




















































Scoring Guide 
Solution: Both bars drawn correctly. ("Line" bars are acceptable.)

Score & Description  
 

In this question the student needed to read information presented in a table and complete a bar graph representing the given information. The student was first required to select the appropriate values from the table. Finally, the student needed to determine the correct height for the bars representing scores of 90 and 95 and draw the bars on the graph. 
Correct  Student Response 
1 
Use the information in the table above to complete the bar graph below. 
Incorrect  Student Response 
1 
Use the information in the table above to complete the bar graph below. 
Scoring Guide 
Solution: 
Score & Description  
 

In this question the student needed to fill in missing entries in a pattern of the letters "A" and "B." The student was told that the pattern repeats in groups of 3, and enough information was given for the student to find the one correct sequence. 
Correct  Student Response 
2 
Peter wrote down a pattern of A's and B's that repeats in groups of 3. Here is the beginning of his pattern with some of the letters erased. Fill in the missing letters. 
Incorrect  Student Response 
2 
Peter wrote down a pattern of A's and B's that repeats in groups of 3. Here is the beginning of his pattern with some of the letters erased. Fill in the missing letters. 
Scoring Guide 
Solution: Dot correctly placed or student labels "3/4" where the dot should be placed OR

Score & Description  
 

In this question the student needed to locate the position of 3/4 on a number line. The number line was marked from 0 to 1 in increments of 1/8, with the point 1/2 marked for reference. 
Correct  Student Response 
3 
On the portion of the number line below, a dot shows where 1/2 is. Use another dot to show where 3/4 is. 
Incorrect  Student Response 
3 
On the portion of the number line below, a dot shows where 1/2 is. Use another dot to show where 3/4 is. 
Scoring Guide 
Solution: 2 1/2 inches OR 2 1/2" OR 2 1/2 in OR 2 1/2 OR 2.5 OR 10/4 
Score & Description  
 
 
 

In this question the student needed to determine the
length of a toothpick displayed above a portion of a ruler. One end of the
toothpick was above the 8inch mark on the ruler, and the other end of the
toothpick was located above the 10 1/2inch mark on the ruler. The student
could subtract to find the length or else count the number of inches from
8 to 10 1/2.
*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct  Student Response 
4 
What is the length of the toothpick in the figure above? 
Incorrect #3  Student Response 
4 
What is the length of the toothpick in the figure above? 
Incorrect #2  Student Response 
4 
What is the length of the toothpick in the figure above? 
Incorrect #1  Student Response 
4 
What is the length of the toothpick in the figure above? 
Scoring Guide 
Solution: Any obtuse angle, such as:
OR

Score & Description  
 
 

In this question the student was asked to draw an angle
that is larger than 90° (an obtuse angle). Full credit was earned for a
drawing of either an obtuse angle or a closed figure containing an obtuse
angle.
*The use of more than one correct category in this question enabled NAEP to gather data on different ways students responded correctly to this question. Any one of these responses that fell into one of these correct categories earned full credit. 
Correct #1  Student Response 
5 
In the space below, draw an angle that is larger than 90°. 
Correct #2  Student Response 
5 
In the space below, draw an angle that is larger than 90°. 
Incorrect  Student Response 
5 
In the space below, draw an angle that is larger than 90°. 
Scoring Guide 
Solution: 
Score & Description  
 
 

In this question the student needed to demonstrate an
understanding of the ordering of real numbers by graphing an interval—not
individual points—on the number line.
*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct  Student Response 
6 
On the number line below, shade the part of the line that shows the set of all numbers greater than or equal to 1 and less than or equal to 3. 
Incorrect #2  Student Response 
6 
On the number line below, shade the part of the line that shows the set of all numbers greater than or equal to 1 and less than or equal to 3. 
Incorrect #1  Student Response 
6 
On the number line below, shade the part of the line that shows the set of all numbers greater than or equal to 1 and less than or equal to 3. 
Scoring Guide 
Solution: A correct pair may be repeated as long as all 9 correct pairs are present and no incorrect pairs are included.

Score & Description  
 
 
 
 
 

In this question the student needed to list all 9
possible combinations of drawing 3 chips from a box with replacement.
Determining a sample space is a prerequisite skill for the study of
probability.
*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct  Student Response 
7 
A box contains 3 chips numbered 1 through 3. One chip will
be taken at random from the box and then put back into the box. Then a
second chip will be taken from the box.
In the space provided below, list all possible pairs of chips. 
Incorrect #5  Student Response 
7 
A box contains 3 chips numbered 1 through 3. One chip will
be taken at random from the box and then put back into the box. Then a
second chip will be taken from the box.
In the space provided below, list all possible pairs of chips. 
Incorrect #4  Student Response 
7 
A box contains 3 chips numbered 1 through 3. One chip will
be taken at random from the box and then put back into the box. Then a
second chip will be taken from the box.
In the space provided below, list all possible pairs of chips. 
Incorrect #3  Student Response 
7 
A box contains 3 chips numbered 1 through 3. One chip will
be taken at random from the box and then put back into the box. Then a
second chip will be taken from the box.
In the space provided below, list all possible pairs of chips. 
Incorrect #2  Student Response 
7 
A box contains 3 chips numbered 1 through 3. One chip will
be taken at random from the box and then put back into the box. Then a
second chip will be taken from the box.
In the space provided below, list all possible pairs of chips. 
Incorrect #1  Student Response 
7 
A box contains 3 chips numbered 1 through 3. One chip will
be taken at random from the box and then put back into the box. Then a
second chip will be taken from the box.
In the space provided below, list all possible pairs of chips. 
Scoring Guide 
Solution: 6.5 or 6 1/2 
Score & Description  
 

In this question the student needed to read the weight of a can placed on a scale marked in increments of 1/2 unit. 
Correct  Student Response 
8 
According to the indicator on the scale above, what is the weight in ounces of the can of tuna on the scale? 
Incorrect  Student Response 
8 
According to the indicator on the scale above, what is the weight in ounces of the can of tuna on the scale? 
Scoring Guide 
Solution: A. Cheaper at Price Pleasers At Price Pleasers the stereo would be $80 after 2 weeks. OR Successive 10% reductions of the original price will yield greater savings than successive reductions of 10% of the reduced price. 
Score & Description  
 
 

In this question the student was asked to compare the sale price of a stereo, after 3 weeks, based on two different ways for reducing the price. In one store, the price was reduced each week by a fixed amount (10% of $100, or $10). In the other store the price was reduced each week by a varying amount (10% of the current price, which is less each week). To earn full credit, the student needed to indicate that the price would be less at the first store after 3 weeks and explain how the solution was obtained. Students were permitted to use a calculator. 
Correct  Student Response 
9 
One store, Price Pleasers, reduces the price each
week of a $100 stereo by 10 percent of the original price.
Another store, Bargains Plus, reduces the price each week of the same $100 stereo by 10 percent of the previous week's price. After 2 weeks, how will the prices at the two stores compare? 
Partial  Student Response 
9 
One store, Price Pleasers, reduces the price each
week of a $100 stereo by 10 percent of the original price.
Another store, Bargains Plus, reduces the price each week of the same $100 stereo by 10 percent of the previous week's price. After 2 weeks, how will the prices at the two stores compare? 
Incorrect  Student Response 
9 
One store, Price Pleasers, reduces the price each
week of a $100 stereo by 10 percent of the original price.
Another store, Bargains Plus, reduces the price each week of the same $100 stereo by 10 percent of the previous week's price. After 2 weeks, how will the prices at the two stores compare? 
Scoring Guide 
Solution: 69 
Score & Description  
 
