
 
1. 
Which of the following lists the angles shown above in order of measure from smallest to largest?  
A)  1, 2, 3, 4  
B)  2, 3, 4, 1  
C)  3, 2, 1, 4  
D)  3, 1, 4, 2  
E)  4, 2, 1, 3  


 
5. 
What is the area of the shaded figure?  
A)  9 square centimeters  
B)  11 square centimeters  
C)  13 square centimeters  
D)  14 square centimeters  


8. 
A rectangular playground has a perimeter of 390 feet. The width of the playground is 75 feet. What is its length?  
A)  5.2 feet  
B)  97.5 feet  
C)  120 feet  
D)  130 feet  
E)  240 feet  
 
9. 
What temperature would be 15° F more than the temperature shown on the thermometer above?  
 
A)  20° F  
B)  10° F  
C)  10° F  
D)  15° F  
E)  20° F  
 
10. 
In the figure above, which object is heaviest?  
A)  The metal ball  
B)  The sandwich  
C)  The bag of potato chips  
D)  The puppy  
11. 
The perimeter of a square is 36 inches. What is the length of one side of the square?  
A)  4 inches  
B)  6 inches  
C)  9 inches  
D)  18 inches  
13. 
Length can be measured to within 0.05 centimeter accuracy by using a certain type of measuring instrument. A reading of 3.7 centimeters on this instrument means that the actual length is at least  
A)  3.20 centimeters  
B)  3.65 centimeters  
C)  3.69 centimeters  
D)  3.70 centimeters  
E)  3.75 centimeters  

1 mile = 5,280 feet  
15. 
How many feet are in 15 miles?  
A)  352  
B)  35,200  
C)  79,200  
D)  84,480  
E)  89,760  
Did you use the calculator on this question? 

 
17. 
Which of the following numerical expressions gives the area of the rectangle above?  
A)  4 × 6  
B)  4 + 6  
C)  2(4 × 6)  
D)  2(4 + 6)  
E)  4 + 6 + 4 + 6  
Did you use the calculator on this question? 
18. 
The cruise ship Titanic was 882 feet long. Which of the following is closest to that length?  
A)  Two movingvan lengths  
B)  Fifty car lengths  
C)  One hundred skateboard lengths  
D)  Five hundred schoolbus lengths  
E)  One thousand bicycle lengths  
 
19. 
The following steps are used
to read the electric meter shown above.
(1) On each dial, the pointer moves in the direction of the arrow for that dial. (2) On each dial, the number that the pointer has just passed is that dial's reading. (3) To obtain the meter reading, the dials are read from left to right. What is the reading on the meter?  
A)  2,975 kwh  
B)  3,086 kwh  
C)  5,792 kwh  
D)  5,803 kwh  
E)  6,803 kwh  



23. 
Of the following, which is the best unit to use when measuring the growth of a plant every other day during a 2week period?  
A)  Centimeter  
B)  Meter  
C)  Kilometer  
D)  Foot  
E)  Yard  
Did you use the calculator on this question? 

25. 
A car odometer registered 41,256.9 miles when a highway sign warned of a detour 1,200 feet ahead. What will the odometer read when the car reaches the detour? (5, 280 feet = 1 mile)  
A)  42,456.9  
B)  41,279.9  
C)  41,261.3  
D)  41,259.2  
E)  41,257.1  
Did you use the calculator on this question? 
 
26. 
The weights of three objects were compared using a pan balance. Two comparisons were made as shown in the figure above. Which object is the heaviest?  
A)  A  
B)  B  
C)  C  
D)  Not enough information is given.  


29. 
A rectangular carpet is 9 feet long and 6 feet wide. What is the area of the carpet in square feet?  
A)  15  
B)  27  
C)  30  
D)  54  


 
33. 
In the figure above, a circle with center O and radius of length 3 is inscribed in a square. What is the area of the shaded region?  
A)  3.86  
B)  7.73  
C)  28.27  
D)  32.86  
E)  36.00  
Did you use the calculator on this question? 
 
