Teacher NotesIs it Worth It?

84 - Is It Worth It?

Lesson Focus / The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.
Materials / NavNet, ActivityCenter
Grouping / Groups of 3 or 4
Prerequisite Knowledge and Skills / Usesymbols to represent unknowns and variables
Use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions
Overview of the Lesson / Students will compare the costs of printing t-shirts on two different machines and whether the change in the function is worth buying a new machine.
Time / Suggested time for Activity 1: 50 – 55 minutes
Suggested time for Activity 2: 30 – 45 minutes
Suggested time for Activity 3: 45 – 50 minutes

Procedure:

Activity 1

1. The class should be divided into pairs. Each student will be given Activity Sheet 1.Tell the students to determine their responses to the questions and that you will ask them to submit their tables when everyone is finished.

2. The students will work on finding the function rule for their t-shirt machine and making their tables and graphs. If a student is struggling, these questions could be asked:

• How much would it cost to purchase 5 t-shirts? What did you enter in your calculator to get that answer? How would that change if you want to know the cost to purchase 10 t-shirts?
• What are the constants in this situation?
• What are the variables? Which is the independent? Dependent? What is a reasonable domain and range?

3. After the students have completed their own table and function rule have log in to NavNet and go to the ActivityCenter. They will then submit their table as two lists.

Directions for ActivityCenter configuration:

• Go to the List tab.
• Contribute: List
• Configure: List properties:
• Group lists as a Data Set.
• 3: Number of lists (L1, L2, L3)
• OK
• Main settings:
• Choose from Data Sets
• Data Set 1: (L1, L2, L3)
• Configure Plots:
• Plot 1: X-List = L1, Y-List = L2
• Plot 2: X-List = L1, Y-List = L3
• OK
• Start Activity.

4. Students should analyze the tables and be ready to answer questions like:

• What observations can you make about the information that we created in our tables?
• What does each table column represent?
• If Management makes only 55 t-shirts, which company is better to use? Why?
• If Management makes 125 t-shirts, which company is better to use? Why?
• Which machine would allow the Management to save the most money? Why?
• How many shirts need to be made in order for the cost to be the same? Why is this information important? Where do you see this in the table of information?
• What does the graph of the information look like? (Continuous/Discreet? why?) What type of correlation?
• If we graph the two functions, how does the graph show when the costs were the same for the two companies?

5. Have the students compare the sketches of their graph to the List-Graph Screen. Make sure to set your graph to include all data from the tables. Ex. X-min = -10, X-max = 150, Y-min=-10, Y-max=200.

• What are the differences between your graphs?
• Where do you find the solution to the system? What are those coordinates? What do they mean with the scenario?

6. Students should correct graph and label the point of intersection. Have students write a verbal description of the intersection as a solution to the scenario.

Activity 2

1. Have the students answer the questions on Activity 2 Sheet. They should be prepared to share with the rest of the class ways to remember this technique of solving a system.

• Describe how you can use a table to determine the solution of the system.
• Explain how a graph can be used to determine the solution of the system.
• Explain how to tell if a solution you found is correct.

Activity 3

1. Distribute Activity 3 Sheet. Allow times for partners or groups of 3 to determine the function rule and ask them to submit.

• Go to ActivityCenter.
• Go to Graph-Equation.
• Contribute: Equations
• Configure: Main Settings:
• Number of equations per student = 1
• Let students view graphs of equations.
• Empty equations.
• OK
• Start Activity

2. Use the Equation tab to see the tables created by the students’ functions by using the pull down menu next to the x column.

3. Discuss their solutions.

• Explain how you decided which function rule to use.
• Why did you choose this y-intercept?
• Explain how you decided which slope to use.
• What is the meaning of the slope in your equation?
• Explain how you knew that your function rule would have the same intersection point (120, 170).

TI-Navigator™ Activity© 2006 Texas Instruments Incorporated

Algebra 1 1

Activity 1Is it Worth It?

Navigator

Is It Worth It?

The setup cost of a machine (A) that prints t-shirts is \$50. After setup, it costs\$1.00 to print each shirt. Management is considering the purchase of a larger machine (B) that can produce the same shirt at a cost of \$0.75 per shirt. If the setup cost of the larger machine is \$80, how many shirts would the company have to produce to make the purchase worthwhile?

1. Write a function rule for each machine.

2. Create a table to help you determine how many t-shirts the company would have to produce to make the purchase of the larger machine worthwhile. Record your table values below. Your teacher will ask you to submit your information through the Navigator.

Number of Shirts / Total cost using Machine B / Total cost using Machine A
x

3. Sketch a graph of both machine’s functions in the space below. Make sure to label the graph appropriately.

4. Explain how the graph helps you determine how many t-shirts the company would have to produce to make the purchase of the larger machine worthwhile.

5. Describe the appropriate domain for each of the function rules. Do all the points on this graph represent the situation?

TI-Navigator™ Activity© 2006 Texas Instruments Incorporated

Algebra 1 1

Activity 2Is it Worth It?

Activity 2

Be prepared to share with the rest of the class ways to remember this technique of solving a system.

1. Describe how you can use a table to determine the solution of the system.

2. Explain how a graph can be used to determine the solution of the system.

3. Explain how to tell if a solution you found is correct.

TI-Navigator™ Activity© 2006 Texas Instruments Incorporated

Algebra 1 1

Activity 3Is it Worth It?

Activity 3

You and your partner will create a function rule for the costs for a machine that satisfies the following:

• The cost to produce 120 shirts is the same as the cost for Machine A and Machine B.
• To produce fewer than 120 shirts the cost is between the costs of Machine A and Machine B.