### 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

Try the problem Investigating the Dilution Series.

### Possible support

Work though a particular example as a group before attempting individual practice. Show the answer first and try to work backwards.