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Work with numbers big and small to estimate and calulate various quantities in biological contexts.

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Bigger or Smaller?

When you change the units, do the numbers get bigger or smaller?

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Bio Graphs

What biological growth processes can you fit to these graphs?

Natural Shapes

Age 14 to 16 Challenge Level:

Why do this problem ?

Approximating physical quantities by idealised mathematical shapes is a commonly used tool in mathematical biology. By thinking about these issues and categorising the shapes, students will learn that various shapes occur both naturally and frequently in nature. Students will intuitively have some concept as to how 'good' an representation might be; by explicitly discussing the concepts, understanding of the strengths and limitations of these representations will grow.

Possible approach

This question could be posed individually or for group discussion. This problem also works effectively when students are given time to reflect. Ask the question and let students consider it over, say, a week. What shapes have they noticed in nature? This results might make an effective display.

Key questions

  • How reasonable is the mathematical idealisation?
  • Are there any objects which are particularly well represented by a certain shape?
  • What order of magnitude checks could you make to test that your answer is sensible?

Possible extension

Can students think of good evolutionary reasons for the shapes that certain organisms take?

Possible support

Students might struggle with the 'open' nature of the question, as there is no 'complete' answer.To begin, they might like to read the Student Guide to Getting Started with Rich Tasks