









































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 the student could 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: 3 bicycles and 2 wagons have 6 + 8 = 14 wheels Possible acceptable responses include: 14, 14 wheels, 14 wheels in yard 
Score & Description  
 
 

In this question the student needed to determine the total number of wheels on 3 bicycles and 2 wagons. The student needed to know or observe from the picture that each bicycle has 2 wheels and each wagon has 4 wheels, and then determine and carry out an appropriate method for determining the total number of wheels. Students were permitted to use a calculator. 
Correct  Student Response 
6 
On Monday there were 3 bicycles and 2 wagons in the school yard. How many wheels were in the school yard? 
Partial  Student Response 
6 
On Monday there were 3 bicycles and 2 wagons in the school yard. How many wheels were in the school yard? 
Incorrect  Student Response 
6 
On Monday there were 3 bicycles and 2 wagons in the school yard. How many wheels were in the school yard? 
Scoring Guide 
Solution: Any two of the following correct responses: 0 bicycles, 6 wagons 
Score & Description  
 
 

In this question the student was told that there were bicycles and wagons in a school yard and that there were a total of 24 wheels. The student was asked to find two different combinations of bicycles and wagons that would have a total of 24 wheels. The student needed to know or observe from the picture that each bicycle has 2 wheels and each wagon has 4 wheels, and then determine two ways there could be a total of 24 wheels. Students were permitted to use a calculator. 
Correct  Student Response 
7 
On Tuesday the total number of wheels in the school yard was 24. There are several ways this could happen. 
Partial  Student Response 
7 
On Tuesday the total number of wheels in the school yard was 24. There are several ways this could happen. 
Incorrect  Student Response 
7 
On Tuesday the total number of wheels in the school yard was 24. There are several ways this could happen. 
Scoring Guide 
Solution: They can both be right because 1/4 of 20 = 5 and 20  5 = 15. OR 1/4 is 5 and 3/4 is 15. OR

Score & Description  
 
 

In this question the student was given information in two different ways—a fractional part and a number of items—and the student needed to justify that these two interpretations of the same situation were consistent. To answer the question, the student needed to observe that the fractional part has meaning in terms of the number of items, or that the number of items can be represented as a fractional part of the whole amount. Students were permitted to use a calculator. 
Correct  Student Response 
8 
Together, Sara and Brendan have 20 pencils. Sara says 1/4 of the pencils are hers. Brendan says 15 of the pencils belong to him. Explain how they both could be right. Use words or drawings. 
Partial  Student Response 
8 
Together, Sara and Brendan have 20 pencils. Sara says 1/4 of the pencils are hers. Brendan says 15 of the pencils belong to him. Explain how they both could be right. Use words or drawings. 
Incorrect  Student Response 
8 
Together, Sara and Brendan have 20 pencils. Sara says 1/4 of the pencils are hers. Brendan says 15 of the pencils belong to him. Explain how they both could be right. Use words or drawings. 
Scoring Guide 
Solution: Any one of these pairs: 3, 42 6, 21 7, 18 9, 14 
Score & Description  
 
 

In this question the student was asked to write 126 as the product of two whole numbers, each of which is greater than 2. The student was required only to identify one of several possible factorizations of 126 for credit. Students were permitted to use a calculator. 
Correct  Student Response 
9 
Two whole numbers, each greater than 2, are multiplied together. The product is 126. What could the two numbers be? 
Partial  Student Response 
9 
Two whole numbers, each greater than 2, are multiplied together. The product is 126. What could the two numbers be? 
Incorrect  Student Response 
9 
Two whole numbers, each greater than 2, are multiplied together. The product is 126. What could the two numbers be? 
Scoring Guide 
Solution: Figure must be closed and have 5 sides and 2 or more right angles. Right angles do not have to be marked, but should appear to be right angles. Two right angles must be on the inside of the figure.

