NAEP Mathematics
Grade 8
Sample Assessment Block
West Virginia Department of Education
West Virginia Board of Education
2011-2012
L. Wade Linger Jr., President
Gayle C. Manchin, Vice President
Robert W. Dunlevy, Secretary
Michael I. Green, Member
Priscilla M. Haden, Member
Lloyd G. Jackson II, Member
Lowell E. Johnson, Member
Jenny N. Phillips, Member
William M. White, Member
Brian E. Noland, Ex Officio
Chancellor
West Virginia Higher Education Policy Commission
James L. Skidmore, Ex Officio
Chancellor
West Virginia Council for Community and Technical College Education
Jorea M. Marple, Ex Officio
State Superintendent of Schools
West Virginia Department of Education
NAEP Mathematics - Grade 8
Table of Contents
Sample Assessment...................................................................................................................... 3
Framework Overview................................................................................................................ 19
Individual Item Analysis............................................................................................................ 21
2| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
These pieces would be printed on card stock paper. Eighth grade students who received this booklet would have
received a perforated sheet with these shapes on it. The students are expected to punch out the shapes during
the timed assessment.
Eighth grade students would see the following directions for this block of questions. “With this test booklet you
will receive a sheet of pieces labeled R, T, and X. You will use these pieces in answering the questions. You
can turn the pieces in any way or flip them over. You may use drawings to help explain your answers.”
3| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
Directions for students:
This part has 18 questions. Mark your answers in your booklet. You will have to fill in an oval or write
your answer as directed. In those questions where you must write an answer, it is important that your
answer be clear and complete and that you show all of your work, since partial credit may be awarded.
With this test booklet you will receive a sheet of pieces labeled R, T, and X. You will use the pieces in
answering questions 1-5. You can turn the pieces in any way or flip them over. You may use drawing to
help explain your answer.
4| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
You will need four pieces labeled R and two pieces labeled T to answer this question.
1.Use these pieces to cover the figure below.
Draw the lines to show where the pieces meet.
Label the pieces on the figure.
5| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Reading - Grade 8
You will need two pieces labeled X to answer this question.
2.Use the pieces to make a shape that has these properties.
• It has four sides.
• No pieces overlap.
• No two sides are parallel.
In the space below, trace the shape.
Draw the line to show where the two pieces meet.
6| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Reading - Grade 8
You will need one piece labeled X, one piece labeled T, and one piece labeled R to answer this
question.
3.Which of the pieces has an angle greater than a right angle?
A. Only
B. Only
C. Only
D. Both
7| Page
X
R
T
R and T
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
You will need pieces labeled R, T, and X to answer this question.
4.The figure above is made of one piece labeled T and two pieces labeled X. This figure has the same
total area as
A. one piece labeled R
B. two pieces labeled X
C. three pieces labeled X
D. one piece labeled R and one piece labeled T
8| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
For this question, you may want to use your pieces labeled X.
5.The figure below shows two triangles, labeled 1 and 2.
Which one of the following describes a way to move triangle 1 so that it completely covers triangle
2?
A. Turn (rotate) 180 degrees about point P.
B. Flip (reflect) over line .
C. Slide (translate) 5 units to the right followed by 8 units down.
D. Flip (reflect) over line m.
E. Slide (translate) 10 units to the right followed by 16 units down.
9| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
You may now put your packet of pieces away.
6.What number should be put in the box to make the number sentence above true?
Answer: _________________________
7.Write a three-digit number using the digits 2, 4, and 6 so that the digit 4 means four tens and the
digit 6 means six hundreds.
Answer: _________________________
10| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
8.A loaded trailer truck weighs 26,643 kilograms. When the trailer truck is empty, it weighs 10,547
kilograms. About how much does the load weigh?
A. 14,000 kilograms
B. 16,000 kilograms
C. 18,000 kilograms
D. 36,000 kilograms
9.Marty has 6 red pencils, 4 green pencils, and 5 blue pencils. If he picks out one pencil without looking,
what is the probability that the pencil he picks will be green?
A. 1 out of 3
B. 1 out of 4
C. 1 out of 15
D. 4 out of 15
11| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
10.Which picture shows that
is the same as
A.
B.
C.
D. 11.Write the next two numbers in the number pattern.
1 6 4 9 7 12 10 ____ ____
Write the rule that you used to find the two numbers you wrote.
12| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
12.A turkey is put in the oven at 10:30 a.m. If the turkey takes
taken out of the oven?
A. 12:15 p.m.
B. 12:45 p.m.
C. 1:15 p.m.
D. 1:45 p.m.
hours to cook, at what time should it be
NAEP Mathematics - Grade 8
13.Susie said, “I have 83¢ but fewer than 10 coins.” Show in the chart how many of each coin she could
have to total 83¢.
14| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
14.Jorge left some numbers off the number line below. Fill in the numbers that should go in A, B, and C.
15.In the right triangle above, what is the length of AB?
A. 8.5
B. 12
C. 13
D. 17
E. 30
15| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
16.Which of the following is always an odd integer?
A. The product of two odd integers
B. The product of two consecutive integers
C. The sum of three even integers
D. The sum of two odd integers
E. The sum of three consecutive integers
17.How many square tiles, 5 inches on a side, does it take to cover a rectangular area that is 50 inches wide
and 100 inches long?
Answer: _________________________
16| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
18.Leroy has one quarter, one dime, one nickel, and one penny. Two of the coins are in his left pocket and
the other two coins are in his right pocket. The coins have been randomly placed in the two pockets.
What is the probability that Leroy will be able to purchase a 30-cent candy bar with the two coins in his
left pocket?
Using the coins, explain your reasoning. 17| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
If you need more room for your work, use the space below.
18| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
NAEP Mathematics Framework Overview Information
The National Assessment of Educational Progress (NAEP) assesses students’ understanding of mathematical
content. The framework for the mathematics assessment is anchored in five broad areas of mathematics.
Broad Area of Mathematics
Includes but is not limited to
Number Properties and Operations
Computation
Understanding of number concepts
Measurement
Use of instruments
Application of processes
Concepts of area and volume
Geometry
Spatial reasoning
Applying geometric properties
Data Analysis, Statistics, and Probability
Graphical display
Statistics
Algebra
Representations
relationships
These divisions are not intended to separate mathematic into discrete elements. Rather, they are intended to
provide a helpful classification scheme that describes the full spectrum of mathematical content assessed by
NAEP. Classification of items into one primary content area is not always clear-cut, but it helps ensure that
important mathematical concepts and skills are assessed in a balanced way.
Item Distribution by Content Area
Content Area
Grade 4
Grade 8
Grade 12
Number Properties and Operations
40%
20%
10%
Measurement
20%
15%
Geometry
15%
20%
Data Analysis, Statistics, and Probability
10%
15%
25%
Algebra
15%
30%
35%
19| Page
30%
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
Mathematical Complexity
Items are the NAEP mathematics assessment are categories by mathematical complexity. Mathematical
complexity is an indication of the demands on students’ thinking. The demand on thinking that an item
expects—what it asks the student to recall, understand, reason about, and do—assume that students are familiar
with the mathematics of the task. Mathematical complexity deals with what the students are asked to do in a
task. It does not take into account how they might undertake it.
NAEP has three levels of complexity—high, moderate, low—forming an ordered description of the demands
an item may make on a student. Items at the low level of complexity, for example, may ask a student to recall a
property. At the moderate level, an item may ask the student to make a connection between two properties; at
the high level, an item may ask a student to analyze the assumptions made in a mathematical model.
At each grade level, the percent of testing time at each complexity level is the same. One half the testing time
is expected to be spent on moderate complexity level. One quarter of the testing time is expected to be spent on
low complexity items and the remaining quarter on high complexity items.
Item Type
NAEP assessment in mathematics has three formats or item types: multiple-choice, short constructed response,
and extended constructed response.
• Multiple-choice items require students to read, reflect, or compute and then to select the alternative that
best expresses the answer. Multiple-choice items for grade 4 have four choices, and at grades 8 and 12,
there are five choices.
• Short constructed-responses require students to give either a numerical result or the correct name or
classification for a group of mathematical objects, draw an example of a given concept, or possibly write
a brief explanation for a given result.
• Extended Constructed-response items require students to consider a situation that requires more than a
numerical response or a short verbal communication. The student may be asked, for example, to describe
a situation, analyze a graph or table of values or an algebraic equation, or compute specific numerical
values.
The NAEP assessment is divided evenly between multiple-choice and both types of constructed-response items.
