OPEN RESPONSE QUESTION FROM MCAS SPRING 2003

GRADE 10, #17

The following is an “Open Response” question. It is important to practice

these types of questions in preparat9ion for the state mandated

MCAS. This exercise will help you walk through solving one of these questions. There are also some links to some web

sites that might help you.

INTRODUCTIONINTRODUCTION

HOW TO ANSWER AN OPEN HOW TO ANSWER AN OPEN RESPONSE QUESTIONRESPONSE QUESTION

BE SURE TO: Read all parts of each

question carefully. Make each response as clear,

complete and accurate as you can.

Check all your work! Did you answer the question?!?!

TOPICTOPICSolve everyday problems that can

be modeled using systems of linear equations or inequalities. Apply

algebraic and graphical methods to the solutions.

NO NO CALCULATORS CALCULATORS

ALLOWED!!ALLOWED!!This problem was given during the NO CALCULATOR

section

QUESTION #17QUESTION #17Larissa plans to select one of the two mobile phone

services described in the chart below. Each of the two companies charges a fixed monthly fee plus an additional

charge for each minute in excess of the free time allowance.

Larissa plans to use her mobile phone as her only phone and predicts that she will use it between 600 and 900

minutes per month. To find t, the total monthly charge for each company based on m minutes of phone use, Larissa

wrote the two equations shown below.Cellco: t = 35 + (m – 300)(0.08) for m 300Firstfone: t = 22 + (m – 400)(0.15) for m 400

MOBIL PHONE SERVICE

CompanyMonthly

Fee

Free Minute Allowance per

Month

Cost for Each Additional

Cellco $35 300 $0.08

Firstfone $22 400 $0.15

ACellco: t = 35 + (m – 300)(0.08) for m 300Firstfone: t = 22 + (m – 400)(0.15) for m 400

PART A: Which is the less expensive plan for 600 minutes of phone use per month? Show or explain

how you obtained your answer.

MOBIL PHONE SERVICE

CompanyMonthly

FeeFree Minute Allowance

per MonthCost for Each

Additional

Cellco $35 300 $0.08

Firstfone $22 400 $0.15

part A HintCellco: t = 35 + (m – 300)(0.08) for m 300Firstfone: t = 22 + (m – 400)(0.15) for m 400

PART A: Which is the less expensive plan for 600 minutes of phone use per month? Show or explain

how you obtained your answer.

MOBIL PHONE SERVICE

CompanyMonthly

FeeFree Minute Allowance

per MonthCost for Each

Additional

Cellco $35 300 $0.08

Firstfone $22 400 $0.15

Remember that m is the number of minutes of phone use.

Substitute into the equations.

BCellco: t = 35 + (m – 300)(0.08) for m 300Firstfone: t = 22 + (m – 400)(0.15) for m 400

PART B: Which is the less expensive plan for 900 minutes of phone use per month? Show or explain

how you obtained your answer.

MOBIL PHONE SERVICE

CompanyMonthly

FeeFree Minute Allowance

per MonthCost for Each

Additional

Cellco $35 300 $0.08

Firstfone $22 400 $0.15

part B HintCellco: t = 35 + (m – 300)(0.08) for m 300Firstfone: t = 22 + (m – 400)(0.15) for m 400

PART B: Which is the less expensive plan for 900 minutes of phone use per month? Show or explain

how you obtained your answer.

MOBIL PHONE SERVICE

CompanyMonthly

FeeFree Minute Allowance

per MonthCost for Each

Additional

Cellco $35 300 $0.08

Firstfone $22 400 $0.15

Remember that m is the number of minutes of phone use.

Substitute into the equations.

CCellco: t = 35 + (m – 300)(0.08) for m 300Firstfone: t = 22 + (m – 400)(0.15) for m 400

Part C: Determine the number of minutes for which the monthly charges for the two companies would be exactly the same amount. Show or explain how you

obtained your answer.

MOBIL PHONE SERVICE

CompanyMonthly

FeeFree Minute Allowance

per MonthCost for Each

Additional

Cellco $35 300 $0.08

Firstfone $22 400 $0.15

part C HintCellco: t = 35 + (m – 300)(0.08) for m 300Firstfone: t = 22 + (m – 400)(0.15) for m 400

Part C: Determine the number of minutes for which the monthly charges for the two companies would be exactly the same amount. Show or explain how you

obtained your answer.

MOBIL PHONE SERVICE

CompanyMonthly

FeeFree Minute Allowance

per MonthCost for Each

Additional

Cellco $35 300 $0.08

Firstfone $22 400 $0.15

Try setting the two equations equal to each other.

If that doesn’t work, how about a table of values?

DCellco: t = 35 + (m – 300)(0.08) for m 300Firstfone: t = 22 + (m – 400)(0.15) for m 400

Part D: How can Larissa use the results of parts a, b and c to make her selection of a cell phone

company? Explain your reasoning.

MOBIL PHONE SERVICE

CompanyMonthly

FeeFree Minute Allowance

per MonthCost for Each

Additional

Cellco $35 300 $0.08

Firstfone $22 400 $0.15

part D HintCellco: t = 35 + (m – 300)(0.08) for m 300Firstfone: t = 22 + (m – 400)(0.15) for m 400

Part D: How can Larissa use the results of parts A, B and C to make her selection of a cell phone

company? Explain your reasoning.

MOBIL PHONE SERVICE

CompanyMonthly

FeeFree Minute Allowance

per MonthCost for Each

Additional

Cellco $35 300 $0.08

Firstfone $22 400 $0.15

Is one company always better than the other one?

What should Larissa consider before she makes her decision?

Student ScoresThe numbers below are possible scores. Click on one to

see an example of someone’s work who earned that score. You will also see the guideline that the graders

followed.

Click on the link below to see some web sites that can help you understand some of the concepts from this

problem

Score of 4

What is a 4?The student response demonstrates an

exemplary understanding of the Patterns,

Relations, and Algebra concepts involved in

mathematical modeling with systems of linear

equations.

Score of 3

What is a 3?The student response demonstrates a good understanding of the Patterns, Relations, and Algebra concepts involved in mathematical modeling with systems of linear equations. Although there is significant evidence that the student was able to recognize and apply the concepts involved, some aspect of the response is flawed. As a result the response merits 3 points.

Score of 2

What is a 2?The student response contains fair evidence of an understanding of the Patterns, Relations, and Algebra concepts involved in mathematical modeling with systems of linear equations. While some aspects of the task are completed correctly, others are not. The mixed evidence provided by the student merits 2 points.

Score of 1

What is a 1?The student response contains only minimal

evidence of an understanding of the Patterns, Relations, and Algebra concepts involved in

mathematical modeling with systems of linear equations.

Score of 0

What is a 0?The student response contains insufficient

evidence of an understanding of the Patterns, Relations, and Algebra concepts involved in

mathematical modeling with systems of linear equations to merit any points.

REFERENCESREFERENCESIf you are having any trouble with this problem there are some links below that will help you with the concepts involved with this question:http://mathforum.org/dr.math/

http://www.algebra.com/algebra/homework/coordinate/

http://school.discovery.com/homeworkhelp/webmath/

http://www.doe.mass.edu/mcas/

CONCLUSIONCONCLUSIONHopefully, this has been a helpful experience for you. The only way to improve is to practice and

there are other problems like this one available for you to try if you are up to the challenge!

-- or--

Call a friend, have them do the same problem and you can talk about it.

-- or --

Take a break, you earned it!