Score & Description  
 
 
 

In this question the student needed to show geometric
understanding by drawing a closed figure with 5 sides and at least 2 right
angles. Students did not have a ruler or protractor.
*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 
In the space below, draw a closed figure with 5 sides. Make 2 of the angles right angles. 
Incorrect #3  Student Response 
10 
In the space below, draw a closed figure with 5 sides. Make 2 of the angles right angles. 
Incorrect #2  Student Response 
10 
In the space below, draw a closed figure with 5 sides. Make 2 of the angles right angles. 
Incorrect #1  Student Response 
10 
In the space below, draw a closed figure with 5 sides. Make 2 of the angles right angles. 
Scoring Guide 
Solution: 5 × 7 = (or other symbol, such as 5 × 7 = ? ) OR 5 × 7 = 35 OR 5 × 7 = _ OR 5 × 7 Note: 5 × 7 can be written as 7 × 5. Other solutions are possible, such as 7 × 2 + 7 × 3 or any equivalent expression, as long as it involves multiplication. 
Score & Description  
 
 

This was a modeling question in which the student was asked to write a number sentence about the problem rather than to solve the problem. To answer this question, the student needed to recognize the relationship between repeated addition and multiplication. 
Correct  Student Response 
11 
Kim wants to give 7 stickers to each of her 5 friends. To
find out how many stickers she needs, she writes the number sentence 7 + 7
+ 7 + 7 + 7 = .
Write a number sentence with multiplication that she could use to find the number of stickers she needs. 
Partial  Student Response 
11 
Kim wants to give 7 stickers to each of her 5 friends. To
find out how many stickers she needs, she writes the number sentence 7 + 7
+ 7 + 7 + 7 = .
Write a number sentence with multiplication that she could use to find the number of stickers she needs. 
Incorrect  Student Response 
11 
Kim wants to give 7 stickers to each of her 5 friends. To
find out how many stickers she needs, she writes the number sentence 7 + 7
+ 7 + 7 + 7 = .
Write a number sentence with multiplication that she could use to find the number of stickers she needs. 
Scoring Guide 
Solution: 361 
Score & Description  
 

In this question the student needed to apply subtraction to solve a word problem. 
Correct  Student Response 
12 
The band members have a goal to sell 625 candy bars. If they have sold 264 so far, how many more candy bars do they have to sell to reach their goal? 
Incorrect  Student Response 
12 
The band members have a goal to sell 625 candy bars. If they have sold 264 so far, how many more candy bars do they have to sell to reach their goal? 
Scoring Guide 
Solution: 
Score & Description  
 
 

In this question the student was asked to locate 2 points on a coordinate grid. A sample point illustrated how the ordered pair is related to the axes for the first and second numbers in the pair. 
Correct  Student Response 
13 
On the same grid draw the point with coordinates (4,7) and the point with coordinates (8,0). 
Partial  Student Response 
13 
On the same grid draw the point with coordinates (4,7) and the point with coordinates (8,0). 
Incorrect  Student Response 
13 
On the same grid draw the point with coordinates (4,7) and the point with coordinates (8,0). 
Scoring Guide 
Solution: 84 or 84° 
Score & Description  
 
 

In this question the student needed to read the
temperature from a thermometer scale with each mark representing 2
degrees.
*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 
14 
What is the temperature reading shown on the thermometer? 
Incorrect #2  Student Response 
14 
What is the temperature reading shown on the thermometer? 
Incorrect #1  Student Response 
14 
What is the temperature reading shown on the thermometer? 
Scoring Guide 
Score & Description  
 

Correct  Student Response 
15 
How many fourths make a whole? 
Incorrect  Student Response 
15 
How many fourths make a whole? 
Scoring Guide 
Solution: Note: This question is listed as a short constructedresponse question. It should be considered a multiplechoice question with multiple parts. Which of these instruments best measures each of the following? 
Score & Description  
 
 
 

3 Right  Student Response 
16 
Which of these instruments best measures each of the following? 
2 Right  Student Response 
16 
Which of these instruments best measures each of the following? 
1 Right  Student Response 
16 
Which of these instruments best measures each of the following? 
0 Right  Student Response 
16 
Which of these instruments best measures each of the following? 
Scoring Guide 
Solution: 2 Scoring Guide: In this question, a student needed to interpret the meaning of a remainder in a division problem. Dividing 34 by 8 gives an answer of 4 with a remainder of 2. Therefore, Ms. Hernandez would form 4 teams with 8 students on each and have 2 students left as substitutes. If the student was not able to interpret the meaning of a remainder and gave an answer of 4 (or 4 remainder 2 or any other response), without the correct interpretation of the remainder 2, then the response was scored incorrect. 
Score & Description  
 

