Lesson Title: Car Depreciation
Date: _____________ Teacher(s): ____________________
Course: Algebra II, Unit 2
Start/end times: _________________________
Lesson Standards/Objective(s): What mathematical skill(s) and understanding(s) will be developed? Which
Mathematical Practices do you expect students to engage in during the lesson?
MP1:
MP2:
MP3:
MP4:
MP6:
MP7:
MP8:
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
F.BF.A.2 Write geometric sequences both recursively and with an explicit formula, use them to model situations,
and translate between the two forms.
F.LE.A.2 Construct exponential functions, including geometric sequences, given a graph, a description of a
relationship, or two input-output pairs (include reading these from a table).
Common Core Algebra II, Unit 2
Lesson Launch Notes: Exactly how will you use the first five
minutes of the lesson?
Students will generate, as a group, a list of their 10 favorite new
car make and models.
Lesson Closure Notes: Exactly what summary
activity, questions, and discussion will close the
lesson and connect big ideas? List the questions.
Provide a foreshadowing of tomorrow.
For Discussion:
As a student scribe records the list, research the MSRP at
http://www.edmunds.com/newcars/?mktcat=genauto&kw=new+auto+invoice&mktid=ga2436
22
Record the new car prices of each.
OR
Pre-select 10 popular new cars from the site above and record
their names and prices on strips that students will select
randomly for task.
Who could benefit from the information in the
sequence?
What factors could impact the value of a car
during its “life” span?
Can a term potentially have a negative value?
If so, what does it mean in the context of this
lesson?
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations, problems,
questions, or tasks will students be working on during the lesson? Be sure to indicate strategic connections to
appropriate mathematical practices.
1. Project the following web page on the screen http://www.edmunds.com/car-buying/how-fast-does-my-new-carlose-value-infographic.html without revealing the image below.
2. After allowing the students to make sense of the information, direct students to an analysis of the values on the
ticket prices for each year to determine if a noticeable pattern exists in the data. (Look for evidence of MP1.)
3. Give the students five minutes to predict and justify with a partner the value of the car after 10 years. Have
students report out their predictions and justifications. (The assumption will be that the car will have no value in
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student achievement.
Portsmouth, NH: Heinemann.
Lesson Title: Car Depreciation
Date: _____________ Teacher(s): ____________________
Course: Algebra II, Unit 2
Start/end times: _________________________
10 years based on the given images of the line and pie graph.) (Look for evidence of MP2 and MP3.)
4. Now, reveal the bottom of the page to the students (that which shows the image below).
http://www.edmunds.com/car-buying/how-fast-does-my-new-car-lose-value-infographic.html
5. Discuss the challenges and suggestions that would aid in making “better” predictions (common depreciation
value – a common r value). (Look for evidence of MP3.)
6. Decide as a group (or preselect) on an average depreciation value that will be used for the task.
7. In groups of three, have students use the information from the edmunds.com site to generate the value of the car
that they were assigned (or selected) for each year, over the next five years (recursive geometric sequence).
Have students write the formula for the value of the car both recursively and explicitly. Have students explain
how they determined these formulas. (Look for evidence of MP6, MP7 and MP8.)
8. Have students graph their car data and compare its image to that of the one projected from the Edmunds website
(Edmunds’ graph appears linear.) (Look for evidence of MP4.)
9. Once groups have generated and graphed their data, have the class: (Look for evidence of MP3.)
● Discuss why it is not correct to begin with the new car value as the first term in the sequence.
● Discuss the need for knowledge of the prior year’s value (n-1) to calculate the current year.
● Write a formula that models the process used to generate the car values each year (recursive geometric
function).
● Discuss the possibility of predicting the value of the car in year 10.
● Discuss what information would be needed to make the prediction.
Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I
measure student success? That is, deliberate consideration of what performances will convince you (and any outside
observer) that your students have developed a deepened and conceptual understanding.
Students will be able to identify how and when to apply a recursive geometric formula when presented with a
problem. Students will demonstrate success if they are able to write and apply the formula for calculating the
depreciation of a car given the average rate of depreciation.
Notes and Nuances: Vocabulary, connections, anticipated misconceptions (and how they will be addressed), etc.
Vocabulary
Depreciation – loss in value of an asset
MSRP – Manufacturer’s Suggested Retail Price
Edmunds – private publisher of automotive specifications
Geometric
Recursive
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student achievement.
Portsmouth, NH: Heinemann.
Lesson Title: Car Depreciation
Date: _____________ Teacher(s): ____________________
Course: Algebra II, Unit 2
Start/end times: _________________________
Define the meaning of the subscripts 1 and n-1.
Define the meaning of the superscript n-1.
Connection: Students were introduced to geometric and exponential functions in Algebra I. This lesson will help to
apply their understanding to a real-world situation of car depreciation.
Note: Students may forget to make the first term of the sequence the value of the car after the first depreciation.
Remind students that the car depreciates immediately after driven off the lot so the MSRP is not the first term. The
initial depreciation is 11% but (for the purpose of this lesson), will average 15% per year over the next five years.
Resources: What materials or resources are essential for
students to successfully complete the lesson tasks or
activities?
Homework: Exactly what follow-up homework
tasks, problems, and/or exercises will be assigned
upon the completion of the lesson?
board, flip chart, document camera or overhead projector,
internet access, Edmunds New Car Value Website
http://www.edmunds.com/newcars/?mktcat=genauto&kw=new+auto+invoice&mktid=ga24
3622
Have students reflect and write responses to the last
two bullets from the whole-group discussion: “is it
possible to predict the value of the car in year 10?”
and “what information would be needed to make the
prediction?”
Lesson Reflections: How do you know that you were effective? What questions, connected to the lesson
standards/objectives and evidence of success, will you use to reflect on the effectiveness of this lesson?
Did students understand what contributes to the rate of depreciation of a vehicle, thus the need for the use of
“average” depreciation? Did students write a formula and apply it correctly to generate the value of the car and
distinguish between this and the amount of depreciation? Were students asking questions that indicated that they
were thinking about alternative methods for finding the value of the car for any given year without knowing the prior
year?
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student achievement.
Portsmouth, NH: Heinemann.