Conjecturing and generalising

  • Count The Digits
    problem

    Count the digits

    Age
    5 to 11
    Challenge level
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    In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

  • At least one...
    problem

    At least one...

    Age
    11 to 14
    Challenge level
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    Imagine flipping a coin a number of times. Can you work out the probability you will get a head on at least one of the flips?

  • 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?

  • Area and perimeter
    problem

    Area and perimeter

    Age
    7 to 11
    Challenge level
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    What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

  • What does random look like?
    problem

    What does random look like?

    Age
    11 to 14
    Challenge level
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    Engage in a little mathematical detective work to see if you can spot the fakes.

  • Mathsland National Lottery
    problem

    Mathsland national lottery

    Age
    14 to 16
    Challenge level
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    Can you work out the probability of winning the Mathsland National Lottery?

  • Sitting round the party tables
    problem

    Sitting round the party tables

    Age
    5 to 11
    Challenge level
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    Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

  • Difference Dynamics
    problem

    Difference dynamics

    Age
    14 to 18
    Challenge level
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    Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?
  • Do you feel lucky?
    problem

    Do you feel lucky?

    Age
    11 to 14
    Challenge level
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    Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?