From Maura – I taught both sections today.
I reviewed weighted averages, with the objective of showing them both how interesting and how subtle weighted averages are. We started with an example of a course grade, calculated based on weighted grades for homework (15%), a project (20%), a midterm (25%) and a final exam (40%). Some students took the four grades (homework, project, midterm and final) and averaged those. This led to a good discussion of why this is not the right approach (even though sometimes the answer is close to what we get when we do the weighted average calculation – but that’s a coincidence). It made more sense to them when we talked about the final exam as being worth twice as much as the project. We then experimented with a question that the professor always gets: “what do I have to do on the final to get an A (or B, or Pass) for the class?” This worked better in Ethan’s class because I made up better numbers and skewed it so that it was impossible for the student to earn an A. One student suggested (facetiously) that the student could get 200% on the final. I tried not to digress into my annoyance with my children’s grade school teachers who regularly award 115% on exams. In Ethan’s class the students were also more comfortable using algebra to solve for the exam grade.
We also worked through a GPA example based on problem 5.2: a student has 55 credits and a 1.8 GPA. If the student takes 12 credits, what GPA does she need to get her cumulative GPA above 2.0? The first class found this difficult – I was surprised. We ended up working it out together. The second class made better progress with it and again several students were comfortable using algebra to find the answer. I then gave them a more dramatic (but real) situation: a student has 100 credits with a cumulative GPA of 1.4. Students need at least 120 credits to graduate. Can this student be in good standing at the end of 120 credits? Even if the student earns all A’s on those last 20 credits (highly unlikely, given the student’s previous record), the cumulative GPA would only be 1.83. I told both classes that I do see students in this situation and that it’s a challenge to know how to proceed as they will need many semesters before they can graduate. On the other hand, we as an institution have already invested a lot in them (as they have invested with us) and does that give us an obligation to continue working with them?
One more comment on the arithmetic: students agreed that it was tedious to do these calculations with their calculator. That’s fine, since we will start Excel very soon and they should see the power of Excel for doing tedious work like this. It also underscored the importance of the order of operations. For these calculations, students need to remember to simplify the numerator before dividing by the denominator. It was a good reminder of that.
We spent the last part of class talking about section 5.4 from the text. This example brings out the subtleties of weighted averages: the average vehicle price went down, but both the average car price and the average truck price went up. This can happen when the weights change. We talked this through and I think they found it surprising. It’s a good example (although unfortunately with made up numbers in most of it) of how we need to be careful when working with weighted averages.
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