Here's a performance task that's a great way to tie in what students know about exponential functions.
Big Idea
Students are given the following task:
Determine if there is a significant difference in value over time for two types
of cars by determining and examining their approximate rates of depreciation
and using that and other factors to determine which car would be a better value
for your needs.
Setting the Stage
First it's a good idea to brainstorm how students might compare two cars they are interesting in purchasing to determine which is the better deal. Is it enough to compare purchase price? Are there other factors they should be considering? Get a good conversation going, have students list things they should consider on their papers and then share in whole group on the board.Students have learned about car depreciation in a general way. If they are still uncertain as to what that is you can search on youtube for a possible video to show them. I have students read this article on depreciation. I tell students they are going to compare two types of cars to see which is the better value. They will use depreciation rate as one way of comparing and then choose one other characteristic. We'll have time in class to collect data on the "Kelley Blue Book" site.
Then usually have students then read the article for HW and also read over the performance task details. They are also to think about two types of cars they might want to compare. They might want to compare SUVs and mini-vans. Or two-door sports cars vs 4 door sedans. Or american made vs foreign made. There are a lot of possibilities and encourage them to discuss with their parents about what they think. Students should come in with a general thesis question next class. They do not have to collect data yet or even choose specific makes of cars yet. We'll do that the next class. I also tell students they can work in pairs (this is the ONLY PT they can work together on. I hate having students work together on a graded assignment but every year students beg me to let them do this. And every year there are students who end up doing most of the work for their group who come to me to complain. Sigh. But I figure one PT for them to do together will appease them and it will be less grading for me. I do a big stern talk about being sure you carry your weight if you work in pairs, etc).
Collecting Data
The next class students come in all ready to collect data and start this PT - so we have a computer lab day. Students will collect data on the internet. I have to plan ahead to do this in our school, we don't have many full class sets of computers and I have to be sure to sign up a few weeks ahead of time. Warning - if you have students use ipads to access the site the "tablet" site is a bit different from the general webpage. So be sure you are familiar with what that looks like and how to navigate.HUGE DISCLAIMER
This can be a little confusing. We really cannot collect true data for calculating depreciation because we can't buy a car and then record its value each year for 5 years. We have about an hour to collect our data. So you have to explain this very clearly and carefully to students so they understand how we are sort of fudging our data but that its still valuable to us even though we aren't truly tracking the value of a single car over time.
What are doing is collecting data on two cars that have been manufactured for at least five years. Students will choose two specific cars, go to Kelley Blue Book (http://www.kbb.com/) and find the new price of their first car. I strongly recommend that you work through this yourself on the site before you have students do this. My performance task directions are pretty specific but they may redesign their site so things change (and tablet or phone mobile sites look different).
I give students a data collection worksheet to record their data. They will use tables that look like this:
So the new price goes in for the y-value of "New". Then they look up the price of the same make & model car for the previous year and that goes for the y-value of a 1 year old car (x = 1) and so on with the used car prices. They will use the x values noted in the table when inputting data in their calculator NOT the actual year of the car.
They do this for both cars.
Warning - all sorts of things can happen when students are collecting data. They can find that one of their cars was not manufactured for a given year or that the value is lower for a newer year than an older year. Weird stuff can happen. So you have to think on your feet and decide what they should. Sometimes they have to start over and find another car model.
I know some teachers in my school limit students to a dozen different cars to choose from that the teacher researches ahead of time to be sure the data makes sense for those cars. This is a good idea. I have advanced students so I like them to learn about the quirks and limitations of working with the internet. They are pretty good-natured about having to start over so it has worked out fine for me.
Pulling it All Together
Now students have collected data and they have information about two cars. They need to create a nice table of all their data and get pictures of each of their cars. They should have something like this:
Then they have to apply the algebra they've learned, collect some more information about their cars and pull it all together to make a comparison. See the performance task details to see very specifically what they are doing.
The next class I like to talk briefly about what they do next. They need to have some sort of presentation of their results. They can turn it in as a powerpoint, as a booklet or as a poster. They do not have to present in class. Sometimes I get a pair of students who wants to present their powerpoint and I give them the opportunity as long as they can do it in ten minutes or less. But generally students want to just turn it in. It's a great idea for them to present their results but I'm always am working with time constraints - so much to cover, so little time. Anyhow, I show students this PowerPoint that gives a "sample presentation". I won't post this on line for students to refer to because I want them to have things in their own words but I like them to have a good idea of what makes a good and complete presentation. I don't give students any more class time to complete this task. They have about a week to turn in their final work.
How I grade this
I have a teacher rubric with details on how I grade this. Feel free to contact me for this and I will send it out to you.
