Q and A – Grades 6-8 Mathematics Tests (2008)

Global clarification

Q: At times, a student will show two or more separate bodies of work, one which is incorrect and one which is correct or appropriate, but doesn’t cross out either body of work. Which body of work do we evaluate?
A: If both correct and incorrect procedures are demonstrated within a ‘Show your work’ item, evaluate only the body of work leading to the answer on the answer line. The body of work includes all work associated with the procedure leading to the final answer, including any check on the final answer.

Grade 6

Item #26

Q6-26-1: In the annotation for Guide Paper #4 (Vol. 1, p.10), the first sentence states, "This response is incorrect." Shouldn't it state, "This response is only partially correct?"
A6-26-1: Yes. The first line should read,"This response is only partially correct."

Item #27

Q6-27-1: On Practice Set 7 Part A, why isn’t the paper lowered to a score point 1 for having incorrect mathematical statements? Isn’t the statement 6 x 10 = 120 considered a calculation error?
A6-27-1: A partial understanding is demonstrated. Holistically, using incorrect mathematical statements or notation errors does not detract from a partial understanding of the mathematical concept embodied in the task. The statement 6 x 10 = 120 is considered a notation error, as the remainder of the procedure is not reflective of a calculation error.

Item #28

Q6-28-1: If a student correctly plots the coordinate points, draws and identifies the trapezoid, and provides an adequate explanation, can the paper receive a score point 3 if the student does not label the points?
A6-28-1: No. In order for a response to be considered complete and correct, all elements of the task must be addressed correctly. The response must include the use of labels, either with letters or the appropriate coordinate pairs, in order to demonstrate a thorough understanding.

Item #30

Q6-30-1: Does a response need to show the final conversion from decimal to percent as a bridge to the final answer?
A6-30-1: No. The conversion of decimal to percent is an exception according to Scoring Policy 14.

Q6-30-2: Practice Set 25 does not show the final division calculation to arrive at the answer of 80%. Isn’t it necessary for a paper to show the final bridge to receive full credit?
A6-30-2: For this particular item, if the response includes the correct setup of the proportion and clear evidence of the correct cross multiplication procedure necessary to arrive at the correct answer, the final division calculation is not necessary.

Q6-30-3: If the response only contains a correct proportion, can the paper receive any credit?
A6-30-3: Yes. Setting up the correct proportion on its own is enough to demonstrate a limited understanding of the task.

Item #35

Q6-35-1: Why does Practice Set 50 receive credit? Wasn’t the answer arrived at using an incorrect procedure?
A6-35-1: This response receives a score point 1 because there is not enough work on the page to ascertain whether or not an incorrect procedure was used to arrive at the correct answer of 80.

Grade 7

Item #31

Q7-31-1: Why is Practice Set 5 a score point 1 response, but Practice Sets 3 and 4 are score point 0 responses?
A7-31-1: Using the answer from Part A within the Part B work is not appropriate. However, if the student uses the correct operation, the process used is considered valid and demonstrates a limited understanding.

Item #34

Q 7-34-1: Can you explain Practice Set 16b?
A7-34-1: The numbers of students who chose each sport are added (17 + 13) to find the answer of 30. Next, the number who chose both sports is subtracted from 30 (30 – 8), resulting in an answer of 22. The answer of 22 is then subtracted from the total number of campers (30 – 22), resulting in the correct number (8) who did not select either sport. In other words, if Set A represents the number of students who enjoy baseball and Set B represents the number of students who enjoy swimming, then the number of students who enjoy both baseball and swimming is represented by the intersection of the two sets.
n(A) = 17, n(B) = 13, n(A ∩ B) = 8.
The formula for the union of the two sets is
n(A ∪ B) = n(A) + n(B) – n(A ∩ B) = 17 + 13 – 8 = 22

If we now subtract 22 from the total number of students (30 – 22), we can find the number of students who did not choose either of the two sports.

Item #35

DVD and annotation clarification

Guide Paper #3 (Vol. 1, p. 52) has more than one calculation error (the annotation states a single error). The response still demonstrates a partial understanding, as all procedures are sound. The inappropriate expression of π as a rational number does not detract from a partial understanding.

Item #37

Q7-37-1: If students did not fill in the chart, but filled in the graph correctly, can they receive credit?
A7-37-1: Yes. Three labeled angles graphed within tolerance, regardless of the number of correct table values, would be sufficient for partial credit.

Q7-37-2: Is mislabeling the yellow sector on Guide Paper #3b (Vol. 1, p. 81) a conceptual error?
A7-37-2: No.

Item #38

Q7-38-1: There is only one range listed in Part C of Guide Paper #4b (Vol. 1, pp. 98-99). If the student is using the table on the previous page, shouldn’t two ranges be listed?
A7-38-1: One range is sufficient for partial credit, as the prompt only requests one range.

Grade 8

Item #33

Q8-33-1: Can the student demonstrate a partial understanding if the table is correctly filled in, but the graph is incorrect as in Practice Set 28?
A8-33-1: No. As Guide Paper #5 demonstrates, although the table is filled in correctly, holistically it is not enough to demonstrate a partial understanding of the task.

Q8-33-2: Is either a properly plotted line or ray acceptable for full credit?
A8-33-2: Yes. Although the prompt requests a line segment, properly plotted lines (with arrows) or rays are acceptable for full credit. Due to various interpretations of the question, it was deemed unfair not to accept a line or ray.

Item #34

Q8-34-1: Why does Practice Set 32 receive full credit when it is missing the final step, when Scoring Policy 14 says it must have it?
b There is no bridging procedure or step omitted; only calculations are omitted. All necessary procedures are clearly displayed.

Item #39

Q8-39-1: Does the student need to refer to the freezing point or freezing temperature in their explanation to receive full credit?
A8-39-1: No. As demonstrated in the Guide Papers and Practice Set, “freezing point” or “freezing temperature” is not needed within the explanation.

Item #41

Q8-41-1: Would the student have demonstrated a partial understanding in Guide Paper #5 (Vol. 2, p. 69) if they had correctly labeled the polygon with prime marks?
A8-41-1: Yes. If the student had appropriately labeled the figure with primes it would have been sufficient to demonstrate a partial understanding.

Q8-41-2: Why does Guide Paper #6 (Vol. 2, p. 70) not demonstrate a partial understanding?
A8-41-2: The figure drawn contains a conceptual error because the shape of the figure has changed by more than one grid mark. Although 3 of the 5 points are translated correctly, and there are appropriate labels with primes, changing the shape to this extend prevents the student from demonstrating a partial understanding.

Item #42

Q8-42-1: In Practice Set 75, why doesn’t the student receive full credit when an abbreviated label is used in the proportion?
A8-42-1: Although labels can be used with their corresponding numeric values within the proportion (as demonstrated in Guide Paper #1), at this grade level, the abbreviated label might be interpreted as a variable and detracts from demonstrating a thorough understanding of the task.

Item #43

Q8-43-1: Why doesn’t the student receive some credit in Guide Paper #6 (Vol. 2, pp. 96-97) when he/she correctly plots a triangle using the incorrect coordinates?
A8-43-1: The coordinates given by the student are incorrect. The student must understand that the length of the sides must change to demonstrate the concept of dilation. In Guide Paper #6, the student is merely translating instead of showing dilation.