Mini Practice Set Responses ~ Algebra/Data Analysis ~ Item 11


	Item 11 Mini Practice Set Responses

A city bus company requires exact change or a token to ride a bus. The company conducted a random survey of 100 passengers to determine how they paid their bus fare. The survey results are shown in the table below.

Complete the following in the Answer Book:

Last week 2,000 passengers rode the bus. Based on this survey, how many of these passengers would be expected to use exact change to pay the bus fare? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
Mr. Blake, a bus driver for the city bus company, reported that 44 passengers who rode on his bus one morning paid using a token. Based on this survey, estimate how many passengers rode on his bus that morning. Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
Should a different city use these survey results to predict the number of bus passengers that would be expected to use exact change to ride the bus in their city? Use mathematics to justify your answer.

Score Level 1 Paper
This response indicates little application of a reasonable strategy. The number of exact-change passengers (1260) is correct. The explanation supports the solution (multiplying 100 by 20 and you get 2000. Then you multiply both 63 + 37 by 20 because that's how many times 100 goes into 2000). The number of passengers on Blake's bus (114) is incorrect. The explanation reveals a flaw in reasoning. (There's a difference of 7 between 37 + 44 {people using tokens} so I figured that the people paying exact change would go up by 7 too.) Although the student indicates that the survey's results should be used, the justification reveals a flaw in reasoning. This response demonstrates a minimal understanding and analysis of the problem. (Compare to this Level 1 anchor paper.)
Score Level 4 Paper
This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The number of exact-change passengers (1,260) is correct. The explanation is clearly presented, fully developed, and supports the solution (63/100 passengers used exact change. I converted this to 63% or .63. Of the 2000 passengers, 63%, or 1,260 people, could be expected to use exact change). The number of passengers on Blake's bus (around 119) is correct. The explanation is fully developed (37% of the passengers who rode the bus used tokens. This meant that those 44 people were 37% of the people who had ridden the bus. I set up the equation .37x=44 and solved). The student indicates that the survey's results should not be used, and the fully developed justification supports the solution. (The people from that city probably use different methods of transportation, etc. and can be expected to use different methods to pay fares.) This response demonstrates a complete understanding and analysis of the problem. (Compare to this Level 4 anchor paper.)
Score Level 2 Paper
This response indicates application of an incomplete strategy. Both the number of exact-change passengers (1,260) and the number of passengers on Blake's bus (119) are correct. However, explanations are not provided. The student indicates that the survey's results should not be used. The justification supports the solution, but is incomplete (people may buy more tokens there, or they may not have bus tokens). This response demonstrates a conceptual understanding and analysis of the problem.
Score Level 3 Paper
This response indicates application of a reasonable strategy that leads to some correct solutions. The number of exact-change passengers (1,260) is correct. The explanation supports the solution (finding that 63% used exact change and 37% used tokens. Then I found 63% of 2000 {2000 x .63} and got 1,260 passengers). The number of passengers on Blake's bus (119) is correct, and the explanation supports the solution (doing the equation 44=.37x, letting x= the number of passengers total who rode that morning). The student indicates that the survey's results should be used. The justification reveals a flaw in reasoning (no matter what they factor in {population, not as many buses, etc.}, the percentages will remain the same and could predict how many use exact change). This response demonstrates a clear understanding and analysis of the problem. (Compare to this Level 4 anchor paper.)

Mini Practice Set Papers ~ Algebra/Data Analysis ~ Item 11

Complete the following in the Answer Book:

Last week 2,000 passengers rode the bus. Based on this survey, how many of these passengers would be expected to use exact change to pay the bus fare? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
Mr. Blake, a bus driver for the city bus company, reported that 44 passengers who rode on his bus one morning paid using a token. Based on this survey, estimate how many passengers rode on his bus that morning. Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
Should a different city use these survey results to predict the number of bus passengers that would be expected to use exact change to ride the bus in their city? Use mathematics to justify your answer.

Score Level 1 Paper

This response indicates little application of a reasonable strategy. The number of exact-change passengers (1260) is correct. The explanation supports the solution (multiplying 100 by 20 and you get 2000. Then you multiply both 63 + 37 by 20 because that's how many times 100 goes into 2000). The number of passengers on Blake's bus (114) is incorrect. The explanation reveals a flaw in reasoning. (There's a difference of 7 between 37 + 44 {people using tokens} so I figured that the people paying exact change would go up by 7 too.) Although the student indicates that the survey's results should be used, the justification reveals a flaw in reasoning. This response demonstrates a minimal understanding and analysis of the problem. (Compare to this Level 1 anchor paper.)

Score Level 4 Paper

This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The number of exact-change passengers (1,260) is correct. The explanation is clearly presented, fully developed, and supports the solution (63/100 passengers used exact change. I converted this to 63% or .63. Of the 2000 passengers, 63%, or 1,260 people, could be expected to use exact change). The number of passengers on Blake's bus (around 119) is correct. The explanation is fully developed (37% of the passengers who rode the bus used tokens. This meant that those 44 people were 37% of the people who had ridden the bus. I set up the equation .37x=44 and solved). The student indicates that the survey's results should not be used, and the fully developed justification supports the solution. (The people from that city probably use different methods of transportation, etc. and can be expected to use different methods to pay fares.) This response demonstrates a complete understanding and analysis of the problem. (Compare to this Level 4 anchor paper.)

Score Level 2 Paper

This response indicates application of an incomplete strategy. Both the number of exact-change passengers (1,260) and the number of passengers on Blake's bus (119) are correct. However, explanations are not provided. The student indicates that the survey's results should not be used. The justification supports the solution, but is incomplete (people may buy more tokens there, or they may not have bus tokens). This response demonstrates a conceptual understanding and analysis of the problem.

Score Level 3 Paper

This response indicates application of a reasonable strategy that leads to some correct solutions. The number of exact-change passengers (1,260) is correct. The explanation supports the solution (finding that 63% used exact change and 37% used tokens. Then I found 63% of 2000 {2000 x .63} and got 1,260 passengers). The number of passengers on Blake's bus (119) is correct, and the explanation supports the solution (doing the equation 44=.37x, letting x= the number of passengers total who rode that morning). The student indicates that the survey's results should be used. The justification reveals a flaw in reasoning (no matter what they factor in {population, not as many buses, etc.}, the percentages will remain the same and could predict how many use exact change). This response demonstrates a clear understanding and analysis of the problem. (Compare to this Level 4 anchor paper.)