Conjecturing and generalising

  • Shadow Play
    problem
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    Shadow Play

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

    Here are shadows of some 3D shapes. What shapes could have made them?

  • Lots of Lollies
    problem
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    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?

  • More Numbers in the Ring
    problem
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    More Numbers in the Ring

    Age
    5 to 7
    Challenge level
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    If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

  • Stop the Clock
    problem
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    Stop the Clock

    Age
    5 to 7
    Challenge level
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    This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

  • Odd times Even
    problem
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    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.

  • Stop the Clock for Two
    game

    Stop the Clock for Two

    Age
    5 to 7
    Challenge level
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    Stop the Clock game for an adult and child. How can you make sure you always win this game?
  • Generalising
    list

    Generalising

    Age
    5 to 11
    These tasks give learners chance to generalise, which involves identifying an underlying structure.
  • Circles, Circles
    problem
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    Circles, Circles

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

    Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

  • Always, Sometimes or Never?
    problem
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    Always, Sometimes or Never?

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

    Are these statements relating to odd and even numbers always true, sometimes true or never true?