Conjecturing and generalising

  • Odd times Even
    problem
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    Odd Times Even

    Age
    5 to 11
    Challenge level

    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

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

  • Roman Numerals
    problem
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    Roman Numerals

    Age
    7 to 11
    Challenge level

    Can you find some examples when the number of Roman numerals is fewer than the number of Arabic numerals for the same number?

  • Satisfying Four Statements
    problem
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    Satisfying Four Statements

    Age
    7 to 11
    Challenge level

    Can you find any two-digit numbers that satisfy all of these statements?

  • Tumbling Down
    problem
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    Tumbling Down

    Age
    7 to 11
    Challenge level

    Watch this animation. What do you see? Can you explain why this happens?

  • Dicey Operations in Line
    game
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    Dicey Operations in Line

    Age
    7 to 11
    Challenge level

    In these addition, subtraction, multiplication and division games, you'll need to think strategically to get closest to the target.

  • Doplication
    problem
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    Doplication

    Age
    7 to 11
    Challenge level

    We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

  • A section of a bracelet made of colourful beads.
    problem
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    Bracelets

    Age
    7 to 11
    Challenge level

    Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

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