Conjecturing and generalising

  • Different Sizes
    problem
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    Different Sizes

    Age
    5 to 11
    Challenge level
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    A simple visual exploration into halving and doubling.

  • Digit Addition
    problem
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    Digit Addition

    Age
    5 to 11
    Challenge level
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    Try out this number trick. What happens with different starting numbers? What do you notice?

  • Dicey Array
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    Dicey Array

    Age
    5 to 11
    Challenge level
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    Watch the video of this game being played. Can you work out the rules? Which dice totals are good to get, and why?

  • Make 37 Poster
    problem
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    Make 37

    Age
    5 to 11
    Challenge level
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    Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick ten numbers from the bags so that their total is 37?

  • Hundred Square Poster
    problem
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    Hundred Square

    Age
    5 to 11
    Challenge level
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    A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

  • problem
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    How Odd

    Age
    5 to 11
    Challenge level
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    This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

  • Three Squares
    problem
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    Three Squares

    Age
    5 to 11
    Challenge level
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    What is the greatest number of squares you can make by overlapping three squares?

  • Shadow Play
    problem
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    Shadow Play

    Age
    5 to 11
    Challenge level
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    Here are shadows of some 3D shapes. What shapes could have made them?

  • Odd times Even
    problem
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    Odd Times Even

    Age
    5 to 11
    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.

  • Build it up
    problem
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    Build It Up

    Age
    7 to 11
    Challenge level
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    Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.