naep mathematics grade 4 - west virginia department of...

NAEP MathematicsGrade 4

Sample Assessment Block

West Virginia Department of Education

West Virginia Board of education

2011-2012

L. Wade Linger Jr., PresidentGayle C. Manchin, Vice President

Robert W. Dunlevy, Secretary

Michael I. Green, MemberPriscilla M. Haden, MemberLloyd G. Jackson II, MemberLowell E. Johnson, MemberJenny N. Phillips, MemberWilliam M. White, Member

Brian E. Noland, Ex OfficioChancellor

West Virginia Higher Education Policy Commission

James L. Skidmore, Ex OfficioChancellor

West Virginia Council for Community and Technical College Education

Jorea M. Marple, Ex OfficioState Superintendent of Schools

West Virginia Department of Education

Sample Assessment .....................................................................................................................3

Framework Overview ...............................................................................................................15

Individual Item Analysis ...........................................................................................................17

Table of Contents

NAEP Mathematics - Grade 4

Students are expected to answer the following 16 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.


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.



1. 301

– 75

A. 226

B. 235

C. 236

D. 374



2. What number does n represent in the table?

A. 2

B. 3

C. 4

D. 5



3. Michelle has a container with 3 quarts of juice. She pours 1 cup of juice for each person. At most, how many people can she serve? (1 quart = 4 cups)

A. 4

B. 7

C. 8

D. 12

• Fred planted 8 trees.

• Yolanda planted 12 trees

4. Make a pictograph of the information above. Use to represent 2 trees

NAEP Reading - Grade 8


5. One student will be chosen at random from the list above. What is the probability that the student's name begins with the letter P?

A. 1 out of 3

B. 1 out of 10

C. 3 out of 7

D. 3 out of 10



6. It takes Ms. Wylie 15 minutes to drive from her house to the store. Which is the best estimate of the distance from her house to the store?

A. 5 feet

B. 5 miles

C. 20 feet

D. 200 miles

7. On the number line, what number does P represent?

A.

B.

C. 1

D. 1



8. Kiara set her beads on a table to make a repeating pattern. Some of the beads rolled off the table.

Here is what was left.

Which of the following should Kiara use to replace the missing beads in the pattern?

A.

B.

C.

D.



9. Which figure has the greatest area?

A. A

B. B

C. C

D. D

10. What is the shape of the shaded figure inside the star?

A. Hexagon

B. Pentagon

C. Quadrilateral

D. Triangle



11. Sam did the following problems.

2 + 1 = 3

6 + 1 = 7

Sam concluded that when he adds 1 to any whole number, his answer will always be odd.

Is Sam correct? __________

Explain your answer.



12. Divide:

A. 85 R1

B. 95 R1

C. 96

D. 135 R1



13. A pattern of dots is shown above. How many dots would be in the 6th picture?

Answer: ________________

Explain how you found your answer.


14. Emily needs to measure the length of a table. She has a dollar bill that is about 6 inches long. It fits, end to end, 10 times along the length of the table. Which is the best estimate for the length of the table?

A. 5 feet

B. 6 feet

C. 10 feet

D. 12 feet

15. Which fraction has a value closest to ?

A.

B.

C.

D.



16. On the grid below, plot the points that have coordinates (B, 1), (B, 3), and (D, 5).

Plot 3 more points on the grid so that when you connect all 6 points you will make a rectangle.

List the coordinates for the 3 new points. _______ _______ _______ Connect the 6 points to show your rectangle.



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 toNumber Properties and Operations Computation

Understanding of number conceptsMeasurement Use of instruments

Application of processesConcepts of area and volume

Geometry Spatial reasoningApplying geometric properties

Data Analysis, Statistics, and Probability Graphical displayStatistics

Algebra Representationsrelationships

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 12Number Properties and Operations 40% 20% 10%Measurement 20% 15%

30%Geometry 15% 20%Data Analysis, Statistics, and Probability 10% 15% 25%Algebra 15% 30% 35%



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 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.



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. Number Properties and Operations

West Virginia National PublicA* 59% 67%B 6% 6%C 15% 14%D 18% 12%

Omitted 2% 2%

301 – 75

A. 226B. 235C. 236D. 374



2. Algebra

West Virginia National PublicA 4% 4%B* 81% 83%C 5% 4%D 10% 9%

Omitted Rounds to Zero 1%

What number does n represent in the table?

