Additional Materials (1)



Additional Materials (2)



Additional Materials (3)



Additional Materials (4)



Additional Materials (5)



Additional Material (1)
Additional Material



1.   

The results of a class survey on whether students liked a new television show are as follows.

     25 students liked the new show.

     15 students disliked the new show.

      5 students had no opinion on the new show.

On the graph below, each smiley face represents 5 students. Draw the correct number of faces to illustrate the results of the class survey.


 
 

class survey graph



Question 2 refers to Additional Materials (5)

2.   

Draw bars on the graph below so that the number of dogs is twice the number of cats and the number of hamsters is one-half the number of cats.


 
 

bar graph of dogs, cats, and hamsters.  Cats=6



Question 3 refers to Additional Materials (5)

3. 

Each of the 6 faces of a certain cube is labeled either R or S. When the cube is tossed, the probability of the cube landing with an R face up is 1/3 .

How many faces are labeled R ?

 
A)  Five
B)  Four
C)  Three
D)  Two
E)  One
 



4. 

The prices of gasoline in a certain region are $1.41, $1.36, $1.57, and $1.45 per gallon. What is the median price per gallon for gasoline in this region?
 
A)  $1.41
B)  $1.43
C)  $1.44
D)  $1.45
E)  $1.47
 



5.   

A package of candies contained only 10 red candies, 10 blue candies, and 10 green candies. Bill shook up the package, opened it, and started taking out one candy at a time and eating it. The first 2 candies he took out and ate were blue. Bill thinks the probability of getting a blue candy on his third try is 10/30 or 1/3.

Is Bill correct or incorrect?


 
 
Explain your answer.



               pie graph of elements that make up the earth's crust

6. 

According to the graph above, which element forms the second greatest portion of the earth's crust?

 

 
A)  Oxygen
B)  Silicon
C)  Aluminum
D)  Iron
E)  Calcium
 



Stimulus Image

7. 

The pie chart above shows the portion of time Pat spent on homework in each subject last week. If Pat spent 2 hours on mathematics, about how many hours did Pat spend on homework altogether?
 
A)  4
B)  8
C)  12
D)  16
 



FINAL TEST SCORES
Score Number of Students
95 50
90 120
85 170
80 60
75 10

 

8.   

Use the information in the table above to complete the bar graph below.
 
 
Stimulus Image

 
 



9.   

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.
 

 
Number on First Chip Number on Second Chip
 

 
 



10. 

4, 8, 3, 2, 5, 8, 12

What is the median of the numbers above?

 
A)  4
B)  5
C)  6
D)  7
E)  8
 



Stimulus Image

11. 

According to the graph above, how many times did the yearly increase of the price of a hamburger exceed 10 cents?
 
A)  None
B)  One
C)  Two
D)  Three
E)  Four
 
Did you use the calculator on this question?



Score Number of Students
90 1
80 3
70 4
60 0
50 3

 

12.   

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?
 
  Answer: _________________________
 
 
Did you use the calculator on this question?



Stimulus Image

13. 

There are 1,200 students enrolled in Adams Middle School. According to the graph above, how many of these students participate in sports?
 
A)  380
B)  456
C)  760
D)  820
E)  1,162
 
Did you use the calculator on this question?



14.   

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.
 
 



Did you use the calculator on this question?



POPULATION
Clear Lake 8,000
Rancho Santa Fe 4,000
Bull Shoals 1,500
Beaver City 750
Jeffersonville 500

 

15. 

A pictogram of the data above is to be drawn using as the symbol that represents 500 people. How many would it take to represent the population of Rancho Santa Fe?
 
A)  1
B)  4
C)  8
D)  80
E)  4,000
 



16. 

Gloria's diving scores from a recent competition are represented in the stem-and-leaf plot shown below. In this plot, 3 | 4 would be read as 3.4.

5 2   5
6 1
7 7
8 0   2

What was her lowest score for this competition?
 
A)  0.02
B)  1.0
C)  2.5
D)  5.2
E)  8.0
 



Stimulus Image

17.   

