Teacher: Maple So School: Herron High School. Comparing the Usage Cost of Electric Vehicles Versus Internal Combustion Vehicles

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1 Teacher: Maple So School: Herron High School Name of Lesson: Comparing the Usage Cost of Electric Vehicles Versus Internal Combustion Vehicles Subject/ Course: Mathematics, Algebra I Grade Level: 9 th 10 th Grades Lesson Abstract: Students will compare the usage cost of electric vehicles versus internal combustion vehicles. They will use the slope-intercept form of linear equations to make a cost analysis of the two types of vehicles. After creating their mathematical models, students will interpret the graphs using key mathematical terms and see how the models affect their vehicle choices. Additionally, students will be working on additional linear applications that are related to sustainability energy topics. Learning Outcomes: Students can use a linear mathematical model to do a cost analysis when comparing two decisions. Students can apply key mathematical terms to relate features of linear equations in slope-intercept form to real-life implications. Problem Statement: How can linear equations help people make a choice between buying an electric or internal combustion vehicle? Key Mathematical Terms Linear Equation Slope Y-Intercept Y-axis X-axis Intersect X-Intercept Cost Rate Change Units Content and Skills Standards: College & Career Ready Indiana Academic Standards for Mathematics: Algebra I Process Standards for Mathematics PS.4: Model with mathematics. Mathematically proficient students apply the mathematics they know to solve problems arising in everyday life, society, and the workplace using a variety of appropriate strategies. They create and use a variety of representations to solve problems and to organize and communicate mathematical ideas. PS.6: Attend to precision. Mathematically proficient students communicate precisely to others. They use clear definitions, including correct mathematical language, in discussion with others and in their own reasoning. Algebra I Skills Standards AI.L.2: Represent real-world problems using linear equations and inequalities in one variable and solve such problems. Interpret the solution and determine whether it is reasonable. AI.L.4: Represent linear functions as graphs from equations (with and without technology), equations from graphs, and equations from tables and other given information (e.g., from a given point on a line and the slope of the line). AI.L.5: Represent real-world problems that can be modeled with a linear function using equations, graphs, and tables; translate fluently among these representations, and interpret the slope and intercepts. AI.L.6: Translate among equivalent forms of equations for linear functions, including slopeintercept, point-slope, and standard. Recognize that different forms reveal more or less information about a given situation.

2 Lesson Sequence: Approximate Time Needed: 5.5 hours Introduce the problem statement and key mathematical terms. TIME NEEDED: 3 minutes Pre-assess the students knowledge of the key mathematical terms in a class discussion. TIME NEEDED: 7 minutes Warm-up exercise about the gallons of gas required for a road trip using a 2014 Toyota Tundra. TIME NEEDED: 5 minutes White Board Practice Problems TIME NEEDED: 10 minutes Guided Notes of Linear Story Problems TIME NEEDED: 15 minutes Odd One Out: 3 Examples of Linear Graphs TIME NEEDED: 6 minutes Think-Pair-Share Missing Information Needed to Solve Story Problems TIME NEEDED: 9 minutes Exit Quiz TIME NEEDED: 15 minutes Think-Pair Compare Activity: Electric vs. Internal Combustion Vehicles TIME NEEDED: 25 minutes Cost Analysis Project: Electric vs. Internal Combustion Vehicles TIME NEEDED: 60 minutes Come Up With Interview Questions for the Car Dealership TIME NEEDED: 10 minutes Visiting the Car Dealership & Interview the Salesperson TIME NEEDED: 90 minutes Linear Story Problem Test TIME NEEDED: 60 minutes Materials Needed: Classroom set of about dry erase markers Classroom set of about individual mini whiteboards Classroom set of about old socks (erasers for the mini whiteboards) Classroom set of about rulers Computer and internet access for students sheets of graph paper

