    Age
    14 to 18
    Challenge level
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    Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

  • Making Spirals
    problem

    Making spirals

    Age
    7 to 11
    Challenge level
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    Can you make a spiral for yourself? Explore some different ways to create your own spiral pattern and explore differences between different spirals.

  • Constructing Triangles
    problem

    Constructing triangles

    Age
    11 to 14
    Challenge level
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    Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

  • Interpolating polynomials
    problem

    Interpolating polynomials

    Age
    16 to 18
    Challenge level
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    Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.
  • Different Sizes
    problem

    Different sizes

    Age
    5 to 11
    Challenge level
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    A simple visual exploration into halving and doubling.

  • Take three numbers
    problem

    Take three numbers

    Age
    7 to 11
    Challenge level
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    What happens when you add three numbers together? Will your answer be odd or even? How do you know?

  • Odd times Even
    problem

    Odd times even

    Age
    5 to 7
    Challenge level
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    This problem looks at how one example of your choice can show something about the general structure of multiplication.