1
NAEP 2009 Math – Grade 4 Released Items
Math
2009
Grade 4 Released Items
Additional materials [1]
Content: Geometry / Type / Grade / DifficultyDescription: Determine how many given pieces cover a shape / MC / 4 / Easy
Question 1 refers to additional materials [1]
The following question 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.
- How many of the pieces labeled X are needed to cover the piece labeled R?
- Two
- Three
- Four
- Six
2009 Percentage of 4th Grade Students in Each Response Category
Public Schools / Choice A / Choice B / Choice C* / Choice D / Omitted
National / 11% / 6% / 77% / 4% / 2%
Delaware / 9% / 4% / 80% / 4% / 2%
Content: Geometry / Type / Grade / Difficulty
Description: Recognize type of transformation from picture / MC / 4 / Easy
Question 2 refers to additional materials [1]
The following question refers to pieces R, T and X.
You will need the piece labeled X to answer this question.
- Which word best describes how to move the piece labeled X from position 1 to position 2?
- Flip
- Fold
- Slide
- Turn
2009 Percentage of 4th Grade Students in Each Response Category
Public Schools / Choice A / Choice B / Choice C* / Choice D / Omitted
National / 15% / 3% / 74% / 8% / 1%
Delaware / 18% / 2% / 70% / 8% / 3%
Content: Geometry / Type / Grade / Difficulty
Description: Arrange given pieces to cover a figure / SRC / 4 / Easy
The following question refers to pieces R, T and X.
You will need four pieces labeled R and two pieces labeled T to answer this question.
- Use these pieces to cover the figure below.
Draw the lines to show where the pieces meet.
Label the pieces on the figure.
Public Schools / Incorrect / Partial / Correct / Omitted / Off task
National / 14% / 40% / 41% / 5% / #
Delaware / 10% / 36% / 50% / 3% / #
Scoring Guide
Solution:
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
Correct - Student Responses
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Assessment.
Duncan G. SmithDelaware Department of EducationMarch 5, 2011
1
NAEP 2009 Math – Grade 4 Released Items
Student response #1
Use these pieces to cover the figure below.
Draw the lines to show where the pieces meet.
Label the pieces on the figure.
Student response #2
Use these pieces to cover the figure below.
Draw the lines to show where the pieces meet.
Label the pieces on the figure.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Assessment.
Duncan G. SmithDelaware Department of EducationMarch 5, 2011
1
NAEP 2009 Math – Grade 4 Released Items
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 Responses
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Assessment.
Duncan G. SmithDelaware Department of EducationMarch 5, 2011
1
NAEP 2009 Math – Grade 4 Released Items
Student response #1
Use these pieces to cover the figure below.
Draw the lines to show where the pieces meet.
Label the pieces on the figure.
Student response #2
Use these pieces to cover the figure below.
Draw the lines to show where the pieces meet.
Label the pieces on the figure.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Assessment.
Duncan G. SmithDelaware Department of EducationMarch 5, 2011
1
NAEP 2009 Math – Grade 4 Released Items
Scorer Comments:
Theseresponses 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.
Incorrect - Student Responses
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Assessment.
Duncan G. SmithDelaware Department of EducationMarch 5, 2011
1
NAEP 2009 Math – Grade 4 Released Items
Student response #1
Use these pieces to cover the figure below.
Draw the lines to show where the pieces meet.
Label the pieces on the figure.
Student response #2
Use these pieces to cover the figure below.
Draw the lines to show where the pieces meet.
Label the pieces on the figure.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Assessment.
Duncan G. SmithDelaware Department of EducationMarch 5, 2011
1
NAEP 2009 Math – Grade 4 Released Items
Scorer Comments:
These responsesused anincorrect number of pieces.
Content: Geometry / Type / Grade / DifficultyDescription: Use given pieces to make shape with certain properties / SCR / 4 / Medium
- 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.
Public Schools / Incorrect / Partial / Correct / Omitted / Off task
National / 29% / 44% / 21% / 5% / #
Delaware / 21% / 53% / 22% / 3% / #
Scoring Guide
Solution:
Score & Description
Correct
Correct response
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
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Assessment.
Duncan G. SmithDelaware Department of EducationMarch 5, 2011
1
NAEP 2009 Math – Grade 4 Released Items
Correct - Student Responses
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Assessment.
Duncan G. SmithDelaware Department of EducationMarch 5, 2011
1
NAEP 2009 Math – Grade 4 Released Items
Student response #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.
Student response #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.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Assessment.
Duncan G. SmithDelaware Department of EducationMarch 5, 2011
1
NAEP 2009 Math – Grade 4 Released Items
Scorer Comments:
These responses correctly showed a four-sided figure with no pieces that overlapped and no two sides that were parallel.
Partial - Student Responses
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Assessment.
Duncan G. SmithDelaware Department of EducationMarch 5, 2011
1
NAEP 2009 Math – Grade 4 Released Items
Student response #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.
Student response #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.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Assessment.
Duncan G. SmithDelaware Department of EducationMarch 5, 2011
1
NAEP 2009 Math – Grade 4 Released Items
Scorer Comments:
These responses showed partially correct figures where each had a line drawn where the two pieces met.
Incorrect - Student Responses
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Assessment.
Duncan G. SmithDelaware Department of EducationMarch 5, 2011
1
NAEP 2009 Math – Grade 4 Released Items
Student response #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.
Student response #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.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Assessment.
Duncan G. SmithDelaware Department of EducationMarch 5, 2011
1
NAEP 2009 Math – Grade 4 Released Items
Scorer Comments:
These responses were incorrect. Piece Xwas not used to make the shapes.
Content: Geometry / Type / Grade / DifficultyDescription: Identify given piece with angle greater than 90 degrees / MC / 4 / Medium
Question 5 refers to additional materials [1]
The following question refers to pieces R, T and X.
You will need one piece labeled X, one piece labeled T, and one piece labeled R to answer this question.
- Which of the pieces has an angle greater than a right angle?
- Only X
- Only R
- Only T
- Both R and T
2009 Percentage of 4th Grade Students in Each Response Category
Public Schools / Choice A / Choice B* / Choice C / Choice D / Omitted
National / 18% / 44% / 6% / 30% / 1%
Delaware / 17% / 45% / 4% / 31% / 3%
Content: Geometry / Type / Grade / Difficulty
Description: Make a design using given shapes and solve problem / ECR / 4 / Hard
Question 6 refers to additional materials [1]
The following question refers to pieces R, T and X.
You will need the pieces labeled T and X to answer this question.
- 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.
Public Schools / Incorrect / Minimal / Partial / Satisfactory / Extended / Omitted / Off task
National / 47% / 28% / 9% / 10% / 4% / 3% / #
Delaware / 44% / 27% / 7% / 12% / 6% / 3% / #
Scoring Guide
Solution:
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.
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
Extended - Student Responses
Student Response #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.
Student response #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.
Satisfactory - Student Responses
Student response #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.
Student response #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.
Partial - Student Response
Student response #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.
Student response #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.
Minimal - Student Response
Student response #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.
Student response #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.