Academy of Best Practices: Day 1

Today is the first day of what a friend helped me label a "mathcation." I get to travel to a new place, go to dinner every night, and do a bunch of math and teacher training during the day. Personally I can't think of two things I'd rather combine! Today's focus was on grouping strategies and multiple representations.

One of our tasks was a remake of one I had done before. Given different sized circles, measure the circumference and diameter and record the results.  The primary goal is to allow students to find that the circumference is a little more than three times the diameter. Or said another way, the ratio of circumference to diameter is about 3.14 to 1. Today we created our circles in a way I had never seen before. We used bubbles! We were given some homemade bubble solution, poured a little on our desk, dipped a straw in the solution and blew a bubble on the desk.

We, of course, tried to create the biggest bubble possible. After the bubble popped, it left a circular mark on the desk. We were then given string and a centimeter ruler to determine the circumference and diameter. Of course, the teacher across from me talked about how to make the diameter more accurate, since the center of the circle was hard to find. She recommended we take an average of diameters within one circle including a length and width one. Yes, I thought to myself, this really is a mathcation with like-minded people who probably considers it one as well.

We recorded our results in a table, and then plotted them on a graph. I enjoyed using the sticky dots to represent our data point, and think students would feel the same way. Who doesn't like stickers?!

Then we were asked to calculate the ratio of our circumference to diameter. The results were recorded on the board. We got surprisingly close for the most part. I was off by quite a bit, with my inaccurate measuring skills due to frustration with a wet string and unimpressive fine motor skills. I think I calculated 3.4.  Luckily, the activity compensates for the butterfingered participant and we averaged the results and got around 3.2. Pretty impressive using bubbles and string.

What I really liked about this activity was the graphical representation. It connects rather nicely to the line of best fit, proportional reasoning, and the meaning of slope (about 3.14 in circumference over one diameter). What a lovely unit rate!

Even though I have seen an activity like this before, a new twist was exactly what I needed to be able to connect this discovery to many more mathematical concepts. I can't wait to blow bubbles in class!

This is just a snippet out of my day. Looking forward to more tomorrow!

We were given quite an interesting homework problem to discuss tonight: Very Woodstocky for the young crowd I am surrounded by who probably think of Woodstock as a bird (or maybe not even that!)  We also have some reading to do tonight, so I will most likely finish that first and save the problem for homework dessert!  

Solve this math problem: A rock festival was attended by 50,000 young people, 24,000 boys, 20,000 barefooted, 27,000 listening to the music. If there were 12,000 barefoot boys, 10,000 barefoot listeners, 11,000 boys listening, and 4,000 barefoot boys listening, then how many barefoot girls were there? How many shod boys not listening?