 
 

In this question the student needed to find the average
of 11 test scores. Since only 5 different scores were given, the student
needed either to find a weighted average or include each score an
appropriate number of times in the computation. Students were permitted to
use a calculator.
*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct  Student Response 
10 
The table above shows the scores of a group of 11 students on a history test. What is the average (mean) score of the group to the nearest whole number? 
Incorrect #3  Student Response 
10 
The table above shows the scores of a group of 11 students on a history test. What is the average (mean) score of the group to the nearest whole number? 
Incorrect #2  Student Response 
10 
The table above shows the scores of a group of 11 students on a history test. What is the average (mean) score of the group to the nearest whole number? 
Incorrect #1  Student Response 
10 
The table above shows the scores of a group of 11 students on a history test. What is the average (mean) score of the group to the nearest whole number? 
Scoring Guide 
Solution: No. The opinions would likely be biased in favor of those who like baseball. NOTE: Answer may or may not have a reason for the bias, but it must, in some way, indicate that a bias could exist. 
Score & Description  
 
 

This question required the student to demonstrate an
understanding of sampling bias in the design of a survey.
*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct  Student Response 
11 
A survey is to be taken in a city to determine the most popular sport. Would sampling opinions at a baseball game be a good way to collect this data? Explain your answer. 
Incorrect #2  Student Response 
11 
A survey is to be taken in a city to determine the most popular sport. Would sampling opinions at a baseball game be a good way to collect this data? Explain your answer. 
Incorrect #1  Student Response 
11 
A survey is to be taken in a city to determine the most popular sport. Would sampling opinions at a baseball game be a good way to collect this data? Explain your answer. 
Scoring Guide 
Solution: 24 
Score & Description  
 

In this question the student needed to solve a long division problem, dividing a 2digit number into a 3digit number. 
Scoring Guide 
Solution: $525 or 525 
Score & Description  
 

In this question the student needed to apply multiplication to solve a word problem, multiplying $5.25 by 100. 
Correct  Student Response 
13 
Movie tickets cost $5.25 each. If 100 tickets were sold, how much money was collected? 
Incorrect  Student Response 
13 
Movie tickets cost $5.25 each. If 100 tickets were sold, how much money was collected? 
Scoring Guide 
Solution: 418 ÷ 11 = 38 per bus which is 3 more students than 35, or 3 more students would have to fit in each bus OR is 3 more students than can fit in a bus OR buses (must include .9) OR 11 × 35 is less than 418 
Score & Description  
 

In this question the student needed to apply multiplication or division to solve a word problem, and then interpret the answer in the context of the question. To earn full credit the student needed to explain either that there were not enough seats on 11 buses for 418 students or that 418 students would require more than 11 buses. 
Correct  Student Response 
14 
A high school orders 11 buses to transport 418 students. If
each bus can seat 35 students, will the number of buses ordered be enough
to provide a seat for each student?
()Yes ()No 
Incorrect  Student Response 
14 
A high school orders 11 buses to transport 418 students. If
each bus can seat 35 students, will the number of buses ordered be enough
to provide a seat for each student?
()Yes ()No 
Scoring Guide 
Solution: Triangles 1 and 2 may be interchanged. Triangles need not be labeled with numbers.

Score & Description  
 

In this question the student needed to demonstrate spatial visualization and reasoning skills to show how to rearrange (touching, but not overlapping) three given triangles to form a parallelogram. 
Correct  Student Response 
15 
Draw lines on the figure below to show how triangles 1, 2, and 3 can be rearranged without overlap to form this parallelogram. 
Incorrect  Student Response 
15 
Draw lines on the figure below to show how triangles 1, 2, and 3 can be rearranged without overlap to form this parallelogram. 
Scoring Guide 
Solution: Triangles 1 and 2 may be interchanged. Triangles need not be labeled with numbers. 
Score & Description  
 

In this question the student needed to demonstrate spatial visualization and reasoning skills to show how to rearrange (touching, but not overlapping) three given triangles to form a rectangle. 
Correct  Student Response 
16 
Draw lines on the figure below to show how triangles 1, 2, and 3 can be rearranged without overlap to form this rectangle. 
Incorrect  Student Response 
16 
Draw lines on the figure below to show how triangles 1, 2, and 3 can be rearranged without overlap to form this rectangle. 
Scoring Guide 
Solution: 8 hours. Graphical Solution: Extend both lines to the right until they intersect. Then read the horizontal coordinate of the point of intersection. Note: If lines are extended correctly until they intersect, this will serve as sufficient justification. No words are required in this situation. Algebraic Solution: 
Score & Description  
 
 

This question could be solved using either a numerical, graphical, or algebraic approach. Whatever solution path was selected required the student to recognize that the water in tank T is decreasing at a rate of 50 gallons per hour and the water in tank W is increasing at a rate of 25 gallons per hour. These rates could be used to determine when there are equal amounts of water in the two tanks by using any one of several methods, for example, by numerically comparing values for the amount of water in the tanks at different times, by extending the given graphs until they intersect, or by setting up and solving an equation. 
Correct  Student Response 
17 
Two large storage tanks, T and W, contain water. T starts losing water at the same time additional water starts flowing into W. The graph below shows the amount of water in each tank over a period of hours. 
Partial  Student Response 
17 
Two large storage tanks, T and W, contain water. T starts losing water at the same time additional water starts flowing into W. The graph below shows the amount of water in each tank over a period of hours. 
Incorrect  Student Response 
17 
Two large storage tanks, T and W, contain water. T starts losing water at the same time additional water starts flowing into W. The graph below shows the amount of water in each tank over a period of hours. 
Scoring Guide 
Solution: 6 miles east and 5 miles north of the tree 
Score & Description  
 
 

In this question, presented in context, the student
needed to determine the effect of horizontal and vertical translations on
a point in a coordinate plane.
*The use of more than one correct category in this question enabled NAEP to gather data on different ways students responded correctly to this question. Any one of these responses that fell into one of these correct categories earned full credit. 
Correct #1  Student Response 
18 
What is the position of the treasure chest with respect to the tree? 
Correct #2  Student Response 
18 
What is the position of the treasure chest with respect to the tree? 
Incorrect  Student Response 
18 
What is the position of the treasure chest with respect to the tree? 
Scoring Guide 
Solution: Note: This question is listed as a short constructedresponse question. It should be considered a multiplechoice question with multiple parts. A bag contains two red candies and one yellow candy. Kim takes out one candy and eats it, and then Jeff takes out one candy. For each sentence below, fill in the oval to indicate whether it is possible or not possible. 
Score & Description  
 
 
 
 

