Today's lesson picks up where yesterday's lesson left off. Yesterday, we investigated what happens to the value of a car over time. We saw that there are many different factors that affect the value of a car, and that we can use the word parameters to describe all of these influencing factors that can change for a specific case.
Changing parameters will once again be a focal point of today's lesson, as we will investigate the factors that affect the terms of an auto loan, and how each one contributes to the total amount we'll pay for a car over time.
To begin today's lesson, students will build background knowledge (BBK) by identifying the parameters at play when we're talking auto loans. The opener is a reading called "How to Finance a Car and Get a Car Loan". You can use this slightly dated version of the article, or see an up-to-date version at U.S. News and World Report. As students arrive, I distribute copies of this activity packet, and I direct students to get a computer and to find the article online.
"Today, we're going to talk about how to pay for a car," I say. "Yesterday I said you had to choose a popular car. Today you can choose the car of your dreams, and then you're going to figure out how you're going to pay for it!"
Students work through the first three questions in the packet. For the first, they identify their "dream car" and use edmonds.com to find the MSRP of that car. I wait for students to set the terms for our discussion of question #2, "What is a car loan?" If kids get this conversation going, I'll run with it. If they don't, or really have no idea how auto loans work, they should start reading the article right away. Either way, after a brief discussion or not, students read the article and answer all parts of question #3. As with yesterday's lesson, my goals today are to show students how to research and make the kinds of real-world decisions that are in their near future, in addition to exposing them to some important mathematics.
About the Activity
This activity is from a curriculum developed by Laguardia Community College. It's all great reading. Today's handouts come from this document, on pages s-25 through s-35. There's an overview of the lessons on pages s25-s27, followed by the activity on s28-s31, then the opening reading is on pages s34-s35. Also in the same document is an exploration of student loan debt that follows a similar outline to this one, and that could also be useful in a course like this.
If you like these activities, check out the rest of the pages that I haven't referenced, and a larger sample of similar activities here: http://ctl.laguardia.edu/pql/sampler/activities.htm.
The BBK continues as we identify the parameters of an auto loan, which continues our work from yesterday, when we investigated the factors that contributed to the value of a car over time.
When students are done reading the article, I ask them to name the parameters of an auto loan, and I record their notes on the board. If students have questions about what these terms mean, I'll answer them now.
The Parameters of an auto loan:
In addition to these quantitative variables that factor into the loan formula, students will note that there are other parameters that can change these values. For example, students just read that someone's credit score can affect the interest rate they're offered, and that different loan providers can offer different interest rates to the same consumer, so it's worth it to shop around.
From this conversation, we move onto looking together at a specific example.
In addition to learning about auto loans and laying foundations for a lesson about recursive function rules tomorrow, students will also see the magic of spreadsheets work in today's lesson.
To get started, we'll look at an example together. As students identify and research the prices of their dream cars, I look for a student who has chosen a particularly expensive one. I take their example, and as they finish up, I create a chart like this on the board.
Usually, when you get a loan, you have some options for loan term, and then the monthly payment is based on that. But what if we could start by saying what we wanted to pay each month? After I find a student who has chosen an expensive dream car, I construct the chart on the board. "What do you want your monthly payment to be?" I ask. "What do you think is reasonable?" Then, we can start the chart here, to see how everything works before creating the chart in Excel. Referring back to the list of parameters that we've identified previously, I now show students how to calculate the amount of interest that is added to their principle each month, and how the month ending balance is determined by subtracting the monthly payment and adding the interest.
We soon recognize that doing all this work by hand will take a while, "and that," I tell everyone, "is where Excel becomes a really useful tool." In this narrative video, I describe how I demonstrate the use of spreadsheet software to students. When they continue questions #4-7 in the investigation packet, students will use Excel on their own. I find that sharing this example is a great way to frame their individual work. Here is the example spreadsheet that I work with in the video.
Once we have a tool like this spreadsheet, it's really easy to change parameters and gauge their affect on the loan. In this video, you can see how I demonstrate this to students. Once students see this, they can't wait to run their own experiments.
After students have seen the example, they're ready to go on the rest of the investigation. I give students the rest of the class to work with their own dream car to complete tasks #4-7 in the investigation packet.
As students work, I circulate to troubleshoot, but by this point the activity really runs itself. Students are motivated to figure out how someone might go about paying for a car, and it's invigorating to hear their insights as they learn how how auto loans work. We are also laying foundations for our work with function rules tomorrow. Loan payments are much easier to model recursively than otherwise, and this is a nice way into that.
I don't have a specific exit task today: the reflection that I'd look for in an exit slip is built into this task, so when I collect it I'll see what students understand. Hopefully, they'll finish it today; if they don't I'll invite them to come to an after-school session, or if I have to, I'll give some time tomorrow to finish up.