50% of the testing time is expected to be spent of multiple-choice items and the other 50% on the constructedresponse items.
Note: No one student takes the entire mathematics assessment. Some blocks of assessment items may not
contain all types of items, particularly the extended constructed response.
20| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
Individual Item Analysis
For each question in the sample block, the cognitive target is given. In addition the percentage of students
selecting each answer choice for multiple choice or scoring at each score point are indicated for public school
students in West Virginia and the nation. The correct multiple choice answer is indicated with an asterisk. In
order for a question to be considered “omitted,” the student did not answer the question but answered a question
or questions after it.
You will need four pieces labeled R and two pieces labeled T to answer this question.
1.Geometry—This question was a cross-grade questions. It was included on both the 4th grade and 8th
grade assessment. Student performance data are shown for both grades.
4th Grade
8th Grade
West Virginia
National Public
West Virginia
National Public
Incorrect
18%
14%
6%
7%
Partial
40%
40%
36%
31%
Correct
37%
41%
55%
60%
Omitted
4%
5%
2%
2%
Off Task
Rounds to Zero
Rounds to Zero
Rounds to Zero
Rounds to Zero
Use these pieces to cover the figure below.
Draw the lines to show where the pieces meet.
Label the pieces on the figure.
21| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
Scoring Rubric
Score & Description
Correct
Correct response
Sample Correct Responses:
Partial
Uses any combination of at least one R and at least one T (but not four R’s and two T’s) to cover the figure. No
labels are necessary (and mislabels may be present), but lines must be shown. Somewhat poor tracing OK.
OR
Draws lines correctly but does not label.
OR
Writes labels only for four R’s and two T’s in correct locations, but does not draw lines.
Incorrect
Incorrect response Correct - Student Response
Exemplar 1
Use these pieces to cover the figure below.
Draw the lines to show where the pieces meet.
Label the pieces on the figure.
22| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
Exemplar 2
Use these pieces to cover the figure below.
Draw the lines to show where the pieces meet.
Label the pieces on the figure.
Scorer Comments:
These responses correctly used the four pieces labeled R and two pieces labeled T and had the lines drawn
where the pieces met to completely cover the figure.
Partial - Student Response
Exemplar 1
Use these pieces to cover the figure below.
Draw the lines to show where the pieces meet.
Label the pieces on the figure.
Exemplar 2
Use these pieces to cover the figure below.
Draw the lines to show where the pieces meet.
Label the pieces on the figure.
Scorer Comments:
These responses used combinations of at least one R and at least one T to cover the figure with the lines drawn
on where the pieces met.
23| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
2.Geometry—This question was a cross-grade questions. It was included on both the 4th grade and 8th
grade assessment. Student performance data are shown for both grades.
Grade 4
Grade 8
West Virginia
National Public
West Virginia
National Public
Incorrect
34%
29%
23%
17%
Partial
43%
44%
53%
52%
Correct
20%
21%
22%
28%
Omitted
3%
5%
2%
4%
Off Task
Rounds to Zero
Rounds to Zero
Rounds to Zero
Rounds to Zero
Use the pieces to make a shape that has these properties.
• It has four sides.
• No pieces overlap.
• No two sides are parallel.
In the space below, trace the shape.
Draw the line to show where the two pieces meet.
Scoring Rubric
Score & Description
Correct
Correct response
Sample Correct Responses:
Partial
A four-sided figure with parallel sides with meeting lines drawn
OR
A correct shape but meeting line is incorrect.
OR
24| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
A 3-sided figure or a figure with more than four sides, and the sides are not parallel with meeting lines drawn.
OR
Either of the correct shapes is drawn without the line where the pieces meet.
Incorrect
Incorrect response
Correct - Student Response
Exemplar 1
Use the pieces to make a shape that has these properties.
• It has four sides.
• No pieces overlap.
• No two sides are parallel.
In the space below, trace the shape.
Draw the line to show where the two pieces meet.
Exemplar 2
Use the pieces to make a shape that has these properties.
• It has four sides.
• No pieces overlap.
• No two sides are parallel.
In the space below, trace the shape.
Draw the line to show where the two pieces meet.
Scorer Comments:
These responses correctly showed a four-sided figure with no pieces that overlapped and no two sides were
parallel.
Partial - Student Response
Exemplar 1
Use the pieces to make a shape that has these properties.
