LONG DISTANCE TELEPHONE PLAN

Enduring Understanding: Develop a better understanding that using systems of equations in graphical form is appropriate in determining a solution. Develop a better understanding of how to support a recommendation with mathematical information from a graph.

Essential Questions:

  • What is an informative title for a graph?
  • What is an appropriate interval for the x- and y-axes?
  • How is an algebraic equation written from the information given in a contextual scenario?
  • What does the y-intercept of the graph represent in the context of a given situation?
  • How can a graph be used to make predictions?
  • How can a conclusion be supported using mathematical information and calculations?

Lesson Overview:

  • Before allowing the students the opportunity to start the activity: access their prior knowledge with regards to telephone plans and their costs (local and long distance charges along with various taxes and add-ons). What about cell phones? What plans exist for cell phones? What effect have they had on in-home telephone plans and offerings? Show students a copy of cell phone bill and an in-home telephone bill that includes long distance charges.
  • When reading a graph, where are the x- and y-intercepts? What is the relationship between the intercepts and the context of any problem?
  • What is meant when graphs intersect?
  • 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:

1.4.4

1.5.4

1.5.6

2.2.2

3.3.2

5.1.2

5.3.1

Item Specifications: PS03; AS02; AS03; SR02; SR05; MC01

Assessment:

  • Use WASL format items that link to what is being covered by the classroom activity
  • Include multiple choice questions

Long Distance Telephone Plan

Your friend has asked you for help in making a decision regarding what long distance calling plan to accept. Recently, Ray was sent information from three competing companies regarding changing his present long distance telephone carrier to their plan. Ray spent considerable time trying to decide. He finally turned to you for help because he knew that you are a math whiz and would be able to determine what is best for him.

He outlines to you the essential elements of the three plans:

Plan A: $4.95 per month and $.07 per minute on all long distance calls

Plan B: $0.15 per minute on all long distance calls

Plan C: $20.00 per month regardless of the number of minutes used

  1. Determine an algebraic equation for each plan.

Plan A equation: ______

Plan B equation: ______

Plan C equation: ______

  1. Graph each equation on the same graph. Differentiate the three lines by use of color and labeling.

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  1. Determine the y-intercept for each plan:

Plan A y-intercept: ______

Plan B y-intercept: ______

Plan C y-intercept: ______

4. What does the y-intercept represent in the context of this situation?

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  1. A person with Plan A talks long distance for 127 minutes in a month. How much is the long

distance charges on the phone bill? ______

Show your work or explain how the graph was used to determine your answer:

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  1. A person with Plan B talks long distance for 82 minutes in a month. How much is the long

distance charges on the phone bill ? ______

Show your work or explain how the graph was used to determine your answer:

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  1. A person with Plan C talks long distance for 91 minutes in a month. How much is the long

distance charges on the phone bill ? ______

Show your work or explain how the graph was used to determine your answer:

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  1. Your graph should show three points of intersection. What does that mean in terms of these telephone plans?

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  1. Explain what factors Ray should consider in deciding which plan would best fit his needs. Be sure to include data from the graph to support your explanation.

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  1. Plan C is unavailable where Ray lives. Write a letter to Ray giving him your recommendation and why you are recommending Plan A or Plan B. Use mathematical information from the graph to support your recommendation.

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10. The graph of an equation is shown below.

Which equation is represented by this graph?

O A.

O B.

O C.

O D.

11. The graph represents the number of repair calls the Cold Air Service Company received each day and the high temperature for that day.

Which is the best estimate of the number of repair calls the company would receive on a day when the high temperature is 85°F?

O A.43

O B.50

O C.60

O D.11