A. 2B. 3C. 4D. 5



3. Measurement

West Virginia National PublicA 23% 20%B 7% 6%C 9% 7%

D* 60% 67%Omitted 1% 1%

Michelle has a container with 3 quarts of juice. She pours 1 cup of juice for each person. At most, how many people can she serve? (1 quart = 4 cups)

A. 4B. 7C. 8D. 12

4. Data Analysis and Probability

West Virginia National PublicIncorrect 28% 24%Correct 71% 75%Omitted 1% 2%Off Task Rounds to Zero Rounds to Zero

• Fred planted 8 trees. • Yolanda planted 12 trees

Make a pictograph of the information above. Use to represent 2 trees



Scoring Rubric

Score & DescriptionCorrectCorrect response

Sample Correct Responses:

Fred: 4 treesYolanda: 6 treesMust show some kind of pictograph.

IncorrectIncorrect response

Correct - Student ResponseExemplar 1




Exemplar 2


Scorer Comments:These responses correctly drew 4 trees for Fred and 6 trees for Yolanda.



5. Data Analysis and Probability


D* 64% 66%Omitted Rounds to Zero 1%

One student will be chosen at random from the list above. What is the probability that the student's name begins with the letter P?

A. 1 out of 3B. 1 out of 10C. 3 out of 7D. 3 out of 10



6. Measurement


Omitted Rounds to Zero 1%

It takes Ms. Wylie 15 minutes to drive from her house to the store. Which is the best estimate of the distance from her house to the store?

A. 5 feetB. 5 milesC. 20 feetD. 200 miles





D* 40% 46%Omitted Rounds to Zero 1%

On the number line, what number does P represent?

A.

B.

C. 1

D. 1



8. Algebra

West Virginia National PublicA 12% 14%B 6% 6%C* 72% 71%D 9% 8%

Omitted 1% 1%

Kiara set her beads on a table to make a repeating pattern. Some of the beads rolled off the table. Here is what was left.

Which of the following should Kiara use to replace the missing beads in the pattern?

A. B.

C.

D.



9. Measurement


Omitted 1% 1%

Which figure has the greatest area?A. AB. BC. CD. D



10. Geometry

West Virginia National PublicA 27% 23%B* 61% 69%C 11% 7%D Rounds to Zero Rounds to Zero

Omitted 1% 1%

What is the shape of the shaded figure inside the star?A. HexagonB. PentagonC. QuadrilateralD. Triangle




West Virginia National PublicIncorrect 62% 58%Correct 37% 41%Omitted 1% 1%Off Task 1% Rounds to Zero

Sam did the following problems. 2 + 1 = 3 6 + 1 = 7Sam concluded that when he adds 1 to any whole number, his answer will always be odd. Is Sam correct? __________ Explain your answer.

Scoring Rubric

Score & DescriptionCorrectCorrect answer

Sample Correct Responses:Provides a counterexample or an explanation such as adding 1 to an odd number gives an even number.




Correct - Student Response

Exemplar 1Sam did the following problems.

Exemplar 2Sam did the following problems.

Scorer Comments:These responses correctly stated that Sam is not correct and provided a correct explanation.





Omitted 2% 2%

Divide: A. 85 R1B. 95 R1C. 96D. 135 R1

13. AlgebraWest Virginia National Public

Incorrect 50% 43%Partial 1 28% 34%Partial 2 8% 7%Correct 13% 15%Omitted 1% 1%Off Task Rounds to Zero Rounds to Zero

A pattern of dots is shown above. How many dots would be in the 6th picture?

Answer: ________________

Explain how you found your answer.



Scoring Rubric

Score & Description

CorrectCorrect response: 21 dots with a correct explanation.

Sample Correct Responses:21 dots. The 5th picture would have 15 dots, 5 more than the 4th. The 6th picture would have 21 dots, 6 more than the 5th. An acceptable explanation may be given by drawings, words, and/or numbers.Pictures drawn by the students need to follow the pattern of dots shown in the first four pictures in order to be considered correctly drawn. Just having the correct number of dots (but not following the pattern) is not sufficient to earn full credit.

There are two types of correct explanations.

• First type: The geometric explanation. For this, the student has presented correct drawings for the 5th and 6th pictures, the numbers 15 and 21, and a correct supporting explanation.• Second type: The numerical explanation. For this, the student has not presented any drawings for the 5th and 6th pictures, but does have the correct numbers (15 and 21) with a correct supporting explanation like "It goes +2 + 3 + 4 + 5 + 6."

