Day 4: Why is slope so important?

I started class by having kids read the standards we were going to be working on this week (S1.1 & S1.6). I reminded them about the different grading scale and talked about how the unit would progress over the next couple of weeks. 

Then I solicited answers to the question: "Where might you use slope outside of a math class?" I wrote anything anyone said on the board and their responses ranged from architecture to predicting trends for business. 

I varied with exactly how I intro'd the challenge, but I was happiest with this method: Start by asking one group to stand up and form a line. When they've settled, ask someone from the rest of the class to describe that line. Continue, asking probing questions when appropriate until they class feels they've created a specific-enough description that the line could be recreated by an outsider. 

The challenge (with a description already written on the board behind me) is for every group to make their own line and write down their own description (on a whiteboard) that is specific enough to be recreated by another group. Give the groups 5-10 mins to make their lines and walk around the room checking on progress, asking leading questions where necessary. 

My classes are all above 32, so I have 7 or 8 groups in each class which can make things tricky. Thankfully I have a lab class (for physics), so I have plenty of room to spread out. 

When everyone is done, I asked students to return to their seats and I grabbed a group's whiteboard at random and read it aloud to the class. I then called on a group at random and had them attempt to recreate the line in the center of the room. I first check with the class as a whole if the line was recreated accurately to what was given on the whiteboard. I then ask the group that created the line if the new line looks *exactly* like theirs did. We repeated this for 3 or 4 groups (no need to do every group if the point is coming across). 

I then asked some students (at random) if they had any ideas why we did that. There was a stark contrast here between my two Honors classes and my one "regular" class. I could generally get kids to come around to the idea that being able to describe a line accurately is an important skill (and harder than it looks). 

Finally, I try to get students to connect the descriptions used in our lines (N, S, E, W mostly) to descriptions of lines commonly seen in math class. The honors kids quickly jumped on the "slope as direction" connection, but the regular class had to be led there more directly. 

In general, students seemed to have a basic understanding of slope before class, but few readily made the connection to something other than math class. I was fairly satisfied with how the day went - obviously there are things I will do differently next year, but not bad for a first try. 

Tomorrow I hope to lead a discussion of where slope-intercept form comes from, show some examples and get them practicing on their own.