4 Right  Student Response 
19 
A bag contains two red candies and one yellow candy. Kim takes out one candy and eats it, and then Jeff takes out one candy. For each sentence below, fill in the oval to indicate whether it is possible or not possible. 
3 Right  Student Response 
19 
A bag contains two red candies and one yellow candy. Kim takes out one candy and eats it, and then Jeff takes out one candy. For each sentence below, fill in the oval to indicate whether it is possible or not possible. 
2 Right  Student Response 
19 
A bag contains two red candies and one yellow candy. Kim takes out one candy and eats it, and then Jeff takes out one candy. For each sentence below, fill in the oval to indicate whether it is possible or not possible. 
1 Right  Student Response 
19 
A bag contains two red candies and one yellow candy. Kim takes out one candy and eats it, and then Jeff takes out one candy. For each sentence below, fill in the oval to indicate whether it is possible or not possible. 
0 Right  Student Response 
19 
A bag contains two red candies and one yellow candy. Kim takes out one candy and eats it, and then Jeff takes out one candy. For each sentence below, fill in the oval to indicate whether it is possible or not possible. 
Scoring Guide 
Solution: 17 Scoring Guide In this question a student needed to demonstrate an understanding of diagonals of polygons. A diagonal of a polygon is a segment that joins two nonadjacent vertices.(A vertex is a common endpoint of two sides of the polygon). To answer the question it was expected that a student would observe that the number of diagonals from any vertex is 3 less than the number of sides. That is, from any vertex of a convex polygon a diagonal can be drawn to any of the other vertices of that polygon except the two adjacent vertices. For a 20sided polygon, the answer is 20  3 = 17. 
Score & Description  
 

Correct  Student Response 
20 
How many diagonals can be drawn from any vertex of a 20sided polygon? 
Incorrect  Student Response 
20 
How many diagonals can be drawn from any vertex of a 20sided polygon? 
Scoring Guide 
Solution: Between 6 and 7 Between 7 and 6 is also a correct answer. Scoring Guide This question involved the use of estimation skills by using a given unit of length to find the perimeter (distance around) of the 4sided figure. The correct answer is between 6 and 7 (or 7 and 6). There are different types of incorrect responses. If a student overestimated the perimeter as between 7 and 8, then a score of incorrect # 3 is earned. If a student underestimated the perimeter as between 5 and 6, then a score of incorrect # 2 is earned. Any other response is an incorrect # 1. 
Score & Description  
 
 
 

* The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of these incorrect categories earned no credit. 
Correct  Student Response 
21 
Use the unit of length below to estimate the perimeter of the figure shown. Between which two consecutive wholenumber units does the perimeter lie? 
Incorrect #3  Student Response 
21 
Use the unit of length below to estimate the perimeter of the figure shown. Between which two consecutive wholenumber units does the perimeter lie? 
Incorrect #2  Student Response 
21 
Use the unit of length below to estimate the perimeter of the figure shown. Between which two consecutive wholenumber units does the perimeter lie? 
Incorrect #1  Student Response 
21 
Use the unit of length below to estimate the perimeter of the figure shown. Between which two consecutive wholenumber units does the perimeter lie? 
Scoring Guide 
Solution: The explanation must include either one of the following diagrams; The diagram should include or illustrate the idea that B is halfway
between A and C. Scoring Guide In this question a student needed to reason about the possible positions of points on a line and present the conclusion in the form of a diagram. A correct response needed to show that B is halfway between A and C (or C and A). 
Score & Description  
 
 

* The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of these incorrect categories earned no credit. 
Correct  Student Response 
22 
Jaime knows the following facts about points A, B,
and C.
Is Jaime's conclusion correct? 
22 
Jaime knows the following facts about points A, B,
and C.
Is Jaime's conclusion correct? 
Incorrect #2  Student Response 
22 
Jaime knows the following facts about points A, B,
and C.
Is Jaime's conclusion correct? 
Incorrect #1  Student Response 
22 
Jaime knows the following facts about points A, B,
and C.
Is Jaime's conclusion correct? 
22 
Jaime knows the following facts about points A, B,
and C.
Is Jaime's conclusion correct? 
Scoring Guide 
Solution: N is a square (but P and Q are triangles.) OR N has four sides, (or vertices or points or angles), (but P and Q each have 3). OR All the sides of N are =, (but not so with P and Q). OR All the angles of N are = (or, all right angles), (not so with P and Q.) Must mention both P and Q or neither P nor Q plus N is a square or give other characteristics of N. 
Score & Description  
 
 

Note to scorers:
*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct  Student Response 
23 
Laura was asked to choose 1 of the 3 shapes N, P, and Q that is different from the other 2. Laura chose shape N. Explain how shape N is different from shapes P and Q. 
23 
Laura was asked to choose 1 of the 3 shapes N, P, and Q that is different from the other 2. Laura chose shape N. Explain how shape N is different from shapes P and Q. 
Incorrect #2  Student Response 
23 
Laura was asked to choose 1 of the 3 shapes N, P, and Q that is different from the other 2. Laura chose shape N. Explain how shape N is different from shapes P and Q. 
23 
Laura was asked to choose 1 of the 3 shapes N, P, and Q that is different from the other 2. Laura chose shape N. Explain how shape N is different from shapes P and Q. 
Incorrect #1  Student Response 
23 
Laura was asked to choose 1 of the 3 shapes N, P, and Q that is different from the other 2. Laura chose shape N. Explain how shape N is different from shapes P and Q. 
23 
Laura was asked to choose 1 of the 3 shapes N, P, and Q that is different from the other 2. Laura chose shape N. Explain how shape N is different from shapes P and Q. 
Scoring Guide 
Solution: The square may be tilted. Space between is acceptable. Scoring Guide In this question, a student needed to visualize how to form a square using two isosceles right triangles. 
Score & Description  
 

Correct  Student Response 
24 
You will need the 2 pieces labeled Q. Please find
those 2 pieces now.
Use the 2 pieces labeled Q to make a square. Trace the square and draw the line to show where the 2 pieces meet. 
24 
You will need the 2 pieces labeled Q. Please find
those 2 pieces now.
Use the 2 pieces labeled Q to make a square. Trace the square and draw the line to show where the 2 pieces meet. 
Incorrect  Student Response 
24 
You will need the 2 pieces labeled Q. Please find
those 2 pieces now.
Use the 2 pieces labeled Q to make a square. Trace the square and draw the line to show where the 2 pieces meet. 
24 
You will need the 2 pieces labeled Q. Please find
those 2 pieces now.
Use the 2 pieces labeled Q to make a square. Trace the square and draw the line to show where the 2 pieces meet. 
Scoring Guide 
Solution: Examples of correct response #1 (see note below score & description) Examples of correct response #2 (see note below score &
description) Space between pieces is acceptable. Scoring Guide In this question, a student needed to take 2 isosceles triangles and construct a 4sided figure that was not a square or a rhombus. A student had to manipulate 2 figures, form a shape other than a square or rhombus, and draw a line of separation in order to earn a score of correct #1. To earn a correct #2, a student had to manipulate 2 figures with some overlapping possible, form a shape that was not a square or rhombus, but did not have to drawn a line of separation. 
Score & Description  
 
 