Correct  Student Response 
17 
Ms. Hernandez formed teams of 8 students each from the 34 students in her class. She formed as many teams as possible, and the students left over were substitutes. How many students were substitutes? 
Incorrect  Student Response 
17 
Ms. Hernandez formed teams of 8 students each from the 34 students in her class. She formed as many teams as possible, and the students left over were substitutes. How many students were substitutes? 
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 equal (but not so with P and Q). OR All the angles of N are equal (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. Scoring Guide:
In this question, a student needed to compare the shapes with respect to a common attribute such as number of sides or angles or vertices. The student could choose which attribute he or she wished to use. 
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 
18 
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. 
18 
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 
18 
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. 
18 
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 
18 
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: 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 
19 
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. 
19 
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 
19 
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. 
19 
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 
19 
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. 
19 
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: The square may be tilted. Diagonal must be shown. Pieces may or may not be labeled. Space between is acceptable. Freehand drawings are 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 
20 
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. 
20 
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 
20 
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. 
20 
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 a 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 
21 
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. 
21 
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 
21 
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 
21 
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: 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 the incorrect categories earned no credit. 
Correct  Student Response 
22 
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. 
22 
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 
22 
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. 
22 
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 
22 
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. 
22 
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 
22 
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. 
22 
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: An adequate explanation with or without Bob. May say "neither" or "both". Parts of P overlaps N, and part sticks out. 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 different ways on common student errors. Any response that fell into one of the incorrect categories earned no credit. 
Correct  Student Response 
23 
Bob, Carmen, and Tyler were comparing the areas of N and P. 
23 
Bob, Carmen, and Tyler were comparing the areas of N and P. 
Incorrect #2  Student Response 
23 
Bob, Carmen, and Tyler were comparing the areas of N and P. 
23 
Bob, Carmen, and Tyler were comparing the areas of N and P. 
Incorrect #1  Student Response 
23 
Bob, Carmen, and Tyler were comparing the areas of N and P. 
23 
Bob, Carmen, and Tyler were comparing the areas of N and P. 
Scoring Guide 
Solution: 752 The multiplication key Scoring Guide: In the first part of the question a student needed to know that the meaning of the word "sum"is the result of adding numbers. The sum of the two numbers is 752. The second part of the question focused on aspects of number sense, specifically on magnitude of numbers. Students are expected to realize that a result in the hundred thousands would occur only when 489 and 263 are multiplied. 
Score & Description  
 
 

Correct  Student Response 
24 
Mark tried to add the numbers 489 and 263 on his calculator. What is the sum of these numbers? 
24 
Mark tried to add the numbers 489 and 263 on his calculator. What is the sum of these numbers? 
Partial  Student Response 
24 
Mark tried to add the numbers 489 and 263 on his calculator. What is the sum of these numbers? 
Incorrect  Student Response 
24 
Mark tried to add the numbers 489 and 263 on his calculator. What is the sum of these numbers? 
24 
Mark tried to add the numbers 489 and 263 on his calculator. What is the sum of these numbers? 
Scoring Guide 
Solution: For 1 day, the sum is $1.75. For 5 days, the sum is $8.75. Therefore, he should ask his mother for nine onedollars bills (or one $5 bill and four $1 bills). Answer may be given pictorially. Scoring Guide: In this question a student needed to add together the cost of a juice, the cost of a sandwich, and the cost of a piece of fruit for one day. The total cost for lunch each day is $1.75. Once the total is found for each day, the student needs to multiply the total for each day by 5 days. This gives a total for the week of $8.75. The least number of dollar bills that Sam's mother needs to give him is 9. To earn full credit the student needed to give an answer of nine $1 bills (or one $5 bill and four $1 bills). Partial credit could be earned in a variety of ways, such as giving only the total for 5 days ($8.75), or rounding the per day total to $2 and multiplying by 5 days, which would have given an answer of $10. The question presented students with an opportunity to demonstrate their understanding of money in a realworld situation. 
Score & Description  
 