• It has four sides.
• No pieces overlap.
• No two sides are parallel.
In the space below, trace the shape.
Draw the line to show where the two pieces meet.
25| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
Exemplar 2
Use the pieces to make a shape that has these properties.
• It has four sides.
• No pieces overlap.
• No two sides are parallel.
In the space below, trace the shape.
Draw the line to show where the two pieces meet.
Scorer Comments:
These responses showed partially correct figures where each had a line drawn where the two pieces met.
3.Measurement—This question was a cross-grade questions. It was included on both the 4th grade and 8th
grade assessment. Student performance data are shown for both grades.
Grade 4
Grade 8
West Virginia
National Public
West Virginia
National Public
A
22%
18%
11%
9%
B*
38%
44%
64%
72%
C
6%
6%
4%
3%
D
33%
30%
19%
14%
Omitted
1%
1%
1%
2%
Which of the pieces has an angle greater than a right angle?
A. Only
B. Only
C. Only
D. Both
26| Page
X
R
T
R and T
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
4. Measurement
West Virginia
National Public
A*
35%
43%
B
9%
9%
C
18%
12%
D
36%
33%
Omitted
2%
2%
The figure above is made of one piece labeled T and two pieces labeled X. This figure has the same total
area as
A. one piece labeled R
B. two pieces labeled X
C. three pieces labeled X
D. one piece labeled R and one piece labeled T
27| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
5.Geometry
West Virginia
National Public
A*
61%
65%
B
17%
15%
C
7%
7%
D
12%
8%
E
3%
2%
Omitted
Rounds to Zero
2%
The figure below shows two triangles, labeled 1 and 2.
Which one of the following describes a way to move triangle 1 so that it completely covers triangle 2?
A. Turn (rotate) 180 degrees about point P.
B. Flip (reflect) over line .
C. Slide (translate) 5 units to the right followed by 8 units down.
D. Flip (reflect) over line m.
E. Slide (translate) 10 units to the right followed by 16 units down.
28| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
6.Algebra—This question was a cross-grade questions. It was included on both the 4th grade and 8th grade
assessment. Student performance data are shown for both grades.
Grade 4
Grade 8
West Virginia
National Public
West Virginia
National Public
Incorrect
33%
30%
18%
13%
Correct
65%
68%
81%
85%
Omitted
2%
1%
1%
2%
Off Task
Rounds to Zero
Rounds to Zero
Rounds to Zero
Rounds to Zero
What number should be put in the box to make the number sentence above true?
Answer: _________________________
Scoring Rubric
Sample Correct Responses:
Score & Description
Correct
Correct response
29 OR 29 − 8 = 21
OR 29 in the box and response area blank.
Incorrect
Incorrect response
Correct - Student Response
What number should be put in the box to make the number sentence above true?
Answer: _________________________
Scorer Comments:
These responses correctly listed 29 as the number that should be put in the box.
29| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
7. Number Properties and Operations—This question was a cross-grade questions. It was included on both
the 4th grade and 8th grade assessment. Student performance data are shown for both grades.
Grade 4
Grade 8
West Virginia
National Public
West Virginia
National Public
Incorrect
32%
29%
40%
32%
Correct
65%
69%
59%
63%
Omitted
2%
2%
1%
4%
Off Task
Rounds to Zero
Rounds to Zero
Rounds to Zero
Rounds to Zero
Write a three-digit number using the digits 2, 4, and 6 so that the digit 4 means four tens and the digit 6
means six hundreds.
Answer: _________________________
Scoring Guide
Score & Description
Correct
Correct response: 642
Incorrect
Incorrect response Correct - Student Response
Write a three-digit number using the digits 2, 4, and 6 so that the digit 4 means four tens and the digit 6 means
six hundreds.
Answer: _________________________
Scorer Comments:
These responses had the correct answer of 642.
30| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
8. Number Properties and Operations—This question was a cross-grade questions. It was included on both
the 4th grade and 8th grade assessment. Student performance data are shown for both grades.
Grade 4
Grade 8
West Virginia
National Public
West Virginia
National Public
A
10%
8%
4%
3%
B*
47%
52%
77%
83%
C
14%
10%
8%
4%
D
28%
28%
11%
9%
Omitted
1%
2%
1%
1%
A loaded trailer truck weighs 26,643 kilograms. When the trailer truck is empty, it weighs 10,547
kilograms. About how much does the load weigh?
