Ratio, Proportion and Rates of Change: Age 11-16

This is part of our collection of favourite rich tasks arranged by topic.

If you are a teacher, you can find the whole collection on our Secondary Curriculum teacher page.
Alternatively, if you are a student, you'll find the same problems on our Secondary Curriculum student page.


  • Mixing Lemonade
    problem
    Favourite

    Mixing Lemonade

    Age
    11 to 14
    Challenge level
    1 out of 3

    Can you work out which drink has the stronger flavour?

  • Olympic Measures
    problem
    Favourite

    Olympic Measures

    Age
    11 to 14
    Challenge level
    1 out of 3

    These Olympic quantities have been jumbled up! Can you put them back together again?

  • Fractions Rectangle
    problem
    Favourite

    Fractions Rectangle

    Age
    11 to 14
    Challenge level
    1 out of 3

    The large rectangle is divided into quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?

  • Mixing Paints
    problem
    Favourite

    Mixing Paints

    Age
    11 to 14
    Challenge level
    2 out of 3

    Can you work out how to produce different shades of pink paint?

  • All in a jumble
    problem
    Favourite

    All in a Jumble

    Age
    11 to 14
    Challenge level
    2 out of 3

    My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.

  • Thousands and Millions
    problem
    Favourite

    Thousands and Millions

    Age
    11 to 14
    Challenge level
    2 out of 3

    Here's a chance to work with large numbers...

  • Triathlon and Fitness
    problem
    Favourite

    Triathlon and Fitness

    Age
    11 to 14
    Challenge level
    2 out of 3

    The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?

  • Nutrition and Cycling
    problem
    Favourite

    Nutrition and Cycling

    Age
    14 to 16
    Challenge level
    1 out of 3

    Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

  • The Legacy
    problem
    Favourite

    The Legacy

    Age
    14 to 16
    Challenge level
    2 out of 3

    Your school has been left a million pounds in the will of an ex-pupil. What model of investment and spending would you use in order to ensure the best return on the money?

  • Speeding boats
    problem
    Favourite

    Speeding Boats

    Age
    14 to 16
    Challenge level
    2 out of 3

    Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

  • Mixing More Paints
    problem
    Favourite

    Mixing More Paints

    Age
    14 to 16
    Challenge level
    3 out of 3

    Can you find an efficent way to mix paints in any ratio?

  • Dating made Easier
    problem
    Favourite

    Dating Made Easier

    Age
    14 to 16
    Challenge level
    3 out of 3

    If a sum invested gains 10% each year how long before it has doubled its value?

  • Areas and Ratios
    problem
    Favourite

    Areas and Ratios

    Age
    16 to 18
    Challenge level
    2 out of 3

    Do you have enough information to work out the area of the shaded quadrilateral?