Anchor Papers ~ Algebra/Data Analysis ~ Item 6


	Item 6 Anchor Papers

The Knitwear Company wants to know what sock colors teenagers will buy. The company is considering the three options below for collecting data.

Option 1:      Spend five days in the sock department of a randomly selected store and ask every person who enters what color socks they buy.
Option 2:      Spend one day in the sock departments of five randomly selected stores in randomly selected cities and ask every teenager who enters what color socks they buy.
Option 3:      Spend one day in eight randomly selected shopping centers and ask ten randomly selected teenagers at each shopping center what color socks they buy.

Complete the following in the Answer Book:

Which option gives the company the most representative sample of sock colors that teenagers will buy?
Use mathematics to justify why the other two options do not give the company the most representative sample.

Score Level 1 Anchor Paper
This response indicates little attempt to apply a reasonable strategy. The student correctly chooses Option 2 as the most representative sample of sock colors. The justification hints at the concept of variety ("asking different people in different cities to get different opinions"), but lacks the necessary specificity that would apply to this problem. This 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 correctly chooses Option 2 as the most representative sample of sock colors. The statement "this is because with option 2 your spending the day asking every teenager not just random selections such as in option 3" is an unclear justification for why Option 3 is not the most representative. The justification for Option 1 is logically sound. ("Also, option one won't be that good either because in this one you asking everyone, meaning even non-teenagers.") This 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 correctly chooses Option 2 as the most representative sample of sock colors. The justification for Option 3 is a restatement of the question. ("Option 3 says randomly ten teenagers what color sock they like.") The justification for Option 1 ("Option 1 says every person and they want teenagers") identifies that the wrong population is being sampled. This 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 chooses Option 2 as the most representative sample of sock colors. No justification is needed for why Option 2 gives the most representative sample, but the student correctly states that Option 2 "is representing many cities + not just one." This shows an understanding that variety is necessary in a representative sample. The justification for Option 1 correctly states that the wrong population is being sampled ("they are asking every person that enters the store; so that isn't representative of teenagers"). The justification for Option 3 is plausible, but not fully developed, since it does not recognize that the sample size for Option 3 is smaller than the sample size for Option 2. This 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 chooses Option 2 as the most representative sample of sock colors. The justification for Option 3 is that the sample size is too small ("only giving them eighty teenagers"). The justification for Option 1 is that the wrong population is sampled ("in option one they were going to ask every person who walks into the store. Even if they were seventy or five and they're just looking for teenagers"). Although both of these justifications support the solution, neither addresses the concept of variety. This 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 chooses Option 2 as the most representative sample of sock colors. The response shows a clear understanding that variety is necessary in a representative sample ("sample 2 takes place in 5 randomly selected stores. That would incorporate a wide variety of opinion"). The justification for Option 3 ("Option 3 would only be asking 80 teens total") is clearly presented and indicates that the sample size is too small. Fully developed justification is given for Option 1 ("Option 1 asks everybody who enters the 1 store whether they're teenagers or not"), which indicates that the wrong population is being sampled. This 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 chooses Option 2 as the most representative sample of sock colors. A fully developed justification, which indicates that the wrong population is being sampled, is given for Option 1. ("Option 1 says ask every person who enters; every person is not a teenager.") The justification for Option 3 is logically sound ("they're only getting eighty opinions") and indicates that the sample size is too small. The student also shows an understanding that variety is necessary to a representative sample by referencing the fact that Option 2 takes place in multiple cities. ("They would be getting the opinion of more teenagers in different cities.") This response demonstrates a complete understanding and analysis of the problem.

Anchor Papers ~ Algebra/Data Analysis ~ Item 6

The Knitwear Company wants to know what sock colors teenagers will buy. The company is considering the three options below for collecting data.

Complete the following in the Answer Book:

Which option gives the company the most representative sample of sock colors that teenagers will buy?
Use mathematics to justify why the other two options do not give the company the most representative sample.

Score Level 1 Anchor Paper

This response indicates little attempt to apply a reasonable strategy. The student correctly chooses Option 2 as the most representative sample of sock colors. The justification hints at the concept of variety ("asking different people in different cities to get different opinions"), but lacks the necessary specificity that would apply to this problem. This 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 correctly chooses Option 2 as the most representative sample of sock colors. The statement "this is because with option 2 your spending the day asking every teenager not just random selections such as in option 3" is an unclear justification for why Option 3 is not the most representative. The justification for Option 1 is logically sound. ("Also, option one won't be that good either because in this one you asking everyone, meaning even non-teenagers.") This 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 correctly chooses Option 2 as the most representative sample of sock colors. The justification for Option 3 is a restatement of the question. ("Option 3 says randomly ten teenagers what color sock they like.") The justification for Option 1 ("Option 1 says every person and they want teenagers") identifies that the wrong population is being sampled. This 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 chooses Option 2 as the most representative sample of sock colors. No justification is needed for why Option 2 gives the most representative sample, but the student correctly states that Option 2 "is representing many cities + not just one." This shows an understanding that variety is necessary in a representative sample. The justification for Option 1 correctly states that the wrong population is being sampled ("they are asking every person that enters the store; so that isn't representative of teenagers"). The justification for Option 3 is plausible, but not fully developed, since it does not recognize that the sample size for Option 3 is smaller than the sample size for Option 2. This 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 chooses Option 2 as the most representative sample of sock colors. The justification for Option 3 is that the sample size is too small ("only giving them eighty teenagers"). The justification for Option 1 is that the wrong population is sampled ("in option one they were going to ask every person who walks into the store. Even if they were seventy or five and they're just looking for teenagers"). Although both of these justifications support the solution, neither addresses the concept of variety. This 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 chooses Option 2 as the most representative sample of sock colors. The response shows a clear understanding that variety is necessary in a representative sample ("sample 2 takes place in 5 randomly selected stores. That would incorporate a wide variety of opinion"). The justification for Option 3 ("Option 3 would only be asking 80 teens total") is clearly presented and indicates that the sample size is too small. Fully developed justification is given for Option 1 ("Option 1 asks everybody who enters the 1 store whether they're teenagers or not"), which indicates that the wrong population is being sampled. This 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 chooses Option 2 as the most representative sample of sock colors. A fully developed justification, which indicates that the wrong population is being sampled, is given for Option 1. ("Option 1 says ask every person who enters; every person is not a teenager.") The justification for Option 3 is logically sound ("they're only getting eighty opinions") and indicates that the sample size is too small. The student also shows an understanding that variety is necessary to a representative sample by referencing the fact that Option 2 takes place in multiple cities. ("They would be getting the opinion of more teenagers in different cities.") This response demonstrates a complete understanding and analysis of the problem.