3 Activities: 1. White Board Practice Problems The objective of the activity is to quickly review the features of lines in slope-intercept form. The teacher will have 5 problems that focus on one aspect for each problem. Graphing a line with a positive slope. Graphing a line with a negative slope. Graphing a line with a positive y-intercept. Graphing a line with a negative y-intercept. Evaluating a linear equation given a specific input value of x. 2. Guided Notes of Linear Story Problems Teacher will show students techniques to pick out important information in a story problem and organize the problem solving process in a graphic organizer. a) The story problem in the guided notes will be read aloud by a student. Afterwards, the teacher will ask students to mark up what the story problem is asking. i. The focus is to push students to identify the question in the story problem. ii. After students successfully identifies the question, the teacher will ask students to write down important information that is needed to answer the question in the story problem. iii. If students identified all the numerical values as important information, the teacher needs to ask the following questions. Why are the numerical values important to the problem? Identify the relationship that the numerical values have with the slope-intercept form of a line. How will the numerical values be used to solve the story problem? b) Students will then work on another story problem with a partner using the graphic organizer. When students finish the story problem, debrief as a class with the following questions. Reflection Method Did your solution answer what the story problem asked for? How can you verify that your answer makes sense? If you made a mistake, where can you review in your work to correct your mistake? 3. Odd One Out: 3 Examples of Linear Graphs The teacher will show three examples of graphs of linear equations on the board. Each example will display three choices; the student needs to identify what he or she think is the choice that does not belong in the example based on a characteristic that stands alone compared to the other choices. Students will write down their answer for each example and justify their answer. Reflection Method: Before moving on to a new example, ask the following questions. Why did you select that choice as the odd one out? What can be changed about the choice that you selected, so it can fit in with the other choices in the example? The focus of this activity is to push students to identify features of a line graph by using mathematical terms in justifying their answer. 4. Think-Pair-Share Missing Information Needed to Solve Story Problems

4 The teacher will show three cases of different story problems that have purposely omitted important information to solving the problem. Students will silently read the story problem on the board to themselves, think about what crucial information is omitted in the problem and pair up with a peer to write down what additional information is needed to solve the word problems. 5. Exit Quiz In this activity, students will be given a story problem with information about the monthly fixed cost of a residential solar panel system and the price that the electric company pays to the household per kwh of surplus electricity produced. Students will do the following. Read the question. Identify the problem. Mark up crucial information. Set up the necessary equations to the solution. Write out the thought process to solving the problem using key mathematical terms without physically computing exact numerical values for the answer. KEY MATHEMATICAL TERMS Linear Equation Slope Y-Intercept Y-axis X-axis Intersect X-Intercept Cost Rate Change Units Assessments: Formative Assessments 1. Warm-Up Exercise Students will create a linear model to figure out how many gallons of gas will be needed for a 2014 Toyota Tundra for a 200-mile road trip. The purpose of this exercise is to refresh the concept of slope in the context of a practical, real-life example. 2. Think-Pair-Compare Activity a) Students will pair up with a partner and decide on a style of car that they want to buy. The style of car refers to compact, midsize, large size or a sports utility vehicle. b) Once students have decide on one style of car, one student will research a model of electric car for the particular style while the other student researches a model of internal combustion vehicle. Use the following links for the research process. Fuel Economy Information Consumer Reports Article c) Each student will create a linear equation for their car and graph their linear models together on Desmos Graphing Calculator. d) Students may not know how to adjust the window size to make the linear graphs visible on the graphing calculator. At this point, the teacher needs to use the following guiding questions. GUIDING QUESTIONS FOR ADJUSTING WINDOW SIZE OF A GRAPH

