Conjecturing and generalising

  • Can it be?
    problem

    Can it be?

    Age
    16 to 18
    Challenge level
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    When if ever do you get the right answer if you add two fractions by adding the numerators and adding the denominators?
  • Lots of Lollies
    problem

    Lots of lollies

    Age
    5 to 7
    Challenge level
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    Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

  • Share Bears
    problem

    Share bears

    Age
    5 to 7
    Challenge level
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    Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

  • Shadow Play
    problem

    Shadow play

    Age
    5 to 7
    Challenge level
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    Here are shadows of some 3D shapes. What shapes could have made them?

  • The Bridges of Konigsberg
    problem

    The bridges of Konigsberg

    Age
    11 to 18
    Challenge level
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    Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.

  • Tourism
    problem

    Tourism

    Age
    11 to 14
    Challenge level
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    If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

  • Painted Cube
    problem

    Painted cube

    Age
    14 to 16
    Challenge level
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    Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

  • Tilted Squares
    problem

    Tilted squares

    Age
    11 to 14
    Challenge level
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    It's easy to work out the areas of most squares that we meet, but what if they were tilted?

  • Coordinate Patterns
    problem

    Coordinate patterns

    Age
    11 to 14
    Challenge level
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    Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

  • Seven Squares - Group-worthy Task
    problem

    Seven squares - group-worthy task

    Age
    11 to 14
    Challenge level
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    Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?