Today was a neat lesson because the students were asked to "break away" from the Overland Trail theme and consider using lines of best fit to analyze data considering the budgets of 3 college students who share an apartment.
Common mistakes today:
1. "connecting the dots" instead of drawing a line of best fit
2. not extending the lines of best fit to touch the x and y axes...even though one of their data points was (0, $ that each student had at the beginning of the month)!!
3. Scaling their axes incorrectly - by this I mean one "box" was 100 and then later on they spread 100 over 2 boxes
4. When answering #3 several of the students looked at how much money the guys were projected to have on April 21st instead of how much extra they had on April 30th.
5. One student started all of her lines at some random starting point on the y-axis because her group had Who Will Make It last week and all of the families started 330 miles away from the Green River...
I got frustrated today because I expected a higher percentage of the students to "get it" since we have been working on similar types of problems for 2 or 3 days now. I was disappointed to see students connecting the dots and not extending their lines to the axes. I felt like I had done such a better job covering this because of the experiences they have already had with "lines of best fit." I also need help on reacting better when my students are way off the mark. I am so good sometimes...and then other times I know they can see it all over my face and hear it in my voice that I am frustrated... This is my confession day I guess!
On a positive note...I had some students that flew through the activity and had a very good conceptual understanding of what was going on! The rules were difficult for everyone but we went over them today and I know that we will continue to work on writing rules and equations as we go.
**It is good to use chart paper and leave some of the graphs hanging up in the room. I still had several graphs from Previous Travelers hanging up in the room so we used them to compare the graphs that start from the origin with those that don't (like in The Basic Student Budget).
My 5th period today did Vermillion Crossing in class and I introduced Ox Expressions and assigned it as a bonus for the student with the most meaningful algebraic expressions.