Exponential functions have a connection to geometric sequences and series, but it is not always clear to students why we study them as two separate topics. For the lesson's warm-up I ask students to answer some questions about geometric functions, some questions about geometric functions. When they have completed these questions, I spend time discussing the connection between geometric sequences and exponential functions The most important point I try to drive home is that geometric sequences ARE special exponential functions. They are geometric functions with a domain restriction of x = 1, 2, 3, ...
For the Drinking and Driving Activity, students will need an internet-enabled device, a graphing calculator and a pencil.
The goal of the activity is threefold:
The day before this activity, I select groups of 3 students that will work together. They will receive a group grade for this work, so its important that I arrange students in groups that will participate equally. I also arrange students so that there is sure to be at least one student in each group with easy internet access. I arrange the groups on a powerpoint slide so that I can show the slide to students when I ready for them to move.
I start the activity by introducing the idea of probability of an accident. We talk about what factors affect the likelihood of getting into a car accident. Because many of my algebra 2 students are in drivers ed, this is a topic that they have been thinking about recently. The topic of alcohol generally comes up in this conversation, but if it did not, I would steer the conversation in that direction. At this point I introduce the activity, writing the exponential function introduced in the activity on the board and discussing some of its features. We examine
After we have examined the function in this way, students are ready to jump in because the activity is laid out in a step-y-step way in the document Drinking and Driving Activity.docx