34. 
Chris wishes to carpet the rectangular room shown above. To the nearest square yard, how many square yards of carpet are needed to carpet the floor of the room if the closet floor will not be carpeted? (1 square yard = 9 square feet)  
A)  8  
B)  10  
C)  11  
D)  19  
E)  22  
Did you use the calculator on this question? 
37. 
The length of a trail that Pat hiked in one day could have been  
A)  5 milliliters  
B)  5 centimeters  
C)  5 meters  
D)  5 kilometers  

 
39. 
If the area of the shaded triangle shown above is 4 square inches, what is the area of the entire square?  
A)  4 square inches  
B)  8 square inches  
C)  12 square inches  
D)  16 square inches  
E)  Not enough information given  
40. 
For each figure below, the lengths of 3 sides are given. Which figure could have a perimeter of 28?  
A)  
B)  
C)  
D)  
E)  
 
42. 
In the figure above, the tube was filled to the 0 mark at the start. How much liquid has been let out?  
A)  10 milliliters  
B)  15 milliliters  
C)  25 milliliters  
D)  40 milliliters  
E)  50 milliliters  
43. 
If a measurement of a rectangular box is given as 48 cubic inches, then the measurement represents the  
A)  distance around the top of the box  
B)  length of an edge of the box  
C)  surface area of the box  
D)  volume of the box  
44. 
In the model town that a class is building, a car 15 feet long is represented by a scale model 3 inches long. If the same scale is used, a house 35 feet high would be represented by a scale model how many inches high?  
A) 
 
B)  3  
C)  5  
D)  7  
E) 
 
Did you use the calculator on this question? 
 
45. 
A certain rectangle has area equal to the sum of the areas of the four rectangles shown above. If its length is 4, what is its width?  
A)  2  
B)  2¼  
C)  2½  
D)  3  
E)  3½  
Did you use the calculator on this question? 

Scoring Guide 
Solution:

Score & Description  
 
 


Correct  Student Response 
2 
The weather service reported a tornado 75° south of west. On the figure below, use your protractor to draw an arrow from P in the direction in which the tornado was sighted.  
Scorer Comments: This response received full credit because the student drew an arrow in the correct direction and at the correct angle. 

Partial  Student Response 
2 
The weather service reported a tornado 75° south of west. On the figure below, use your protractor to draw an arrow from P in the direction in which the tornado was sighted.  
Scorer Comments: This response received partial credit because the student drew the arrow in the correct direction, but with an incorrect angle measure. 

Incorrect  Student Response 
2 
The weather service reported a tornado 75° south of west. On the figure below, use your protractor to draw an arrow from P in the direction in which the tornado was sighted.  
Scorer Comments: This response received no credit because the arrow is drawn in the wrong direction and the angle measure is incorrect. 

Scoring Guide 
Solution: Tolerance of inch on all measurements. 
Score & Description  
 
 


Correct  Student Response 
3 
The figure above shows a picture and its frame. In the space below, draw a rectangular picture 2 inches by 3 inches and draw a 1inchwide frame around it.  
Scorer Comments: This response received full credit because both the picture and the frame were drawn with the correct dimensions. 

Partial  Student Response 
3 
The figure above shows a picture and its frame. In the space below, draw a rectangular picture 2 inches by 3 inches and draw a 1inchwide frame around it.  
Scorer Comments: This response received partial credit because the picture was drawn correctly, but the frame was not drawn correctly. 

Incorrect  Student Response 
3 
The figure above shows a picture and its frame. In the space below, draw a rectangular picture 2 inches by 3 inches and draw a 1inchwide frame around it.  
Scorer Comments: This response received no credit because both the picture and the frame were drawn incorrectly. 

