
	Item 27 Anchor Papers

HSA 2008 Algebra/Data Analysis Item 27

CID: CID1738cca495c306cc36e5c1561af4c921
itemNum: 27
initialLetter
itemType: BCR
itemAnswerKey: N/A
itemMaxScorePoints: 3
origNum: 36

The president of the student government wants to survey the students in the school about their satisfaction with the 36 after-school activities. There are 1,000 students in the school—200 freshmen, 200 sophomores, 300 juniors, and 300 seniors. The president suggested three different sampling methods.

Method A: Randomly choose three students from each of the 36 after-school activities for the survey.

Method B: Randomly select 100 students from the honor roll list to survey.

Method C: Randomly select 20 freshmen, 20 sophomores, 30 juniors, and 30 seniors for the survey.

Complete the following in the Answer Book:

Which method provides the most representative sample of the student population? Use mathematics to justify your answer.
Use mathematics to justify why each of the other two methods does not provide a representative sample.

Score Level 1 Anchor Paper
This response indicates little attempt to apply a reasonable strategy. The student incorrectly chooses Method A as providing the most representative sample. However, the justification for choosing Method A is relevant (its choosing people from each activity) since the student recognizes that all of a population must be represented. The response demonstrates a minimal understanding and analysis of the problem.
Score Level 1 Anchor Paper
This response indicates little attempt to apply a reasonable strategy. The student incorrectly chooses Method A as providing the most representative sample. Because the survey described in the item is asking about satisfaction with after-school activities, the student thinks only students in after-school activities should be able to answer the survey. The justification for choosing Method A shows that the student is drawing the sample from the wrong population; that is, students in after-school activities instead of the whole student body. However, this answer still shows some understanding of representative sampling. The justifications for not choosing Methods B and C also focus on the fact that the students selected may not be in after-school activities. The response demonstrates a minimal understanding and analysis of the problem.
Score Level 2 Anchor Paper
This response indicates an incomplete application of a reasonable strategy. The student correctly selects Method C as providing the most representative sample but gives no justification. Justification is given for why Method A does not provide the most representative sample (not every student in the school stays for after school activities). Justification is also given for why Method B does not provide the most representative sample (not all students are on the honor roll). The response demonstrates a conceptual understanding and analysis of the problem.
Score Level 2 Anchor Paper
This response indicates an incomplete application of a reasonable strategy. The student correctly selects Method C as providing the most representative sample and gives fully developed justification (you have a number of students from each grade + each number of students from that grade is 1/10 of the grade). No justification is given for why Methods A and B do not provide the most representative sample. The response demonstrates a conceptual understanding and analysis of the problem.
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. The student correctly selects Method C as providing the most representative sample and gives justification (each class is represented by 1/10 of it’s population). Justification is provided as to why A and B were not chosen (because they bias by selecting only certain groups). The response demonstrates a complete understanding and analysis of the problem.
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. The student correctly selects Method C as providing the most representative sample and gives a justification (you are surveying a lot of students, some from each grade). Complete justification is given for why Method A does not provide the most representative sample (you are only asking kids that are in the after school activity). Fully developed justification is also given for why Method B does not provide the most representative sample (you are only surveying kids on the honor roll, not kids who aren’t). The response demonstrates a complete understanding and analysis of the problem.

Anchor Papers ~ Algebra/Data Analysis ~ Item 27

HSA 2008 Algebra/Data Analysis Item 27

CID: CID1738cca495c306cc36e5c1561af4c921
itemNum: 27
initialLetter
itemType: BCR
itemAnswerKey: N/A
itemMaxScorePoints: 3
origNum: 36

Method A: Randomly choose three students from each of the 36 after-school activities for the survey.

Method B: Randomly select 100 students from the honor roll list to survey.

Method C: Randomly select 20 freshmen, 20 sophomores, 30 juniors, and 30 seniors for the survey.

Complete the following in the Answer Book:

Which method provides the most representative sample of the student population? Use mathematics to justify your answer.
Use mathematics to justify why each of the other two methods does not provide a representative sample.

Score Level 1 Anchor Paper

This response indicates little attempt to apply a reasonable strategy. The student incorrectly chooses Method A as providing the most representative sample. However, the justification for choosing Method A is relevant (its choosing people from each activity) since the student recognizes that all of a population must be represented. The response demonstrates a minimal understanding and analysis of the problem.

Score Level 1 Anchor Paper

This response indicates little attempt to apply a reasonable strategy. The student incorrectly chooses Method A as providing the most representative sample. Because the survey described in the item is asking about satisfaction with after-school activities, the student thinks only students in after-school activities should be able to answer the survey. The justification for choosing Method A shows that the student is drawing the sample from the wrong population; that is, students in after-school activities instead of the whole student body. However, this answer still shows some understanding of representative sampling. The justifications for not choosing Methods B and C also focus on the fact that the students selected may not be in after-school activities. The response demonstrates a minimal understanding and analysis of the problem.

Score Level 2 Anchor Paper

This response indicates an incomplete application of a reasonable strategy. The student correctly selects Method C as providing the most representative sample but gives no justification. Justification is given for why Method A does not provide the most representative sample (not every student in the school stays for after school activities). Justification is also given for why Method B does not provide the most representative sample (not all students are on the honor roll). The response demonstrates a conceptual understanding and analysis of the problem.

Score Level 2 Anchor Paper

This response indicates an incomplete application of a reasonable strategy. The student correctly selects Method C as providing the most representative sample and gives fully developed justification (you have a number of students from each grade + each number of students from that grade is 1/10 of the grade). No justification is given for why Methods A and B do not provide the most representative sample. The response demonstrates a conceptual understanding and analysis of the problem.

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. The student correctly selects Method C as providing the most representative sample and gives justification (each class is represented by 1/10 of it’s population). Justification is provided as to why A and B were not chosen (because they bias by selecting only certain groups). The response demonstrates a complete understanding and analysis of the problem.

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. The student correctly selects Method C as providing the most representative sample and gives a justification (you are surveying a lot of students, some from each grade). Complete justification is given for why Method A does not provide the most representative sample (you are only asking kids that are in the after school activity). Fully developed justification is also given for why Method B does not provide the most representative sample (you are only surveying kids on the honor roll, not kids who aren’t). The response demonstrates a complete understanding and analysis of the problem.