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How much peel does an apple have?

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Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.

Robot Camera

Age 14 to 16
Challenge Level

Why do this problem ?

Nanotechnology is an important area of research for new products.  This problem uses a medical context for students to think about estimation and orders of magnitude.  These are crucial mathematical skills in the sciences.  This problem could be tackled by individual students or it could be tackled jointly by a whole class.

Possible approach

The first two questions will help students in working with very small numbers, including finding out what the units mean.  The class could then discuss whether they think it is possible in principle to make a camera suitable for injecting into an artery, before embarking on any calculations.

Key questions

Do you have all the information you need?  If not, where can you find out what you need?
What formulae will you need to use?
How accurate do you think your answer is?
What 'order of magnitude' checks could you make to test that your answer is sensible?

Possible extension

Students could come up with their own idea for a new product, and find out how feasible it is.

Possible support

Revise units and orders of magnitudes, starting from metres, then millimetres, and so on, using standard form.  Students could suggest objects which would be measured in each unit.