Reasoning, convincing and proving

  • Bryony's Triangle
    problem

    Bryony's triangle

    Age
    7 to 11
    Challenge level
    filled star empty star empty star

    Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

  • Fit for photocopying
    problem

    Fit for photocopying

    Age
    14 to 16
    Challenge level
    filled star filled star filled star

    Explore the relationships between different paper sizes.

  • missing multipliers
    problem

    Missing multipliers

    Age
    7 to 14
    Challenge level
    filled star empty star empty star

    What is the smallest number of answers you need to reveal in order to work out the missing headers?

  • Which solids can we make?
    problem

    Which solids can we make?

    Age
    11 to 14
    Challenge level
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    Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

  • Archimedes Numerical Roots
    problem

    Archimedes numerical roots

    Age
    16 to 18
    Challenge level
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    How did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

  • Journeys in Numberland
    problem

    Journeys in Numberland

    Age
    7 to 11
    Challenge level
    filled star empty star empty star

    Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

  • The add and take-away path
    problem

    The add and take-away path

    Age
    5 to 7
    Challenge level
    filled star empty star empty star

    Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

  • What does random look like?
    problem

    What does random look like?

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    Engage in a little mathematical detective work to see if you can spot the fakes.

  • problem

    The car that passes

    Age
    7 to 11
    Challenge level
    filled star empty star empty star

    What statements can you make about the car that passes the school gates at 11am on Monday? How will you come up with statements and test your ideas?

  • problem

    Inky cube

    Age
    7 to 14
    Challenge level
    filled star filled star filled star

    This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?