Teaching Ratios: Gestation to Life Span

Is there a link between the gestation period of an animal, and how long it lives?

This was the question inspired by the Connected Mathematics unit: Comparing and Scaling.

It is a problem hidden within the homework section, but which deserved more attention. I find it to be an excellent example of using real world information to practice and apply ratios. It also lent itself to a relatively easy set up on the Smartboard, so that we can stay away from doing math solely from a math book.

Based on the following table, my students created a list of ratios comparing life spans to gestation periods.

 We looked at our lists and discussed whether we saw any direct relationship between life span and gestation. Based on my initial observations, there may be some sort of relatively weak correlation between the two, but it is not as obvious.

I then showed my students how to reduce their ratios to unit rates, comparing days of gestation to one year of life by dividing both sides by life span. This is similar to fractions, but does not require both numbers to share factors. It is an occasion where ratios look like fractions but act under their own special rules.

When we calculated these unit rates, we found that the poor giraffe has a huge cost in gestation days when compared to life span, while humans get off fairly scott free in that category.

Still, this type of data begs to be graphed to "see" if there is a correlation.

Here is what my admittedly rushed graph looked like on the Smartboard.

Based on the data, I would only be able to say that there may be some weak and not terribly useful correlation. Discussing it with a colleague, we wondered if the correlation is actually more of a curved line, indicating that throwing more gestation days into the pot only give marginally better results.

What do you think? Are we way off?