Item 6 Anchor Papers    

HSA 2007 Algebra/Data Analysis Item 6

CID
CID286c93a95f470354e71834fd1a4e4d06
itemNum
6
initialLetter
itemType
BCR
itemAnswerKey
N/A
itemMaxScorePoints
3
origNum
x

The graph below shows the height of a ball in one-second intervals. The curve of best fit has been drawn.

Complete the following in the Answer Book:

  • According to the curve of best fit, what is the height of the ball at 4.5 seconds? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
  • According to the curve of best fit, when will the ball be at a height of 100 feet? 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. Although a correct answer of 40 feet is given for the height of the ball at 4.5 seconds, the explanation shows a serious flaw in reasoning. Finding the halfway point between the height at 4 seconds and the height at 5 seconds (80 divided by ½) would only be logically sound for a linear equation. One correct answer is given for when the ball will be at a height of 100 feet (.3 seconds) but the student does not provide the second answer or an explanation. 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. A correct answer is given for the height of the ball at 4.5 seconds (40 feet) but the explanation is incomplete. An incorrect answer is given for when the ball will be at a height of 100 feet (4 seconds). The student does not provide the second answer and the explanation is incomplete. 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. A correct answer is given for the height of the ball at 4.5 seconds (40 feet) but there is no explanation. One correct answer is given for when the ball will be at a height of 100 feet (3.5 seconds). The student does not provide the second answer or the explanation. 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 is given for the height of the ball at 4.5 seconds (40 feet). There is no explanation. Two correct answers are given for when the ball will be at a height of 100 feet (.5 seconds, 3.5 seconds). There is no explanation. 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. An incorrect answer is given for the height of the ball at 4.5 seconds (80 feet). The explanation is also incorrect because it indicates that the student looked for the plotted point closest to 4.5 seconds instead of where the curve was at 4.5 seconds. Two correct answers are given for when the ball will be at a height of 100 feet (.5 seconds and 3.5 seconds) and the explanation is complete. 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. A correct answer is given for the height of the ball at 4.5 seconds (40 feet). The explanation is complete (I went over to 4.5 on the chart and went up until it hit the line and went across and got 40). Two correct answers are given for when the ball will be at a height of 100 feet (.5 seconds and 3.5 seconds). There is no explanation. 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. A correct answer is given for the height of the ball at 4.5 seconds (45 feet) and the explanation is complete. One correct answer is given for when the ball will be at a height of 100 feet (3.8 seconds) but there is no second answer. The explanation is complete for the answer of 3.8. 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 is given for the height of the ball at 4.5 seconds (40 feet). The explanation is fully developed (going half way between 4 & 5 to 4.5, then I went straight up until I ran into the line. Then when I went straight over the line was lined up across from 40 ft.). Two correct answers are given for when the ball will be at a height of 100 feet (.5 seconds; 3.5 seconds). The explanation is fully developed (I got my answer by setting my ruler down at the 100 mark horizontal. Then I went straight down from both marks and got .5 seconds and 3.5 seconds). 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 is given for the height of the ball at 4.5 seconds (40 feet) and the explanation is fully developed. Two correct answers are given for when the ball will be at a height of 100 feet (.5 and 3.5 seconds) and the explanation is fully developed. 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 is given for the height of the ball at 4.5 seconds (40 ft.). The explanation is fully developed (I followed the x-axis to 4.5 seconds. Then, I went up in a straight line until I reached the curve, which was at 40 feet). Two correct answers are given for when the ball will be at a height of 100 feet (about 0.25 seconds and 3.75 seconds). The explanation is fully developed (I followed the y-axis up to 100 feet. Then, I drew a straight, horizontal line across the graph at 100 ft. Where the 100 ft. mark crossed the curve was how many seconds the answers were). The response demonstrates a complete understanding and analysis of the problem.

image of student response
 

Anchor Papers ~ Algebra/Data Analysis ~ Item 6

HSA 2007 Algebra/Data Analysis Item 6

CID
CID286c93a95f470354e71834fd1a4e4d06
itemNum
6
initialLetter
itemType
BCR
itemAnswerKey
N/A
itemMaxScorePoints
3
origNum
x

The graph below shows the height of a ball in one-second intervals. The curve of best fit has been drawn.

Complete the following in the Answer Book:

  • According to the curve of best fit, what is the height of the ball at 4.5 seconds? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
  • According to the curve of best fit, when will the ball be at a height of 100 feet? 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. Although a correct answer of 40 feet is given for the height of the ball at 4.5 seconds, the explanation shows a serious flaw in reasoning. Finding the halfway point between the height at 4 seconds and the height at 5 seconds (80 divided by ½) would only be logically sound for a linear equation. One correct answer is given for when the ball will be at a height of 100 feet (.3 seconds) but the student does not provide the second answer or an explanation. 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. A correct answer is given for the height of the ball at 4.5 seconds (40 feet) but the explanation is incomplete. An incorrect answer is given for when the ball will be at a height of 100 feet (4 seconds). The student does not provide the second answer and the explanation is incomplete. 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. A correct answer is given for the height of the ball at 4.5 seconds (40 feet) but there is no explanation. One correct answer is given for when the ball will be at a height of 100 feet (3.5 seconds). The student does not provide the second answer or the explanation. 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 is given for the height of the ball at 4.5 seconds (40 feet). There is no explanation. Two correct answers are given for when the ball will be at a height of 100 feet (.5 seconds, 3.5 seconds). There is no explanation. 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. An incorrect answer is given for the height of the ball at 4.5 seconds (80 feet). The explanation is also incorrect because it indicates that the student looked for the plotted point closest to 4.5 seconds instead of where the curve was at 4.5 seconds. Two correct answers are given for when the ball will be at a height of 100 feet (.5 seconds and 3.5 seconds) and the explanation is complete. 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. A correct answer is given for the height of the ball at 4.5 seconds (40 feet). The explanation is complete (I went over to 4.5 on the chart and went up until it hit the line and went across and got 40). Two correct answers are given for when the ball will be at a height of 100 feet (.5 seconds and 3.5 seconds). There is no explanation. 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. A correct answer is given for the height of the ball at 4.5 seconds (45 feet) and the explanation is complete. One correct answer is given for when the ball will be at a height of 100 feet (3.8 seconds) but there is no second answer. The explanation is complete for the answer of 3.8. 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 is given for the height of the ball at 4.5 seconds (40 feet). The explanation is fully developed (going half way between 4 & 5 to 4.5, then I went straight up until I ran into the line. Then when I went straight over the line was lined up across from 40 ft.). Two correct answers are given for when the ball will be at a height of 100 feet (.5 seconds; 3.5 seconds). The explanation is fully developed (I got my answer by setting my ruler down at the 100 mark horizontal. Then I went straight down from both marks and got .5 seconds and 3.5 seconds). 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 is given for the height of the ball at 4.5 seconds (40 feet) and the explanation is fully developed. Two correct answers are given for when the ball will be at a height of 100 feet (.5 and 3.5 seconds) and the explanation is fully developed. 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 is given for the height of the ball at 4.5 seconds (40 ft.). The explanation is fully developed (I followed the x-axis to 4.5 seconds. Then, I went up in a straight line until I reached the curve, which was at 40 feet). Two correct answers are given for when the ball will be at a height of 100 feet (about 0.25 seconds and 3.75 seconds). The explanation is fully developed (I followed the y-axis up to 100 feet. Then, I drew a straight, horizontal line across the graph at 100 ft. Where the 100 ft. mark crossed the curve was how many seconds the answers were). The response demonstrates a complete understanding and analysis of the problem.

image of student response