The following 16 Sample Student Responses represent a range of score points.

Score for Sample Student Response #1: Rubric Score 1

Annotation: This response indicates little application of a reasonable strategy. The number of votes for Marie (25) is incorrect, and the explanation reveals an inappropriate strategy (dividing 300 by 12). Although the student states that Paul is incorrect, the justification reveals a strategic flaw (dividing 300 by both of their votes, and Nick actually won by 3). Paul's survey is chosen as the more reliable, and the justification supports the solution (it's not fair, that only people for chorus so vote for them; it should be open to everybody). The response demonstrates a minimal understanding and analysis of the problem. Compare to Anchor Paper #2.

Score for Sample Student Response #2: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to some correct solutions. The number of votes for Marie (72 votes) is correct and the symbolic explanation supports the solution (300÷50= 12×6=72). The student indicates that Paul is correct. The symbolic justification reveals a reasonable strategy (300÷50=12×14=168; 300÷50=12×16=192). However, a significant mathematical error is made in the number of expected votes when the student divides 300 by 50 and arrives at 12, rather than 6. The difference of (24 more votes) is consistent with the student's numbers. The student indicates that Paul's is the more reliable survey. The justification supports the solution, but is incomplete (he asked any 11^th graders not just chorus). This response demonstrates a clear understanding and analysis of the problem.

Score for Sample Student Response #3: Rubric Score 4

Annotation: This response indicates application of a reasonable strategy that leads to correct solutions within the context of the problem. The number of votes for Marie is correct (72 votes). The explanation is clearly presented, fully developed and supports the solution (you multiply 50x6=300 so you would multiply 12 or Marie's votes by 6 too and you get 72). The student states that Paul is incorrect, and the justification supports the solution (16×6=96 and 14×6=84 and 96−84=12). The student indicates that Paul's is the more reliable survey. The justification is fully developed (it surveys the entire student body and gives an equal chance. Where if Loren asks 50 of the chorus students, their opinions might lean toward 1 person because they are all friends with that person or because the chorus people are friends they might choose a certain person because of someone else picking him or her). This response demonstrates a complete understanding and analysis of the problem.

Score for Sample Student Response #4: Rubric Score 1

Annotation: This response indicates little application of a reasonable strategy. The number of votes for Marie (93) is incorrect, and no explanation is provided. The student states that Paul is correct, and no justification is given. Paul's survey is chosen as the more reliable, and the justification supports the solution (he didn't ask a general group he asked any person in the school). The response demonstrates a minimal understanding and analysis of the problem. Compare to Anchor Paper #2.

Score for Sample Student Response #5: Rubric Score 2

Annotation: This response indicates application of an incomplete strategy. The number of votes for Marie (72 votes) is correct, and the explanation supports the solution (multiplying 12 × 6 because all the votes on the graph added up=50 and 300÷5=6 so I did 12•6 and I got 72). The student states that Paul is incorrect; the justification supports the solution. (Nick will recive 84 votes and Bertha will recive 96.) No answer is given to the third part of the question. The response demonstrates a conceptual understanding and analysis of the problem. Compare to Anchor Paper #4.

Score for Sample Student Response #6: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to some correct solutions. The number of votes for Marie is correct. The fully developed explanation supports the solution (I added together all the people they serveyed and there was a total of 50. Then I saw she had recieved 12 out of the 50 votes. There are 300 students that will vote and if Marie gets 12 out of every 50 votes she will get 72 out of 300). The student states that Paul is correct, and the justification reveals a flaw in reasoning (as you calculate and the numbers go up as long as they follow the same pattern then Nick and Bertha will be two points away). Paul's survey is chosen as the more reliable, and the justification supports the solution (she did not ask anyone outside of chorus and those people could be bias toward one canadate or another). The response demonstrates a clear understanding and analysis of the problem. Compare to Anchor Paper #6.

Score for Sample Student Response #7: Rubric Score 4

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The number of votes for Marie is correct. The symbolic explanation is clearly presented, fully developed, and supports the solution (12/50=.24=6/25 → 300×.24=72). An additional explanation is given. (I simplified the number of students voting for Marie to .24, then multiplied 300 by .24 to get 72 votes.) The student states that Paul is incorrect; the fully developed justification supports the solution. The student calculates the number of votes that each candidate can expect to receive and then notes (Bertha would get 12 more votes, not 2 more). Paul's survey is chosen as the more reliable, and the justification is fully developed. (This is biased because not every eleventh-grade student takes chorus, so not everyone would have an equal opportunity to be surveyed.) The response demonstrates a complete understanding and analysis of the problem.

Score for Sample Student Response #8: Rubric Score 2

Annotation: This response indicates application of an incomplete strategy. The number of votes for Marie (72 votes) is correct, and the symbolic explanation supports the solution; the student sets up the appropriate proportion and solves for x. The student states that Paul is incorrect. The justification supports the solution. (Bertha should receive 96 votes in the election, and Nick should receive 84 votes in the election. That means that Bertha will get 12 more votes than Nick.) No answer is given to the third part of the question. The response demonstrates a conceptual understanding and analysis of the problem. Compare to Anchor Paper #4.

