NAEP Mathematics
Grade 4
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 4
Table of Contents
Sample Assessment.................................................................................................... 3
Framework Overview.............................................................................................. 19
Individual Item Analysis.......................................................................................... 21
1 | 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 4
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 4
These pieces would be printed on card stock paper. Prior to the assessment, the shapes would be separated and
placed in small zip-closure baggie.
Fourth grade students would see the following directions for this block of questions. “With this test booklet you
will receive a packet 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 4
Students are expected to answer these 15 questions in 25 minutes.
Directions for students:
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 packet of pieces labeled R, T, and X. You will use these
pieces in any way or flip them over. You may use drawings to help explain your answers.
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 Mathematics - Grade 4
Question 1-6 refers to pieces R, T and X.
Please remove the pieces from your packet and put them on your desk.
You can cover the piece labeled R with two of the pieces labeled T.
1. How many of the pieces labeled X are needed to cover the piece labeled R?
A. Two
B. Three
C. Four
D. Six
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 Mathematics - Grade 4
You will need the piece labeled X to answer this question.
2.Which word best describes how to move the piece labeled X from position 1 to position 2?
A.Flip
B.Fold
C.Slide
D.Turn
7 | 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 4
You will need four pieces labeled R and two pieces labeled T to answer this question.
3.Use these pieces to cover the figure below.
Draw the lines to show where the pieces meet.
Label the pieces on the figure.
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 4
You will need two pieces labeled X to answer this question.
4.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.
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 4
You will need one piece labeled X, one piece labeled T, and one piece labeled R to answer this
question.
5.Which of the pieces has an angle greater than a right angle?
A. Only
B. Only
C. Only
D. Both
10 | 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 4
You will need the pieces labeled T and X to answer this question.
6.Kylena made a design from the pieces and called it a "shy dog." Each dog design used 1 piece
labeled T and 2 pieces labeled X. It looked like this.
How many of each of the pieces would she need to make 26 shy dog designs?
Piece T ____________________
Piece X ____________________
If Kylena had only 11 pieces labeled T and only 15 pieces labeled X, how many shy dog designs
could she make?
Answer: ___________________
Use drawings, words, or numbers to explain how you found the number of shy dog designs she
could make.
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 4
If you need more room for your work, use the space below.
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 4
You may now put your packet of pieces away.
7.What number should be put in the box to make the number sentence above true?
Answer: _________________________
8.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: _________________________
13 | 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 4
9.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
10.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
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 4
11.Which picture shows that
is the same as
A.
B.
C.
D. 12.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.
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 4
13.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.
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 4
14.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¢.
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 4
15.Jorge left some numbers off the number line below. Fill in the numbers that should go in A, B,
and C.
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 4
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 4
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 constructedresponse items. 50% of the testing time is expected to be spent of multiple-choice items and
the other 50% on the constructed-response 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 4
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.
1. Geometry
West Virginia
National Public
A
10%
11%
B
4%
6%
C*
79%
77%
D
5%
4%
Omitted
2%
2%
How many of the pieces labeled X are needed to cover the piece labeled R?
A.Two
B.Three
C.Four
D.
Six
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 4
2.Geometry
West Virginia
National Public
A
15%
15%
B
3%
3%
C*
74%
74%
D
6%
8%
Omitted
1%
1%
Which word best describes how to move the
piece labeled X from position 1 to position 2 ?
A. Flip
B. Fold
C. Slide
D. Turn
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 4
3. 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.
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 4
Scoring Rubric
Sample Correct Responses:
Score & Description
Correct
Correct response
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
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 4
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.
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.
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 4
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.
26 | 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 4
4. 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.
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 4
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
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
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 4
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 that were parallel.
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 4
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.
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.
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 4
5. 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 X
B. Only R
C. Only T
D. Both R and T
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 4
6. Number Properties and Operations
West Virginia
National Public
Incorrect
56%
47%
Minimal
27%
28%
Partial
6%
9%
Satisfactory
8%
10%
Extended
1%
4%
Omitted
2%
3%
Off Task
Rounds to Zero
Rounds to Zero
Kylena made a design from the pieces and called it a "shy dog." Each dog design used 1 piece
labeled T and 2 pieces labeled X. It looked like this.
How many of each of the pieces would she need to make 26 shy dog designs?
Piece T ____________________
Piece X ____________________
If Kylena had only 11 pieces labeled T and only 15 pieces labeled X, how many shy dog designs
could she make?
Answer: ___________________
Use drawings, words, or numbers to explain how you found the number of shy dog designs she
could make.
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 4
Scoring Rubric
Sample Correct Responses:
Part A:
Piece T - 26
Piece X - 52
Part B:
7 (accept 7R1)
Explanation:
Kylena could make 7 shy dogs with the pieces she has. She needs 2 X's for each dog.
15 ÷ 2 = 7.5 so there are only enough X's for 7.
There are enough T's for more than 7.
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 4
Score & Description
Extended
Correct response
Satisfactory
Both parts correct, but explanation is incomplete.
OR
Has 52 for piece X but piece T is incorrect and has 7 for part B and explanation is completely
correct.
OR
Part A completely correct and explanation completely correct but does not answer 7 for part B.
Partial
Part A is completely correct and there is some correct work in the explanation, but does not have
7 on answer line.
OR
Shows three answers 26, 52, and 7 with no explanation.
OR
Part A is incorrect and part B is correct and explanation is completely correct.
Minimal
Has part A correct
OR
Answers 7 for part B with no explanation, incorrect explanation or incomplete explanation.
OR
Answers 52 for piece X (and number for piece T is incorrect or missing).
OR
Explanation completely correct with no other correct work.