The graph above represents Marisa's riding speed throughout her 80-minute bicycle trip. Use the information in the graph to describe what could have happened on the trip, including her speed throughout the trip.
 
  During the first 20 minutes, Marisa ______________________________________________________

From 20 minutes to 60 minutes, she _____________________________________________________

From 60 minutes to 80 minutes, she _____________________________________________________


 
 



18.   

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.
 
 
Stimulus Image

 
 



19. 

A poll is being taken at Baker Junior High School to determine whether to change the school mascot. Which of the following would be the best place to find a sample of students to interview that would be most representative of the entire student body?
 
A)  An algebra class
B)  The cafeteria
C)  The guidance office
D)  A French class
E)  The faculty room
 


Question 20 refers to Additional Material (1)

20.   

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.
 

 
  Class 1 Class 2 Class 3
Shape N 9 14 11
Shape P 1 9 17
Shape Q 22 7 2

Using the information in the chart, Mr. Bell must select one of the shapes to be the symbol. Which one should he select and why?

The shape Mr. Bell should select:____________________

Explain:
 

 






This question requires you to show your work and explain your reasoning. You may use drawings, words, and numbers in your explanation. Your answer should be clear enough so that another person could read it and understand your thinking. It is important that you show all of your work.

METRO RAIL COMPANY
Month Daily Ridership
October 14,000
November 14,100
December 14,100
January 14,200
February 14,300
March 14,600

The data in the table above has been correctly represented by both graphs shown below.
 

Stimulus Image

21.   

Which graph would be best to help convince others that the Metro Rail Company made a lot more money from ticket sales in March than in October?

Explain your reason for making this selection.


 
 

 

 

 

 

 

Why might people who thought that there was little difference between October and March ticket sales consider the graph you chose to be misleading?
 
 




Did you use the calculator on this question?



22. 

In a bag of marbles, 1/2 are red, 1/4 are blue, 1/6 are green, and 1/12 are yellow. If a marble is taken from the bag without looking, it is most likely to be
 
A)  red
B)  blue
C)  green
D)  yellow
 



23. 

From a shipment of 500 batteries, a sample of 25 was selected at random and tested. If 2 batteries in the sample were found to be dead, how many dead batteries would be expected in the entire shipment?
 
A)  10
B)  20
C)  30
D)  40
E)  50
 



Stimulus Image

24. 

The total distances covered by two runners during the first 28 minutes of a race are shown in the graph above. How long after the start of the race did one runner pass the other?
 
A)  3 minutes
B)  8 minutes
C)  12 minutes
D)  14 minutes
E)  28 minutes
 



Stimulus Image

25. 

The graph above shows how many of the 32 children in Mr. Rivera's class are 8, 9, 10, and 11 years old. Which of the following is true?
 
A)  Most are younger than 9.
B)  Most are younger than 10.
C)  Most are 9 or older.
D)  None of the above is true.
 



26.   

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.
 
 
y stands for one
yellow marble.
First
Marble
Second
Marble
b stands for one
blue marble.
y b

 
 



27.   

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.
 
 
Stimulus Image

 
 



Stimulus Image

28. 

The entire circle shown above represents a total of 2,675 radios sold. Of the following, which is the best approximation of the number of radios represented by the shaded sector of the circle?
 
A)  70
B)  275
C)  985
D)  25,880
E)  98,420
 
Did you use the calculator on this question?



Stimulus Image

29. 

In the graph above, each dot shows the number of sit-ups and the corresponding age for one of 13 people. According to this graph, what is the median number of sit-ups for these 13 people?
 
A)  15
B)  20
C)  45
D)  50
E)  55
 
Did you use the calculator on this question?



Stimulus Image

30.   

The pictograph shown above is misleading. Explain why.
 
  Answer:
 
 






31. 

The average weight of 50 prize-winning tomatoes is 2.36 pounds. What is the combined weight, in pounds, of these 50 tomatoes?
 
A)  0.0472
B)  11.8
C)  52.36
D)  59
E)  118
 



Stimulus Image

32. 