A. 14,000 kilograms
B. 16,000 kilograms
C. 18,000 kilograms
D. 36,000 kilograms
31| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
9. Data Analysis and Probability—This question was a cross-grade questions. It was included on both the
4th grade and 8th grade assessment. Student performance data are shown for both grades.
Grade 4
Grade 8
West Virginia
National Public
West Virginia
National Public
A
15%
13%
6%
4%
B
24%
24%
9%
6%
C
25%
23%
10%
12%
D*
34%
38%
75%
77%
Omitted
2%
2%
1%
1%
Marty has 6 red pencils, 4 green pencils, and 5 blue pencils. If he picks out one pencil without looking,
what is the probability that the pencil he picks will be green?
A. 1 out of 3
B. 1 out of 4
C. 1 out of 15
D. 4 out of 15
32 Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
10.Number Properties and Operations—This question was a cross-grade questions. It was included on both
the 4th grade and 8th grade assessment. Student performance data are shown for both grades.
Grade 4
Grade 8
West Virginia
National Public
West Virginia
National Public
A*
47%
56%
66%
74%
B
18%
12%
13%
9%
C
11%
9%
7%
5%
D
21%
20%
13%
11%
Omitted
3%
3%
1%
1%
Which picture shows that
is the same as
A.
B.
C.
D. 33| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
11.Algebra—This question was a cross-grade questions. It was included on both the 4th grade and 8th grade
assessment. Student performance data are shown for both grades.
4th
8th
West Virginia
National Public
West Virginia
National Public
Incorrect
47%
39%
17%
14%
Partial
18%
16%
18%
16%
Correct
27%
37%
61%
66%
Omitted
8%
8%
3%
4%
Off Task
Rounds to Zero
Rounds to Zero
Rounds to Zero
Rounds to Zero
Write the next two numbers in the number pattern.
1 6 4 9 7 12 10 ____ ____
Write the rule that you used to find the two numbers you wrote.
Scoring Rubric
Score & Description
Correct
Correct response
15, 13
Add 5 to previous number for even places and subtract 2 from previous number to get odd places,
OR
+5, −2
OR
The odd terms increase by 3 and the even terms increase by 3. (“Every other number skips 3” is acceptable.)
Partial
Gives 15 and 13 but not the rule
OR
Just gives evidence that they know the rule but omits or gets incorrect the 15 and/or 13
OR
Gives 8 and 13 with rule −2, + 5
Incorrect
Incorrect response
34| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
Correct - Student Response
Exemplar 1
Write the next two numbers in the number pattern.
Exemplar 2
Write the next two numbers in the number pattern.
Scorer Comments:
These responses correctly extended the pattern and gave the correct rule.
35| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
Partial - Student Response
Exemplar 1
Write the next two numbers in the number pattern.
Exemplar 2
Write the next two numbers in the number pattern.
Scorer Comments:
These responses either extended the pattern correctly or gave the correct rule. 36| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
12.Measurement—This question was a cross-grade question. It was included on both the 4th grade and 8th
grade assessment. Student performance data are shown for both grades.
4th
8th
West Virginia
National Public
West Virginia
National Public
A
19%
19%
9%
8%
B
42%
42%
38%
30%
C*
27%
27%
46%
54%
D
9%
9%
5%
6%
Omitted
2%
3%
2%
2%
A turkey is put in the oven at 10:30 a.m. If the turkey takes
taken out of the oven?
hours to cook, at what time should it be
A. 12:15 p.m.
B. 12:45 p.m.
C. 1:15 p.m.
D. 1:45 p.m.
37| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
13.Number Properties and Operations—This question was a cross-grade question. It was included on both
the 4th grade and 8th grade assessment. Student performance data are shown for both grades.
4th
8th
West Virginia
National Public
West Virginia
National Public
Incorrect
35%
35%
14%
13%
Partial
10%
9%
4%
6%
Correct
54%
55%
80%
78%
Omitted
Rounds to Zero
1%
2%
3%
Off Task
Rounds to Zero
Rounds to Zero
Rounds to Zero
Rounds to Zero
Susie said, “I have 83¢ but fewer than 10 coins.” Show in the chart how many of each coin she could
have to total 83¢.
