Conjecturing and generalising

  • Roman Numerals
    problem
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    Roman Numerals

    Age
    7 to 11
    Challenge level
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    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
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    Satisfying Four Statements

    Age
    7 to 11
    Challenge level
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    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
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    Watch this animation. What do you see? Can you explain why this happens?

  • Dicey Operations in Line
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    Dicey Operations in Line

    Age
    7 to 11
    Challenge level
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    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
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    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?

  • The Great Tiling Count
    problem

    The Great Tiling Count

    Age
    7 to 11
    Challenge level
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    Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.
  • A section of a bracelet made of colourful beads.
    problem
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    Bracelets

    Age
    7 to 11
    Challenge level
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    Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

  • problem
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    Sweets in a Box

    Age
    7 to 11
    Challenge level
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    How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?