The nine chips shown above are placed in a sack and then mixed up. Madeline draws one chip from this sack. What is the probability that Madeline draws a chip with an even number?
 
A) 
1
9
B) 
2
9
C) 
4
9
D) 
1
2
E) 
4
5
 



33. 

There are 15 girls and 11 boys in a mathematics class. If a student is selected at random to run an errand, what is the probability that a boy will be selected?
 
A) 
 4 
26
B) 
11
26
C) 
15
26
D) 
11
15
E) 
15
11
 



HAIR COLOR SURVEY
RESULTS
Color of
Hair
Percentage
Blond
Brown
Black
17
50
33
Totals 100

 

34.   

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.
 
 
Stimulus Image

 
 
Did you use the calculator on this question?




Question 1

Scoring Guide
 
Solution:

All categories correct.

In order for a category to be counted as correct, it must have the correct number of faces (but the eyes and mouth do not have to be drawn). The use of numbers rather than faces is an incorrect response.

Liked

   smiley face     smiley face     smiley face     smiley face     smiley face

Disliked

   smiley face     smiley face     smiley face

No Opinion

   smiley face

Score & Description
  Correct
 

Correct response.

  Incorrect #3
 

Appears as though each student is represented by one face.

  Incorrect #2
 

Two categories correct.

  Incorrect #1
 

Any incorrect response other than those described in 2 and 3.


*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

1  

The results of a class survey on whether students liked a new television show are as follows.

     25 students liked the new show.

     15 students disliked the new show.

      5 students had no opinion on the new show.

On the graph below, each smiley face represents 5 students. Draw the correct number of faces to illustrate the results of the class survey.

  Response Image
   Scorer Comments:
This response was scored as correct because the student drew the correct number of faces for each category.
 
 
 
  Incorrect #3 - Student Response

1  

The results of a class survey on whether students liked a new television show are as follows.

     25 students liked the new show.

     15 students disliked the new show.

      5 students had no opinion on the new show.

On the graph below, each smiley face represents 5 students. Draw the correct number of faces to illustrate the results of the class survey.

  Response Image
   Scorer Comments:

In this paper, the student drew a face for every person. This particular response was coded to gather data on common student errors, but the paper received no credit.


 
 
 
  Incorrect #2 - Student Response

1  

The results of a class survey on whether students liked a new television show are as follows.

     25 students liked the new show.

     15 students disliked the new show.

      5 students had no opinion on the new show.

On the graph below, each smiley face represents 5 students. Draw the correct number of faces to illustrate the results of the class survey.

  Response Image
   Scorer Comments:
In this paper, the student had two of the three categories correct. This particular response was coded to gather data on common student errors, but the paper received no credit.
 
 
 
  Incorrect #1 - Student Response

1  

The results of a class survey on whether students liked a new television show are as follows.

     25 students liked the new show.

     15 students disliked the new show.

      5 students had no opinion on the new show.

On the graph below, each smiley face represents 5 students. Draw the correct number of faces to illustrate the results of the class survey.

  Response Image
   Scorer Comments:

Papers scored as incorrect #1 received no credit and represent incorrect responses different than those described under incorrect #3 and incorrect #2.


 
 
 


Question 2

Scoring Guide
 
Solution:
Both dog and hamsters correct.

Any type of shading bars is acceptable. (no shading is also acceptable.)

Top edge of hamsters should fall between 2 and 4 (anywhere) but not 2 or 4.

graph of dogs, cats, and hamsters.  Dog=12, cats=6, hamster=3

Note: Vertical lines that are the same length as the appropriate bars are acceptable.

Score & Description
  Correct
  Correct response
  Incorrect #3
  Only bar for hamsters correct.
  Incorrect #2
  Only bar for dogs correct.
  Incorrect #1
  Incorrect response – no bars correct.

*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

2  

Draw bars on the graph below so that the number of dogs is twice the number of cats and the number of hamsters is one-half the number of cats.

  Response Image
   Scorer Comments:
This paper was scored as correct because the student correctly added the bars for the number of dogs and hamsters.
 