* The use of more than one correct category in this question enabled NAEP to gather data on different ways in which students responded correctly to this question. Any response that fell into one of these correct categories earned full credit. 
Correct #1  Student Response 
25 
Use the 2 pieces labeled Q to make a 4sided shape that is not a square. Trace the shape and draw the line to show where the 2 pieces meet. 
25 
Use the 2 pieces labeled Q to make a 4sided shape that is not a square. Trace the shape and draw the line to show where the 2 pieces meet. 
Correct #2  Student Response 
25 
Use the 2 pieces labeled Q to make a 4sided shape that is not a square. Trace the shape and draw the line to show where the 2 pieces meet. 
25 
Use the 2 pieces labeled Q to make a 4sided shape that is not a square. Trace the shape and draw the line to show where the 2 pieces meet. 
Incorrect  Student Response 
25 
Use the 2 pieces labeled Q to make a 4sided shape that is not a square. Trace the shape and draw the line to show where the 2 pieces meet. 
25 
Use the 2 pieces labeled Q to make a 4sided shape that is not a square. Trace the shape and draw the line to show where the 2 pieces meet. 
Scoring Guide 
Solution:
Scoring Guide In this question, a student needed to visualize where to place 4 of the 6 given shapes (2 squares, 2 isosceles triangles, and 2 right triangles) so that they formed a 6sided shape that was already given to the student. 
Score & Description  
 
 

* The use of more than one correct category in this question enabled NAEP to gather data on different ways in which students responded correctly to this question. Any response that fell into one of these correct categories earned full credit. 
Correct #1  Student Response 
26 
For this question you will need some of the pieces labeled
N, P, and Q.
Use 4 of the 6 pieces labeled N, P, and Q to make the shape shown below. Draw the lines to show where the pieces meet and label the pieces. 
26 
For this question you will need some of the pieces labeled
N, P, and Q.
Use 4 of the 6 pieces labeled N, P, and Q to make the shape shown below. Draw the lines to show where the pieces meet and label the pieces. 
Correct #2  Student Response 
26 
For this question you will need some of the pieces labeled
N, P, and Q.
Use 4 of the 6 pieces labeled N, P, and Q to make the shape shown below. Draw the lines to show where the pieces meet and label the pieces. 
26 
For this question you will need some of the pieces labeled
N, P, and Q.
Use 4 of the 6 pieces labeled N, P, and Q to make the shape shown below. Draw the lines to show where the pieces meet and label the pieces. 
Incorrect  Student Response 
26 
For this question you will need some of the pieces labeled
N, P, and Q.
Use 4 of the 6 pieces labeled N, P, and Q to make the shape shown below. Draw the lines to show where the pieces meet and label the pieces. 
26 
For this question you will need some of the pieces labeled
N, P, and Q.
Use 4 of the 6 pieces labeled N, P, and Q to make the shape shown below. Draw the lines to show where the pieces meet and label the pieces. 
Scoring Guide 
Solution: An adequate explanation with or without Bob. Parts of P overlaps N, and part sticks out. The sticking out part is equal to the left out part of N. OR Two P's match two N's therefore they have the same area. (Therefore, one N has the same area as one P.) OR Areas are equal because height of P is the same as the height of N, and the base of P is twice the base of N. OR Either of these two figures alone are acceptable. Scoring Guide In this question, a student has to compare two given shapes with respect to their area. A student needed to realize that area meant the amount of surface a shape covers. They also needed to know how to compare the areas of the shapes. Using pictures and words to make the comparison between the areas of N and P, a student could have given a variety of explanations such as two shape P's match with two shape N's; therefore, one N has the same area as one P. They also could have used the geometric shapes placed one on top of the other to see how their areas compared. 
Score & Description  
 
 

* The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of these incorrect categories earned no credit. 
Correct  Student Response 
27 
Bob, Carmen, and Tyler were comparing the areas of N and P. Bob said that N and P have the same area. Carmen said that the area of N is larger. Tyler said that the area of P is larger. 
27 
Bob, Carmen, and Tyler were comparing the areas of N and P. Bob said that N and P have the same area. Carmen said that the area of N is larger. Tyler said that the area of P is larger. 
Incorrect #2  Student Response 
27 
Bob, Carmen, and Tyler were comparing the areas of N and P. Bob said that N and P have the same area. Carmen said that the area of N is larger. Tyler said that the area of P is larger. 
27 
Bob, Carmen, and Tyler were comparing the areas of N and P. Bob said that N and P have the same area. Carmen said that the area of N is larger. Tyler said that the area of P is larger. 
Incorrect #1  Student Response 
27 
Bob, Carmen, and Tyler were comparing the areas of N and P. Bob said that N and P have the same area. Carmen said that the area of N is larger. Tyler said that the area of P is larger. 
27 
Bob, Carmen, and Tyler were comparing the areas of N and P. Bob said that N and P have the same area. Carmen said that the area of N is larger. Tyler said that the area of P is larger. 
Scoring Guide 
Solution: P has the longest perimeter. Adequate explanation e.g. hold pieces up to each other, moving edges around to match
up, OR Copy the sides of each piece in a line as shown below, and compare lengths
Scoring Guide In this question, a student has to estimate the perimeter of each shape and then compare perimeters to see which shape has the longest perimeter. This question requires a student to come up with some method to determine the perimeter of the shapes without the use of a ruler and to explain why he or she selected the shape. 
Score & Description  
 
 

* The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of these incorrect categories earned no credit. 
Correct  Student Response 
28 
Which of the shapes N, P, and Q has the longest perimeter (distance around)? 
28 
Which of the shapes N, P, and Q has the longest perimeter (distance around)? 
Incorrect #2  Student Response 
28 
Which of the shapes N, P, and Q has the longest perimeter (distance around)? 
28 
Which of the shapes N, P, and Q has the longest perimeter (distance around)? 
Incorrect #1  Student Response 
28 
Which of the shapes N, P, and Q has the longest perimeter (distance around)? 
28 
Which of the shapes N, P, and Q has the longest perimeter (distance around)? 
Scoring Guide 
Solution: N, because more students chose it. OR N, because it was first choice in one class and second choice in the other classes. "Majority" is acceptable (taken to mean most.) If student says the most classes, do not accept. Scoring Guide In this question, a student has to read and interpret information from a chart. A student then has to make a decision on which of the shapes should be the choice for the class. To earn full credit the student has to tell which of the three pieces should be the choice for the class and then explain why he or she chose that shape. 
Score & Description  
 
 
 

* The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of these incorrect categories earned no credit. 
Correct  Student Response 
29 
This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results. 
29 
This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results. 
Incorrect #3  Student Response 
29 
This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results. 
29 
This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results. 
Incorrect #2  Student Response 
29 
This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results. 
29 
This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results. 
Incorrect #1  Student Response 
29 
This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results. 
29 
This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results. 
Scoring Guide 
Solution: 1571 Scoring Guide In this question, a student needed to interpret that the lowest point of the St. Lawrence River is a negative number and the highest point of Mt. Jacques Cartier is a positive number (both with respect to sea level). To find the difference between the highest point and the lowest point and to earn full credit, a student needed to subtract the two numbers. To earn partial credit, a student would have had to show the correct procedure using positive and negative numbers, but made a computation error. 
Score & Description  
 
 

