From Maura:
I filled in for Ethan today, who couldn’t make it. He gave me two problems to have the class work on, so that’s what we did. Both problems were about weighted averages. I passed them out and asked them to work in groups to solve them. (They are in the book: Problems 5.7.4 and 5.7.8.)
The first problem built on what the class had done with GPA calculations before the exam. The essential problem is that a student has 55 credits and a GPA of 1.8 (this is a cumulative GPA – should have emphasized that). The student will take 12 credits and needs to raise the GPA above 2.0 to avoid academic suspension. What semester GPA does the student need to earn?
While they had done an example last week on calculating semester GPA, the students for the most part weren’t able to make the leap to using cumulative and semester GPA information together. Some got stuck on the number of courses that could make up 12 credits and what individual grades the student should earn. I suggested they keep it simple and just think of a 12-credit course. The other issue was that quite a few groups proposed a semester GPA of 2.2 and argued that since (1.8+2.2)/2 = 2.0, that GPA should work. The tutor and I talked them through the importance of weighting the 1.8 GPA by the 55 credits and how they would do that. Once the groups heard that, they got the right idea. Most of the groups used algebra to solve the problem, but a few did the guess-and-check approach. Both are valid approaches. The algebra approach has the advantage of giving the answer as the lowest possible GPA the student needs to earn. As for guess-and-check, many students took a 4.0 semester GPA and established that this would raise the overall GPA above 2.0. Well, yes, but that’s not too realistic for a student who is on academic probation. I encouraged them to refine their guess to get a bit closer to the minimum GPA – most settled on 3.0 as close enough. I asked the groups to put their answers on the board and then we talked them through. While all three groups used the algebra approach, one group used percentages to represent the weights. This was for part (c), where the student takes 6 credits. The group argued that 55 out of 61 credits represents just over 90% of the credits, while 6 out of 61 represents just under 10%. Then they finished the calculation. I liked this approach as it illustrated very clearly how much weight is placed on the 1.8 GPA and should help students see how the 1.8 GPA is pulling the overall GPA down.
This exercise took a lot longer than I expected – almost 45 minutes. Part of the time was spent talking about what they think they would do in that situation. Would they try 12 credits or focus on only 6? The answers varied, with good reasoning for both sides. I told them that I’m the one who sends out the probation and suspension letters and my experience is that it’s better for students to focus on a small number of classes and do well. I then told them that if they repeat a course, the grade for the repeat is what’s included in their GPA and the first grade is taken out of their GPA. They seemed surprised to hear this. The point is that if you are selective and careful about courses you repeat, you can raise your GPA fairly quickly.
Some of them had already moved on to the second question so I gave them some more time on that. This is a paradoxical one. We have two students, Alice and Bob. Alice’s semester GPA is better than Bob’s in both the fall and spring semesters, but overall Bob has the higher cumulative GPA. It’s hard to imagine how this could be, until you start to take it apart. The initial approach of many of the students was to keep everything the same in the two semesters – for example, Alice takes 15 credits each semester and earns a 3.7 GPA each semester, while Bob takes 12 credits each semester and earns a 3.5 each semester. With this approach, Alice’s cumulative GPA will always be higher than Bob’s. To give Bob the edge, he needs to have a lot of credits (that is, a large weight) with a GPA that is higher than one of Alice’s GPAs. And Alice needs to have a lot of credits associated to that GPA. The trick is that Bob’s fall semester GPA could be higher than Alice’s spring semester GPA. When we talked it through in class, people protested that this wasn’t allowed. But in fact it’s legal and the only way to give Bob a higher cumulative GPA. One student put an example on the board for us and we could see how the weights made it work. As an extreme example, I encouraged them to think of Bob taking 15 credits with a high GPA in one semester and only 1 credit with a low GPA in the other semester. Balance Alice’s credits and GPA accordingly, and Bob will end up the winner.
It was fun to revisit this group, several weeks after the beginning of the semester. It’s a good group and I was impressed again at how well they were engaged with the material.
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