Lesson Title: __Car Mileage: Which is a better buy?______________
Course: __Common Core 6 (MSM1)____
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Lesson Objective(s): What mathematical skill(s) and understanding(s) will be developed?
6.RP.2: Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the
context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is
a ¾ cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”
6.RP.3b: Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took
7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns
being mowed?
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
Put the pictures of the five cars under the document
camera. Activate any background knowledge by
asking students what they know about these cars.
Which one would they consider to have the best gas
mileage and why?
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and provide
a foreshadowing of tomorrow? List the questions.



How did we determine which car was the most
efficient?
How did we utilize unit rate? What unit rate did
we use? Why?
What were some of the strategies we used to find
unit rates?
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students be working on during the lesson?
1. Show students the list of cars (Camry, Hummer, Accord, Prius, and Mustang). Ask them what gas mileage
is and what it means. Have a brief conversation about why gas mileage is given as a statistic for car
performance. Now give students a few minutes to order the cars from the lowest gas mileage to the highest
gas mileage. Next, show them the attached paper with the cars and the number of miles the cars can travel
with the given amount of gas. Give students 60 seconds to see if they want to change their order of
efficiency. Remove the paper from view of the students in order to prevent them from moving ahead and
performing any calculations. Ask the class if anyone made any changes and ask them why he/she made
those changes.
2. Solve the first problem together (for the Camry). Scaffold the entire process as follows and think aloud.
 Ask the class if it would make more sense to find miles per gallon or gallons per mile. Encourage
students to think about it—does it make sense to find the fraction of a gallon of gas it takes to drive one
mile?
 Begin the process by talking about how one would calculate how many miles you could drive on one
gallon of gas. Ask for student suggestions and record their thinking. Ask questions as necessary in
order to ensure the class understands the strategy. “Does this strategy work?”
 Once the gas mileage has been computed, ask the students to interpret their findings. Ask, “What does
gas mileage tell us? Is it better to have higher or lower gas mileage?”
3. Students should now work with their group (or partner) in solving for the rest of the gas mileages. They can
use any strategy they wish. However, they must show their work. Emphasize the necessity of including
units and labels.
4. Regroup as a class and go over the gas mileages. Ask for students to share different strategies they used in
order to solve for the gas mileages.
 Refer back to their predictions. Ask, “How do the actual gas mileages compare to your predictions?”
 Ask, “If you had a car in the wrong place in your original order, why did you place it there?”
 Ask, “What generalizations can we make from the data of gas mileages that we now have?”
5. Extension: Give students the prices and cargo capacity for each of the five cars. Give them a minute to look
at the data. If you want to get the most efficient car for your money, which would you choose? Why? What
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: __Car Mileage: Which is a better buy?______________
Course: __Common Core 6 (MSM1)____
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
if you want a car that can carry a lot of tools or gear? Give students some time to look at the data and
discuss with their groups. Do not provide a lot of structure here. Instead, let students try and work through
the problem on their own. Encourage students to make generalizations based on all of the information/data.
If students seem to be struggling, regroup and talk through the first car. Allow this to be a time for students
to share their thinking with each other (as a class) and then proceed accordingly.
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 mastery? That is, deliberate consideration of what performances will convince you (and any outside
observer) that your students have developed a deepened (and conceptual) understanding.
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Students should be able to articulate gas mileage as a unit rate since we are solving for the number of
miles per one gallon of gas. They should also be able to articulate that a higher gas mileage is better
because you can drive farther on just one gallon of gas.
Students should also be able to verbalize: to determine the most efficient car for your money, one would
need to look at and compare gas mileage AND price.
Notes and Nuances: Vocabulary, connections, common mistakes, typical misconceptions, etc.


Vocabulary: gas mileage, unit rate, “per one”
Common mistakes/misconceptions: Students who chose to use proportions (or other strategies) may
invert the division number sentence and inadvertently solve for the fraction of a gallon per mile.
Students who do not have a firm grasp on gas mileage may confuse the meaning of a high gas mileage
versus a low gas mileage.
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?
Resource sheets with cars’ gas mileage, price, and
cargo capacity (included); paper, pencil
Lesson Reflections: What questions, connected to the lesson objectives and evidence of success, will you use to
reflect on the effectiveness of this lesson?


Did students demonstrate a conceptual understanding of unit rate in being able to articulate how and why
they were solving for unit rate and what it means in the context of the problem?
Did every student find and use at least one strategy for solving the problem?
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: __Car Mileage: Which is a better buy?______________
Course: __Common Core 6 (MSM1)____
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Which car has the best gas mileage?
Camry
392 mi, 14 gal
Hummer
176 mi, 11 gal
Accord
312 mi, 12 gal
Prius
Mustang
400 mi, 8 gal
368 mi, 16 gal
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: __Car Mileage: Which is a better buy?______________
Course: __Common Core 6 (MSM1)____
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Which car is the better buy?
Camry
$21,955
Hummer
$45,000
Accord
$21,380
Prius
Mustang
$24,000
$26,310
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: __Car Mileage: Which is a better buy?______________
Course: __Common Core 6 (MSM1)____
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Which car has the best cargo capacity?
Camry
15.4 cubic feet
Hummer
30.7 cubic feet
Accord
14.7 cubic feet
Prius
Mustang
21.6 cubic feet
13.4 cubic feet
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.