# A Review of Mr. Stadel’s Rolling Tires

The teachers in my grade level were instructed to insert a circle unit (just the basics folks) into the scope and sequence for the advanced classes this year. The idea of teaching circles made me happy because I loved teaching circles to my fifth graders; back when I taught at the elementary level. One activity based on the now defunct Growing with Mathematics program involved students’ self-discovery of the pi ratio. Although I used the activity as a brief introduction, I knew I needed to up my game for my seventh graders.

Upon my searching of all circle lessons (wow there are so many!), I stumbled across Andrew Stadel’s 3-Act Math plan for Rolling Tires. Essentially, Mr. Stadel is rolling two different sized tires towards a tower of toilet paper on a makeshift table. That is the premise:  toilet paper and tires. Naturally the students were captivated.

I had rehearsed my 3 act math questioning technique with a few Dan Meyer lessons already, so I felt prepared. I showed act one and asked the students to discuss the questions that came to mind. Oh my goodness, they couldn’t get their questions out fast enough. “Will the tire knock down all of the toilet paper? Will the tire hit the target? Is the tower of toilet paper sitting on a table or something else? How quickly are the tires rolling? What is the diameter of each tire? What is the circumference? How many times does each tire need to rotate to get to the target?”

Many students asked me to replay the video over and over again. I was instructed to pause it at certain points, and conversation exploded in the room. The conversations were all about math, geometry, and calculations in real life and it must be said, the students and I were happy.

I asked my student investigators, before showing act two, to consider what specific pieces of information they would want to be provided with in order to satisfy their own varying levels of curiosity. It was the moments following that question which proved Mr. Stadel created a genius lesson. Without saying another word, my math family began to debate each other about the merits of having the radius, diameter, or circumference of each circle. In the middle of the debate, one of the students (I will call her Jan) interjected, “Hey, it doesn’t matter which piece of information we have, if we have the radius, we can find the area, circumference, and diameter. We already know pi is a constant ratio.”

Boom. Just like that, that one student changed the course of the classroom conversation. I asked the other students to clarify Jan’s comments to each other as I walked around and listened in on their dialogue. As I checked in with the students, it became clear that they all understood what she meant and I had this lesson to thank for the reinforcement.

I then showed act 2, which presented the diameter of each tire, the distance of the tire track, and the distance from the tire to the target (if it actually hit the bullseye). The question Mr. Stadel presented, which many students had asked in their own inquiry, was how many rotations would it take for each tire to hit the target and would it actually hit the target?

The students worked furiously and shouted out numbers to each other regarding the circumference. One student started to calculate the area and her partner corrected her with a visual. She actually rolled her water bottle on its side and demonstrated why circumference (kind of like the perimeter) would be important information to answer the question.  She asked if I still had string left over from the other lesson and showed her how the length of the string would be helpful to see the distance each rotation covered on the ground.

When most students arrived at their own conclusions (most saw no reason that both tires would not hit the target, but questioned whether or not the force would be powerful enough from the smaller tire to knock all of the toilet paper over), I asked if they were ready to view act three and most responded yes. However, one student protested, “No, don’t show it yet, wait!!! I am not done!” This is a math teacher’s dream.

We all agreed to wait a few more minutes, and then I played act three. The students screamed when the big tire hit the target and complained endlessly when the small tire missed the target. Questions continued to abound.

“Why did he miss? Was his aim bad? Did it have something to do with the tire being smaller? Why did he highlight the central angle of the circle? Why is that significant?”

I don’t need to describe this lesson any further because it is clear that it had students going beyond any math textbook exercise and yet still provided so much actual understanding of a concept. As I continue to search for lessons that produce results like these I must give Mr. Stadel a huge and grateful shout out for this lesson. Mr. Stadel, I am officially a big fan!!!