Score for Sample Student Response #9: Rubric Score 4

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The number of votes for Marie is correct. The explanation is clearly presented, fully developed, and supports the solution. The student sets up an appropriate proportion and then continues. (You will get 3600 after multiplying 12 + 300. You'll have 3600=50x. Then divide 3600 by 50, getting 72=x.) The student believes that Paul is incorrect, and the fully developed justification supports the solution. The student calculates the number of votes that each candidate can expect to receive, then notes that the difference is 12 votes. Paul's survey is chosen as the more reliable. The justification is fully developed (Loren only asks chorus students, not giving all eleventh-grade students an equal chance in the survey). The response demonstrates a complete understanding and analysis of the problem.

Score for Sample Student Response #10: Rubric Score 2

Annotation: This response indicates application of an incomplete strategy. The number of votes for Marie (72 votes) is correct, and the explanation supports the solution. (I looked to see how many times 50 went into 300. My answer was 6. Next, I multiplied 12 by 6 and got 72.) The student states that Paul is incorrect. The justification supports the solution. (Bertha will receive 12 more votes than Nick.) No answer is given to the third part of the question. The response demonstrates a conceptual understanding and analysis of the problem. Compare to Anchor Paper #4.

Score for Sample Student Response #11: Rubric Score 1

Annotation: This response indicates little application of a reasonable strategy. The number of votes for Marie (25) is incorrect. The explanation reveals an inappropriate strategy (there's 300 people ÷ into 12). Although the student indicates that Paul is correct, the justification reveals a strategic flaw (Bertha because she got 18.75 rounded to 19. Nick got 21.42 rounded to 21. 300÷14 for Nick= 21.42 300÷16 for Bertha=18.75). Paul's survey is chosen as the more reliable, and the justification supports the solution (Loren's only used 11^th grade students who took chorus every 11th grader doesn't take chorus so Loren survey is bias). The response demonstrates a minimal understanding and analysis of the problem. Compare to Anchor Paper #2.

Score for Sample Student Response #12: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to correct solutions. The number of votes for Marie (72 votes) is correct, and the explanation supports the solution. (I got this from 12 out of 50 × 24% × 300=72.) The student states that Paul is incorrect, and the justification supports the solution (Nick will recieve 84 votes and Bertha will receive 96 votes). Paul's survey is chosen as the more reliable. An incomplete justification supports the solution (because one of the candidates my be in chorus). The response demonstrates a clear understanding and analysis of the problem.

Score for Sample Student Response #13: Rubric Score 4

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution within the context of the problem. The number of votes for Marie is correct. The explanation is clearly presented, fully developed, and supports the solution (out of the 50 random students Marie got 12 votes, 12/50. If 300 kids are in Paul's school 300÷50=6 so you multiply 6×12 to get 72 votes). The student states that Paul is incorrect, and the fully developed justification supports the solution. The student calculates the number of votes that each candidate can expect to receive, then notes that the difference is 12 votes. Paul's survey is chosen as the more reliable. The justification is fully developed (in Loren's survey, she only asked chorus people not random students in the school like Paul did. Paul gave everyone an equal chance at being surveyed; Loren didn't). The response demonstrates a complete understanding and analysis of the problem.

Score for Sample Student Response #14: Rubric Score 1

Annotation: This response indicates little application of a reasonable strategy. Although the number of votes for Marie (194 votes) is incorrect, the explanation reveals an appropriate strategy. The student finds the correct percentage of students who would vote for Marie (.24), but multiplies that by 800, instead of 300. The student believes that Paul is correct, and the justification reveals a flaw in reasoning (the data shows she beats him by 2 votes and the data is correct because that is 50 total votes). The student indicates that both surveys are reliable, and the justification reveals a flaw in reasoning. (They Both have 50 students, but the only difference is that Loren's survey can have more candidates.) The response demonstrates a minimal understanding and analysis of the problem. Compare to Anchor Paper #1.

Score for Sample Student Response #15: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to some correct solutions. The number of votes for Marie (72 votes) is correct, and the explanation supports the solution (by first trying at see how many 50s added if it will make 300. It did it took 6 50s to add up to 300 so I multiplied 12 by 6). The student states that Paul is correct, and the justification reveals a flaw in reasoning. (In the chart it shows that Nick has 14 votes and Bertha has 16. When you minus 16 by 14, it is 2.) Paul's survey is chosen as the more reliable, and the justification supports the solution (Loren's survey is full of just chorus students. Pauls is a whole bunch of different students from different classes. Loren's survey might just show that if Bertha was in chorus and had many friends there she would get all the votes). The response demonstrates a clear understanding and analysis of the problem. Compare to Anchor Paper #6.

Score for Sample Student Response #16: Rubric Score 2

Annotation: This response indicates application of an incomplete strategy. The number of votes for Marie (72 votes) is correct, and the explanation supports the solution (300 students/50 selected=6 votes 6×12 original votes=72). The student believes that Paul is incorrect, and the justification supports the solution. The student calculates the number of votes each candidate would receive, thus proving that the difference is not 2. The student indicates that both surveys are reliable, and the justification reveals a flaw in reasoning (because they both use the same techniques to find the data). This response demonstrates a conceptual understanding and analysis of the problem. Compare to Anchor Paper #4.

Anchor Papers used in scoring