Scoring Rubric
Score & Description
Correct
Gives one or more correct solutions
Sample Correct Responses
Partial
Combination of coins equals $.83 but total number of coins is incorrect (has 10 or more).
OR
Has at least one correct solution but one or more incorrect solutions (half or more of the solutions are incorrect).
Incorrect
Incorrect response
38| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
Correct - Student Response
Exemplar 1
Susie said, “I have 83¢ but fewer than 10 coins.” Show in the chart how many of each coin she could have to
total 83¢.
Exemplar 2
Susie said, “I have 83¢ but fewer than 10 coins.” Show in the chart how many of each coin she could have to
total 83¢.
Scorer Comments:
These responses showed the correct number of coins and the correct total number of coins.
39| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
Partial - Student Response
Exemplar 1
Susie said, “I have 83¢ but fewer than 10 coins.” Show in the chart how many of each coin she could have to
total 83¢.
Exemplar 2
Susie said, “I have 83¢ but fewer than 10 coins.” Show in the chart how many of each coin she could have to
total 83¢.
Scorer Comments:
These responses showed the correct combination of coins but the total number of coins had to be fewer than 10
coins.
40| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
14.Number Properties and Operations—This question was a cross-grade question. It was included on both
the 4th grade and 8th grade assessment. Student performance data are shown for both grades.
4th
8th
West Virginia
National Public
West Virginia
National Public
Incorrect
57%
48%
23%
17%
Partial
8%
8%
5%
5%
Correct
34%
44%
63%
71%
Omitted
Rounds to Zero
Rounds to Zero
8%
6%
Off Task
Rounds to Zero
Rounds to Zero
Rounds to Zero
Rounds to Zero
Jorge left some numbers off the number line below. Fill in the numbers that should go in A, B, and C.
41| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
Scoring Rubric
Score & Description
Correct
Correct response
is acceptable for A (or any equivalent)
is acceptable for B (or any equivalent)
is acceptable for C (or any equivalent)
Partial
2 of 3 entries correct
Incorrect
Incorrect response
Correct - Student Response
Exemplar 1
Jorge left some numbers off the number line below. Fill in the numbers that should go in A, B, and C.
42| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
Exemplar 2
Jorge left some numbers off the number line below. Fill in the numbers that should go in A, B, and C.
Scorer Comments:
These responses had the correct numbers in each box.
Partial - Student Response
Exemplar 1
Jorge left some numbers off the number line below. Fill in the numbers that should go in A, B, and C.
Exemplar 2
Jorge left some numbers off the number line below. Fill in the numbers that should go in A, B, and C.
Scorer Comments:
These responses had two correct entries in boxes B and C.
43| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
15.Geometry
West Virginia
National Public
A
8%
7%
B
21%
17%
C*
32%
40%
D
33%
30%
E
5%
5%
Omitted
1%
1%
In the right triangle above, what is the length of AB?
A. 8.5
B. 12
C. 13
D. 17
E. 30
44| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
16.Number Properties and Operations
West Virginia
National Public
A*
27%
36%
B
20%
18%
C
14%
12%
D
22%
17%
E
17%
16%
Omitted
1%
2%
Which of the following is always an odd integer?
A. The product of two odd integers
B. The product of two consecutive integers
C. The sum of three even integers
D. The sum of two odd integers
E. The sum of three consecutive integers
17.Measurement
West Virginia
National Public
Incorrect
(Responses of 1000)
87%
73%
Incorrect
(other)
3%
7%
Correct
7%
16%
Omitted
2%
2%
Off Task
1%
1%
How many square tiles, 5 inches on a side, does it take to cover a rectangular area that is 50 inches wide
and 100 inches long?
45| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
Scoring Rubric
Score & Description
Correct
Correct response
Sample Correct Responses:
200 or 200 tiles
Incorrect
1,000
Incorrect
Any incorrect response other than 1,000
Correct - Student Response
Exemplar 1
How many square tiles, 5 inches on a side, does it take to cover a rectangular area that is 50 inches wide and
100 inches long?
Answer: _________________________
46| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
Exemplar 2
How many square tiles, 5 inches on a side, does it take to cover a rectangular area that is 50 inches wide and
100 inches long?
Answer: _________________________
Scorer Comments:
These responses correctly answered 200.
