Geometric sequences

  • Investigating Pascal's Triangle
    problem

    Investigating Pascal's triangle

    Age
    7 to 11
    Challenge level
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    In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.

  • Production Equation
    problem

    Production equation

    Age
    16 to 18
    Challenge level
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    Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
  • Smaller and Smaller
    problem

    Smaller and smaller

    Age
    7 to 14
    Challenge level
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    Can you predict, without drawing, what the perimeter of the next shape in this pattern will be if we continue drawing them in the same way?
  • Von Koch Curve
    problem

    Von Koch curve

    Age
    16 to 18
    Challenge level
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    Make a poster using equilateral triangles with sides 27, 9, 3 and 1 units assembled as stage 3 of the Von Koch fractal. Investigate areas & lengths when you repeat a process infinitely often.

  • Magic Plant
    problem

    Magic plant

    Age
    5 to 7
    Challenge level
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    On Friday the magic plant was only 2 centimetres tall. Every day it doubled its height. How tall was it on Monday?

  • problem

    The amazing splitting plant

    Age
    5 to 7
    Challenge level
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    Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

  • The tomato and the bean
    problem

    The tomato and the bean

    Age
    5 to 7
    Challenge level
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    At the beginning of May, Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

  • The Great Tiling Count
    problem

    The great tiling count

    Age
    7 to 11
    Challenge level
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    Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.
  • Pocket money
    problem

    Pocket money

    Age
    11 to 14
    Challenge level
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    Which of these pocket money systems would you rather have?