Fractions

  • Ben's Game
    problem
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    Ben's Game

    Age
    11 to 16
    Challenge level
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    Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

  • Counting Fish
    problem

    Counting Fish

    Age
    14 to 16
    Challenge level
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    I need a figure for the fish population in a lake. How does it help to catch and mark 40 fish?

  • The genes of Gilgamesh
    problem

    The Genes of Gilgamesh

    Age
    14 to 16
    Challenge level
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    Can you work out the parentage of the ancient hero Gilgamesh?

  • Rationals Between...
    problem

    Rationals Between...

    Age
    14 to 16
    Challenge level
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    What fractions can you find between the square roots of 65 and 67?
  • Fair Shares?
    problem
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    Fair Shares?

    Age
    14 to 16
    Challenge level
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    A mother wants to share some money by giving each child in turn a lump sum plus a fraction of the remainder. How can she do this to share the money out equally?

  • Geometry and Measure - Short Problems
    problem

    F'arc'tion

    Age
    14 to 16
    Challenge level
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    At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and paper.

  • Archimedes and numerical roots
    problem

    Archimedes and Numerical Roots

    Age
    14 to 16
    Challenge level
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    The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
  • Tiny Nines
    problem
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    Tiny Nines

    Age
    14 to 16
    Challenge level
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    What do you notice about these families of recurring decimals?

  • Repetitiously
    problem
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    Repetitiously

    Age
    14 to 16
    Challenge level
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    Can you express every recurring decimal as a fraction?

  • What a Joke
    problem

    What a Joke

    Age
    14 to 16
    Challenge level
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    Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?