# My First Foray Into Three Act Math

I recently returned to teaching after an extended maternity leave. As much as I love my girls, it was tough for me to be out of the classroom for almost a year. A lot can happen in a year and a lot did happen in a year in our math world. We adopted a Singapore inspired program, embraced the mathematical practice standards, and had Yeap Ban Har train us in a better way to teach math. It was at Ban Har’s workshop where my mind truly experienced a renaissance, if a mind can experience such a phenomenon. Of course, by the time Ban Har reshaped my focus I had already been trained via staff developers of the Math in Focus program. Every lesson structure we discussed and I witnessed allowed little light bulbs in my head to flicker. When I returned to my classroom this past August, I was determined to change everything.

Anyone who has been in teaching will tell you that changing everything, for lack of a better term, is stupid. As true as that may be, I knew the type of math teacher of which I was aspiring to become, so I attempted such a transformation. I furiously researched my new textbook topics and scoured the Internet for lessons that were already brilliantly designed and would complement the objectives I knew I must meet. It was this search that led me back to Dan Meyer.

I had seen Mr. Meyer’s Ted Talk discussing how math instruction must change. But like most people, I need to be introduced and reintroduced to something multiple times before I truly embrace and understand it. I re-watched Dan Meyer’s Ted Talk and then went further to watch examples of his 3-Act Math. In a nutshell (apologies to Dan Meyer here for not doing this explanation justice), three act math includes a conflict/hook, a problem where students must develop ways to overcome the obstacles presented, and a resolution. There are various ways to get that hook, and it is our job as instructors to find it and lead our students’ interest in our direction.

Upon searching for something to do with integers and absolute value, I came across one of his lessons that had students guessing ages of celebrities. Like all teachers out there, I “stole” his idea, and modified it to make it my own. I spent hours debating which celebrities to use in my presentation and how many I needed. Then, realizing that I would be at a different pace with each of my classes; I figured I needed to make at least two versions of this lesson so the celebrities would be different for each class.

Here is what happened in my first class.

I asked the students how good they thought they would be at guessing somebody’s age. The responses varied from, “I am so good at that, to, I am the worst.” After they polled each other quickly on their anticipated success or failure at such a task, I posted a slide with lots of celebrity pictures with the challenge:  Let’s examine your talents. On the slide, I showed Barack Obama, Daniel Radcliffe, Donald Trump, Oprah Winfrey, Selena Gomez, Serena Williams, Michael Strahan, and Tom Brady.

Next, I distributed a table with the following categories:  Name, Age Guess, About, Difference.

I then posted one slide at a time of each celebrity and the students had about 30 seconds to record their age guess.

The students were excitedly shouting out their guesses and arguing with each other as each celebrity was shown on the screen. After they recorded their guesses, I posted the actual age of each celebrity in a table that matched the one I created for them. After they filled it out, they were instructed to determine the difference between the actual age of the celebrity and their age guess. We figured out who was the best in the class at this game and who was the worst guesser. Both students were celebrated by a round of vigorous applause. The discussion led to the fact that there was never a consideration as to whether the guesses were too high or too low, just the distance from the actual age.

Eventually, students figured out that this was an example of absolute value because they were measuring the distance from the actual age.

Students were then asked the following question:  “If provided the exact birthday of any of the celebrities from the previous slides, how could you find a more precise difference between your guess and the actual age? For example, Donald Trump’s actual birthday is June 14, 1946. Use this information to find a more precise difference between your guess and the actual age of Donald Trump. Discuss, explain, and problem solve.

Students soon realized that they were dealing with rational numbers. Some students decided to post the information in fraction form out of 12 months, others used 365 as the denominator and were showing the age difference to the exact day, and still others tried to tie in hours! They were all on a mission to be the most precise and my classroom was alive.

Since that lesson, I have referred to the age activity when reminding students about the concept of absolute value. This lesson became one of those lessons. The lessons teachers dream about. Students were inspired to perform all of the problem solving, research, and data gathering independently and collaboratively, without much from me. Most of my work was in the lesson structure and observation. The rest was up to them.

That was a good day.