The Vacation Problem

TALK, SAVE, AND PLAY TEACHER EDITION

List of Activities for this Unit:

ACTIVITY STRAND DESCRIPTION Write, evaluate, and manipulate a 1 – Talk, Talk, Talk AS linear function for cell phone use. 2 – Talk Easy and Talk Cheap AS Compare two linear functions. Use graphing to solve a system of 3 – The Vacation AS equations. Writing a linear function for a 4 – Multiple Choice Items AS given situation.

Pow-Wow Planning COE Connections Savings Account

Calculators MATERIALS Rulers

Warm-Ups Play it Again (in Segmented Extras Folder)

Vocabulary: Mathematics & ELL

Appropriate Axes Consistent Coordinates Equation Intersection Origin Process Column

Length of the Lesson: 150 minutes

Essential Questions:

 Why is it important to define the variables that are being used?  What is an informative title for a graph?  How is an appropriate scale for a graph determined?  What is an appropriate interval for the x- and y-axes?  How is information in a situation translated into an equation that represents the information?  How is a table of values created? How can the table assist in graphing and determining an answer to a question?  How can a graph be used to make predictions?  How can a conclusion be supported using mathematical information and calculations?

Teacher: Ch 9 “Talk, Save and Play” 1  How can a system of equations be used to answer a question?  What is meant when two graphs intersect?

Lesson Overview:

 Before allowing the students the opportunity to start the activity: assess their prior knowledge with regards to them saving money. Have any students gone on a vacation or trip where they had to save money in order to go? Who has traveled to Portland or Disney World or Europe or Mexico or elsewhere? What was it like to take such a trip?  How can you support a conclusion that you make? What evidence from graphs can be used to support/justify your conclusion?  Use resources from your building.

Performance Expectations:

5.4.B Write a rule to describe the relationship between two sets of data that are linearly related. 5.4.D Graph ordered pairs in the coordinate plane for two sets of data related by a linear rule and draw the line they determine. 6.2.A Write a mathematical expression or equation with variables to represent information in a table or given situation. 6.2.B Draw a first-quadrant graph in the coordinate plane to represent information in a table or given situation. 6.2.D Apply the commutative, associative, and distributive properties, and use the order of operations to evaluate mathematical expressions. 7.5.A Graph ordered pairs of rational numbers and determine the coordinates of a given point in the coordinate plane. 8.1.C Represent a linear function with a verbal description, table, graph, or symbolic expression, and make connections among these representations. 8.1.D Determine the slope and y-intercept of a linear function described by a symbolic expression, table, or graph. 8.1.E Interpret the slope and y-intercept of the graph of a linear function representing a contextual situation. 8.1.F Solve single- and multi-step word problems involving linear functions and verify the solutions. A1.1.A Select and justify functions and equations to model and solve problems. A1.1.B Solve problems that can be represented by linear functions, equations, and inequalities. A1.1.C Solve problems that can be represented by a system of two linear equations or inequalities. A1.4.B Write and graph an equation for a line given the slope and the y-intercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations. A1.4.C Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines. A1.4.D Write and solve systems of two linear equations and inequalities in two variables. A1.6.D Find the equation of a linear function that best fits bivariate data that are linearly related, interpret the slope and y-intercept of the line, and use the equation to make predictions. G.6.F Solve problems involving measurement conversions within and between systems, including those involving derived units, and analyze solutions in terms of reasonableness of solutions and appropriate units.

Teacher: Ch 9 “Talk, Save and Play” 2 Performance Expectations and Aligned Problems:

Chapter 9 “Talk, 1- Talk, Talk, 2- Talk Easy and 3- The 4- MC Items Save, and Play” Talk Talk Cheap Vacation Subsections: Problems Supporting: 8, 9 2 8, 9 PE 5.4.B ≈ 6.2.A Problems Supporting: 2 Graph for 8, 9 3 PE 5.4.D ≈6.2.B ≈ 7.5.A Problems Supporting: 1, 5 10-12, 15 1, 6 PE 6.2.D Problems Supporting: 2-7 8-12, 15 1, 3-6 7-9 PE 8.1.C ≈ 8.1.F ≈ A1.1.B Problems Supporting: PE 8.1.D ≈ 8.1.E 2, 4 8, 9, 13, 18, 19 2, 3 7, 9 ≈ A1.4.B ≈ A1.4.C Problems Supporting: 1, 2 8, 9, 13 2, 3 7-9 PE A1.1.A (weakly) Problems Supporting: 1, 2, 4 8, 9, 13, 18, 19 2, 3 7-9 PE A1.6.D (weakly) Problems 2-7 Supporting: (Linear eqns. in PE G.6.F context are 8-12, 15 1, 3-6 7-9 conversion problems.)

Assessment: Use the multiple choice and short answer items from Algebraic Sense and Number Sense that are included in the CD. They can be used as formative and/or summative assessments attached to this lesson or later when the students are being given an overall summative assessment.

