Last year when I taught slope for the first time I introduced the concept using a silly drawing of Mt. Doom. This year I tried to remember how the lesson went last time and make some adjustments. I think it went better this time.
Here I must once again this year tip my hat to Dan Meyer for his “Math Class Needs A Makeover” video, since this lesson approach to slope is very obviously a rip-off of his ski slopes deconstruction.
I started by setting the scene from Lord Of The Rings (for the students who were unfamiliar) and recited the One Ring incantation in the Black Speech of Mordor (they were, sadly, not impressed). Then I showed them the following clip of Sam and Frodo on Mt. Doom.
Then I passed out the first page of this small handout. (I had four graphs to a sheet. It was big enough too see and write on, but small enough to be economical with my prints.) I emphasized that what I was interested in was the REASONING for picking a certain section to be the most steep and not necessarily a looking the “correct” section of the mountain.
I gave the students some time to think and talk about this. Of course, there was some off-task behaviors, but most of the students in both blocks of Foundations discussed with classmates and wrote down an answer. I even got some good reasons out of them (although I had to coach/coax/coerce them into actually writing the reasons down instead of just saying them outloud to classmates or me). In fact in several cases the students really debated amongst themselves about why the tiny vertical portion was the steepest. They related it back to literally climbing a mountain so I was happy with the time that I spent explaining LOTR and watching the video clip. (Besides, it’s LOTR.) The only downside was that they got a little sidetracked worrying about carrying someone on your back (which made the vertical portion “impossible”.) But then again, this emphasized the extreme slope of that part of the graph.
As has been the pattern all semester, I got better engagement and discussion out of my first block than my second block, but both blocks did well. I was pleased and they seemed to get it. And even better, some students labeled points or asked about names without any prompting from me. Once I had given them a chance to work individually and we moved to whole class discussion, this was the first thing I brought up. I called on the students who had asked about labels or written labels and had them share what they did with the class. I prodded the rest of the class about why that was useful and then had everyone label using the same scheme.
After I was sure we all had a labeling scheme I asked the students to share which section they chose and why. Generally classes were split between the first segment (from point 1 to point 2) and the fifth segment (from point 5 to point 6), but students struggled to say anything past “It’s vertical” or “It’s nearly vertical”.
Still! That’s exactly what I wanted.
I then followed up by giving them the second sheet and emphasizing that it was the exact same picture with some helpful additions. (I don’t know if I quite created enough of a “headache” here for which a graph would be the aspirin. Maybe next time I will force the students to rank the slopes from greatest to least and submit there answers. This may create a greater need for more information.) But overall I was pleased.
Once I had the second graph I upped the amount of guidance I was giving to help them figure out how to use the graph to make an argument. I don’t know if this was too much help or not, but they seemed to get it. I drew a table on the board with “Segment Name”, “Up”, and “Down” and asked the class to identify the pieces and then use the numbers to compare.
I was tempted to print the document front-to-back to save paper, but I knew that if I did that, I would have students who would start on the wrong side and make it difficult, so I am glad I spent the extra 11 sheets and classtime to hand out two different slips. Next time I think I will give less help during this portion, but I was happy with how much better this activity flowed and connected for the students this time around compared to last year.
I moved from this intro into notes on the definition and formula for slope and then we did some practice problems.
Also I just noticed that I introduced the topic of slope a full 10 days later this year. I wonder how much of that is the new pacing guide we have for the district and how much is me being behind.
Thanks for reading.