5 i. What does the x-axis represent on the graph? What is the range of realistic values that the x-axis can represent in the context of this example? ii. What does the y-axis represent on the graph? What is the range of realistic values that the y-axis represent in the context of this example? iii. How does the number of tick marks on the axes help you clearly read the graph? e) Reflection Method: After creating their mathematical models, students will need to respond to the following questions in writing. Each answer must be supported with specific evidence from their mathematical model and use key mathematical terms as stated below. Summative Assessment QUESTIONS FOR THE STUDENT i. Which vehicle cost more as the mileage of the car increases? How do you know? ii. Why is it important to compare the same style of car (i.e. a compact electric car with a compact regular car)? iii. Can we do a cost comparison of an electric sedan with a regular sports utility vehicle? How is this a fair or unfair comparison? SUMMATIVE ASSESSMENT A: COST ANALYSIS PROJECT 1. Creating Mathematical Models Students will select one electric vehicle and one internal combustion vehicle. They will create a linear model in slope-intercept form for each vehicle to do a cost analysis of the two choices. The presentation of the solution will follow the diamond format graphic organizer. Use the following links for the research process in finding two cars to compare. Fuel Economy Information Consumer Reports Article 2. Analyzing the Mathematical Model After creating their mathematical models, students will need to respond to the following questions in writing. Reflection Method: Each answer must be supported with specific evidence from their mathematical model and use key mathematical terms as stated below. KEY MATHEMATICAL TERMS Linear Equation Slope Y-Intercept Y-axis X-axis Intersect X-Intercept Cost Rate Change Units QUESTIONS FOR THE STUDENT Refer to your mathematical model and consider the mileage of the vehicles, under what circumstance would owning an electric car be a better choice than a regular car?

6 Refer to your mathematical model and consider the mileage of the vehicles, under what circumstance would owning a regular car be a better choice than an electric car? Under what circumstance would owning either an electric or regular car not matter based strictly on the linear models? Why? SUMMATIVE ASSESSMENT B: LINEAR STORY PROBLEMS TEST Students will demonstrate mastery of the algebra skills in linear equations in a written test. The questions will address the following content. Identify graphs and equations of lines with positive or negative rate of change. Identify the slope and intercepts of a linear equation and explain their features on a graph. Solve linear equation story problem by identifying the question, marking up crucial information and explaining why their solution makes sense.

7 Warm Up Exercise Your family is on a 200-mile road trip to visit a lake, driving the 2014 Toyota Tundra. The truck can travel 20 miles per gallon of gasoline. After traveling 50 miles, your family needs to fill up the gasoline. What is the minimum number of gallons of gasoline needed to complete the remainder of the road trip?

8 White Board Practice Problems Whiteboard Problem 1. Create a linear equation in slope-intercept form that has increasing y-values as x-values get larger. Graph the linear equation on the x-y coordinate plane. Whiteboard Problem 2. Create a linear equation in slope-intercept form that has decreasing y-values as x-values get larger. Graph the linear equation on the x-y coordinate plane. Whiteboard Problem 3. Create a linear equation in slope-intercept form with an upward slope and a positive y-intercept. Graph the linear equation on the x-y coordinate plane. Whiteboard Problem 4. Create a linear equation in slope-intercept form with a downward slope and a negative y-intercept. Graph the linear equation on the x-y coordinate plane.

9 Whiteboard Problem 5. Consider the equation y= 5x +10. What is the y-value when x= 2? What would be the value of x if y= 30?

10 Name Date Period Guided Notes: Story Problems Involving Linear Equations SKILL: I can apply linear models to solve story problems in real-life applications. *Underlined and bold, red text should be blank spaces to be filled out during note-taking. STRATEGIES TO BEGIN SET UP A STORY PROBLEM 1. Read the entire story problem. 2. Mark up the question in the problem. 3. Write down the important information that is needed to answer the problem. 4. Arrange all the information in the graphic organizer using the appropriate headings: question, variables & important details, relevant equations, math work and interpretation of solution. EXAMPLE 1. Jenny and Harry each own a bike-pedaled power electric generator. The time that Jenny spends to set up the machine before she can charge a cell phone is about 5 minutes. She takes about 4 minutes to charge a cell phone. The time that Harry spends to set up the machine before he can charge a cell phone is about 10 minutes. He uses about 2 minutes to charge a cell phone. If a customer has 5 phones, who will take less time to charge all the phones? If a customer has 2 phones, who will take less time to charge all phones? Create a general rule in who to choose when a customer needs to charge k number of cell phones. As you mark up the important information, answer the questions below. o Why are the numerical values important to the problem? o Identify the relationship that the numerical values have with the slope-intercept form of a line. How will the numerical values be used to solve the story problem?

11 EXAMPLE 2. Karen is trying to decide whether she should buy an incandescent light bulb or a LED light bulb. An incandescent light bulb cost $1.50 and $0.02 per KWh. A LED light bulb cost $20 and $0.002 per KWh. Which light bulb is a better purchase? Why? o Did your solution answer what the story problem asked for? o How can you verify that your answer makes sense? o If you made a mistake, where can you review in your work to correct your mistake?

