ALEX Lesson Plan

Comparing Fuel Economy (adapted from CMP "Comparing and Scaling" Investigation 4.1)

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  This lesson provided by:  
Author:Mark Baynes
System: Tallassee City
School: Southside Middle School
The event this resource created for:GEMS
  General Lesson Information  
Lesson Plan ID: 23976

Title:

Comparing Fuel Economy (adapted from CMP "Comparing and Scaling" Investigation 4.1)

Overview/Annotation:

In this lesson students will explore rates. They will use the concept of rates to compute and compare fuel economy.
This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.

 Associated Standards and Objectives 
Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 4
3. Determine and justify solutions for multi-step word problems, including problems where remainders must be interpreted.

a. Write equations to show solutions for multi-step word problems with a letter standing for the unknown quantity.

b. Determine reasonableness of answers for multi-step word problems, using mental computation and estimation strategies including rounding.


Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.1 Solve one-step word problems involving real-life situations using the four operations within 100 without regrouping and select the appropriate method of computation when problem solving.


Mathematics
MA2019 (2019)
Grade: 7
1. Calculate unit rates of length, area, and other quantities measured in like or different units that include ratios or fractions.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.7.1 Calculate a unit rate (limited to whole numbers under 100).


Mathematics
MA2019 (2019)
Grade: 7
2. Represent a relationship between two quantities and determine whether the two quantities are related proportionally.

a. Use equivalent ratios displayed in a table or in a graph of the relationship in the coordinate plane to determine whether a relationship between two quantities is proportional.

b. Identify the constant of proportionality (unit rate) and express the proportional relationship using multiple representations including tables, graphs, equations, diagrams, and verbal descriptions.

c. Explain in context the meaning of a point (x,y) on the graph of a proportional relationship, with special attention to the points (0,0) and (1, r) where r is the unit rate.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.7.2 Use a ratio to model or describe a real-world relationship.


Local/National Standards:

NCTM Number and Operations Standard Grades 6–8 Understand numbers, ways of representing numbers, relationships among numbers, and number systems: - Understand and use ratios and proportions to represent quantitative relationships.

Primary Learning Objective(s):

Students will use rates to compute fuel economy and gas mileage.

Additional Learning Objective(s):

 
 Preparation Information 

Total Duration:

31 to 60 Minutes

Materials and Resources:

You will need transparencies (attached). These can also be used as slides in a PowerPoint.

Technology Resources Needed:

You will need a overhead projector (ELMO or LCD projector, if available) and a computer with Internet access.

Background/Preparation:

The students should be able to complete long division problems.

  Procedures/Activities: 
1.)Put the rates transparency on the overhead (see attachment). Read each statement to the class and ask students to interpret each of the statements. Ask students what is being compared? Are the quantities the same kinds of measures (or counts) or are they different? Tell the students that each statement on the transparency compares two different things.....Let the students identify the two things in each statement. Tell the students that these are called rates because they tell us the rate at which something happened.

2.)Now discuss with the students how a rate can be scaled up or down to find an equivalent rate. Read this problem: My brand new car gets 30 miles to the gallon in the city. How much gas will my car use if I drive it 240 miles in the city? Place methods transparency on overhead and discuss the two possible ways listed on the over head. Ask the question: Which way did you think was best? Why? Can you think of another way of finding this rate?

3.)Talk to students about their experiences with cars and travel. Ask them if they know any drivers who worry about gas mileage.

4.)Put the story of Johnny and Fred on the overhead. Read the story aloud and direct the students to the table above. Tell them the table shows where Johnny and Fred live. It also shows the route they will take to visit their mom and dad. Point out the distances between cities and how this could be very important later in who wins the competition. Pose the question: "Which car is more fuel efficient on the highway?" Have students work in pairs on the problem. If some are struggling redirect them to the question/problem in step #2. It's the same kind of problem. Remind students that you are interested in explanations and why they think their answers are correct.

5.)Have students report their answers and share their thought process while solving the problem. In any solution, students should take into account two quantities: gallons used and miles traveled. The ratio of total miles to total gallons is typically used to report fuel efficiency and commonly represented as miles per gallon. Some students may compute gallons per mile and make perfectly good sense out of these rates. Miles per gallon is more common, but gallons per mile (gpm) is fine as long as students can explain what rate they have computed and what it means.

6.)During this activity each student will be given a certain vehicle and a destination. They must research (in the computer lab) this vehicle to show what kind of fuel economy it gets. (for example: 2006 F-150 SuperCrew gets 18 miles to the gallon on the highway.) Use the Mapquest hyperlink to help find the car's mpg. Using the cars estimated miles per gallon, the student must find how many gallons of gas it will take to drive round trip to their destination. They will need to calculate how much they will spend in fuel cost with the price of gas being $3.95 per gallon. Example: A student is given a slip of paper with the statement: You have a 2008 Chevy Tahoe and you are going to visit your aunt in Seattle, Washington. How much fuel will be needed to travel there and back? If gas is $3.95 per gallon, what will be the cost of fuel for your trip?
(Fuel Economy)

7.)After students complete their assignment, they will make class presentations to share their results. Allow small group discussions using the following questions: How does the rising fuel cost affect our economy? What do you think about fuel shortages? Identify any changes in your lifestyle that have occurred due to the rise in fuel cost.


Attachments:
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  Assessment  

Assessment Strategies

Teacher observation and test (see attached.)

Acceleration:

If a student has mastered the primary learning objective of this lesson they can research the concept of unit rates and how they are useful in real life situations. This research could be published in their math journals or on a sheet of paper to be turned in.

Intervention:

Students who need remediation in this area can access the following website. What is Your Rate?


View the Special Education resources for instructional guidance in providing modifications and adaptations for students with significant cognitive disabilities who qualify for the Alabama Alternate Assessment.