Powers and Roots: 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.


  • A glue stick with the lid off.
    problem
    Favourite

    Sticky Numbers

    Age
    11 to 14
    Challenge level

    Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

  • Pocket money
    problem
    Favourite

    Pocket Money

    Age
    11 to 14
    Challenge level

    Which of these pocket money systems would you rather have?

  • Power Countdown
    problem
    Favourite

    Power Countdown

    Age
    14 to 16
    Challenge level

    In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.

  • Generating Triples
    problem
    Favourite

    Generating Triples

    Age
    14 to 16
    Challenge level

    Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

  • Standard Index Form Matching
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    Favourite

    Standard Index Form Matching

    Age
    14 to 16
    Challenge level

    Can you match these calculations in Standard Index Form with their answers?

  • A question of scale
    problem
    Favourite

    A Question of Scale

    Age
    14 to 16
    Challenge level

    Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

  • Negative 3 to the power of negative 3.
    problem
    Favourite

    Negative Powers

    Age
    14 to 18
    Challenge level

    What does this number mean? Which order of 1, 2, 3 and 4 makes the highest value? Which makes the lowest?

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