THE VACATION
Enduring Understanding: Develop a better understanding of how to develop an equation from written information and then graph the equation. Develop a better understanding of how to solve a system of equations graphically and algebraically.
Essential Questions:
· Is it very important to define the variables that are being used? Why?
· What is an informative title for a graph?
· 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?
· How can a system of equations be used to answer a question?
Lesson Overview:
· Before allowing the students the opportunity to start the activity: access 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?
· What is meant when two graphs intersect?
· A good warm-up could be Play it Again.
· 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.
EALRs/GLEs
1.4.5
1.5.1
1.5.2
1.5.4
1.5.6
2.2.2
3.2.2
5.1.1
Item Specifications: PS03; AS01; AS02; AS03; SR02; SR04; SR05
Assessment:
· Use WASL format items that link to what is being covered by the classroom activity
· Include multiple choice questions
The Vacation
Today is Monday, Jan 24, 2005. Starting now, Alicia and Brent have promised to deposit a certain amount of money in their savings accounts every Friday at 9 am. 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 pm 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. 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: ______
Ø Defined variables for the equation: ______
______
Equation for Brent: ______
Ø Defined variables for the equation: ______
______
2. Complete a table of values for each person.
3. Graph the two equations on the same graph. Use different colors and label the two graphs.
______
4. Where will they go on vacation? ______
Support your answer using information from your equations, tables and/or graphs.
______
______
______
______
5. On what date will they leave? ______
Support your answer using information from your equations, tables and/or graphs.
______
______
______
______
6. Chris has $430.50 in savings on January 24, 2005. How much will Chris have to save each week
in order to join them on the trip? ______
Support your answer using words, number and/or diagrams.
______
______
______
______
______
______
7. Show how you could algebraically solve a system of equations to confirm which week Alicia and Brent have the same amount of money.
8. 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 ChargesCompany / 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?
O A. 35 miles
O B. 50 miles
O C. 70 miles
O D. 100 miles
9. 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?
O A.
O B.
O C.
O D.