Teacher: Ch 9 “Talk, Save and Play” 3 Talk, Talk, Talk

A few years ago, Juanita was going to get a cell phone. The Call-A-Lot cellular phone company had a special plan for high school seniors. The plan charges a flat fee of $15.00 per month and a charge of $0.05 per minute for each phone call.

1. Complete the table for the first month:

Number of Total cell Minutes Process Column phone cost per Talking month   $15.00 0 15  0.05 0   $15.20 4 15  0.05 4   $15.50 10 15  0.05 10   $15.75 15 15  0.05 15   $16.25 25 15  0.05 25   $17.50 50 15  0.05 50   $18.75 75 15  0.05 75   $20.00 100 15  0.05 100   n 15  0.05 n

2. Graph the data from the table. Be sure to include an appropriate title, labels for the axes, consistent and appropriate scales, and accurate data display.

______

Teacher: Ch 9 “Talk, Save and Play” 4 3. If she spends $35.00 per month on her phone bill, how many minutes will she be able to talk? ______400 minutes______Support your answer using words, numbers and/or information from the graph.

15  0.05n  35 0.05n  20 n  400 minutes 4. How much would she owe the Call-A-Lot cellular phone company for the first month if she didn’t use any minutes? ____$15.00______

a. What is the ordered pair that represents this situation? ____(0, 15)______Support your answer using words, numbers and/or information from the graph.

15  0.050  cost

5. If Juanita talks for 1 hour, what will she owe the Call-A-Lot cellular phone company? __$18.00__

a. What is the ordered pair that represents this situation? ___(60, 18)______Support your answer using words, numbers and/or information from the graph.

15  0.0560  cost cost = $18.00

6. If Juanita can only spend $35.00 on her cellular phone bill every month. How many additional minutes could she talk if the Call-A-Lot cellular phone company decides to lower the cost per minute to $0.04 per minute? ____100 additional minutes____ Support your answer using words, numbers and/or diagrams. 15  0.04n  35 500 minutes – 400 minutes = 100 minutes 0.04n  20 n  500 minutes

7. The Call-A-Lot cellular phone company decides to raise the flat fee from $15.00 to $25.00 and keep the cost per minute at $0.05. Juanita wants to keep her monthly bill at $35.00. How many minutes can she talk? _____200 minutes______Support your answer using words, numbers and/or diagrams.

25 + 0.05n = 35 0.05n = 10 n = 200 minutes

Teacher: Ch 9 “Talk, Save and Play” 5 Talk Easy and Talk Cheap

During that same time frame and in a different state, Mrs. Kim decided to buy her son, Jason (Juanita’s cousin), a cellular phone so that he can easily communicate with his parents when he is away from home. Mrs. Kim found two companies that offer special rates for students. Talk Cheap cellular phone service has no monthly basic fee, but charges $0.55 per minute used. Talk Easy cellular phone service charges a basic monthly fee of $35.00 plus $0.20 per minute used. Both companies do not round the time to the nearest minute like many competitors do. They charge for the exact amount of time used. Build a table (include a title), make a graph and write a rule to represent the cost of cellular phone service for each company.

______Comparisons of Cellular Phone Plans______

Number of 0 30 60 90 120 150 180 Minutes Talk $0.00 $16.50 $33.00 $49.50 $66.00 $82.50 $99.00 Cheap Talk $35.00 $41.00 $47.00 $53.00 $59.00 $65.00 $71.00 Easy

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0.55n = cost 8. Rule for Talk Cheap: ______

35 + 0.20n = cost 9. Rule for Talk Easy: ______

Teacher: Ch 9 “Talk, Save and Play” 6 10. How much would each company charge for 20 minutes?

Talk Cheap: ____$11.00______Talk Easy: _____$39.00______Support your answer using words, numbers and/or diagrams.

0.5520 = $11.00 35 + 0.2020 = $39.00

11. How much would each company charge for 50 minutes?

Talk Cheap: ___$27.50______Talk Easy: _____$45.00______Support your answer using words, numbers and/or diagrams.

0.5550 = $27.50 35 + 0.2050 = $45.00

12. How much would each company charge for 200 minutes?

Talk Cheap: ___$110.00______Talk Easy: ____$75.00______Support your answer using words, numbers and/or diagrams.

0.55200 = $110.00 35 + 0.20200 = $75.00

13. Why does one line on your graph include the origin, but the other does not? ____The Talk Cheap plan includes the origin because it does not have a basic monthly fee. If you do not use your phone (minutes = zero) you will not have a bill for that month from Talk Cheap. The

Talk Easy plan does have a basic monthly fee. Even if you do not use your phone you will owe $35

for the month. ______

Teacher: Ch 9 “Talk, Save and Play” 7 14. If price is the only factor in deciding which company to choose, which plan is better? It depends on how many minutes you use Talk Cheap <100 and Talk Easy >100______Support your answer using words, numbers and/or diagrams.

.55x = 35 + .20x .35x = 35 x = 100

If you use less than 100 minutes the Talk Cheap plan is less expensive. If you use more than 100___ minutes the Talk Easy plan is less expensive. ______

______

15. Jason knows the cost of each plan for 20 minutes. Can he double this cost to determine the cost for 40 minutes? ___No______Support your answer using words, numbers and/or diagrams.

