Reasoning, convincing and proving

  • Fit for photocopying
    problem

    Fit for photocopying

    Age
    14 to 16
    Challenge level
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    Explore the relationships between different paper sizes.

  • missing multipliers
    problem

    Missing multipliers

    Age
    7 to 14
    Challenge level
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    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?

  • Journeys in Numberland
    problem

    Journeys in Numberland

    Age
    7 to 11
    Challenge level
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    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
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    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?
  • problem

    The car that passes

    Age
    7 to 11
    Challenge level
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    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
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    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?

  • problem

    Pairs of numbers

    Age
    5 to 7
    Challenge level
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    If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

  • Curious number
    problem

    Curious number

    Age
    7 to 11
    Challenge level
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    Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

  • Takeaway Time
    problem

    Takeaway time

    Age
    14 to 16
    Challenge level
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    Pizza, Indian or Chinese takeaway? If everyone liked at least one, how many only liked Indian?