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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Dilution Series Calculator

### 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

### Key questions

### Possible extension

### Possible support

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Age 14 to 16

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

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.

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?

Try the problem Investigating the
Dilution Series.

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

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?