0.5520 = $11.00 35 + 0.2020 = $39.00 0.5540 = $22.00 35 + 0.2040 = $43.00 39(2)  43

16. What are the coordinates of the point of intersection of the two equations? __(100, 55)______

17. What is the significance of this point?

___The point of intersection on the graph is when the two plans cost the same amount for the______

month.______

______

Teacher: Ch 9 “Talk, Save and Play” 8 18. Talk Cheap will begin charging a basic fee. Describe how the graph stays the same and how it changes.

__The slope will remain the same, but the y-intercept will go up on the y-axis to the basic fee._____

______

19. Talk Easy is going to raise the amount they charge per minute. Describe how the graph stays the same and how it changes?

__The y-intercept will remain the same, but the slope of the line will be steeper.______

______

Teacher: Ch 9 “Talk, Save and Play” 9 The Vacation

Today is Monday, Jan 22, 2007. Starting now, Alicia and Brent have promised to deposit a certain amount of money in their savings accounts every Friday at 9 a.m. As soon as they have exactly the same amount of money, they will each withdraw all their money and buy vacation packages to the most expensive vacation spot they can afford. They will withdraw their money at 2 p.m. that Friday, buy the package, and fly away the next morning.

As of today, Alicia has $51 in her account and Brent has $292.50 in his account. Alicia plans to save $36 a week. Brent plans to save $25.50 a week. Vacation package prices are:

Destination Vacation package prices (per person) Portland $320 Disney World $478 Cabo San Lucas $598 Oaxaca, Mexico $690 Costa Rica $754 Bahamas $832 London $967 Paris $1190

1. Complete a table of values for each person.

Number of Show your Amount Show your work Amount Weeks work Saved for (Brent) Saved for (Alicia) Alicia Brent

1 51 + 361 $87.00 292.50 + 25.501 $318.00 2 51 + 362 $123.00 292.50 + 25.502 $343.50 3 51 + 363 $159.00 292.50 + 25.503 $369.00 5 51 + 365 $231.00 292.50 + 25.505 $420.00 10 51 + 3610 $411.00 292.50 + 25.5010 $547.50 15 51 + 3615 $591.00 292.50 + 25.5015 $675.00

Teacher: Ch 9 “Talk, Save and Play” 10 20 51 + 3620 $771.00 292.50 + 25.5020 $802.50 25 51 + 3625 $951.00 292.50 + 25.5025 $930.00

2. Write an equation for each person that will allow you to determine the amount of money saved in relation to the amount of time needed to travel. Define the variables.

Equation for Alicia: ___ 51 + 36(m) = s ______m = months s = savings______

______

Equation for Brent: __ 292.50 + 25.50(m) = s ____ m = months s = savings ______

______

3. Graph the two equations on the same graph. Use different colors and label the two graphs.

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Teacher: Ch 9 “Talk, Save and Play” 11 4. How many weeks will it take them to save enough money for their vacation? ______23 Weeks______Support your answer using information from your equations, tables and/or graphs. 51 + 36m  = 292.50 + 25.50m  10.5m  = 241.50 m = 23 months ______

______

5. Where will they go on vacation? ___Bahamas______Support your answer using information from your equations, tables and/or graphs.

______

Teacher: Ch 9 “Talk, Save and Play” 12 6. Chris has $430.50 in savings on January 22, 2007. How much will Chris have to save each week

in order to join them on the trip? ____ $19.50 ______Support your answer using words, number and/or diagrams.

430.50 + (x)(23) = 879 23x = 448.50 x = 19.50

______

Multiple Choice

7. Both of the rental car companies Myra can use on her business trips charge a fixed daily fee, plus an additional charge for each mile the car is driven. The two companies’ charges are shown in the chart below.

Rental Car Charges Company Fixed Daily Fee Charge per Mile Paragon $35 $0.14 Atlas $34 $0.16

Myra plans to rent a car for one day.

Which is the number of miles driven by Myra that would result in her being charged the same total amount by either of the two companies?

 A. 35 miles

 B. 50 miles

 C. 70 miles

 D. 100 miles

8. A mountain bike costs $75 more than 3 times the amount a street bike costs. The mountain bike sells for $1,500.

Which equation can be used to find the price of the street bike?

Teacher: Ch 9 “Talk, Save and Play” 13  A. 3x + 75 = 1500

 B. 3x = 1500 +75

 C. 3(x + 75) = 1500

 D. 3x – 75 = 1500

9. Eddie’s Towing Company charges $40 to hook a vehicle to the tow truck and $1.70 for each mile the vehicle is towed.

Which equation represents the relationship between the number of miles towed, m, and the total charges, c?

 A. c = 40 + 1.70  B. c = 40 + 1.70m  C. c = 40m + 1.70m  D. c = 40m + 1.70

Teacher: Ch 9 “Talk, Save and Play” 14