Correct  Student Response 
30 
The lowest point of the St. Lawrence River is 294 feet below sea level. The top of Mt. Jacques Cartier is 1,277 feet above sea level. How many feet higher is the top of Mt. Jacques Cartier than the lowest point of the St. Lawrence River? Show your work. 
30 
The lowest point of the St. Lawrence River is 294 feet below sea level. The top of Mt. Jacques Cartier is 1,277 feet above sea level. How many feet higher is the top of Mt. Jacques Cartier than the lowest point of the St. Lawrence River? Show your work. 
Partial  Student Response 
30 
The lowest point of the St. Lawrence River is 294 feet below sea level. The top of Mt. Jacques Cartier is 1,277 feet above sea level. How many feet higher is the top of Mt. Jacques Cartier than the lowest point of the St. Lawrence River? Show your work. 
30 
The lowest point of the St. Lawrence River is 294 feet below sea level. The top of Mt. Jacques Cartier is 1,277 feet above sea level. How many feet higher is the top of Mt. Jacques Cartier than the lowest point of the St. Lawrence River? Show your work. 
Incorrect  Student Response 
30 
The lowest point of the St. Lawrence River is 294 feet below sea level. The top of Mt. Jacques Cartier is 1,277 feet above sea level. How many feet higher is the top of Mt. Jacques Cartier than the lowest point of the St. Lawrence River? Show your work. 
30 
The lowest point of the St. Lawrence River is 294 feet below sea level. The top of Mt. Jacques Cartier is 1,277 feet above sea level. How many feet higher is the top of Mt. Jacques Cartier than the lowest point of the St. Lawrence River? Show your work. 
Scoring Guide 
Solution: Brian (constant difference) Scoring Guide In this question, a student has to use mathematical reasoning to construct different justifications that support Darlene’s and Brian’s claims. In this realworld problem, students have to construct an appropriate method for supporting each claim in the question. One such method uses proportional thinking as well as percentages to explain how a conclusion could be reached, while the other involves comparing differences in growth by subtraction. Partial credit is earned if a student just gives a correct justification for Brian’s or Darlene’s claim, but not both, or shows a limited understanding of how to proceed with the problem. 
Score & Description  
 
 

Correct  Student Response 
31 
In 1980, the populations of Town A and Town B were 5,000 and
6,000, respectively. The 1990 populations of Town A and Town B were 8,000
and 9,000, respectively.
Brian claims that from 1980 to 1990 the populations of the two towns grew by the same amount. Use mathematics to explain how Brian might have justified his claim. Darlene claims that from 1980 to 1990 the population of Town A had grown more. Use mathematics to explain how Darlene might have justified her claim. 
Partial  Student Response 
31 
In 1980, the populations of Town A and Town B were 5,000 and
6,000, respectively. The 1990 populations of Town A and Town B were 8,000
and 9,000, respectively.
Brian claims that from 1980 to 1990 the populations of the two towns grew by the same amount. Use mathematics to explain how Brian might have justified his claim. Darlene claims that from 1980 to 1990 the population of Town A had grown more. Use mathematics to explain how Darlene might have justified her claim. 
31 
In 1980, the populations of Town A and Town B were 5,000 and
6,000, respectively. The 1990 populations of Town A and Town B were 8,000
and 9,000, respectively.
Brian claims that from 1980 to 1990 the populations of the two towns grew by the same amount. Use mathematics to explain how Brian might have justified his claim. Darlene claims that from 1980 to 1990 the population of Town A had grown more. Use mathematics to explain how Darlene might have justified her claim. 
Incorrect  Student Response 
31 
In 1980, the populations of Town A and Town B were 5,000 and
6,000, respectively. The 1990 populations of Town A and Town B were 8,000
and 9,000, respectively.
Brian claims that from 1980 to 1990 the populations of the two towns grew by the same amount. Use mathematics to explain how Brian might have justified his claim. Darlene claims that from 1980 to 1990 the population of Town A had grown more. Use mathematics to explain how Darlene might have justified her claim. 
Scoring Guide 
Solution: 283 Scoring Guide In this question, a student is given the formula for the volume of a cylinder. To earn full credit, a student needed to give an answer of 283 (with or without work) which has been rounded to the nearest cubic inch. To earn partial credit, the correct substitutions would have been made but the student did not round his or her answer correctly. 
Score & Description  
 
 

Correct  Student Response 
32 
A cereal company packs its oatmeal into cylindrical containers. The height of each container is 10 inches and the radius of the bottom is 3 inches. What is the volume of the box to the nearest cubic inch? (The formula for the volume of a cylinder is ) 
32 
A cereal company packs its oatmeal into cylindrical containers. The height of each container is 10 inches and the radius of the bottom is 3 inches. What is the volume of the box to the nearest cubic inch? (The formula for the volume of a cylinder is ) 
Partial  Student Response 
32 
A cereal company packs its oatmeal into cylindrical containers. The height of each container is 10 inches and the radius of the bottom is 3 inches. What is the volume of the box to the nearest cubic inch? (The formula for the volume of a cylinder is ) 
Incorrect  Student Response 
32 
A cereal company packs its oatmeal into cylindrical containers. The height of each container is 10 inches and the radius of the bottom is 3 inches. What is the volume of the box to the nearest cubic inch? (The formula for the volume of a cylinder is ) 
32 
A cereal company packs its oatmeal into cylindrical containers. The height of each container is 10 inches and the radius of the bottom is 3 inches. What is the volume of the box to the nearest cubic inch? (The formula for the volume of a cylinder is ) 
Scoring Guide 
Solution: They will both reach points A and B at the same time because their rates are equal. Scoring Guide In this question, a student needed to use proportional thinking to solve this problem. The student should have reasoned that both Victor’s rate and Sharon’s rate are equal. To earn full credit the student needed to answer both parts of the question correctly with the correct justification for each. To earn partial credit, a student could have just answered one part correctly with the correct justification or answered both parts with no justification or incorrect justifications. 
Score & Description  
 
 

Correct  Student Response 
33 
Victor's van travels at a rate of 8 miles every 10 minutes.
Sharon's sedan travels at a rate of 20 miles every 25 minutes.
If both cars start at the same time, will Sharon's sedan reach point A, 8 miles away, before, at the same time, or after Victor's van? Explain your reasoning. 
33 
Victor's van travels at a rate of 8 miles every 10 minutes.
Sharon's sedan travels at a rate of 20 miles every 25 minutes.
If both cars start at the same time, will Sharon's sedan reach point A, 8 miles away, before, at the same time, or after Victor's van? Explain your reasoning. 
Partial  Student Response 
33 
Victor's van travels at a rate of 8 miles every 10 minutes.
Sharon's sedan travels at a rate of 20 miles every 25 minutes.
If both cars start at the same time, will Sharon's sedan reach point A, 8 miles away, before, at the same time, or after Victor's van? Explain your reasoning. 
33 
Victor's van travels at a rate of 8 miles every 10 minutes.
Sharon's sedan travels at a rate of 20 miles every 25 minutes.
If both cars start at the same time, will Sharon's sedan reach point A, 8 miles away, before, at the same time, or after Victor's van? Explain your reasoning. 
Incorrect  Student Response 
33 
Victor's van travels at a rate of 8 miles every 10 minutes.
Sharon's sedan travels at a rate of 20 miles every 25 minutes.
If both cars start at the same time, will Sharon's sedan reach point A, 8 miles away, before, at the same time, or after Victor's van? Explain your reasoning. 
33 
Victor's van travels at a rate of 8 miles every 10 minutes.
Sharon's sedan travels at a rate of 20 miles every 25 minutes.
If both cars start at the same time, will Sharon's sedan reach point A, 8 miles away, before, at the same time, or after Victor's van? Explain your reasoning. 
Scoring Guide 
Score & Description  
 
