PBL in Proportional Reasoning

Grade 8 math has been fun and interesting for me to teach. Compared to the algebra and pre-calculus parts of the higher grades, the topics covered in grade 8 seem to be immediately relevant and useful. None more so than proportional reasoning.

My students, for the most part, managed to grasp the concepts of ratios fairly quickly. This shouldn’t be a surprise, given how much scaffolding there is in the BC math curriculum. So when we got to problem solving with proportional reasoning, I decided to use a more ill-defined activity.  Part of this was based on Dan Meyer’s 3 Acts. But really, my approach was based on inquiry and PBL.

The root of the “problem” was a video that I showed of a plane landing in Phoenix, Arizona. While the video was running behind me, I was talking to the students about flight simulators, good airports to practice landing, and other ramblings. The idea was to get students thinking about planes motion and landing. Once the plane in the video had landed, I asked the class if they had any questions about what they saw or about the plane. As sure as it rains in Vancouver, it wasn’t long before students asked how fast the plane was going when it landed. Shazam, we now had a problem to solve.

The class broke up into groups, and their task for the next 10 minutes was to come up with a strategy for figuring out the speed of the plane. Each group was able to come up with a plan. Most groups realized that the plane crossed some large highways. If they could figure out the distance between the highways and how long it took for the plane to cross the highways, they could find the airplane speed

I asked the kids how could they find the distance between highways, and once again the students had an answer at the ready.  They realized that they could use Google Maps to do this. I had anticipated this, and already had map printouts of the area with the map scale on it. Working on whiteboards, each groups came up with a solution within the next 15 minutes. Having worked through this problem, the students grappled with proportional reasoning (map scale) and rates (distance:time). Once the groups had calculated the landing speed, I asked them to figure out how much fuel was used, given that the fuel consumption was 0.05 km/L. Most groups managed to do this quickly as well.

There were many positives in this lesson. First, it was a challenging and moderately interesting problem to work on. Secondly, they analyzed an open-ended problem by coming up with their own question. Thirdly, although it would be rare for someone to actually need to solve this problem in real life, it was a real life situation and similar to something that a person may need to figure out. On the down side, there are a few things that I could have done better. Most importantly, I could have done a better job of having a group summary of what happened. I had asked the students to take what they learned in the problem and apply it to some practice questions in the textbook. And although this wasn’t a hugely bad thing to do, it later became apparent that students have a hard time taking ideas from one situation to another (PBL to other word problems). The second thing I could have done better was assess which kids had struggled with the PBL and didn’t really get the solution.

For sure, many of the students really enjoyed this activity, and made progress towards our learning objectives with it. It was engaging and allowed kids to explore and think imaginatively. For instance, one group contemplated the idea of estimating speed by looking at how the perspective changes in the distance. Some students have asked that we do more of this, which I’d love to do. One downside (sort of), is the time that it takes to do this kind of activity. While another grade 8 math class would spend one day on “covering chapter 5.5 – ratio word problems”, our class ideally would spend one class on the PBL and another class debriefing and extending the activity. So what I’m finding is that these PBL activities take significantly longer.