Scoring Guide 
Solution: 7 boxes Correct process for solution includes evidence of each of the following (may be implied or explicit):
(Note: Steps b and c may be interchanged; if done, this would yield 10 sq. in. and 160 sq. ft., respectively.) 
Score & Description  
 
 
 
 


Extended  Student Response 
4 
The floor of a room shown in the figure above is to be covered with tiles. One box of floor tiles will cover 25 square feet. Use your ruler to determine how many whole boxes of these tiles must be bought to cover the entire floor.  
Scorer Comments: This response received full credit because the number of boxes of tiles was correctly determined and all work was shown. First, the area of the floor was determined by measuring the scaled drawing and converting to square feet. Next, the area of the floor was divided by the area that one box of tiles would cover, which the student then correctly rounded to a whole number. 

Satisfactory  Student Response 
4 
The floor of a room shown in the figure above is to be covered with tiles. One box of floor tiles will cover 25 square feet. Use your ruler to determine how many whole boxes of these tiles must be bought to cover the entire floor.  
Scorer Comments: This response received a satisfactory score. The student correctly converted the scaled dimensions into feet, calculated the area of the room, and divided by 25, but they did not round the final answer to a whole number. 

Partial  Student Response 
4 
The floor of a room shown in the figure above is to be covered with tiles. One box of floor tiles will cover 25 square feet. Use your ruler to determine how many whole boxes of these tiles must be bought to cover the entire floor.  
Scorer Comments: This response received partial credit. The student calculated the area of the room using the scaled dimensions, but did not convert that area into square feet. They knew to divide by 25 and round the answer, but the number is not correct since they were using different units. 

Minimal  Student Response 
4 
The floor of a room shown in the figure above is to be covered with tiles. One box of floor tiles will cover 25 square feet. Use your ruler to determine how many whole boxes of these tiles must be bought to cover the entire floor.  
Scorer Comments: This response received minimal credit because the student correctly determined the area of the room from the scaled drawing. 

Incorrect  Student Response 
4 
The floor of a room shown in the figure above is to be covered with tiles. One box of floor tiles will cover 25 square feet. Use your ruler to determine how many whole boxes of these tiles must be bought to cover the entire floor.  
Scorer Comments: This response received no credit because the answer given is incorrect and there is no relevant supporting work. 


Scoring Guide 
Solution:
Tolerance
Note: Both sides should be the same measure

Score & Description  
 
 


Correct  Student Response 
6 
On the grid below, use piece Q to draw a right triangle. The angles of the right triangle should measure the same as the angles in piece Q. The area of the right triangle should be four times the area of piece Q.  
Scorer Comments: This response received full credit because the student correctly drew a right triangle that has an area four times that of piece Q, also a right triangle. 

Partial  Student Response 
6 
On the grid below, use piece Q to draw a right triangle. The angles of the right triangle should measure the same as the angles in piece Q. The area of the right triangle should be four times the area of piece Q.  
Scorer Comments: This response received partial credit because the student drew a right triangle, but its area is not four times the area of piece Q. 

Incorrect  Student Response 
6 
On the grid below, use piece Q to draw a right triangle. The angles of the right triangle should measure the same as the angles in piece Q. The area of the right triangle should be four times the area of piece Q.  
Scorer Comments: This response received no credit because all the student did was trace piece Q once, so they did not create a right triangle with an area four times that of piece Q. 

Scoring Guide 
Solution: a. 16 square units b. Here are some of the possible correct responses 
Score & Description  
 
 

Correct  Student Response 
7 
a. What is the area, in square units, enclosed by the pentagon above?  
Scorer Comments: This response received full credit because the student correctly determined the area of the given pentagon and drew another, different pentagon with the same area. 

Partial  Student Response 
7 
a. What is the area, in square units, enclosed by the pentagon above?  
Scorer Comments: This response received partial credit because the student correctly determined the area of the given pentagon, but they did not answer part b. 

Incorrect  Student Response 
7 
a. What is the area, in square units, enclosed by the pentagon above?  
Scorer Comments: This response received no credit because part a is incorrect and the pentagon they drew in part b is the same as the one given, but in a different direction. 