 
 
  Incorrect #3 - Student Response

2  

Draw bars on the graph below so that the number of dogs is twice the number of cats and the number of hamsters is one-half the number of cats.

  Response Image
   Scorer Comments:
In this paper, the student correctly added the bar for the number of  hamsters, but the bar for the number of dogs is not correct. This particular response was coded to gather data on common student errors, but the paper received no credit.
 
 
 
  Incorrect #2 - Student Response

2  

Draw bars on the graph below so that the number of dogs is twice the number of cats and the number of hamsters is one-half the number of cats.

  Response Image
   Scorer Comments:
In this paper, the student correctly added the bar for the number of dogs, but the bar for the number of hamsters is not correct. This particular response was coded to gather data on common student errors, but the paper received no credit.
 
 
 
  Incorrect #1 - Student Response

2  

Draw bars on the graph below so that the number of dogs is twice the number of cats and the number of hamsters is one-half the number of cats.

  Response Image
   Scorer Comments:
Papers scored as incorrect #3 received no credit and represent incorrect responses different than those described under incorrect #1 and incorrect #2.
 
 
 


Question 3

Key
 
 3.  

Each of the 6 faces of a certain cube is labeled either R or S. When the cube is tossed, the probability of the cube landing with an R face up is 1/3 .

How many faces are labeled R ?

     
  A)  Five
  B)  Four
  C)  Three
Key Arrow D)  Two
  E)  One




Question 4

Key
 
 4.   The prices of gasoline in a certain region are $1.41, $1.36, $1.57, and $1.45 per gallon. What is the median price per gallon for gasoline in this region?
     
  A)  $1.41
Key Arrow B)  $1.43
  C)  $1.44
  D)  $1.45
  E)  $1.47




Question 5

Scoring Guide
 
Solution:
He is incorrect. Two of the candies that Bill ate were blue, which leaves only 8 blue candies. A total of 28 candies remain, which gives a probability of 8/28 , (4/14 , 2/7 ) or 0.29.

Score & Description
  Correct
  Correct response
  Partial
  Shows some understanding of sampling without replacement (i.e., that the number of blue candies has decreased because he already removed two), but the explanation is not complete enough to earn full credit.
  Incorrect
  Incorrect response

 




  Correct - Student Response

5  

A package of candies contained only 10 red candies, 10 blue candies, and 10 green candies. Bill shook up the package, opened it, and started taking out one candy at a time and eating it. The first 2 candies he took out and ate were blue. Bill thinks the probability of getting a blue candy on his third try is 10/30 or 1/3.

Is Bill correct or incorrect?

  Response Image
   Scorer Comments:
This response received full credit because the student correctly explained that the probability of getting a blue candy will not be the same on the third try and that it will go down since there will be less blue candies each time.
 
 
 
  Partial - Student Response

5  

A package of candies contained only 10 red candies, 10 blue candies, and 10 green candies. Bill shook up the package, opened it, and started taking out one candy at a time and eating it. The first 2 candies he took out and ate were blue. Bill thinks the probability of getting a blue candy on his third try is 10/30 or 1/3.

Is Bill correct or incorrect?

  Response Image
   Scorer Comments:
This response received partial credit because the student showed some understanding of sampling without replacement since they recognized that the number of blue candies was decreasing, but they did not take into account that the total number of candies in the bag was also decreasing each time.
 
 
 
  Incorrect - Student Response

5  

A package of candies contained only 10 red candies, 10 blue candies, and 10 green candies. Bill shook up the package, opened it, and started taking out one candy at a time and eating it. The first 2 candies he took out and ate were blue. Bill thinks the probability of getting a blue candy on his third try is 10/30 or 1/3.

Is Bill correct or incorrect?

  Response Image
   Scorer Comments:
This response received no credit. The student answered that the probability would still be 10 out of 30, which is incorrect because the candies are not being replaced.
 
 
 


Question 6

Key
 
 6.  

According to the graph above, which element forms the second greatest portion of the earth's crust?

