Anchor Papers ~ Algebra/Data Analysis ~ Item 35


	Item 35 Anchor Papers

A high school principal is meeting with the PTA to discuss the amount of time students spend doing homework each day. He asked a teacher to gather data for the parents. The teacher is going to survey 25 students from a student body of 1,000 students. Consider the methods of sampling shown below.

Method 1: randomly select 25 students from honors classes

Method 2: select 25 members of the girls' varsity softball team at random

Method 3: use a random number generator to generate 25 random numbers and use these to select 25 students from a numerical list of the students

Method 4: randomly select 25 classrooms and ask the teacher in each classroom to select a student

Complete the following in the Answer Book:

Which of the above methods of sampling would give the most representative random sample of the student population? Use mathematics to justify your answer. Include in your justification why you chose that method and why you did not choose each of the other three methods.

Score Level 1 Anchor Paper
This response indicates little attempt to apply a reasonable strategy. The student incorrectly chooses Method 4. Because it indicates a lack of variety, the justification for not selecting Method 1 (if they are in an honors class, chances are that they always do their homework) is plausible. The justification for not selecting Method 2 (because she wasn't asking any boys, and maybe the girls team never do their homework) also indicates a lack of variety. The justification for Method 3 shows a flaw in reasoning. 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 correctly chooses Method 3 as giving the most representative sample with some relevant justification. No justification is given for not selecting the other methods. 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 4; however, the statements (it samples people from all over the school; makes a wider outlook) both indicate variety. The justification for not selecting Method 1 (not just… people who obviously do their homework to be able to get in an honors class) also indicates a lack of variety or bias. No justifications are given for Methods 2 and 3. 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 chooses Method 3 and provides justification (it would give more of a variety). The justification for not choosing Method 1 (you would have all honors students) is logical and indicates a lack of variety. The justification for not selecting Method 2 (you would only have all girls) also shows a lack of variety. No justification is given for not selecting Method 4. 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. Although incorrectly choosing Method 4, the student still shows some understanding of what is required in a representative sample. The justification for Method 4, even though applied to the wrong method, contains true statements (it will give many more different types of opinions; from a wider variety of people) about a representative sample. The justification for not selecting Method 1 (It's only giving you a look at one group of children) is logical. The justification for not selecting Method 2 (only gives you a look at one set of children; It doesn't give you diversity) is correct and indicates a lack of variety. Although Method 3 is the best method, the justification for not selecting Method 3 is not entirely incorrect; the students selected could end up all being from the same group. Overall, 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 Method 3; however, no justification is given. The justification for not choosing Method 1 (they are only choosing honor students) is logical and indicates a lack of variety. The justification for not selecting Method 2 (the girl's softball team might not spend as much time on homework because they're out on the field playing softball) also indicates a lack of variety. The justification for not selecting Method 4 (the teachers might choose their hardest working students who might spend more time on their homework) is correct and indicates bias. 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 chooses Method 3 as giving the most representative sample and the justification (it is not bias, or it is not limited to certain students) and (you could be absent, and it includes the whole school) is logically sound. The fully developed justifications for not selecting Method 1 (the honors students would do more homework), Method 2 (is limited to a certain group; only girls, and only the softball team), and Method 4 (the teacher would pick their favorite student) indicate that bias is possible in each method. 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 chooses Method 3, and the justification (It gives each student an equal chance of being picked, so that way every type of student could be represented) is fully developed. The justification for not selecting Methods 1 and 2 (The first two methods are biased towards bright students and girls) is logically sound. The justification for not selecting Method 4 (teacher may have one student she always chooses) indicates bias. The response demonstrates a complete understanding and analysis of the problem.

Anchor Papers ~ Algebra/Data Analysis ~ Item 35

Method 1: randomly select 25 students from honors classes

Method 2: select 25 members of the girls' varsity softball team at random

Method 3: use a random number generator to generate 25 random numbers and use these to select 25 students from a numerical list of the students

Method 4: randomly select 25 classrooms and ask the teacher in each classroom to select a student

Complete the following in the Answer Book:

Which of the above methods of sampling would give the most representative random sample of the student population? Use mathematics to justify your answer. Include in your justification why you chose that method and why you did not choose each of the other three methods.

Score Level 1 Anchor Paper

This response indicates little attempt to apply a reasonable strategy. The student incorrectly chooses Method 4. Because it indicates a lack of variety, the justification for not selecting Method 1 (if they are in an honors class, chances are that they always do their homework) is plausible. The justification for not selecting Method 2 (because she wasn't asking any boys, and maybe the girls team never do their homework) also indicates a lack of variety. The justification for Method 3 shows a flaw in reasoning. 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 correctly chooses Method 3 as giving the most representative sample with some relevant justification. No justification is given for not selecting the other methods. 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 4; however, the statements (it samples people from all over the school; makes a wider outlook) both indicate variety. The justification for not selecting Method 1 (not just… people who obviously do their homework to be able to get in an honors class) also indicates a lack of variety or bias. No justifications are given for Methods 2 and 3. 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 chooses Method 3 and provides justification (it would give more of a variety). The justification for not choosing Method 1 (you would have all honors students) is logical and indicates a lack of variety. The justification for not selecting Method 2 (you would only have all girls) also shows a lack of variety. No justification is given for not selecting Method 4. 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. Although incorrectly choosing Method 4, the student still shows some understanding of what is required in a representative sample. The justification for Method 4, even though applied to the wrong method, contains true statements (it will give many more different types of opinions; from a wider variety of people) about a representative sample. The justification for not selecting Method 1 (It's only giving you a look at one group of children) is logical. The justification for not selecting Method 2 (only gives you a look at one set of children; It doesn't give you diversity) is correct and indicates a lack of variety. Although Method 3 is the best method, the justification for not selecting Method 3 is not entirely incorrect; the students selected could end up all being from the same group. Overall, 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 Method 3; however, no justification is given. The justification for not choosing Method 1 (they are only choosing honor students) is logical and indicates a lack of variety. The justification for not selecting Method 2 (the girl's softball team might not spend as much time on homework because they're out on the field playing softball) also indicates a lack of variety. The justification for not selecting Method 4 (the teachers might choose their hardest working students who might spend more time on their homework) is correct and indicates bias. 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 chooses Method 3 as giving the most representative sample and the justification (it is not bias, or it is not limited to certain students) and (you could be absent, and it includes the whole school) is logically sound. The fully developed justifications for not selecting Method 1 (the honors students would do more homework), Method 2 (is limited to a certain group; only girls, and only the softball team), and Method 4 (the teacher would pick their favorite student) indicate that bias is possible in each method. 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 chooses Method 3, and the justification (It gives each student an equal chance of being picked, so that way every type of student could be represented) is fully developed. The justification for not selecting Methods 1 and 2 (The first two methods are biased towards bright students and girls) is logically sound. The justification for not selecting Method 4 (teacher may have one student she always chooses) indicates bias. The response demonstrates a complete understanding and analysis of the problem.