 

Correct  Student Response 
25 
Sam can purchase his lunch at school. Each day he wants to have juice that costs 50¢, a sandwich that costs 90¢, and fruit that costs 35¢. His mother has only $1.00 bills. What is the least number of $1.00 bills that his mother should give him so he will have enough money to buy lunch for 5 days? 
25 
Sam can purchase his lunch at school. Each day he wants to have juice that costs 50¢, a sandwich that costs 90¢, and fruit that costs 35¢. His mother has only $1.00 bills. What is the least number of $1.00 bills that his mother should give him so he will have enough money to buy lunch for 5 days? 
Partial  Student Response 
25 
Sam can purchase his lunch at school. Each day he wants to have juice that costs 50¢, a sandwich that costs 90¢, and fruit that costs 35¢. His mother has only $1.00 bills. What is the least number of $1.00 bills that his mother should give him so he will have enough money to buy lunch for 5 days? 
25 
Sam can purchase his lunch at school. Each day he wants to have juice that costs 50¢, a sandwich that costs 90¢, and fruit that costs 35¢. His mother has only $1.00 bills. What is the least number of $1.00 bills that his mother should give him so he will have enough money to buy lunch for 5 days? 
Incorrect  Student Response 
25 
Sam can purchase his lunch at school. Each day he wants to have juice that costs 50¢, a sandwich that costs 90¢, and fruit that costs 35¢. His mother has only $1.00 bills. What is the least number of $1.00 bills that his mother should give him so he will have enough money to buy lunch for 5 days? 
25 
Sam can purchase his lunch at school. Each day he wants to have juice that costs 50¢, a sandwich that costs 90¢, and fruit that costs 35¢. His mother has only $1.00 bills. What is the least number of $1.00 bills that his mother should give him so he will have enough money to buy lunch for 5 days? 
Scoring Guide 
Solution: Fold the string in half and cut it. Then fold each piece in half and cut each again. Scoring Guide: This question focused on aspects of measurement sense and geometric reasoning. No ruler is available to the student. A possible full credit explanation would have described folding the string in half and cutting it and then folding each of the two pieces in half and cutting them again. Clear written communication is an essential part of a fullcredit response on this question. 
Score & Description  
 
 

Correct  Student Response 
26 
Brett needs to cut a piece of string into four equal pieces
without using a ruler or other measuring instrument.
Write directions to tell Brett how to do this. 
26 
Brett needs to cut a piece of string into four equal pieces
without using a ruler or other measuring instrument.
Write directions to tell Brett how to do this. 
Partial  Student Response 
26 
Brett needs to cut a piece of string into four equal pieces
without using a ruler or other measuring instrument.
Write directions to tell Brett how to do this. 
26 
Brett needs to cut a piece of string into four equal pieces
without using a ruler or other measuring instrument.
Write directions to tell Brett how to do this. 
Incorrect  Student Response 
26 
Brett needs to cut a piece of string into four equal pieces
without using a ruler or other measuring instrument.
Write directions to tell Brett how to do this. 
26 
Brett needs to cut a piece of string into four equal pieces
without using a ruler or other measuring instrument.
Write directions to tell Brett how to do this. 
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 
27 
In the space below, use your ruler to draw a square with two of its corners at the points shown. 
Correct #2  Student Response 
27 
In the space below, use your ruler to draw a square with two of its corners at the points shown. 
27 
In the space below, use your ruler to draw a square with two of its corners at the points shown. 
Incorrect  Student Response 
27 
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 
28 
In the space below, draw a rectangle 2 inches wide and 3½ inches long. 
Incorrect #4  Student Response 
28 
In the space below, draw a rectangle 2 inches wide and 3½ inches long. 
Incorrect #3  Student Response 
28 
In the space below, draw a rectangle 2 inches wide and 3½ inches long. 
28 
In the space below, draw a rectangle 2 inches wide and 3½ inches long. 
Incorrect #2  Student Response 
28 
In the space below, draw a rectangle 2 inches wide and 3½ inches long. 
Incorrect #1  Student Response 
28 
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 
29 
What is the length in centimeters of one of the longer sides of the rectangle? 
29 
What is the length in centimeters of one of the longer sides of the rectangle? 
Incorrect #2  Student Response 
29 
What is the length in centimeters of one of the longer sides of the rectangle? 
Incorrect #1  Student Response 
29 
What is the length in centimeters of one of the longer sides of the rectangle? 
Scoring Guide 
Score & Description  
 

