Measuring the thickness of a coin
Introducing the idea of measuring multiple objects and finding an average.
Apparatus and materials
For each student group
Large supply of coins (all of one denomination)
Ruler with graduations in mm (e.g. metre rule)
Health & Safety and Technical notes
There is a significant risk that the coins will go missing! You could use steel washers as an alternative if you are concerned about this.
a Estimate the thickness of a single coin.
b Measure one with a ruler.
c Measure a pile of coins stacked on each other. Calculate the average thickness.
1 Each student should try to measure the thickness of a single coin with a ruler with millimetres marked on it. The teacher should ask for results and also ask how reliable students think they are. Then ask for suggestions of improvement. Some may suggest measuring the height of a pile of coins and then calculate the thickness of one.
2 Discuss the general idea of accuracy behind the method by saying:
Suppose you have just one good coin and this ruler marked in millimetres, how thick would you find the coin if you could measure it very carefully? Yes, we do now know that the thickness is, say, 1.3 mm but could you really see that if you had just one coin to measure? Even if you thought you could see it, would that be a safe and fair answer to give? With just one coin what would be the fairest thing to say? If you wanted to be quite safe, what would you say? Yes I agree; all we can say is somewhere between 1 and 2 millimetres.
Now suppose you have 10 coins in a pile and you measure the pile. Even if you make a mistake of 1 millimetre in that measurement, how much of a mistake is that in the thickness of one coin? So if you measure 10 coins you could say that you think each coin is 1.3 millimetres thick. What would you say if you measured 100 coins in a pile?
At an introductory level, you might leave this problem there and come back to it later. Big numbers and small decimals are not easy, and the problem of accuracy is not a particularly interesting one yet.
3 If a student points out that worn coins are thinner than new coins, then it might be worthwhile sorting them into two stacks, using the faces on the heads and the date on the coins. Compare the heights of the stacks. Of course, this kind of experiment is of far greater value if pupils suggest it themselves, or even if the teacher can coax it out of them in a way that makes them feel it is their own suggestion. Then they are doing science. Measuring many atoms in order to find the size of one atom is a skill which scientists have.
4 How Science Works extensions: Point out that it is worthwhile changing and improving an experimental method as you carry out an experiment and that deciding on a method does not preclude subsequent changes.
Collecting the data from the class for the three different measurements of the thickness can be used to prompt discussion about data spread, variation and accuracy.
You could ask students to use the micrometer on a single coin and compare the value measured this way with the value obtained from the stack of coins. If students have not used a micrometer before, allow time for teaching them how it works and have them take sample readings before expecting them to use it confidently.
This experiment was safety-checked in July 2007