|
5. |
There were 90 employees in a company last year. This year the number of employees increased by 10 percent. How many employees are in the company this year? | |
| A) | 9 | |
| B) |
81 | |
| C) |
91 | |
| D) |
99 | |
| E) | 100 | |
| ||||||||||
|
|
12. |
Ms. Thierry and 3 friends ate dinner at a restaurant. The bill was $67. In addition, they left a $13 tip. Approximately what percent of the total bill did they leave as a tip? | |
| A) | 10% | |
| B) | 13% | |
| C) | 15% | |
| D) | 20% | |
| E) | 25% | |
|
| ||
|
13. |
What number is represented by point A on the number line above? | |
| A) | 0.0010 | |
| B) | 0.0054 | |
| C) |
0.0055 | |
| D) |
0.006 | |
| E) |
0.055 | |
|
|
17. |
How much change will John get back from $5.00 if he buys 2 notebooks that cost $1.80 each? | |
| A) | $1.40 | |
| B) | $2.40 | |
| C) | $3.20 | |
| D) | $3.60 | |
|
18. |
Carla has 12 boxes that each weigh the same amount. What would be a quick way for her to find the total weight of the 12 boxes? | |
| A) | Add 12 to the weight of one of the boxes. | |
| B) | Subtract 12 from the weight of one of the boxes. | |
| C) | Divide the weight of one of the boxes by 12. | |
| D) | Multiply the weight of one of the boxes by 12. | |
|
19. |
Six students bought exactly enough pens to share equally among themselves. Which of the following could be the number of pens they bought? | |
| A) | 46 | |
| B) | 48 | |
| C) | 50 | |
| D) | 52 | |
|
20. |
Carl has 3 empty egg cartons and 34 eggs. If each carton holds 12 eggs, how many more eggs are needed to fill all 3 cartons? | |
| A) | 2 | |
| B) | 3 | |
| C) | 4 | |
| D) | 6 | |
|
|
22. |
Jim has 3/4 of a yard of string which he wishes to divide into pieces, each 1/8 of a yard long. How many pieces will he have? | |
| A) | 3 | |
| B) | 4 | |
| C) | 6 | |
| D) | 8 | |
| ||
|
23. |
On the road shown above, the distance from Bay City to Exton is 60 miles. What is the distance from Bay City to Yardville? | |
| A) | 45 miles | |
| B) | 75 miles | |
| C) | 90 miles | |
| D) | 105 miles | |
|
24. |
The Breakfast Barn bought 135 dozen eggs at $0.89 per dozen. What was the total cost of the eggs? | |
| A) | $116.75 | |
| B) | $120.15 | |
| C) | $135.89 | |
| D) | $151.69 | |
Did you use the calculator on this question? | ||
| |||||||||||||||
|
26. |
Fifteen boxes each containing 8 radios can be repacked in 10 larger boxes each containing how many radios? | |
| A) | 8 | |
| B) | 10 | |
| C) | 12 | |
| D) | 80 | |
| E) | 120 | |
| Did you use the calculator on this question? | ||
|
27. |
Consider the statement "If n is an even number, then n is two times an odd number." For which of the following values of n is the statement FALSE? | |
| A) | 2 | |
| B) | 6 | |
| C) | 8 | |
| D) | 10 | |
| E) | 14 | |
| Did you use the calculator on this question? | ||
|
28. |
The diameter of a red blood cell, in inches, is 3 × 10-4. This expression is the same as which of the following numbers? | |
| A) | 0.00003 | |
| B) | 0.0003 | |
| C) | 0.003 | |
| D) | 3,000 | |
| E) | 30,000 | |
| Did you use the calculator on this question? | ||
|
|
|
32. |
Which of the following ratios is equivalent to the ratio of 6 to 4? | |
| A) | 12 to 18 | |
| B) | 12 to 8 | |
| C) | 8 to 6 | |
| D) | 4 to 6 | |
| E) | 2 to 3 | |
|
33. |
Which of the following numbers, when rounded to the nearest thousand, becomes 27,000? | |
| A) | 26,099 | |
| B) | 26,490 | |
| C) | 27,381 | |
| D) | 27,550 | |
| E) | 27,640 | |
|
36. |
Of the following, which is the closest approximation of a 15 percent tip on a restaurant check of $24.99? | |
| A) | $2.50 | |
| B) | $3.00 | |
| C) | $3.75 | |
| D) | $4.50 | |
| E) | $5.00 | |
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|
38. |
Anita is making bags of treats for her sister's birthday party. She divides 65 pieces of candy equally among 15 bags so that each bag contains as many pieces as possible. How many pieces will she have left? | |
| A) | 33 | |
| B) | 5 | |
| C) | 4 | |
| D) | 3 | |
| E) | 0.33 | |
| Did you use the calculator on this question? | ||
|
39. |
If each of the counting numbers from 1 through 10 is multiplied by 13, how many of the resulting numbers will be even? | |
| A) | One | |
| B) | Four | |
| C) | Five | |
| D) | Six | |
| E) | Ten | |
| Did you use the calculator on this question? | ||
