# All the Trees in the Forest

How many trees are in the forest, at Hilton Falls Conservation Area? I swear it wasn’t me who started this conversation, although usually it would be me, going around, trying to mathematize the things around us.

On the path through the forest, leading to the falls, Nancy said, “if I wanted to know how many trees are in this forest, I would start with a 5 square metre section of forest, and count how many trees were in it”. She continued, by saying, she would divide the size of the forest by the number of trees in that 5 metre square. She then corrected herself, after thinking about it, and saying something like: I would figure out how many 5 metre sections would fit in the whole park, and multiply. (I am paraphrasing)

I mentioned Fermi problems, but really, that’s a math teacher thing, and I was just interested in her thinking, and she didn’t need to know that I am doing estimation and Fermi problems for my OAME session.

Fermi began with “how many piano tuners are in the City of Chicago?” This problem, I am sure you agree, needs some updating. Andrew Robinson has his students estimate the weight of all cell phones in the room they are in. It makes sense- a cell phone could have 50 piano apps on it, if you wanted it to, in this day and age.

Technique matters here. We can be several orders of magnitude out, if we don’t choose a good enough initial estimation unit. In the forest example, that unit is the 5 metre square.

Notice in the screen capture below that Google Maps gets us as close as 10 metres above. We have a pretty good idea now that the park is mostly solid forest, barring the parking lot area.

Next I need to identify what kind of information would help me to reach a good estimate.

If we could mark the boundaries of the whole park on this screen cap, we could proceed from our initial estimate, for the 5 metre square. A quick search reveals that the park is 645 hectares, so we can use that information as well.

6, 450,000 square metres is the same as 645 hectares. That’s a whole lot of trees! I would want kids to try and figure out how much to subtract due to the open areas near the entrance, the visitor centre, and the parking lot.

If you are trying this task, here are some things you could ask kids.

How big is a square metre? (we used to lay one out with tape on the classroom floor)

Is our classroom bigger than 5 square metres?

How many trees could it be? Thousands? Millions? Billions? Getting a sense of orders of magnitude, the size of numbers, is a big part of our intuition and “horse sense” of estimation.

Extend this tasks. Go big with it. How many trees in Canada?

I would love hear kids’ thinking here. The tree line matters-at a certain latitude, trees disappear. Some parts don’t have trees. Our cities have less trees. Some areas are logged heavily. What assumptions do you want kids to make?

I want to know if kids think there are millions, billions, or trillions of trees. What do you think?