Big and Small Numbers in Biology

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

Using the Haemocytometer

Stage: 4 Challenge Level:

Why do this problem ?

The haemocytometer is an important piece of scientific apparatus. This interactivity will allow students to practice the relevant skills of proportional reasoning required for its use.The solution to the problem provides lots of scientific insight into the real use of such a piece of equipment,

Possible approach

This resource could be used for whole class or individual use. The configuration for the question is randomly generated each time the refresh button is pressed. This will require students to stay on their toes whilst answering the questions.

Once students have become skilled in the use of the interactivity, you might like to try a race: project a configuration onto the board and the first student to obtain the correct answers is the winner, allowing them to balance speed with accuracy.

There are two key issues involved with using a haemocytometer:

1) The sample chosen on the slide might not uniformly represent the density in the big sample of the medium

2) The cell count might be made difficult due to overlapping cells on the microscope slide.

Students should realise that they always need to consider the questions

1) Is my sample uniform?

2) Are the obscured cells on the microscope slide.

You could discuss these issues with the help of multiple choices of cells and higher or lower density of medium (select these on the interactivitiy). Don't forget that you can zoom in and drag the grid around to focus on issues of overlapping cells.

Key questions

Have you understood the configuration of the grid? How big is the whole grid?

Is there an obvious order in which to work out the various answers? Why?

Given the details for a question, how might you jump straight from the count of the cells on the screen to the number of cells in the original sample?

Possible extension

Can students find algebraic answers to the questions for a general set of inputs?

In what situations might the haemocytometer be more likely to give inaccurate results? How accurate would you expect the results to be in everyday usage?

Possible support

At first, you might like to show the answers and ask students to replicate them.

Complex numbers. STEM - living world. Mathematical reasoning & proof. Calculating with ratio & proportion. chemistry. Interactivities. Games. Making and proving conjectures. physics. Estimating and approximating.

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