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'Dilution Series Calculator' printed from https://nrich.maths.org/
Why do this problem?
This
activity gives repeated practice in the proportional reasoning
required to understand dilution calculations. It is surprising how
even quite skilled mathematicians find this quite tricky. Clear
thinking is required and this will be developed by the problem.
Possible approach
The key is to realise that the calculation is the same step
repeated 4 times. At each step we need to determine the
concentration of cells per ml. This will require a clear pen and
paper calculation and the use of a calculator. Once the concept is
grasped, keep trying until the ideas are firmly understood and the
problem can be solved quickly.
Key questions
How can you work out the effects of a single dilution?
What happens if all of the numbers are set to 100?
What happens if the first number is reduced to 50?
Possible extension
Possible support
Work though a particular example as a group before attempting
individual practice. Show the answer first and try to work
backwards.