Ratio and proportion

  • Once Upon a Time
    problem

    Once upon a time

    Age
    7 to 11
    Challenge level
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    Can you work out the height of Baby Bear's chair and whose bed is whose if all the things the three bears have are in the same proportions?
  • Rod Ratios
    problem

    Rod ratios

    Age
    7 to 11
    Challenge level
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    Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2?
  • Half a Triangle
    problem

    Half a triangle

    Age
    14 to 16
    Challenge level
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    Construct a line parallel to one side of a triangle so that the triangle is divided into two equal areas.
  • Triangle in a Triangle
    problem

    Triangle in a triangle

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    Can you work out the fraction of the original triangle that is covered by the inner triangle?

  • Slippage
    problem

    Slippage

    Age
    14 to 16
    Challenge level
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    A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance up the wall which the ladder can reach?
  • Televisual Technology
    problem

    Televisual technology

    Age
    14 to 16
    Challenge level
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    If a new and an old television have screens of the same area, what is the ratio of their widths?
  • Off the Cuff
    problem

    Off the cuff

    Age
    11 to 14
    Challenge level
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    Can you work out the ratio of shirt types made by a factory, if you know the ratio of button types used?
  • Circuit training
    problem

    Circuit training

    Age
    14 to 16
    Challenge level
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    Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever meet at the start again? If so, after how many circuits?
  • Bus Stop
    problem

    Bus stop

    Age
    14 to 16
    Challenge level
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    Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant and in the ratio 5 to 4. The buses travel to and fro between the towns. What milestones are at Shipton and Veston?
  • problem

    Orange drink

    Age
    7 to 11
    Challenge level
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    A 750 ml bottle of concentrated orange squash is enough to make fifteen 250 ml glasses of diluted orange drink. How much water is needed to make 10 litres of this drink?