| |||||||||
| |||||||||||
| ||
|
42. |
If the string does not cost anything, how much does the necklace above cost? | |
| A) | 10¢ | |
| B) | 24¢ | |
| C) | 28¢ | |
| D) | 34¢ | |
| ||
|
43. |
Carol wanted to estimate the distance from A to D along the path shown on the map above. She correctly rounded each of the given distances to the nearest mile and then added them. Which of the following sums could be hers? | |
| A) | 4 + 6 + 5 = 15 | |
| B) | 5 + 6 + 5 = 16 | |
| C) | 5 + 6 + 6 = 17 | |
| D) | 5 + 7 + 6 = 18 | |
|
44. |
There are 50 hamburgers to serve 38 children. If each child is to have at least one hamburger, at most how many of the children can have more than one? | |
| A) | 6 | |
| B) | 12 | |
| C) | 26 | |
| D) | 38 | |
| ||
|
45. |
Chen had $10 to buy a model plane, glue, and paint as shown above. At which of the following times could an estimate have been used instead of exact numbers? | |
| A) | When Chen tried to decide whether or not he had enough money to buy the plane, glue, and paint | |
| B) | When the clerk entered each amount into the cash register | |
| C) | When the clerk told Chen how much he owed | |
| D) | When Chen counted his change | |
|
46. |
By how much would 217 be increased if the digit 1 were replaced by a digit 5? | |
| A) | 4 | |
| B) | 40 | |
| C) | 44 | |
| D) | 400 | |
|
47. |
Christy has 88 photographs to put in her album. If 9 photographs will fit on each page, how many pages will she need? | |
| A) | 8 | |
| B) | 9 | |
| C) | 10 | |
| D) | 11 | |
|
51. |
If 1 1/3 cups of flour are needed for a batch of cookies, how many cups of flour will be needed for 3 batches? | |
| A) | 4 1/3 | |
| B) | 4 | |
| C) | 3 | |
| D) | 2 2/3 | |
|
|
| ||
|
53. |
If the pattern in the list above continues, what will be the next number after 56? | |
| A) | 54 | |
| B) | 63 | |
| C) | 64 | |
| D) | 65 | |
| E) | 67 | |
| Did you use the calculator on this question? | ||
|
54. |
What is the difference between the smallest positive 3-digit number and the largest positive 2-digit number? | |
| A) | l | |
| B) | 9 | |
| C) | 10 | |
| D) | 90 | |
| E) | 900 | |
| Did you use the calculator on this question? | ||
|
55. |
Ken bought a used car for $5,375. He had to pay an additional 15 percent of the purchase price to cover both sales tax and extra fees. Of the following, which is closest to the total amount Ken paid? | |
| A) | $806 | |
| B) | $5,510 | |
| C) | $5,760 | |
| D) | $5,940 | |
| E) | $6,180 | |
| Did you use the calculator on this question? | ||
|
56. |
Which of the following is both a multiple of 3 and a multiple of 7? | |
| A) | 7,007 | |
| B) | 8,192 | |
| C) | 21,567 | |
| D) | 22,287 | |
| E) | 40,040 | |
| Did you use the calculator on this question? | ||
| |||||||
| |||||||||
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|
60. |
Which of the following is closest to 15 seconds? | |
| A) | 14.1 seconds | |
| B) | 14.7 seconds | |
| C) | 14.9 seconds | |
| D) | 15.2 seconds | |
|
61. |
The census showed that three hundred fifty-six thousand, ninety-seven people lived in Middletown. Written as a number, that is | |
| A) | 350,697 | |
| B) | 356,097 | |
| C) | 356,907 | |
| D) | 356,970 | |
|
62. |
A club held a car wash and washed 21 cars. If the club raised $84, how much did it charge per car? | |
| A) | $0.25 | |
| B) | $4.00 | |
| C) | $5.00 | |
| D) | $1,764.00 | |
|
|
64. |
A certain reference file contains approximately one billion facts. About how many millions is that? | |
| A) | 1,000,000 | |
| B) | 100,000 | |
| C) | 10,000 | |
| D) | 1,000 | |
| E) | 100 | |
|
66. |
Which of the following
figures best illustrates the statement 5 × (6 + 2) = (5 × 6) + (5 × 2)? | |
| A) |  | |
| B) |  | |
| C) |  | |
| D) |  | |
| E) |  | |
|
67. |
The least common multiple of 8, 12, and a third number is 120. Which of the following could be the third number? | |
| A) | 15 | |
| B) | 16 | |
| C) | 24 | |
| D) | 32 | |
| E) | 48 | |
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|
71. |
Kate bought a book for $14.95, a record for $5.85, and a tape for $9.70. If the sales tax on these items is 6 percent and all 3 items are taxable, what is the total amount she must pay for the 3 items, including tax? | |
| A) | $32.33 | |
| B) | $32.06 | |
| C) | $30.56 | |
| D) | $30.50 | |