     
  A)  Oxygen
Key Arrow B)  Silicon
  C)  Aluminum
  D)  Iron
  E)  Calcium




Question 7

Key
 
 7.   The pie chart above shows the portion of time Pat spent on homework in each subject last week. If Pat spent 2 hours on mathematics, about how many hours did Pat spend on homework altogether?
     
  A)  4
Key Arrow B)  8
  C)  12
  D)  16




Question 8

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

Score & Description
  Correct
  Correct response
  Incorrect
  Incorrect or incomplete response—includes one correct bar only or one correct bar and one incorrect bar

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

8  

Use the information in the table above to complete the bar graph below.
  Response Image
 
 
  Incorrect - Student Response

8  

Use the information in the table above to complete the bar graph below.
  Response Image
 
 


Question 9

Scoring Guide
 
Solution:
A correct pair may be repeated as long as all 9 correct pairs are present and no incorrect pairs are included.

Number on First Chip Number on Second Chip
1 1
1 2
1 3
2 1
2 2
2 3
3 1
3 2
3 3

Score & Description
  Correct
  Correct response answer has all 9 ordered pairs correct
  Incorrect #5
  9 correct pairs and at least one erroneous pair
  Incorrect #4
  6-8 correct pairs other than those noted in Incorrect #3
  Incorrect #3
  The 6 correct pairs that do not take the order of draw into account, i.e., no reversed pairs
  Incorrect #2
  1-5 correct pairs
  Incorrect #1
  No correct pairs

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

9  

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.

  Response Image
 
 
  Incorrect #5 - Student Response

9  

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

9  

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.

  Response Image
 
 
  Incorrect #3 - Student Response

9  

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.

  Response Image
 
 
  Incorrect #2 - Student Response

9  

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.

  Response Image
 
 
  Incorrect #1 - Student Response

9  

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.

  Response Image
 
 


Question 10

Key
 
 10.   4, 8, 3, 2, 5, 8, 12

What is the median of the numbers above?

     
  A)  4
Key Arrow B)  5
  C)  6
  D)  7
  E)  8




Question 11

Key
 
 11.   According to the graph above, how many times did the yearly increase of the price of a hamburger exceed 10 cents?
     
  A)  None
  B)  One
  C)  Two
Key Arrow D)  Three
  E)  Four




Question 12

Scoring Guide
 
Solution:
69

Score & Description
  Correct
  Correct response
  Incorrect #3
  69 and any decimal (e.g., 69.09 or 69.0)
  Incorrect #2
  70 (median and mode)
  Incorrect #1
  Any incorrect response other than those described above

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

12  

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?
  Response Image
 
 
  Incorrect #3 - Student Response

12  

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?
  Response Image
 
 
  Incorrect #2 - Student Response

12  

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?
  Response Image
 
 
  Incorrect #1 - Student Response

12  

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?
  Response Image
 
 


Question 13

Key
 
 13.   There are 1,200 students enrolled in Adams Middle School. According to the graph above, how many of these students participate in sports?
     
  A)  380
Key Arrow B)  456
  C)  760
  D)  820
  E)  1,162




Question 14

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
  Correct
  Correct response
OR
A "Yes" response, but explanation clearly indicates that bias would exist
  Incorrect #2
  A "No" response with an incorrect explanation or no explanation
  Incorrect #1
  A "Yes" response with an incorrect explanation or no explanation

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

14  

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.
  Response Image
 
 
  Incorrect #2 - Student Response

14  

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.
  Response Image
 
 
  Incorrect #1 - Student Response

14  

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.
  Response Image
 
 


Question 15

Key
 
 15.   A pictogram of the data above is to be drawn using as the symbol that represents 500 people. How many would it take to represent the population of Rancho Santa Fe?
     
  A)  1
  B)  4
Key Arrow C)  8
  D)  80
  E)  4,000




Question 16

Key
 
 16.   Gloria's diving scores from a recent competition are represented in the stem-and-leaf plot shown below. In this plot, 3 | 4 would be read as 3.4.

5 2   5
6 1
7 7
8 0   2

What was her lowest score for this competition?
     
