Today we started the "Traveling at a Constant Rate" portion of the Overland Trail unit. For Previous Travelers I gave each group one supply to graph. They were provided a table with 4 columns where the 1st one was the number of people and the other 3 told how much of each supply they used. I had them to write their In-Out tables for the supply they were graphing (beans, sugar, or gunpowder) and then graph the points on graph paper. A few things stood out to me:
1. I had several students put the number of people (the input) on the y-axis instead of the x-axis so we had a productive discussion about independent and dependent variables again.
2. I had one student want to have fewer points to graph so she added some of them together and graphed the sums instead...whoa!
3. We still had some people who did not scale their axes appropriately or didn't start with the origin as (0,0) so I got to address that.
4. It REALLY bothered them to have an input to repeat. There were multiple families where the inputs repeated and that threw them for a loop!
5. I discussed the fact (before they started graphing) that the data was discrete instead of continuous since you can't have fractional parts of a person. I wish I would have waited to see what they did with their graphs and let them answer that question for themselves!
We had a Veteran's Day assembly today so 2nd block didn't get to graph their points on chart paper but my 3rd block did. I am excited about doing the line of best fit tomorrow. I don't know if I have ever been "excited" about it before...having the students work within a context makes so much more sense! The way the book develops the idea of using approximations with the data since one rule won't perfectly match all data points is really neat.
Progression for teaching students to graph - We started with "graphing stories" where we interpreted graphs of situations and created graphs for certain situations. Then the book led the students to a discussion about scaling your axes correctly and when to use continuous or discrete points (The Issues Involved). Then the students were given graphs and asked to create tables and then rules for the graphs (Out Numbered). Then the students were given some rules (using In and Out instead of x and y first) and asked to graph them (From Rules to Graphs). Now, with this lesson (Previous Travelers) the authors point out that all "real" data doesn't fit nicely into a rule so approximation must be used. However, with a line of best fit we can still develop a "rule" for the data. There are so many real-life applications to this concept I don't know where to start. The one that comes to mind first is calculating insurance rates. But how about the first time the medical world found "normal" heart rates for certain ages?
My 5th period worked on the More Graphing Sketches activity. We will be finishing it tomorrow.