Item 16 Anchor Papers    

HSA 2006 Algebra/Data Analysis Item 16

CID
CIDde319febffc33de7689c2b4c815a9cf7
itemNum
16
initialLetter
itemType
BCR
itemAnswerKey
NA
itemMaxScorePoints
3
origNum
x

Erin used the equation below to model the price (y) of postage stamps, in cents, between 1950 and 1995. In Erin's model, x represents the number of years since 1950.

y = 0.014x² + 0.09x + 1.28

The graph below models the price of postage stamps, in cents, between 1950 and 1995.

Complete the following in the Answer Book:

  • According to the model, when was the price of a postage stamp 29¢? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
  • According to the model, what was the cost of postage stamps in 1970? Express your answer to the nearest cent. Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

Score Level 1 Anchor Paper

 

This response indicates little attempt to apply a reasonable strategy. The student gives an incorrect answer for when the price of a postage stamp was 29 cents (40 years after 1950) and the explanation is missing. A correct answer of 9 cents is given for the cost of a postage stamp in 1970 but the explanation is missing. The response demonstrates a minimal understanding and analysis of the problem.

image of student response

Score Level 1 Anchor Paper

 

This response indicates little attempt to apply a reasonable strategy. The student gives an answer (After 41 years) for when the price of a postage stamp was 29 cents but does not include that it was 41 years since 1950. The explanation is correct. Both the answer and explanation for the cost of a postage stamp in 1970 are missing. The response demonstrates a minimal understanding and analysis of the problem.

image of student response

Score Level 1 Anchor Paper

 

This response indicates little attempt to apply a reasonable strategy. The student gives a correct answer for when the price of a postage stamp was 29 cents (42 years after 1950) and the explanation supports this answer. Both the answer and explanation for the cost of a postage stamp in 1970 are missing. The response demonstrates a minimal understanding and analysis of the problem.

image of student response

Score Level 2 Anchor Paper

 

This response indicates an incomplete application of a reasonable strategy. A correct answer (1992) is given for when the price of a postage stamp was 29 cents and the explanation supports the solution. A correct answer of 9 cents is given for the cost of a stamp in 1970 but the explanation is missing. The response demonstrates a conceptual understanding and analysis of the problem.

image of student response

Score Level 2 Anchor Paper

 

This response indicates an incomplete application of a reasonable strategy. Although a correct answer is not given for when the price of a postage stamp was 29 cents, the explanation, substituting 29 for "y" in the equation, would support a correct answer. The answer (8.68) for the cost of a stamp in 1970 should be rounded to 9 cents to be completely correct. The explanation, substituting 20 for "x" in the equation, is correct. The response demonstrates a conceptual understanding and analysis of the problem.

image of student response

Score Level 2 Anchor Paper

 

This response indicates an incomplete application of a reasonable strategy. Although an incorrect answer is given for when the price of a postage stamp was 29 cents, the explanation would support a correct answer. A correct answer of 9 cents is given for the cost of a stamp in 1970 and the explanation supports the solution. The response demonstrates a conceptual understanding and analysis of the problem.

image of student response

Score Level 3 Anchor Paper

 

This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. A correct answer (1992) is given for when the price of a postage stamp was 29 cents and the explanation supports the solution. A correct answer (9 ¢) is given for the cost of a stamp in 1970 and substituting 20 for "x" in the equation provides a fully developed explanation. The response demonstrates a complete understanding and analysis of the problem.

image of student response

Score Level 3 Anchor Paper

 

This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. A correct answer (1992) is given for when the price of a postage stamp was 29 cents and the explanation is fully developed. A correct answer (9¢) is given for the cost of a stamp in 1970 and the explanation supports the solution (I followed the graph this time x must = 20 because 1950+20=1970. Following the point is at approx. (20, 9)). The response demonstrates a complete understanding and analysis of the problem.

image of student response

Score Level 3 Anchor Paper

 

This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. A correct answer (1992) is given for when the price of a postage stamp was 29 cents and the explanation is fully developed. A correct answer (9¢) is given for the cost of a stamp in 1970 and the explanation supports the solution. The response demonstrates a complete understanding and analysis of the problem.

image of student response
 

Anchor Papers ~ Algebra/Data Analysis ~ Item 16

HSA 2006 Algebra/Data Analysis Item 16

CID
CIDde319febffc33de7689c2b4c815a9cf7
itemNum
16
initialLetter
itemType
BCR
itemAnswerKey
NA
itemMaxScorePoints
3
origNum
x

Erin used the equation below to model the price (y) of postage stamps, in cents, between 1950 and 1995. In Erin's model, x represents the number of years since 1950.

y = 0.014x² + 0.09x + 1.28

The graph below models the price of postage stamps, in cents, between 1950 and 1995.