  A)  0.02
  B)  1.0
  C)  2.5
Key Arrow D)  5.2
  E)  8.0




Question 17

Scoring Guide
 
Solution:
During the first 20 minutes, Marisa increased her speed from 0 mph to 6 mph.

From 20 to 60 minutes, she remained at 6 mph.

From 60 to 80 minutes, she decreased her speed from 6 mph to 0 mph and stopped. (Must have both decrease and stop for this interval.)

Summary of rate changes: speed up, maintains constant speed, slow down, stop.

Notes:
Responses may be presented in the following ways.

Category A Category B Category C
Speed from 0 to 6 Increase Downhill
Speed at 6 Remained the same Flat road (level)
Speed from 6 to 0; stop Decrease Uphill

  • Responses may mix parts of more than one category.
  • Speed from 0 to 6 may be expressed as 0-6 (likewise for speed from 6 to 0 as 6-0).
  • Responses may include extraneous correct information.
  • "Stop" after 70 minutes may be expressed as "had no speed" or "maintained speed of 0", "stayed at that speed" having stated 0 mph.

Score & Description
  Extended
  All of Category A and all of Category B or Category C
  Satisfactory
  All of Category A and incomplete Category B or Category C
OR
Category A without stop and all of Category B or Category C
  Partial
  All of Category A and no Category B or Category C
OR
All of Category B and Category C, with stop
  Minimal
  Category A without stop
OR
Category B only
OR
Category C only
OR
Response that accounts for each of three parts of trip
  Incorrect
  Incorrect response

In this question the student was asked to translate across representations by interpreting information presented graphically and giving a verbal description (story) of Marisa's bicycle trip. The given graph presented Marisa's speed on the trip as a function of time. To earn full credit, the student needed to give both quantitative and qualitative information about the situation, including the observation that Marisa was at a stop during the last time interval.




  Extended - Student Response

17  

The graph above represents Marisa's riding speed throughout her 80-minute bicycle trip. Use the information in the graph to describe what could have happened on the trip, including her speed throughout the trip.
  Response Image
 
 
  Satisfactory - Student Response

17  

The graph above represents Marisa's riding speed throughout her 80-minute bicycle trip. Use the information in the graph to describe what could have happened on the trip, including her speed throughout the trip.
  Response Image
 
 
  Partial - Student Response

17  

The graph above represents Marisa's riding speed throughout her 80-minute bicycle trip. Use the information in the graph to describe what could have happened on the trip, including her speed throughout the trip.
  Response Image
 
 
  Minimal - Student Response

17  

The graph above represents Marisa's riding speed throughout her 80-minute bicycle trip. Use the information in the graph to describe what could have happened on the trip, including her speed throughout the trip.
  Response Image
 
 
  Incorrect - Student Response

17  

The graph above represents Marisa's riding speed throughout her 80-minute bicycle trip. Use the information in the graph to describe what could have happened on the trip, including her speed throughout the trip.
  Response Image
 
 


Question 18

Scoring Guide
 
Solution:
Note: This question is listed as a short constructed-response question. It should be considered a multiple-choice 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.
answer key

Score & Description
  4 Right
 
  3 Right
 
  2 Right
 
  1 Right
 
  0 Right
 




  4 Right - Student Response

18  

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.
  Response Image
 
 
  3 Right - Student Response

18  

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.
  Response Image
 
 
  2 Right - Student Response

18  

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.
  Response Image
 
 
  1 Right - Student Response

18  

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.
  Response Image
 
 
  0 Right - Student Response

18  

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.
  Response Image
 
 


Question 19

Key
 
 19.   A poll is being taken at Baker Junior High School to determine whether to change the school mascot. Which of the following would be the best place to find a sample of students to interview that would be most representative of the entire student body?
     
  A)  An algebra class
Key Arrow B)  The cafeteria
  C)  The guidance office
  D)  A French class
  E)  The faculty room




Question 20

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
  Correct
  Correct response
  Incorrect #3
  Piece Q chosen, with an explanation that refers to a number of votes.
  Incorrect #2
  Piece N chosen, but explanation not given or is inadequate with incorrect computation.
  Incorrect #1
  Any incorrect response other than those described above.

