I’m going to dive right in.

I am back to teaching high school math this year, after a few years teaching middle school science, and I did a mediocre job first semester. My AP stat class was muddled and confusing and my geometry classes were boring and uninspired.

We’ve been back in class a week and a half, and I’m doing better. I’m feeling charged up by the idea of letting my students struggle with larger problems that don’t have every detail filled in – Problem Based Learning, I guess, as described on http://www.emergentmath.com . I don’t know how I’m going to have the time to do it much in AP Stat – due to my muddling first semester we have a TON of ground to cover before the exam – but geometry is just ripe for this.

I started simple, at the VERY beginning of a chapter on similar polygons. We had reviewed ratios and proportions before doing this problem, but had not actually discussed similar triangles or polygons. I basically improvised this problem, but it worked really well.

It was a sunny day, so I split my girls (I teach at an all-girls school) into teams of 3-4 and told them I was going to take them outside and they would need to measure the height of our athletic field’s flood lights. I gave them three hints:

- They would have a meter stick
- I could use my phone to put “pins” in a Google Map wherever they wanted me too (using satellite view) then measure the distance between pins.
^{1} - It was sunny outside.

This is a very traditional problem, setting up a proportion between objects and their shadows, but I gave them absolutely *no other hints*.

I gave them 5 minutes to strategize, then we walked to the field (it was cold, but nice!) and then I gave them 7 minutes to make their measurements and tell me where to drop pins on the map. Then we returned to the classroom. I gave them the distances they asked me to find, then they found their solutions and wrote it up on a Google Slides presentation that they presented to the class. Here is one example (student’s name was removed and replaced with “student”):

The whole process – setting up the problem, brainstorming, walking, measuring, computing, creating the presentation, and presenting – took about 60 minutes. I was able to give them a useful 10-point classwork grade based on my observations and their presentation. Everybody did well, and felt success. And there was good spring-board potential from the question “Why is the ratio between the object and its shadow the same in both cases?”, which we proved using the AA Similarity Postulate a couple of days later.

It could have been done better, if I had been more ahead of it. But I think it went really well, and it inspired me. We will be doing more things like this. Stay tuned.

** ^{1}**This is a pretty easy and fun trick. Long press on Google maps on your phone, and a pin will drop. Move it exactly where you want. Then you can save the pin to your account by clicking the star. When you log into that account on your computer ,the star will show up, and you can right-click and use “Measure Distance” to measure the distance between any two points on Google Maps. This saved time and effort involved in using the ginormous tape measures from the science labs.