Partial 2Partially correct response21 dots with no explanation, a partially correct explanation, or a partially complete explanation.

Examples of partially correct or partially complete explanations include the following:• You add one more dot to the bottom.• You add 1 each time.• It increased by 1 each time.• I counted the numbers in order.

Partial 1Partially correct responseDoes not get 21 but has a correct explanation.

Examples of correct explanations include the following:• Because the bottom keeps changing to the next number• It goes + 2 + 3 + 4 + 5 + 6.



Correct - Student Response

Exemplar 1A pattern of dots is shown above. How many dots would be in the 6th picture? Answer: ________________ Explain how you found your answer.


Scorer Comments:These responses had the correct answer, the correct drawings for the 5th and 6th picture, and a correct explanation.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.


Partial 2 - Student Response



Scorer Comments:These responses had the correct answer and the correct number of dots on the answer line but only a partial explanation or no explanation at all.



Partial 1 - Student Response





Scorer Comments:These responses did not get 21 for the answer but had the correct numbers for the 5th and 6th picture. The explanation was partially correct.



Omitted 2% 1%

Emily needs to measure the length of a table. She has a dollar bill that is about 6 inches long. It fits, end to end, 10 times along the length of the table. Which is the best estimate for the length of the table?A. 5 feetB. 6 feetC. 10 feetD. 12 feet





Omitted 2% 2%

Which fraction has a value closest to ?

A.

B.

C.

D.



16. Geometry

West Virginia National PublicIncorrect 21% 24%Minimal 36% 32%Partial 5% 3%

Satisfactory 11% 10%Extended 24% 27%Omitted 3% 3%Off Task Rounds to Zero Rounds to Zero

On the grid below, plot the points that have coordinates (B, 1), (B, 3), and (D, 5).

Plot 3 more points on the grid so that when you connect all 6 points you will make a rectangle.

List the coordinates for the 3 new points. _______ _______ _______ Connect the 6 points to show your rectangle.



Scoring Rubric

Score & Description

ExtendedCorrect response

Sample Correct Responses:• Correctly plots the points (B, 1), (B, 3), and (D, 5)• Correctly plots 3 other points that form a rectangle and gives their coordinates• Connects the dots to form a rectangle

SatisfactoryPlots 3 given points and plots 3 new points to form a rectangle, gives correct coordinates of new points, but does not draw the rectangle.

OR Draws rectangle that contains the 3 given points and gives coordinates of 3 other points on the rectangle but one point is not clearly plotted.

OR Plots 3 given points, plots 3 new points, draws rectangle, gives coordinates for 3 new points but one of the coordinates given does not match the point plotted. (e.g., gives (D, 2) instead of (D, 3)).

PartialPlots 3 given points and plots 2 or 3 new points that clearly form a rectangle; gives correct coordinates of 1 or 2 of the new points; may or may not draw the rectangle correctly.

OR Plots 3 given points correctly and gives coordinates of 3 new points that clearly form a rectangle (but does not plot the new points).

OR Plots 3 given points and 3 new points and plots/identifies additional point(s) on rectangle.

MinimalPlots 3 points clearly (either given points or new points or a combination).

OR Plots 2 of the given points correctly and draws a rectangle using those 2 points. Points must be clearly marked.

OR Lists coordinates for 3 new points that would clearly form a rectangle (e.g., (D, 1), (D, 3), (B, 5)) when connected; points may not be plotted.

OR Draws a rectangle that includes the 3 given points, but points may not be clearly plotted.




Extended - Student Response

Exemplar 1On the grid below, plot the points that have coordinates (B, 1), (B, 3), and (D, 5).


Scorer Comments:These responses correctly plotted the 3 given points, correctly plotted and listed 3 other points, and correctly connected the points to form a rectangle.



Satisfactory - Student Response



Scorer Comments:These responses correctly plotted both the 3 given points and the 3 other points and gave the correct coordinates, but they did not connect the points into a rectangle.



Partial - Student Response



Scorer Comments:These responses correctly plotted the 3 given points. The first response correctly listed the coordinates of the other 3 points but did not plot them on the grid to form a rectangle. The second response plotted the other 3 points on the grid but did not correctly list their coordinates.



Minimal - Student Response



Scorer Comments:These responses correctly plotted only the 3 given points.


NAEP MathematicsGrade 4

Jorea M. Marple, Ed.D.State Superintendent of Schools

naep mathematics grade 4 - west virginia department of...

Documents