 

NOTE: All correct answers must contain at least three
equal sides and the figure must appear to be a square.
*The use of more than one correct category in this question enabled NAEP to gather data on different ways students responded correctly to this question. Any one of these responses that fell into one of these correct categories earned full credit. 
Correct #1  Student Response 
34 
In the space below, use your ruler to draw a square with two of its corners at the points shown. 
34 
In the space below, use your ruler to draw a square with two of its corners at the points shown. 
Correct #2  Student Response 
34 
In the space below, use your ruler to draw a square with two of its corners at the points shown. 
Incorrect  Student Response 
34 
In the space below, use your ruler to draw a square with two of its corners at the points shown. 
Scoring Guide 
Score & Description  
 
 
 
 

*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct  Student Response 
35 
In the space below, draw a rectangle 2 inches wide and 3½ inches long. 
Incorrect #4  Student Response 
35 
In the space below, draw a rectangle 2 inches wide and 3½ inches long. 
Incorrect #3  Student Response 
35 
In the space below, draw a rectangle 2 inches wide and 3½ inches long. 
35 
In the space below, draw a rectangle 2 inches wide and 3½ inches long. 
Incorrect #2  Student Response 
35 
In the space below, draw a rectangle 2 inches wide and 3½ inches long. 
Incorrect #1  Student Response 
35 
In the space below, draw a rectangle 2 inches wide and 3½ inches long. 
Scoring Guide 
Score & Description  
 
 

*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct  Student Response 
36 
What is the length in centimeters of one of the longer sides of the rectangle? 
36 
What is the length in centimeters of one of the longer sides of the rectangle? 
Incorrect #2  Student Response 
36 
What is the length in centimeters of one of the longer sides of the rectangle? 
Incorrect #1  Student Response 
36 
What is the length in centimeters of one of the longer sides of the rectangle? 
Scoring Guide 
Score & Description  
 

Correct  Student Response 
37 
What is the length in centimeters of the diagonal from A to B? 
37 
What is the length in centimeters of the diagonal from A to B? 
Incorrect  Student Response 
37 
What is the length in centimeters of the diagonal from A to B? 
Scoring Guide 
Score & Description  
 

Note: Answer need not have the degree symbol. 
Correct  Student Response 
38 
Use your protractor to find the degree measure of the angle shown above. 
Incorrect  Student Response 
38 
Use your protractor to find the degree measure of the angle shown above. 
Scoring Guide 
Score & Description  
 
 

*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct  Student Response 
39 
On the grid below, draw a rectangle with an area of 12 square units. 
Incorrect #2  Student Response 
39 
On the grid below, draw a rectangle with an area of 12 square units. 
Incorrect #1  Student Response 
39 
On the grid below, draw a rectangle with an area of 12 square units. 
Scoring Guide 
Score & Description  
 
 
 

*The use of more than one correct category in this
question enabled NAEP to gather data on different ways students responded
correctly to this question. Any one of these responses that fell into one
of these correct categories earned full credit.
*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct #1  Student Response 
40 
Jill needs to earn $45.00 for a class trip. She earns $2.00 each day on Mondays, Tuesdays, and Wednesdays, and $3.00 each day on Thursdays, Fridays, and Saturdays. She does not work on Sundays. How many weeks will it take her to earn $45.00? 
40 
Jill needs to earn $45.00 for a class trip. She earns $2.00 each day on Mondays, Tuesdays, and Wednesdays, and $3.00 each day on Thursdays, Fridays, and Saturdays. She does not work on Sundays. How many weeks will it take her to earn $45.00? 
Correct #2  Student Response 
40 
Jill needs to earn $45.00 for a class trip. She earns $2.00 each day on Mondays, Tuesdays, and Wednesdays, and $3.00 each day on Thursdays, Fridays, and Saturdays. She does not work on Sundays. How many weeks will it take her to earn $45.00? 
40 
Jill needs to earn $45.00 for a class trip. She earns $2.00 each day on Mondays, Tuesdays, and Wednesdays, and $3.00 each day on Thursdays, Fridays, and Saturdays. She does not work on Sundays. How many weeks will it take her to earn $45.00? 
Incorrect #2  Student Response 
40 
Jill needs to earn $45.00 for a class trip. She earns $2.00 each day on Mondays, Tuesdays, and Wednesdays, and $3.00 each day on Thursdays, Fridays, and Saturdays. She does not work on Sundays. How many weeks will it take her to earn $45.00? 
40 
Jill needs to earn $45.00 for a class trip. She earns $2.00 each day on Mondays, Tuesdays, and Wednesdays, and $3.00 each day on Thursdays, Fridays, and Saturdays. She does not work on Sundays. How many weeks will it take her to earn $45.00? 
Incorrect #1  Student Response 
40 
Jill needs to earn $45.00 for a class trip. She earns $2.00 each day on Mondays, Tuesdays, and Wednesdays, and $3.00 each day on Thursdays, Fridays, and Saturdays. She does not work on Sundays. How many weeks will it take her to earn $45.00? 
40 
Jill needs to earn $45.00 for a class trip. She earns $2.00 each day on Mondays, Tuesdays, and Wednesdays, and $3.00 each day on Thursdays, Fridays, and Saturdays. She does not work on Sundays. How many weeks will it take her to earn $45.00? 
Scoring Guide 
Score & Description  
 
 
 

Note: Any pairs that give a sum other than 2, e.g., (2,2) receive a score of Incorrect #1. Also (0,1) and (1,0) receive a score of Incorrect #1. *The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct  Student Response 
41 
Steve was asked to pick two marbles from a bag of yellow marbles and blue marbles. One possible result was one yellow marble first and one blue marble second. He wrote this result in the table below. List all of the other possible results that Steve could get. 
Incorrect #3  Student Response 
41 
Steve was asked to pick two marbles from a bag of yellow marbles and blue marbles. One possible result was one yellow marble first and one blue marble second. He wrote this result in the table below. List all of the other possible results that Steve could get. 
Incorrect #2  Student Response 
41 
Steve was asked to pick two marbles from a bag of yellow marbles and blue marbles. One possible result was one yellow marble first and one blue marble second. He wrote this result in the table below. List all of the other possible results that Steve could get. 
Incorrect #1  Student Response 
41 
Steve was asked to pick two marbles from a bag of yellow marbles and blue marbles. One possible result was one yellow marble first and one blue marble second. He wrote this result in the table below. List all of the other possible results that Steve could get. 
Scoring Guide 
Score & Description  
 
 
 

