Creating and manipulating expressions and formulae

  • Square Ratio
    problem

    Square Ratio

    Age
    14 to 16
    Challenge level
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    A square is divided into four rectangles and a square. Can you work out the ratio of the side lengths of the rectangles?

  • 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...

  • Simultaneous Multiplying
    problem

    Simultaneous Multiplying

    Age
    14 to 16
    Challenge level
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    If $a \times b=2$, $b \times c=24$, $c \times a=3$ and $a$, $b$ and $c$ are positive, what is the value of $a+b+c$?

  • Alternating Sum
    problem

    Alternating Sum

    Age
    14 to 16
    Challenge level
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    Given that the number 2008 is the correct answer to a sum, can you find n?

  • Algebraic Average
    problem

    Algebraic Average

    Age
    14 to 16
    Challenge level
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    The mean of three numbers x, y and z is x. What is the mean of y and z?

  • Three Fruits
    problem

    Three Fruits

    Age
    14 to 16
    Challenge level
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    Quince, quonce and quance are three types of fruit. Can you work out the order of heaviness of the fruits?

  • Average Surroundings
    problem

    Average Surroundings

    Age
    14 to 16
    Challenge level
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    Can you work out Ali's age based on the diagram?

  • Divisible Expression
    problem

    Divisible Expression

    Age
    14 to 16
    Challenge level
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    Can you show this algebraic expression is divisible by 4?

  • 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?