12 Name Date Period DIRECTIONS: Each example will display three choices A through B. Identify the choice letter that does not belong in each example based on a characteristic that stands alone compared to the other choices. Write down the choice for each example and justify your answer by answering the reflection questions. EXAMPLE 1. Graph A Find the odd one out using Graphs A through C. Explain your answer using the mathematical key terms. Graph B Graph C The odd one out is choice. Why did you select that choice as the odd one out? What can be changed about the choice that you selected, so it can fit in with the other choices in the example?

13 EXAMPLE 2 Equation A Find the odd one out using the Equations A through C. y = 0.75 x Explain your answer using the mathematical key terms. Equation B Equation C y = -9x y = 2x The odd one out is choice. Why did you select that choice as the odd one out? What can be changed about the choice that you selected, so it can fit in with the other choices in the example? EXAMPLE 3 Choice A Find the odd one out using the Choices A through C. y = -3 x + 5 Explain your answer using the mathematical key terms. Choice B Choice C y = 7x + 3 The odd one out is choice. Why did you select that choice as the odd one out? What can be changed about the choice that you selected, so it can fit in with the other choices in the example?

14 Name Date Period DIRECTIONS: There are three story problems that have purposely omitted important information. Read the story each story problem and think about what crucial information is omitted in the problem. Pair up with a peer to write down what important information is needed to solve the word problems using the key mathematical terms. KEY MATHEMATICAL TERMS Linear Equation Slope Y-Intercept Y-axis X-axis Intersect X-Intercept Cost Rate Change Units Story Problem 1. Farmland is measured in acres. Joe owns farmland that grows bushels of corn. Each acre of farmland makes about $172 of profit. How much profit can Joe make on his farmland? What important information is needed to solve the word problem? Story Problem 2. Jack harvested 244 bushels of corn. How much profit did Jack make off of his corn? What important information is needed to solve the word problem? Story Problem 3. Bob pays a fixed monthly rate of $70 for his solar panel system at home. For every unused kilowatt-hour of electricity that the solar panels produced, the electric company deducts $0.25 per kilowatt hour off his monthly bill. How much did Bob pay for one month of electricity? What important information is needed to solve the word problem?

15 Name Date Period DIRECTIONS: Write out the thought process to solving the story problem by using key mathematical terms without physically computing exact numerical values for the answer. KEY MATHEMATICAL TERMS Linear Equation Slope Y-Intercept Y-axis X-axis Intersect X-Intercept Cost Rate Change Units Sonia installed a solar panel system in her home. She pays a fixed monthly rate of $60 for her solar panel system. For every unused kilowatt-hour of electricity that the solar panels produced, the electric company subtracts $0.24 per kilowatt-hour off her monthly bill. How much unused electricity must the solar panel produce for Sonia to pay $0 in her monthly bill?

16 Name Date Period PART 1 Pair up with a partner and decide on a style of car to buy. The style of car refers to compact, midsize, large size or a sports utility vehicle. Research a model of electric car for the particular style while your partner researches a model of internal combustion vehicle. Use the following links for the research process. Miles Per Gallon Information from the U.S. Department of Energy Additional Resource on Consumer Reports Article Partner A Car Type: Electric or Internal Combustion? Price of Car: Cost to Drive Each Mile: Linear Equation Model: Partner B Car Type: Electric or Internal Combustion? Price of Car: Cost to Drive Each Mile: Linear Equation Model: Graph the two linear models on Sketch the graph below, label the axes and the equations next to the graphs.

17 After creating the mathematical models, respond to the following questions. Each answer must be supported with specific evidence from the mathematical model and use key mathematical terms as stated below. KEY MATHEMATICAL TERMS Linear Equation Slope Y-Intercept Y-axis X-axis Intersect X-Intercept Cost Rate Change Units 1. Which vehicle cost more as the mileage of the car increases? How do you know? 2. Why is it important to compare the same style of car (i.e. a compact electric car with a compact regular car)? 3. Can we do a cost comparison of an electric sedan with a regular sports utility vehicle? How is this a fair or unfair comparison?