*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct  Student Response 
42 
Each of the cylinders shown below was cut in a different way. The shaded part shows the shape of the cut. Under each figure, write the name of the shape of the cut. 
42 
Each of the cylinders shown below was cut in a different way. The shaded part shows the shape of the cut. Under each figure, write the name of the shape of the cut. 
Incorrect #3  Student Response 
42 
Each of the cylinders shown below was cut in a different way. The shaded part shows the shape of the cut. Under each figure, write the name of the shape of the cut. 
42 
Each of the cylinders shown below was cut in a different way. The shaded part shows the shape of the cut. Under each figure, write the name of the shape of the cut. 
Incorrect #2  Student Response 
42 
Each of the cylinders shown below was cut in a different way. The shaded part shows the shape of the cut. Under each figure, write the name of the shape of the cut. 
42 
Each of the cylinders shown below was cut in a different way. The shaded part shows the shape of the cut. Under each figure, write the name of the shape of the cut. 
Incorrect #1  Student Response 
42 
Each of the cylinders shown below was cut in a different way. The shaded part shows the shape of the cut. Under each figure, write the name of the shape of the cut. 
42 
Each of the cylinders shown below was cut in a different way. The shaded part shows the shape of the cut. Under each figure, write the name of the shape of the cut. 
Scoring Guide 
Score & Description  
 
 
 

*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct  Student Response 
43 

43 

Incorrect #3  Student Response 
43 

Incorrect #2  Student Response 
43 

43 

Incorrect #1  Student Response 
43 

43 

Scoring Guide 
Solution: Note: This question is listed as a short constructedresponse question. It should be considered a multiplechoice question with multiple parts. 
Score & Description  
 
 
 
 

4 Right  Student Response 
44 
Akira read from a book on Monday, Tuesday, and Wednesday. He read an average of 10 pages per day. Indicate in the ovals below whether each of the following is possible or not possible. 
3 Right  Student Response 
44 
Akira read from a book on Monday, Tuesday, and Wednesday. He read an average of 10 pages per day. Indicate in the ovals below whether each of the following is possible or not possible. 
2 Right  Student Response 
44 
Akira read from a book on Monday, Tuesday, and Wednesday. He read an average of 10 pages per day. Indicate in the ovals below whether each of the following is possible or not possible. 
1 Right  Student Response 
44 
Akira read from a book on Monday, Tuesday, and Wednesday. He read an average of 10 pages per day. Indicate in the ovals below whether each of the following is possible or not possible. 
0 Right  Student Response 
44 
Akira read from a book on Monday, Tuesday, and Wednesday. He read an average of 10 pages per day. Indicate in the ovals below whether each of the following is possible or not possible. 
Scoring Guide 
Score & Description  
 

Correct  Student Response 
45 
The area of rectangle BCDE shown above is 60 square inches. If the length of AE is 10 inches and the length of ED is 15 inches, what is the area of trapezoid ABCD, in square inches? 
45 
The area of rectangle BCDE shown above is 60 square inches. If the length of AE is 10 inches and the length of ED is 15 inches, what is the area of trapezoid ABCD, in square inches? 
Incorrect  Student Response 
45 
The area of rectangle BCDE shown above is 60 square inches. If the length of AE is 10 inches and the length of ED is 15 inches, what is the area of trapezoid ABCD, in square inches? 
45 
The area of rectangle BCDE shown above is 60 square inches. If the length of AE is 10 inches and the length of ED is 15 inches, what is the area of trapezoid ABCD, in square inches? 
Scoring Guide 
Score & Description  
 

Correct  Student Response 
46 
The sum of the measures of the 24 angles in a 24sided regular polygon is 3,960°. What is the measure in degrees of one of the angles? 
46 
The sum of the measures of the 24 angles in a 24sided regular polygon is 3,960°. What is the measure in degrees of one of the angles? 
Incorrect  Student Response 
46 
The sum of the measures of the 24 angles in a 24sided regular polygon is 3,960°. What is the measure in degrees of one of the angles? 
46 
The sum of the measures of the 24 angles in a 24sided regular polygon is 3,960°. What is the measure in degrees of one of the angles? 
Scoring Guide 
Score & Description  
 
 
 

*The use of more than one correct category in this
question enabled NAEP to gather data on different ways students responded
correctly to this question. Any one of these responses that fell into one
of these correct categories earned full credit.
*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct #1  Student Response 
47 
Tracy said, "I can multiply 6 by another number and get an
answer that is smaller than 6." Pat said, "No, you can't. Multiplying 6 by another number always makes the answer 6 or larger." Who is correct? Give a reason for your answer. 
47 
Tracy said, "I can multiply 6 by another number and get an
answer that is smaller than 6." Pat said, "No, you can't. Multiplying 6 by another number always makes the answer 6 or larger." Who is correct? Give a reason for your answer. 
Correct #2  Student Response 
47 
Tracy said, "I can multiply 6 by another number and get an
answer that is smaller than 6." Pat said, "No, you can't. Multiplying 6 by another number always makes the answer 6 or larger." Who is correct? Give a reason for your answer. 
47 
Tracy said, "I can multiply 6 by another number and get an
answer that is smaller than 6." Pat said, "No, you can't. Multiplying 6 by another number always makes the answer 6 or larger." Who is correct? Give a reason for your answer. 
Incorrect #2  Student Response 
47 
Tracy said, "I can multiply 6 by another number and get an
answer that is smaller than 6." Pat said, "No, you can't. Multiplying 6 by another number always makes the answer 6 or larger." Who is correct? Give a reason for your answer. 
47 
Tracy said, "I can multiply 6 by another number and get an
answer that is smaller than 6." Pat said, "No, you can't. Multiplying 6 by another number always makes the answer 6 or larger." Who is correct? Give a reason for your answer. 
Incorrect #1  Student Response 
47 
Tracy said, "I can multiply 6 by another number and get an
answer that is smaller than 6." Pat said, "No, you can't. Multiplying 6 by another number always makes the answer 6 or larger." Who is correct? Give a reason for your answer. 
47 
Tracy said, "I can multiply 6 by another number and get an
answer that is smaller than 6." Pat said, "No, you can't. Multiplying 6 by another number always makes the answer 6 or larger." Who is correct? Give a reason for your answer. 
Scoring Guide 
Score & Description  
 
 
 
 

*The use of more than one correct category in this
question enabled NAEP to gather data on different ways students responded
correctly to this question. Any one of these responses that fell into one
of these correct categories earned full credit.
*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct #1  Student Response 
48 
Raymond must buy enough paper to print 28 copies of a report that contains 64 sheets of paper. Paper is only available in packages of 500 sheets. How many whole packages of paper will he need to buy to do the printing? 
48 
Raymond must buy enough paper to print 28 copies of a report that contains 64 sheets of paper. Paper is only available in packages of 500 sheets. How many whole packages of paper will he need to buy to do the printing? 
Correct #2  Student Response 
48 
Raymond must buy enough paper to print 28 copies of a report that contains 64 sheets of paper. Paper is only available in packages of 500 sheets. How many whole packages of paper will he need to buy to do the printing? 
48 
Raymond must buy enough paper to print 28 copies of a report that contains 64 sheets of paper. Paper is only available in packages of 500 sheets. How many whole packages of paper will he need to buy to do the printing? 
Incorrect #3  Student Response 
48 
Raymond must buy enough paper to print 28 copies of a report that contains 64 sheets of paper. Paper is only available in packages of 500 sheets. How many whole packages of paper will he need to buy to do the printing? 
48 
Raymond must buy enough paper to print 28 copies of a report that contains 64 sheets of paper. Paper is only available in packages of 500 sheets. How many whole packages of paper will he need to buy to do the printing? 
Incorrect #2  Student Response 
48 
Raymond must buy enough paper to print 28 copies of a report that contains 64 sheets of paper. Paper is only available in packages of 500 sheets. How many whole packages of paper will he need to buy to do the printing? 
48 
Raymond must buy enough paper to print 28 copies of a report that contains 64 sheets of paper. Paper is only available in packages of 500 sheets. How many whole packages of paper will he need to buy to do the printing? 
Incorrect #1  Student Response 
48 
Raymond must buy enough paper to print 28 copies of a report that contains 64 sheets of paper. Paper is only available in packages of 500 sheets. How many whole packages of paper will he need to buy to do the printing? 
48 
Raymond must buy enough paper to print 28 copies of a report that contains 64 sheets of paper. Paper is only available in packages of 500 sheets. How many whole packages of paper will he need to buy to do the printing? 
Scoring Guide 
Score & Description  
 