Complete the following in the Answer Book:

  • According to the model, when was the price of a postage stamp 29¢? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
  • According to the model, what was the cost of postage stamps in 1970? Express your answer to the nearest cent. Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

 

Score Level 1 Anchor Paper

 

This response indicates little attempt to apply a reasonable strategy. The student gives an incorrect answer for when the price of a postage stamp was 29 cents (40 years after 1950) and the explanation is missing. A correct answer of 9 cents is given for the cost of a postage stamp in 1970 but the explanation is missing. The response demonstrates a minimal understanding and analysis of the problem.

image of student response

 

Score Level 1 Anchor Paper

 

This response indicates little attempt to apply a reasonable strategy. The student gives an answer (After 41 years) for when the price of a postage stamp was 29 cents but does not include that it was 41 years since 1950. The explanation is correct. Both the answer and explanation for the cost of a postage stamp in 1970 are missing. The response demonstrates a minimal understanding and analysis of the problem.

image of student response

 

Score Level 1 Anchor Paper

 

This response indicates little attempt to apply a reasonable strategy. The student gives a correct answer for when the price of a postage stamp was 29 cents (42 years after 1950) and the explanation supports this answer. Both the answer and explanation for the cost of a postage stamp in 1970 are missing. The response demonstrates a minimal understanding and analysis of the problem.

image of student response

 

Score Level 2 Anchor Paper

 

This response indicates an incomplete application of a reasonable strategy. A correct answer (1992) is given for when the price of a postage stamp was 29 cents and the explanation supports the solution. A correct answer of 9 cents is given for the cost of a stamp in 1970 but the explanation is missing. The response demonstrates a conceptual understanding and analysis of the problem.

image of student response

 

Score Level 2 Anchor Paper

 

This response indicates an incomplete application of a reasonable strategy. Although a correct answer is not given for when the price of a postage stamp was 29 cents, the explanation, substituting 29 for "y" in the equation, would support a correct answer. The answer (8.68) for the cost of a stamp in 1970 should be rounded to 9 cents to be completely correct. The explanation, substituting 20 for "x" in the equation, is correct. The response demonstrates a conceptual understanding and analysis of the problem.

image of student response

 

Score Level 2 Anchor Paper

 

This response indicates an incomplete application of a reasonable strategy. Although an incorrect answer is given for when the price of a postage stamp was 29 cents, the explanation would support a correct answer. A correct answer of 9 cents is given for the cost of a stamp in 1970 and the explanation supports the solution. The response demonstrates a conceptual understanding and analysis of the problem.

image of student response

 

Score Level 3 Anchor Paper

 

This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. A correct answer (1992) is given for when the price of a postage stamp was 29 cents and the explanation supports the solution. A correct answer (9 ¢) is given for the cost of a stamp in 1970 and substituting 20 for "x" in the equation provides a fully developed explanation. The response demonstrates a complete understanding and analysis of the problem.

image of student response

 

Score Level 3 Anchor Paper

 

This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. A correct answer (1992) is given for when the price of a postage stamp was 29 cents and the explanation is fully developed. A correct answer (9¢) is given for the cost of a stamp in 1970 and the explanation supports the solution (I followed the graph this time x must = 20 because 1950+20=1970. Following the point is at approx. (20, 9)). The response demonstrates a complete understanding and analysis of the problem.

image of student response

 

Score Level 3 Anchor Paper

 

This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. A correct answer (1992) is given for when the price of a postage stamp was 29 cents and the explanation is fully developed. A correct answer (9¢) is given for the cost of a stamp in 1970 and the explanation supports the solution. The response demonstrates a complete understanding and analysis of the problem.

image of student response