* 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  

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.

  Response Image
 

20  

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.

  Response Image
 
  Incorrect #3 - Student Response

20  

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.

  Response Image
 

20  

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.

  Response Image
 
  Incorrect #2 - Student Response

20  

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.

  Response Image
 

20  

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.

  Response Image
 
  Incorrect #1 - Student Response

20  

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.

  Response Image
 

20  

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.

  Response Image
 


Question 21

Scoring Guide
 
Solution:

Graph B. It appears to show a large increase from October to March. It is misleading because it exaggerates a relatively small increase (misuse of scale).

Scoring Guide

In this question, a student needed to recognize how given graphs can be both consistent and inconsistent with stated claims. To earn full credit, a student needed to give the correct answer B with a complete explanation that would include both the large October to March increase and how the use of scale could be used to support or refute a claim. Levels of decreasing partial credit could be earned by a student if he or she just answers by giving the correct graph with an incomplete explanation or a missing explanation.

Score & Description
  Correct
  Correct response — with a complete explanation that addresses each of the following two points in the total response
  • B because it (appears to) show(s) a large increase in ridership
  • Misleading because B exaggerates a relatively small increase
  Partial
  B with an incomplete (but partially correct) explanation for the first part or the second part or both parts
  Minimal
  B with missing or incorrect explanation
  Incorrect
  Incorrect response




  Correct - Student Response

21  

Which graph would be best to help convince others that the Metro Rail Company made a lot more money from ticket sales in March than in October?

Explain your reason for making this selection.

  Response Image
 

21  

Which graph would be best to help convince others that the Metro Rail Company made a lot more money from ticket sales in March than in October?

Explain your reason for making this selection.

  Response Image
 
  Partial - Student Response

21  

Which graph would be best to help convince others that the Metro Rail Company made a lot more money from ticket sales in March than in October?

Explain your reason for making this selection.

  Response Image
 

21  

Which graph would be best to help convince others that the Metro Rail Company made a lot more money from ticket sales in March than in October?

Explain your reason for making this selection.

  Response Image
 
  Minimal - Student Response

21  

Which graph would be best to help convince others that the Metro Rail Company made a lot more money from ticket sales in March than in October?

Explain your reason for making this selection.

  Response Image
 

21  

Which graph would be best to help convince others that the Metro Rail Company made a lot more money from ticket sales in March than in October?

Explain your reason for making this selection.

  Response Image
 
  Incorrect - Student Response

21  

Which graph would be best to help convince others that the Metro Rail Company made a lot more money from ticket sales in March than in October?

Explain your reason for making this selection.

  Response Image
 

21  

Which graph would be best to help convince others that the Metro Rail Company made a lot more money from ticket sales in March than in October?

Explain your reason for making this selection.

  Response Image
 


Question 22

Key
 
 22.   In a bag of marbles, 1/2 are red, 1/4 are blue, 1/6 are green, and 1/12 are yellow. If a marble is taken from the bag without looking, it is most likely to be
     
Key Arrow A)  red
  B)  blue
  C)  green
  D)  yellow




Question 23

Key
 
 23.   From a shipment of 500 batteries, a sample of 25 was selected at random and tested. If 2 batteries in the sample were found to be dead, how many dead batteries would be expected in the entire shipment?
     
  A)  10
  B)  20
  C)  30
Key Arrow D)  40
  E)  50




Question 24

Key
 
 24.   The total distances covered by two runners during the first 28 minutes of a race are shown in the graph above. How long after the start of the race did one runner pass the other?
     
  A)  3 minutes
  B)  8 minutes
  C)  12 minutes
Key Arrow D)  14 minutes
  E)  28 minutes




Question 25

Key
 
 25.   The graph above shows how many of the 32 children in Mr. Rivera's class are 8, 9, 10, and 11 years old. Which of the following is true?
     
  A)  Most are younger than 9.
  B)  Most are younger than 10.
Key Arrow C)  Most are 9 or older.
  D)  None of the above is true.