18.Data Analysis and Probability
West Virginia
National Public
Incorrect
64%
52%
Minimal
20%
20%
Partial
3%
5%
Satisfactory
3%
6%
Extended
2%
6%
Omitted
7%
10%
Off Task
1%
1%
Leroy has one quarter, one dime, one nickel, and one penny. Two of the coins are in his left pocket and
the other two coins are in his right pocket. The coins have been randomly placed in the two pockets.
What is the probability that Leroy will be able to purchase a 30-cent candy bar with the two coins in his
left pocket?
Using the coins, explain your reasoning. 47| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
Scoring Rubric
Score & Description
Extended
Complete correct solution that indicates correct probability with a complete explanation. Must indicate the 2
successful combinations (May use conditional probabilities).
Sample Correct Responses:
QP Not able to purchase candy bar with these
QN Able to purchase candy bar with these
QD Able to purchase candy bar with these
PN Not able to purchase candy bar with these
PD Not able to purchase candy bar with these
ND Not able to purchase candy bar with these
The probability is or because there are 6 different possible combinations for the two coins but only 2 of
these have a combined value of 30 cents or more.
Note: Explanation must include correct number of total possible combinations as well as an indication of those
combinations that satisfy 30-cent criteria.
Satisfactory
Response indicates an incorrect probability but explanation implies correct reasoning (sample space of 6).
OR
Response has correct probability for incomplete number of total possible combinations of coins or incomplete
explanation. (Probability agrees with sample space.) For a score of 4, sample space must contain at least 4
different, correct pairs.
Partial
Response gives a correct probability and no explanation.
OR
Less than 4 pairs with agreeing probability.
OR
A correct probability that is based on an incorrect explanation.
Minimal
Response contains evidence that student knows that there is more than one possible combination for the coins in
the left pocket. Probability is missing or incorrect.
Incorrect
Incorrect response
48| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
Extended - Student Response
Exemplar 1
Leroy has one quarter, one dime, one nickel, and one penny. Two of the coins are in his left pocket and the other
two coins are in his right pocket. The coins have been randomly placed in the two pockets.
Exemplar 2
Leroy has one quarter, one dime, one nickel, and one penny. Two of the coins are in his left pocket and the other
two coins are in his right pocket. The coins have been randomly placed in the two pockets.
Scorer Comments:
These responses correctly found the probability of 1/3, indicated the 2 successful combinations, and had a
complete, correct explanation.
49| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
Satisfactory - Student Response
Exemplar 1
Leroy has one quarter, one dime, one nickel, and one penny. Two of the coins are in his left pocket and the other
two coins are in his right pocket. The coins have been randomly placed in the two pockets.
Exemplar 2
Leroy has one quarter, one dime, one nickel, and one penny. Two of the coins are in his left pocket and the other
two coins are in his right pocket. The coins have been randomly placed in the two pockets.
Scorer Comments:
These responses had an incorrect probability but each explanation implied correct reasoning.
50| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
Partial - Student Response
Exemplar 1
Leroy has one quarter, one dime, one nickel, and one penny. Two of the coins are in his left pocket and the other
two coins are in his right pocket. The coins have been randomly placed in the two pockets.
Exemplar 2
Leroy has one quarter, one dime, one nickel, and one penny. Two of the coins are in his left pocket and the other
two coins are in his right pocket. The coins have been randomly placed in the two pockets.
Scorer Comments:
The first response received partial credit because the probability (2/4) is incorrect, but is based (correctly) on the
four given coin combinations. The second response had a correct probability based on an incorrect explanation.
51| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
Minimal - Student Response
Exemplar 1
Leroy has one quarter, one dime, one nickel, and one penny. Two of the coins are in his left pocket and the other
two coins are in his right pocket. The coins have been randomly placed in the two pockets.
Exemplar 2
Leroy has one quarter, one dime, one nickel, and one penny. Two of the coins are in his left pocket and the other
two coins are in his right pocket. The coins have been randomly placed in the two pockets.
Scorer Comments:
These responses contained evidence that there was more than 1 possible combination of coins but the probability
is incorrect.
52| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
53| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
54| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics - Grade 8
55| Page
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics,
National Assessment of Educational Progress (NAEP), 2009 Mathematics Assessment.
NAEP Mathematics
Grade 8
Jorea M. Marple, Ed.D.
State Superintendent of Schools