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 4
Extended - Student Response
Exemplar 1
Kylena made a design from the pieces and called it a "shy dog." Each dog design used 1 piece
labeled T and 2 pieces labeled X. It looked like this.
How many of each of the pieces would she need to make 26 shy dog designs?
Piece T ____________________
Piece X ____________________
If Kylena had only 11 pieces labeled T and only 15 pieces labeled X, how many shy dog designs
could she make?
Answer: ___________________
Use drawings, words, or numbers to explain how you found the number of shy dog designs she
could make.
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 4
Exemplar 2
Kylena made a design from the pieces and called it a "shy dog." Each dog design used 1 piece
labeled T and 2 pieces labeled X. It looked like this.
How many of each of the pieces would she need to make 26 shy dog designs?
Piece T ____________________
Piece X ____________________
If Kylena had only 11 pieces labeled T and only 15 pieces labeled X, how many shy dog designs
could she make?
Answer: ___________________
Use drawings, words, or numbers to explain how you found the number of shy dog designs she
could make.
Scorer Comments:
These responses had the correct number of Piece T and the correct number of Piece X. They
also had the correct answer of 7 for the number of shy dog designs that could be made, and
provided a complete explanation.
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 4
Satisfactory - Student Response
Exemplar 1
Kylena made a design from the pieces and called it a "shy dog." Each dog design used 1 piece
labeled T and 2 pieces labeled X. It looked like this.
How many of each of the pieces would she need to make 26 shy dog designs?
Piece T ____________________
Piece X ____________________
If Kylena had only 11 pieces labeled T and only 15 pieces labeled X, how many shy dog designs
could she make?
Answer: ___________________
Use drawings, words, or numbers to explain how you found the number of shy dog designs she
could make.
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 4
Exemplar 2
Kylena made a design from the pieces and called it a "shy dog." Each dog design used 1 piece
labeled T and 2 pieces labeled X. It looked like this.
How many of each of the pieces would she need to make 26 shy dog designs?
Piece T ____________________
Piece X ____________________
If Kylena had only 11 pieces labeled T and only 15 pieces labeled X, how many shy dog designs
could she make?
Answer: ___________________
Use drawings, words, or numbers to explain how you found the number of shy dog designs she
could make.
Scorer Comments:
These responses had the correct number of pieces for both T and X and the correct number of shy
dog designs that could be made, but they had incomplete explanations.
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 4
Partial - Student Response
Exemplar 1
Kylena made a design from the pieces and called it a "shy dog." Each dog design used 1 piece
labeled T and 2 pieces labeled X. It looked like this.
How many of each of the pieces would she need to make 26 shy dog designs?
Piece T ____________________
Piece X ____________________
If Kylena had only 11 pieces labeled T and only 15 pieces labeled X, how many shy dog designs
could she make?
Answer: ___________________
Use drawings, words, or numbers to explain how you found the number of shy dog designs she
could make.
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 4
Exemplar 2
Kylena made a design from the pieces and called it a "shy dog." Each dog design used 1 piece
labeled T and 2 pieces labeled X. It looked like this.
How many of each of the pieces would she need to make 26 shy dog designs?
Piece T ____________________
Piece X ____________________
If Kylena had only 11 pieces labeled T and only 15 pieces labeled X, how many shy dog designs
could she make?
Answer: ___________________
Use drawings, words, or numbers to explain how you found the number of shy dog designs she
could make.
Scorer Comments:
These responses had the correct number of pieces for both T and X and some correct work in the
explanation, but they did not have the correct number of shy dog designs that could be made.
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 4
Minimal - Student Response
Exemplar 1
Kylena made a design from the pieces and called it a "shy dog." Each dog design used 1 piece
labeled T and 2 pieces labeled X. It looked like this.
How many of each of the pieces would she need to make 26 shy dog designs?
Piece T ____________________
Piece X ____________________
If Kylena had only 11 pieces labeled T and only 15 pieces labeled X, how many shy dog designs
could she make?
Answer: ___________________
Use drawings, words, or numbers to explain how you found the number of shy dog designs she
could make.
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 4
Exemplar 2
Kylena made a design from the pieces and called it a "shy dog." Each dog design used 1 piece
labeled T and 2 pieces labeled X. It looked like this.
How many of each of the pieces would she need to make 26 shy dog designs?
Piece T ____________________
Piece X ____________________
If Kylena had only 11 pieces labeled T and only 15 pieces labeled X, how many shy dog designs
could she make?
Answer: ___________________
Use drawings, words, or numbers to explain how you found the number of shy dog designs she
could make.
Scorer Comments:
These responses had the correct number of pieces for both T and X only.
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 4
7. 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
Score & Description
Correct
Correct response
29
OR
29 − 8 = 21 OR
29 in the box and response area blank.
Incorrect
Incorrect response
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 4
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
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 Rubric
Score & Description
Correct
Correct response: 642
Incorrect
Incorrect response
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 4
9. 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
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 4
10.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
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 4
11.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. 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 4
12.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
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
Sample Correct Responses
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
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 4
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.
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 4
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.
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 4
13.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
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
should it be taken out of the oven?
hours to cook, at what time
A. 12:15 p.m.
B. 12:45 p.m.
C. 1:15 p.m.
D. 1:45 p.m.
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 4
14.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
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¢.
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 4
Scoring Rubric
Score & Description
Correct
Gives one or more correct solutions. Samples given below:
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
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 4
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.
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 4
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.
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 4
15.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
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.
56 | 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 4
Scoring Rubric
Score & Description
Correct
Correct response
Sample Correct Responses:
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
57 | 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 4
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.
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.
58 | 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 4
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.
59 | 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 4
60 | 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 4
61 | 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 4
Jorea M. Marple, Ed.D.
State Superintendent of Schools