Question 26

Scoring Guide
 
Score & Description
  Correct
  yy, bb, by

All 3 outcomes listed.
(A correct pair can be repeated as long as all 3 correct pairs are given and no incorrect pair is included.)

Note: Repeating yb is incorrect, and automatically lowers score to Incorrect #1.

  Incorrect #3
  Uses numbers instead of colors, e.g., one or more of (1,1), (2,0), (0,2).
  Incorrect #2
  1 or 2 correct responses - no incorrect pairs included.
  Incorrect #1
  Any incorrect response other than those described in Incorrect #2, Incorrect #3.

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

26  

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.
  Response Image
 
 
  Incorrect #3 - Student Response

26  

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.
  Response Image
 
 
  Incorrect #2 - Student Response

26  

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.
  Response Image
 
 
  Incorrect #1 - Student Response

26  

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.
  Response Image
 
 


Question 27

Scoring Guide
 
Solution:
Note: This question is listed as a short constructed-response question. It should be considered a multiple-choice question with multiple parts.

Answer Keys: B,A,A,B

Score & Description
  4 Right
 
  3 Right
 
  2 Right
 
  1 Right
 
  0 Right
 




  4 Right - Student Response

27  

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.
  Response Image
 
 
  3 Right - Student Response

27  

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.
  Response Image
 
 
  2 Right - Student Response

27  

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.
  Response Image
 
 
  1 Right - Student Response

27  

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.
  Response Image
 
 
  0 Right - Student Response

27  

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.
  Response Image
 
 


Question 28

Key
 
 28.   The entire circle shown above represents a total of 2,675 radios sold. Of the following, which is the best approximation of the number of radios represented by the shaded sector of the circle?
     
  A)  70
Key Arrow B)  275
  C)  985
  D)  25,880
  E)  98,420




Question 29

Key
 
 29.   In the graph above, each dot shows the number of sit-ups and the corresponding age for one of 13 people. According to this graph, what is the median number of sit-ups for these 13 people?
     
  A)  15
  B)  20
  C)  45
Key Arrow D)  50
  E)  55




Question 30

Scoring Guide
 
Score & Description
  Correct
  Both width and height have been doubled.

     OR

1980 can holds much more than twice the amount of the 1960 can

     OR

Ratio of amount in 1960 can to amount in 1980 can is less than 1/2.

  Incorrect
  Any incorrect response.

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

30  

The pictograph shown above is misleading. Explain why.
  Response Image
 
 
  Incorrect - Student Response

30  

The pictograph shown above is misleading. Explain why.
  Response Image
 

30  

The pictograph shown above is misleading. Explain why.
  Response Image
 


Question 31

Key
 
 31.   The average weight of 50 prize-winning tomatoes is 2.36 pounds. What is the combined weight, in pounds, of these 50 tomatoes?
     
  A)  0.0472
  B)  11.8
  C)  52.36
  D)  59
Key Arrow E)  118




Question 32

Key
 
 32.   The nine chips shown above are placed in a sack and then mixed up. Madeline draws one chip from this sack. What is the probability that Madeline draws a chip with an even number?
     
  A) 
1
9
  B) 
2
9
Key Arrow C) 
4
9
  D) 
1
2
  E) 
4
5




Question 33

Key
 
 33.   There are 15 girls and 11 boys in a mathematics class. If a student is selected at random to run an errand, what is the probability that a boy will be selected?
     
  A) 
 4 
26
Key Arrow B) 
11
26
  C) 
15
26
  D) 
11
15
  E) 
15
11




Question 34

Scoring Guide
 
Score & Description
  Correct
  The brown region should be about 1/2 of the circle.

The blond region should be about 1/2 the black region.

Correct Pie Chart

All three regions must be labeled with the correct colors or with the correct percents.

  Incorrect
  Incorrect answer




  Correct - Student Response

34  

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.
  Response Image
 
 
  Incorrect - Student Response

34  

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.
  Response Image
 

34  

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.
  Response Image