So, as a follow-up to Erastothenes using geometry to calculate the circumference of the Earth, this week I plan to go over how we can use the ratio to Earth to calculate the circumference of the moon!
The lesson idea came from my colleague John. I fleshed it out to scaffold it for my kids. It looks like this, and it ties in nicely both with our school's Grade 9 science curriculum (which teaches astronomy for all of next term), and our current circles unit. I plan to use this lesson the day after our basic circles quiz, when a few of the students will have family members visiting our class. (At our school, this is called Grandparents' Day, even though it is quite possibly not the grandparents that are coming.)
I'm excited!! I've never done this lesson before, but I like how it revisits perpendicular bisectors and makes them seem useful in application.
Addendum 3/26/15: I prepped for this lesson today and it REALLY BOTHERED ME that I got the estimate that the Earth's circumference was about 2.5 times bigger than that of the moon, when in reality it should be about 3.6 times bigger. I did some more digging and worked out a ratio to find out how big the Earth's shadow would be by the time it reaches the moon, and I think it's 9200 km in diameter at that point! That makes my ratio make a lot more sense, because this is only 2.6 times bigger than the moon!!! Go Geometry!