Monday, February 23, 2015

IMP Overland Trail - Water Conservation and stopping to find balance...

My 5th period class is Algebra IA year-round. They should be covering Overland Trail and Cookies before the end of the year. I just realized that they are at a point of Overland Trail where I had to skip some of the activities with my Algebra IA Fall Block classes. I was determined to finish Overland Trail by Christmas in order to start Cookies in January.

The Water Conservation activity is another good one to put on chart paper. Most students will generate a chart in order to answer questions 1 and 2. However, I had some students who graphed the lines first and then tried to go back and answer how many gallons each family had left after a given number of days. This did give us the opportunity to discuss how it is easier to be exact when you use a table instead of the graph due to the estimation that is required when looking at the graphs.

I loved that the group that generated the work shown above included the table and the graph along with their answers to the questions. One of the questions that this group did not address is how to find how much water each family has after x amount of days. This forces them to think about the starting point and rate of change. They know to muliply the amount of water used per day times the number of days but then they have to consider that they are trying to give an expression for the amount of water LEFT not the amount of water consumed.

After covering this lesson I pulled some practice problems where graphs were given and we were asked to find equations. I also talked about the slope formula and had them find the slope given 2 points. I know that I need to take time to stop and explicitly teach topics that we have covered but they may not know the "math vocabulary" so I am going to list them here:

  • graphing from slope-intercept form
  • writing the equation of a line when given a graph
  • finding the slope of a line given 2 points
  • finding the slope of a line given a graph
Our students have done so much more with this curriculum and creating graphs given real-world circumstances. However, when they take the end-of-course exam and the ACT they are going to need to be familiar with how to do these problems when there is NOT a context. After having taught through this unit (Overland Trail) the first time I realized that there are times I needed to stop and teach the students what types of "traditional algebra" problems they might see from the content we have been covering. The problem was that having never been through the curriculum before I did not want to "steal the thunder" of a lesson that we were going to cover in the future. I feel that to teach using the "exploration/inquiry/problem-based" method you have to also find a balance with showing students what the "traditional/worksheet/drill and practice" version of the algebra looks like. I KNOW that I can do a better job of finding a balance between the two.