Creating and manipulating expressions and formulae

  • Areas of parallelograms
    problem
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    Areas of Parallelograms

    Age
    14 to 16
    Challenge level
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    Can you find the area of a parallelogram defined by two vectors?

  • Big Fish
    problem

    Big Fish

    Age
    14 to 16
    Challenge level
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    Granny has taken up deep-sea fishing! Last week, she caught a fish so big that she had to cut it into three pieces in order to weigh it...
  • Nicely Similar
    problem
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    Nicely Similar

    Age
    14 to 16
    Challenge level
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    If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?

  • Gutter
    problem
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    Gutter

    Age
    14 to 16
    Challenge level
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    Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

  • Matchless
    problem
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    Matchless

    Age
    14 to 16
    Challenge level
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    There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value. Can you find that x, y pair?

  • Partly Painted Cube
    problem
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    Partly Painted Cube

    Age
    14 to 16
    Challenge level
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    Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

  • problem
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    Simplifying Doughnut

    Age
    14 to 16
    Challenge level
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    Can you match up these equivalent algebraic expressions?

  • How do you react?
    problem

    How Do You React?

    Age
    14 to 16
    Challenge level
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    To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
  • Robert's spreadsheet
    problem

    Robert's Spreadsheet

    Age
    14 to 16
    Challenge level
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    Robert noticed some interesting patterns when he highlighted square numbers in a spreadsheet. Can you prove that the patterns will continue?
  • Training schedule
    problem
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    Training Schedule

    Age
    14 to 16
    Challenge level
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    The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?