Correct  Student Response 
30 
What is the length in centimeters of the diagonal from A to B? 
30 
What is the length in centimeters of the diagonal from A to B? 
Incorrect  Student Response 
30 
What is the length in centimeters of the diagonal from A to B? 
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 
31 
On the grid below, draw a rectangle with an area of 12 square units. 
Incorrect #2  Student Response 
31 
On the grid below, draw a rectangle with an area of 12 square units. 
Incorrect #1  Student Response 
31 
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 
32 
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? 
32 
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 
32 
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? 
32 
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 
32 
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? 
32 
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 
32 
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? 
32 
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 
33 
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 
33 
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 
33 
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 
33 
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 
34 
Divide 108 by 9. 
34 
Divide 108 by 9. 
Incorrect #4  Student Response 
34 
Divide 108 by 9. 
34 
Divide 108 by 9. 
Incorrect #3  Student Response 
34 
Divide 108 by 9. 
34 
Divide 108 by 9. 
Incorrect #2  Student Response 
34 
Divide 108 by 9. 
34 
Divide 108 by 9. 
Incorrect #1  Student Response 
34 
Divide 108 by 9. 
34 
Divide 108 by 9. 
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 multiplication problem below, write the missing number in the box. 
35 
In the multiplication problem below, write the missing number in the box. 
Incorrect #3  Student Response 
35 
In the multiplication problem below, write the missing number in the box. 
35 
In the multiplication problem below, write the missing number in the box. 
Incorrect #2  Student Response 
35 
In the multiplication problem below, write the missing number in the box. 
35 
In the multiplication problem below, write the missing number in the box. 
Incorrect #1  Student Response 
35 
In the multiplication problem below, write the missing number in the box. 
35 
In the multiplication problem below, write the missing number in the box. 
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. 
Correct #1  Student Response 
36 
Which two of the items above would provide a total of about 600 calories? 
Correct #2  Student Response 
36 
Which two of the items above would provide a total of about 600 calories? 
Incorrect  Student Response 
36 
Which two of the items above would provide a total of about 600 calories? 
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 
37 
What was the total number of points earned from the mathathon? 
37 
What was the total number of points earned from the mathathon? 
Incorrect #3  Student Response 
37 
What was the total number of points earned from the mathathon? 
37 
What was the total number of points earned from the mathathon? 
Incorrect #2  Student Response 
37 
What was the total number of points earned from the mathathon? 
37 
What was the total number of points earned from the mathathon? 
Incorrect #1  Student Response 
37 
What was the total number of points earned from the mathathon? 
37 
What was the total number of points earned from the mathathon? 
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 
38 
Ms. Chen's class earned how many more points from the readathon than from the mathathon? 
38 
Ms. Chen's class earned how many more points from the readathon than from the mathathon? 
Incorrect #2  Student Response 
38 
Ms. Chen's class earned how many more points from the readathon than from the mathathon? 
38 
Ms. Chen's class earned how many more points from the readathon than from the mathathon? 
Incorrect #1  Student Response 
38 
Ms. Chen's class earned how many more points from the readathon than from the mathathon? 
38 
Ms. Chen's class earned how many more points from the readathon than from the mathathon? 
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 
George buys two calculators that cost $3.29 each. If there is no tax, how much change will he receive from a $10 bill? 
Incorrect #2  Student Response 
39 
George buys two calculators that cost $3.29 each. If there is no tax, how much change will he receive from a $10 bill? 
Incorrect #1  Student Response 
39 
George buys two calculators that cost $3.29 each. If there is no tax, how much change will he receive from a $10 bill? 
Scoring Guide 
Score & Description  
 

Correct  Student Response 
40 
If the pattern shown continues, could 375 be one of the products in this pattern? 
Incorrect  Student Response 
40 
If the pattern shown continues, could 375 be one of the products in this pattern? 
Scoring Guide 
Score & Description  
 

