This title also doubles as my future Mitch Albom-esque novel.
I tweeted a picture of student work from this lesson back in November, but I never got around to talking about why it was worth tweeting. I figured now is better than never and I’m still adjusting to summer.
— Tom Hall (@trigoTOMetry) November 20, 2015
This lesson was prepared for my 6th grade accelerated (7th grade content) course. We spent the previous few days working with proportions to solve a myriad of percent problems. I planned for this lesson to be a way to teach percent error without a lot of direct instruction and with a ton of collaborative work. The actual activity (working with M&Ms and calculating percent error) felt old school, but the manner in which I presented the activity would put my money where my mouth was in terms of classroom environment. Would my students rise to the occasion, figure out, and sharpen their understanding of proportions and percent error? Would the lesson flop terribly and leave me with an eternal loathing of chocolate M&Ms?
When students walked into class that Friday before Thanksgiving, the bellwork was estimating the weight of a turkey. Up to this point in the year, I stressed the reasoning aspect for making estimates and asked students how far off they were when I revealed the actual measurement. The start of this day was no different to other days in class, until I asked students to calculate how far away they were from the actual weight of the turkey. Most students were already in the habit of finding their error, but I asked students to be on the safe side. I told students their number for “how far away” is what mathematicians typically call error. Then, I asked students to take a few moments to find their error as a percentage of the actual weight of the turkey.
As I circulated around, I noticed some students started punching numbers in calculators and others jotted down a proportion for the situation. Either way, we were in business.
I asked students to share their percent error and followed up with some questions to formalize percent error. I wrote down these questions in my reflection journal (what I’m using as a reference as I write this post) to remember what I asked:
- How did you find that percentage?
- Why did you use a proportion?
- How did you set up the proportion? Why did you set it up that way?
- How did you know that percentage is reasonable?
With student answers to these questions, I knew it was time to bust out the M&Ms.
Students got a copy of this handout to use for the rest of class. Almost immediately, students noticed the word M&Ms on the page and began to murmur about what they thought they were going to do with the page. In the space at the top, I had students write down a brief summary of percent error and how it could be found with the proportion they knew and loved for percent problems (part/whole = percent/100). This 5 minute span was the only direct instruction for the entire 80 minute class, but students were tuned in because we had already talked through the concept with our estimate (and looking forward to candy). I explained the goal of the activity (see which group of students was the most accurate in predicting the M&Ms in the bag), then I created Visible Random Groupings of students to keep it honest and productive.
I gave groups the bags of M&Ms, asked students to remind me of the expectations for the activity, then set them loose to work through the task. The handout pretty much broke down the process for students, but I knew I would have to scaffold individual students during the activity. I circulated throughout the activity and paused work for clarification/progress checks, but most groups were confident in what to do for finding percent error for their work. I asked groups questions like, “How did you make your estimates? What color do you think is most common? What does your percent error mean about your estimates?” to steer thinking and get feedback about the activity.
The interactions I had with students were the highlight of this lesson and why I decided to write about it after so long. They were making sense of percent error, accurately calculating percent error, and asking good questions. For instance, a student asked how she should count the mutant M&M. Is it 1 candy? Is it 2 candies?
During the blind survey I conducted at the end of the day, most students agreed that the activity allowed them to work with the idea and practice finding percent error (students had to complete 6 calculations for their estimates). Out of the handful of students who disagreed with the majority, some students tended to prefer traditional teaching (step-by-step examples and worksheets). As I thought about the lesson, I think what I loved most was the questions I asked and students asked during the lesson. It was the questions that inspired me to write about this lesson after 6 months.
Then again, maybe I liked the lesson because it involved M&Ms on a Friday.