A few days ago, I was reminded of an epic late 80s film called ‘Honey…I Shrunk the Kids!’ It turns out that you can watch the entire film on youtube – excellent news!
Anyway, there are loads of awesome mathematical questions you could ask and try to answer in class. For example, when the kids have been shrunken by the shrink ray, how long would it take them to walk across the garden in their minature size?
I personally thought that it would be a nice idea to figure out the scale factor between your normal height and miniature height (Have a look at the youtube clip between 1:20:00 and 1:21:00). Then you could take it further by asking what your miniature volume would be? This, I think, would induce some good discussion of how you could find the volume of yourself or indeed any awkward object. After some discussion, you could introduce the students to Archimedes’ ingenius idea of submerging an object in water and measuring the amount of water which has been displaced to find its volume.
Having said this, you don’t actually have to get in a bath to figure out your approximate volume. Since the density of the human body is close to the density of water (1000kg/m³), you can use;
Volume (m³) = Mass (kg)/Density(kg/m³)
Whether you tell them about this formula or about Achimedes’ Principle is your call. It would be interesting to simply show a suitable section of the film, ask them for an approximation of their own miniature volume and see how they get on.
I much prefer this as a lesson/extension to volume scale factors than my approach last year which was based around finding out whether a 2 metre high ant could survive (See previous post: Will Giant Ants ever invade the Planet?). It was fun but I felt as though I had to break the mathematics down a bit too much before I could give it to them as a task.
Of course, once you have a person’s volume you can start asking some interesting questions. For example,
1) If you had the same volume as a blue whale, a football, the moon etc., what would your height be?
2) If your height was the size of a house, the Eiffel Tower etc., what would your volume be?
If anyone else has an interesting way to teach this topic, I’d love to hear about it.