Exponential Thin-Slicing + Quiz Redos

I decided to add a skill to our Exponential Functions unit: writing the equation of an exponential function given two points. First, when one of the points is the y-intercept, and second, when neither point is the y-intercept. I used to save this skill for Pre-Calculus, but I love the application problems for this unit, so I created problems for pairs to do at the VNPS whiteboards. These aren’t exactly ‘thin-slicing’ problems, since they don’t get more difficult as students progress through the series - they’re just presented differently: from a scenario, from a graph, and from a table of values. One requires exponential regression on the TI-84.

These took a little longer to create than I anticipated, but the students enjoyed the real-life context of them so I’ll call it a win. Below is a link to the PDF of the 5 problems I made, and here is the WORD DOC version.

I thought for sure the students would get through all 5 problems in one 47-minute class, but most pairs got through the first three problems. This still gave them good practice on the skill, but I’ll give them 10 more minutes tomorrow before beginning Logarithms.

Before today’s lesson, students watched a video I made yesterday on how to perform this skill. I went through examples of how to do this when the y-intercept is already given and when both ‘a’ and ‘b’ need to be found. I did 5-6 examples for a 13 minute video, and no matter how clearly I think I explain it in the video notes, there’s always a subset of the class that has no idea how to begin the first classwork problem the next day. I’ve learned over time that these are usually the students who consider my video notes as busy work and watch them incorrectly. Some mute the video and mindlessly copy things down. Others hit ‘play’ and walk away from the screen, copying a friend’s notes the next morning instead. Either way, it’s very apparent the next day in class who took the time to process the video while watching it.

What to do with the students who don’t take the time to learn the material initially and then feel the consequences when it’s quiz or test time? Sometimes I’ll offer test revisions, where they can earn half of their points back for fully redoing any problem they missed points on and explaining their error. Sometimes I’ll offer quiz redos, IF extra practice is done beforehand. Sometimes they just keep the score they earned, but I don’t necessarily like this since I know they have not fully mastered the concept. This is why I want to move to Standards Based Grading next school year.

For the quiz they took last week on graphing exponential functions and writing their equations, I am allowing them to fully redo the quiz for a new grade if they want. They get the score of the redo (for better or for worse). This ensures they actually prepare for the quiz and I don’t waste my time regrading quizzes for nothing. Before redoing the quiz, I am having them complete a few different set of extra practice problems after school in my room. Once I’ve checked these with them, they can come in the next day at lunch or after school to redo the quiz.

Click the button below to see the problems I am giving them.

The graphing problems came from The Independent Variable blog.
The other problems came from the Functions Modeling Change textbook.