Posted February 13, 2017
(By Dean Ballard, CORE’s Director of Mathematics)
I was working in a school district near Seattle a few weeks ago, doing lesson studies in middle school math classes. Super fun time. In one sixth grade class I was teaching a lesson on “Finding the Percent of a Number.” As with any type of lesson modeling and even more extensively with lesson study, I met beforehand with teachers to review and revise the lesson as needed and agree on the focus areas for the lesson observation. In this case we were working on three areas – student engagement, discourse, and checking for understanding. We had a team of four teachers, the math coach, and the coordinator, all of whom would watch the lesson and debrief together afterwards.
Using an effective lesson format I not only wanted to be clear about what students were to get out of the lesson, but have a hook to grab their interest. I also needed to do a “warm-up” activity to assess their readiness for the lesson and better prepare them for the lesson. Coincidentally, the week before the lesson I found an article on CNN about a drug maker getting into trouble for hiking the original $40 per vial drug price so that it was now 85,000% (yes, 85 thousand percent!) of the original price. This was the craziest percent I had ever seen in a real situation. I had to use it in the lesson as a hook.
I used individual white boards to have students show what they knew about 50%, 100% and 200% of a number (including $40). The white boards also allowed me to make sure students understood the meaning of these benchmark percents beyond simply doing procedural calculations. The white boards were very engaging for students since I provided each student instant feedback when the boards were held up. I kept a brisk pace, not steam-rolling ahead but also not allowing a lot of pencil twirling time in between problems. I was able to assess what they knew and adjust my next white board question based on what I saw each time.
So we began the lesson itself with me showing the kids the crazy article with 85,000%. I had the kids take a guess at what they thought would be the resulting cost of the drug that originally cost $40. The students wrote their guesses in their notebooks and I wrote them on the board for later reference. The lesson itself that followed led students to see a pattern in what they knew was true about 50%, 100%, and 200% of a number versus the result when they just multiplied the number by the percent. Students recognized that you “drop two zeroes after multiplying the percent times the number” or in other words, move the decimal point two places to the left for the final answer.
However, mid-way through the lesson we returned to the 85,000% cost change and students computed the cost based on a method they had come up with through collaboration and discussion. Their method was to multiply the percent times the number. In this case that meant 85,000 x 40 = $3,400,000. At this point we returned to the benchmark percents they knew with confidence: that 50% of $40 = $20, 100% of $40 = $40, and 200% of $40 = $80. These made sense to them. So I demonstrated applying their technique of multiplying the percent times the number to 50% of 40, 100% of 40 and 200% of 40 (50 x 40 = 2,000; 100 x 40 = 4,000; 200 x 40 = 8,000). They knew these were wrong, and the whole class was intensely looking at me as if to ask, “Why are you doing it that way if you know it’s wrong?” I insisted I was just using their method, just doing what they said to do. Now this smarty pants kid in the front row piped up, “Yeah, but WE are not the boss of YOU…you can’t blame us for this!” HA! TOO FUNNY. Engaged students hot on the trail of learning! After I got done laughing, I focused the class on comparing and analyzing the numbers and discussing in pairs ideas about how the results from “their method” compared to the actual correct answers. They realized that they had to take off two zeroes or move the decimal point two places to the left. They recomputed the drug cost correctly and then I did the reveal on the document camera, showing the full article, so that that they could see they had done the math correctly. The new cost of the drug was $34,000 for a single vial! Next lesson – examining why we move the decimal point.
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