Correct  Student Response 
41 
Multiply: 3 × 405 = 
41 
Multiply: 3 × 405 = 
Incorrect  Student Response 
41 
Multiply: 3 × 405 = 
41 
Multiply: 3 × 405 = 
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 
In 1990 a school had 125 students. Each year the number of students in the school increases by 50. Fill in the table to show the number of students expected for each year. 
42 
In 1990 a school had 125 students. Each year the number of students in the school increases by 50. Fill in the table to show the number of students expected for each year. 
Incorrect #3  Student Response 
42 
In 1990 a school had 125 students. Each year the number of students in the school increases by 50. Fill in the table to show the number of students expected for each year. 
42 
In 1990 a school had 125 students. Each year the number of students in the school increases by 50. Fill in the table to show the number of students expected for each year. 
Incorrect #2  Student Response 
42 
In 1990 a school had 125 students. Each year the number of students in the school increases by 50. Fill in the table to show the number of students expected for each year. 
42 
In 1990 a school had 125 students. Each year the number of students in the school increases by 50. Fill in the table to show the number of students expected for each year. 
Incorrect #1  Student Response 
42 
In 1990 a school had 125 students. Each year the number of students in the school increases by 50. Fill in the table to show the number of students expected for each year. 
42 
In 1990 a school had 125 students. Each year the number of students in the school increases by 50. Fill in the table to show the number of students expected for each year. 
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 
Suppose 120 is a number in column A of the table. Use the same rule to fill in the number in column B. 
43 
Suppose 120 is a number in column A of the table. Use the same rule to fill in the number in column B. 
Incorrect #4  Student Response 
43 
Suppose 120 is a number in column A of the table. Use the same rule to fill in the number in column B. 
43 
Suppose 120 is a number in column A of the table. Use the same rule to fill in the number in column B. 
Incorrect #3  Student Response 
43 
Suppose 120 is a number in column A of the table. Use the same rule to fill in the number in column B. 
43 
Suppose 120 is a number in column A of the table. Use the same rule to fill in the number in column B. 
Incorrect #2  Student Response 
43 
Suppose 120 is a number in column A of the table. Use the same rule to fill in the number in column B. 
43 
Suppose 120 is a number in column A of the table. Use the same rule to fill in the number in column B. 
Incorrect #1  Student Response 
43 
Suppose 120 is a number in column A of the table. Use the same rule to fill in the number in column B. 
43 
Suppose 120 is a number in column A of the table. Use the same rule to fill in the number in column B. 
Scoring Guide 
Score & Description  
 

Correct  Student Response 
44 
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 
44 
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 
45 
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. 
45 
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 
45 
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 
45 
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. 
45 
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  
 
 
 

*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 
46 
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? 
46 
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 
46 
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 
46 
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? 
46 
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 
46 
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? 
46 
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  
 

Scoring Guide 
Score & Description  
 

Correct  Student Response 
48 
In the number sentence above, what number belongs in the? 
Incorrect  Student Response 
48 
In the number sentence above, what number belongs in the? 
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 
49 
A measurement of 60 inches is equal to how many feet? (12 inches = 1 foot) 
Incorrect #1  Student Response 
49 
A measurement of 60 inches is equal to how many feet? (12 inches = 1 foot) 
Incorrect #2  Student Response 
49 
A measurement of 60 inches is equal to how many feet? (12 inches = 1 foot) 
Scoring Guide 
Score & Description  
 

Correct  Student Response 
50 
The table below shows some number pairs. The following rule
was used to find each number in column B.
Rule: Multiply the number in column A by itself and then add 3. Fill in the missing number, using the same rule. 
Incorrect  Student Response 
50 
The table below shows some number pairs. The following rule
was used to find each number in column B.
Rule: Multiply the number in column A by itself and then add 3. Fill in the missing number, using the same rule. 
Scoring Guide 
Score & Description  
 

Correct  Student Response 
51 
What is the distance around the rectangle shown above? 
Incorrect  Student Response 
51 
What is the distance around the rectangle shown above? 
Scoring Guide 
Score & Description  
 