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 
12 
What is the length of the toothpick in the figure above? 
Incorrect #3  Student Response 
12 
What is the length of the toothpick in the figure above? 
Incorrect #2  Student Response 
12 
What is the length of the toothpick in the figure above? 
Incorrect #1  Student Response 
12 
What is the length of the toothpick in the figure above? 

Scoring Guide 
Solution: Possible correct answers include:

Score & Description  
 
 
 
 

In this question the student was asked to draw and
explain three different ways to divide an Lshaped region to determine the
area. The student was also required to give an expression representing the
area for each of the different divisions of the region (however, the
student was not asked to calculate the area of the region). There are many
possible ways to do this, but to earn full credit the student needed to
show three different divisions of the region, label the lengths in each
figure correctly, and write an expression for the area consistent with
each figure. This question requires visualization and knowledge of one or
more formulas for finding area.
Notes: Any division of the figures into rectangles, triangles, trapezoids, or parallelograms is acceptable. Student either needs to show (5 × 5) + (5 × 12), for example OR label all appropriate dimensions in the figure to give credit for 25 + 60. However, "25+60" is not acceptable if dimensions are not labeled. 
Extended  Student Response 
14 
Ted wants to purchase floor covering for the hallway shown above. He knows there are many ways to find the area of the hallway. One way is to divide the hallway into the sections shown below and then add together the area of each section. 
Satisfactory  Student Response 
14 
Ted wants to purchase floor covering for the hallway shown above. He knows there are many ways to find the area of the hallway. One way is to divide the hallway into the sections shown below and then add together the area of each section. 
Partial  Student Response 
14 
Ted wants to purchase floor covering for the hallway shown above. He knows there are many ways to find the area of the hallway. One way is to divide the hallway into the sections shown below and then add together the area of each section. 
Minimal  Student Response 
14 
Ted wants to purchase floor covering for the hallway shown above. He knows there are many ways to find the area of the hallway. One way is to divide the hallway into the sections shown below and then add together the area of each section. 
Incorrect  Student Response 
14 
Ted wants to purchase floor covering for the hallway shown above. He knows there are many ways to find the area of the hallway. One way is to divide the hallway into the sections shown below and then add together the area of each section. 
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 
16 
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 
16 
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: 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 
20 
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 
20 
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 
20 
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 
20 
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: 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 
21 
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. 
21 
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 
21 
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. 
21 
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 
21 
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. 
21 
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 
22 
Which of the shapes N, P, and Q has the longest perimeter (distance around)? 
22 
Which of the shapes N, P, and Q has the longest perimeter (distance around)? 
Incorrect #2  Student Response 
22 
Which of the shapes N, P, and Q has the longest perimeter (distance around)? 
22 
Which of the shapes N, P, and Q has the longest perimeter (distance around)? 
Incorrect #1  Student Response 
22 
Which of the shapes N, P, and Q has the longest perimeter (distance around)? 
22 
Which of the shapes N, P, and Q has the longest perimeter (distance around)? 

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 
24 
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 ) 
24 
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 
24 
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 
24 
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 ) 
24 
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 
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 
27 
What is the length in centimeters of one of the longer sides of the rectangle? 
27 
What is the length in centimeters of one of the longer sides of the rectangle? 
Incorrect #2  Student Response 
27 
What is the length in centimeters of one of the longer sides of the rectangle? 
Incorrect #1  Student Response 
27 
What is the length in centimeters of one of the longer sides of the rectangle? 
Scoring Guide 
Score & Description  
 

Correct  Student Response 
28 
What is the length in centimeters of the diagonal from A to B? 
28 
What is the length in centimeters of the diagonal from A to B? 
Incorrect  Student Response 
28 
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 
30 
Use your protractor to find the degree measure of the angle shown above. 
Incorrect  Student Response 
30 
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 
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  
 

Correct  Student Response 
32 
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? 
32 
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 
32 
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? 
32 
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 
38 
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 
38 
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? 