Correct  Student Response 
49 
Lynn had only quarters, dimes, and nickels to buy her lunch. She spent all of the money and received no change. Could she have spent $1.98? 
Incorrect  Student Response 
49 
Lynn had only quarters, dimes, and nickels to buy her lunch. She spent all of the money and received no change. Could she have spent $1.98? 
Scoring Guide 
Score & Description  
 
 

*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct  Student Response 
50 
On the grid below, the dot at (4, 4) is circled. Circle two other dots where the first number is equal to the second number. 
50 
On the grid below, the dot at (4, 4) is circled. Circle two other dots where the first number is equal to the second number. 
Incorrect #2  Student Response 
50 
On the grid below, the dot at (4, 4) is circled. Circle two other dots where the first number is equal to the second number. 
Incorrect #1  Student Response 
50 
On the grid below, the dot at (4, 4) is circled. Circle two other dots where the first number is equal to the second number. 
50 
On the grid below, the dot at (4, 4) is circled. Circle two other dots where the first number is equal to the second number. 
Scoring Guide 
Score & Description  
 
 
 

Note: 85 is acceptable since not all students are taught to round numbers in the same way. *The use of more than one correct category in this question enabled NAEP to gather data on different ways students responded correctly to this question. Any one of these responses that fell into one of these correct categories earned full credit. *The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct #1  Student Response 
51 
The length of a dinosaur was reported to have been 80 feet (rounded to the nearest 10 feet). What length other than 80 feet could have been the actual length of this dinosaur? 
51 
The length of a dinosaur was reported to have been 80 feet (rounded to the nearest 10 feet). What length other than 80 feet could have been the actual length of this dinosaur? 
Correct #2  Student Response 
51 
The length of a dinosaur was reported to have been 80 feet (rounded to the nearest 10 feet). What length other than 80 feet could have been the actual length of this dinosaur? 
Incorrect #2  Student Response 
51 
The length of a dinosaur was reported to have been 80 feet (rounded to the nearest 10 feet). What length other than 80 feet could have been the actual length of this dinosaur? 
51 
The length of a dinosaur was reported to have been 80 feet (rounded to the nearest 10 feet). What length other than 80 feet could have been the actual length of this dinosaur? 
Incorrect #1  Student Response 
51 
The length of a dinosaur was reported to have been 80 feet (rounded to the nearest 10 feet). What length other than 80 feet could have been the actual length of this dinosaur? 
51 
The length of a dinosaur was reported to have been 80 feet (rounded to the nearest 10 feet). What length other than 80 feet could have been the actual length of this dinosaur? 
Scoring Guide 
Score & Description  
 

Note: 1980 can is really 4 times as big or holds 4 times
as much trash is incorrect. The student must either be inexact, such as "more than twice as much," or must mention "8 times as much." 
Correct  Student Response 
52 
The pictograph shown above is misleading. Explain why. 
Incorrect  Student Response 
52 
The pictograph shown above is misleading. Explain why. 
52 
The pictograph shown above is misleading. Explain why. 
Scoring Guide 
Score & Description  
 

*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct  Student Response 
53 
Explain how you found your answer to question 16. 
Incorrect #1 & 2  Student Response 
53 
Explain how you found your answer to question 16. 
53 
Explain how you found your answer to question 16. 
Scoring Guide 
Score & Description  
 
 

*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct  Student Response 
54 
What is the product of 3.12 and 8^{3}? 
54 
What is the product of 3.12 and 8^{3}? 
Incorrect #1  Student Response 
54 
What is the product of 3.12 and 8^{3}? 
Incorrect #2  Student Response 
54 
What is the product of 3.12 and 8^{3}? 
54 
What is the product of 3.12 and 8^{3}? 
Scoring Guide 
Score & Description  
 

Correct  Student Response 
55 
The weight of an object on the Moon is 1/6 the weight of that object on the Earth. An object that weighs 30 pounds on Earth would weigh how many pounds on the Moon? 
Incorrect  Student Response 
55 
The weight of an object on the Moon is 1/6 the weight of that object on the Earth. An object that weighs 30 pounds on Earth would weigh how many pounds on the Moon? 
Scoring Guide 
Score & Description  
 

Correct  Student Response 
56 
The cost to rent a motorbike is given by the following
formula:
Fill in the table below. 
56 
The cost to rent a motorbike is given by the following
formula:
Fill in the table below. 
Incorrect  Student Response 
56 
The cost to rent a motorbike is given by the following
formula:
Fill in the table below. 
Scoring Guide 
Score & Description  
 
 

*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct  Student Response 
57 
If 12 divides a whole number n without a remainder,
list all whole numbers greater than 1 and less than 12 that must also
divide n without a remainder. 
Incorrect #1  Student Response 
57 
If 12 divides a whole number n without a remainder,
list all whole numbers greater than 1 and less than 12 that must also
divide n without a remainder. 
Incorrect #2  Student Response 
57 
If 12 divides a whole number n without a remainder,
list all whole numbers greater than 1 and less than 12 that must also
divide n without a remainder. 
Scoring Guide 
Score & Description  
 
 

*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct  Student Response 
58 
Plot the point (5, 2) on the grid shown below. 
Incorrect #1  Student Response 
58 
Plot the point (5, 2) on the grid shown below. 
Incorrect #2  Student Response 
58 
Plot the point (5, 2) on the grid shown below. 
Scoring Guide 
Score & Description  
 

Correct  Student Response 
59 
The table above shows the results of a survey of hair color. On the circle below, make a circle graph to illustrate the data in the table. Label each part of the circle graph with the correct hair color. 
Incorrect  Student Response 
59 
The table above shows the results of a survey of hair color. On the circle below, make a circle graph to illustrate the data in the table. Label each part of the circle graph with the correct hair color. 
59 
The table above shows the results of a survey of hair color. On the circle below, make a circle graph to illustrate the data in the table. Label each part of the circle graph with the correct hair color. 
Scoring Guide 
Score & Description  
 
 

*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct  Student Response 
60 
The Zandalia Zoo uses 214,964 kilograms of meat per year. If the meat costs $2.53 per kilogram, how much does the meat cost per week? 
Incorrect #1  Student Response 
60 
The Zandalia Zoo uses 214,964 kilograms of meat per year. If the meat costs $2.53 per kilogram, how much does the meat cost per week? 
Incorrect #2  Student Response 
60 
The Zandalia Zoo uses 214,964 kilograms of meat per year. If the meat costs $2.53 per kilogram, how much does the meat cost per week? 