18 Name Date Period PART 1 Decide on a style of car to buy. The style of car refers to compact, midsize, large size or a sports utility vehicle. Research a model of electric car and internal combustion car for the particular style. Use the following links for the research process. Miles Per Gallon Information from the U.S. Department of Energy Additional Resource on Consumer Reports Article Electric Car Information Car Type: Electric or Internal Combustion? Price of Car: Cost to Drive Each Mile: Linear Equation Model: Internal Combustion Car Information Car Type: Electric or Internal Combustion? Price of Car: Cost to Drive Each Mile: Linear Equation Model: Graph the two linear models on Sketch the graph below, label the axes and the equations next to the graphs.

19 After creating the mathematical models, respond to the following questions. Each answer must be supported with specific evidence from the mathematical model and use key mathematical terms as stated below. KEY MATHEMATICAL TERMS Linear Equation Slope Y-Intercept Y-axis X-axis Intersect X-Intercept Cost Rate Change Units Refer to your mathematical model and consider the mileage of the vehicles, under what circumstance would owning an electric car be a better choice than a regular car? Refer to your mathematical model and consider the mileage of the vehicles, under what circumstance would owning a regular car be a better choice than an electric car? Under what circumstance would owning either an electric or regular car not matter based strictly on the linear models? Why? Compare and contrast the electric car and the internal combustion car using the Venn Diagram and the key mathematical terms. Internal( Combustion( Electric( Car( Car(

20 Name Date Period DIRECTIONS: Come up with 3 questions that you want to ask the car dealership salesman when you visit the local car dealer. Use the table below to organize your questions. ELECTRIC CARS What are some things you want to know more about electric cars? INTERNAL COMBUSTION CARS What are some things you want to know more about internal combustion cars? THE DEALERSHIP What do you want to know more about the dealership?

21 Name Date Class Comparing the Usage Cost of Electric Vehicles Versus Internal Combustion Vehicles For each bullet point met, a box will be checked. CRITERIA Mathematical Content SCORE EXCEEDING (11-12 points) Surpasses Mastery Requirements All mastery requirements PLUS: [ ] All answers to reflection questions uses all key mathematical terms correctly. MASTERY (7-10 points) Surpasses Approaching Requirements All approaching requirements PLUS: [ ] Linear model for electric car is accurate. [ ] Linear model for internal combustion car is accurate. [ ] Graphs are correctly labeled on the axes. APPROACHING (5-6 points) Meets Some Requirements [ ] Research information on prices is complete for both electric and internal combustion vehicles. [ ] Slope for each linear model is identified. [ ] Y-intercept for each linear model is identified. Interpretation Of Model SCORE All mastery requirements PLUS: [ ] Realistic ideas from personal observations are used to justify which vehicle will be purchased. [ ] Venn Diagram includes 2 scientific facts that describe the differences between electric and internal combustion cars. [ ] Answers to reflection questions is at least 70% correct. All approaching requirements PLUS: [ ] Answers to reflection questions are mostly justified (about 70%) by using the key mathematical terms. [ ] Venn Diagram identifies similarities and differences between the two types of cars. [ ] Ideas in reflection questions are partially defended by the model. [ ] Ideas in the reflection questions are partially defended using the key mathematical terms. [ ] Venn Diagram identifies differences between the two types of cars.

22 Name Date Period 1. Identify graphs and equations of lines with positive, negative or constant rate of change. 2. Put the equation in slope-intercept form and graph the equation. 3x + 2y = 6 SLOPE-INTERCEPT FORM: 3. Create a linear equation in slope-intercept form. Graph the equation with the axes labeled correctly. Explain the features in the slope-intercept form of a line. My linear equation is: The slope is, which means: The y-intercept is, which means:

23 4. Solve the story problems. An incandescent light bulb cost $2.00 and $0.02 per KWh. How much does it cost to power 6600 KWh? A LED light bulb cost $35.00 and $0.003 per KWh. How much does it cost to power 6600 KWh? Which type of light bulb is cheaper and by how much?