OPEN RESPONSE QUESTION FROM MCAS SPRING 2003 GRADE 10, #17 INTRODUCTION 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. OPEN RESPONSE QUESTION FROM MCAS SPRING 2003 GRADE 10, #17 NEXT

HOW TO ANSWER AN OPEN RESPONSE 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?!?! NEXT

TOPIC Solve everyday problems that can be modeled using systems of linear equations or inequalities. Apply algebraic and graphical methods to the solutions. NEXT

NO CALCULATORS ALLOWED NO CALCULATORS ALLOWED!! This problem was given during the NO CALCULATOR section NEXT

QUESTION #17 Larissa 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  300 Firstfone: t = 22 + (m – 400)(0.15) for m  400 MOBIL PHONE SERVICE Company Monthly Fee Free Minute Allowance per Month Cost for Each Additional Cellco $35 300 $0.08 Firstfone $22 400 $0.15 NEXT

A Give this problem a try!! move on to I need a HINT Part B Cellco: t = 35 + (m – 300)(0.08) for m  300 Firstfone: 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 Company Monthly Fee Free Minute Allowance per Month Cost for Each Additional Cellco $35 300 $0.08 Firstfone $22 400 $0.15 A Give this problem a try!! Part B move on to I need a HINT

part A Hint Give this problem a try!! move on to I need a HINT Part B Cellco: t = 35 + (m – 300)(0.08) for m  300 Firstfone: 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 Company Monthly Fee Free Minute Allowance per Month Cost for Each Additional Cellco $35 300 $0.08 Firstfone $22 400 $0.15 part A Hint Remember that m is the number of minutes of phone use. Substitute into the equations. Give this problem a try!! Part B move on to I need a HINT

B Now try part B. move on to I need a HINT Part C Cellco: t = 35 + (m – 300)(0.08) for m  300 Firstfone: 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 Company Monthly Fee Free Minute Allowance per Month Cost for Each Additional Cellco $35 300 $0.08 Firstfone $22 400 $0.15 B Now try part B. I need a HINT Part C move on to

part B Hint Now try part B. move on to I need a HINT Part C Cellco: t = 35 + (m – 300)(0.08) for m  300 Firstfone: 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 Company Monthly Fee Free Minute Allowance per Month Cost for Each Additional Cellco $35 300 $0.08 Firstfone $22 400 $0.15 part B Hint Remember that m is the number of minutes of phone use. Substitute into the equations. Now try part B. Part C move on to I need a HINT

C Part C is a bit tougher. move on to I need a HINT Part D Cellco: t = 35 + (m – 300)(0.08) for m  300 Firstfone: 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 Company Monthly Fee Free Minute Allowance per Month Cost for Each Additional Cellco $35 300 $0.08 Firstfone $22 400 $0.15 C Part C is a bit tougher. I need a HINT Part D move on to

part C Hint Part C is a bit tougher. move on to I need a HINT Part D Cellco: t = 35 + (m – 300)(0.08) for m  300 Firstfone: 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 Company Monthly Fee Free Minute Allowance per Month Cost for Each Additional Cellco $35 300 $0.08 Firstfone $22 400 $0.15 part C Hint Try setting the two equations equal to each other. If that doesn’t work, how about a table of values? Part C is a bit tougher. I need a HINT Part D move on to

D Finally, you're on part D. I am all I need a HINT DONE Cellco: t = 35 + (m – 300)(0.08) for m  300 Firstfone: 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 Company Monthly Fee Free Minute Allowance per Month Cost for Each Additional Cellco $35 300 $0.08 Firstfone $22 400 $0.15 D Finally, you're on part D. FIX THE LINK I AM ALL DONE I need a HINT DONE I am all

part D Hint Finally, you're on part D. I need a HINT DONE I am all Cellco: t = 35 + (m – 300)(0.08) for m  300 Firstfone: 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 Company Monthly Fee Free Minute Allowance per Month Cost for Each Additional Cellco $35 300 $0.08 Firstfone $22 400 $0.15 part D Hint Is one company always better than the other one? What should Larissa consider before she makes her decision? Finally, you're on part D. I need a HINT DONE I am all

Best score to worst score Student Scores The 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 4 3 2 1 Best score to worst score Math References

Score of 4 This solution earned a 4 3 2 1 Math References END 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. Math References END

Score of 3 This solution earned a 3 4 2 1 Math References END 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. Math References END

Score of 2 This solution earned a 2 4 3 1 Math References END 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. Math References END

Score of 1 This solution earned a 1 4 3 2 Math References END 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. Math References END

Score of 0 This solution earned a 4 3 2 1 Math References END 4 3 2 1 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. Math References END

REFERENCES If 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/ END

Take a break, you earned it! CONCLUSION Hopefully, 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! click here to TRY ANOTHER PROBLEM