| E) | $ 1.83 | |
| Did you use the calculator on this question? | ||
| |||||||||
|
73. |
Ground beef costs $2.59 per pound. What is the cost of 0.93 pound of ground beef? | |
| A) | $3.52 | |
| B) | $2.78 | |
| C) | $2.47 | |
| D) | $2.41 | |
| E) | $1.66 | |
| Did you use the calculator on this question? | ||
| |||||||||
|
75. |
If the price of a can of beans is raised from 50 cents to 60 cents, what is the percent increase in the price? | |
| A) | 83.3% | |
| B) | 20% | |
| C) | 18.2% | |
| D) | 16.7% | |
| E) | 10% | |
| Did you use the calculator on this question? | ||
|
76. |
If  , then, of the
following, which is closest to n? | |
| A) | 2 .6 1 | |
| B) | 3.83 | |
| C) | 8.76 | |
| D) | 8.82 | |
| E) | 12.11 | |
| Did you use the calculator on this question? | ||
| ||||||||||||||||||||||
| Scoring Guide |
| Solution: Any 2 small rectangles shaded. For example:
|
|
Score & Description | ||||
| ||||
|
| Correct - Student Response |
|
2 |
Shade |
 | |
| Incorrect - Student Response |
|
2 |
Shade |
 | |
| |||||||||||||||||||||||||
| |||||||||||||||||||||||||
| |||||||||||||||||||||||||
| Scoring Guide |
| Solution: 926 |
|
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 |
|
6 |
Subtract:
| |
 | ||
| Scorer Comments: This paper was scored as correct because the student correctly subtracted 46 from 972. |
||
| Incorrect #4 - Student Response |
|
6 |
Subtract:
| |
 | ||
| Scorer Comments: In this paper, the student added instead of subtracted. This particular response was coded to gather data on common student errors, but the paper received no credit. |
||
| Incorrect #3 - Student Response |
|
6 |
Subtract:
| |
 | ||
| Scorer Comments: In this paper, the student made a subtraction error by unnecessarily borrowing from the 9 in the hundreds place and got 826 as their answer. This particular response was coded to gather data on common student errors, but the paper received no credit. |
||
| Incorrect #2 - Student Response |
|
6 |
Subtract:
| |
 | ||
| Scorer Comments: In this paper, the student made a subtraction error and put 934 as their answer. This particular response was coded to gather data on common student errors, but the paper received no credit. |
||
| Incorrect #1 - Student Response |
|
6 |
Subtract:
| |
 | ||
| Scorer Comments: Papers scored as incorrect #1 received no credit and represent incorrect responses different than those described under incorrect #4, incorrect #3, and incorrect #2. |
||
| Scoring Guide |
| Solution: 6.0 or 6 |
|
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 |
|
7 |
On the number line above, what number would be located at point P ? | |
 | ||
| Scorer Comments: This paper was scored as correct because the student correctly identified the number corresponding to point P. |
||
| Incorrect #4 - Student Response |
|
7 |
On the number line above, what number would be located at point P ? | |
 | ||
| Scorer Comments: In this paper, the student gave 61 as their answer. This particular response was coded to gather data on common student errors, but the paper received no credit. |
||
| Incorrect #3 - Student Response |
|
7 |
On the number line above, what number would be located at point P ? | |
 | ||
| Scorer Comments: In this paper, the student gave 5.10 as their answer. This particular response was coded to gather data on common student errors, but the paper received no credit. |
||
| Incorrect #2 - Student Response |
|
7 |
On the number line above, what number would be located at point P ? | |
 | ||
| Scorer Comments: In this paper, the student gave 5.8 as their answer. This particular response was coded to gather data on common student errors, but the paper received no credit. |
||
| Incorrect #1 - Student Response |
|
7 |
On the number line above, what number would be located at point P ? | |
 | ||
| Scorer Comments: Papers scored as incorrect #1 received no credit and represent incorrect responses different than those described under incorrect #4, incorrect #3, and incorrect #2. |
||
| Scoring Guide |
| Solution: 361 |
|
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 |
|
8 |
A club needs to sell 625 tickets. If it has already sold 184 tickets to adults and 80 tickets to children, how many more does it need to sell? | |
 | ||
| Scorer Comments: This paper was scored as correct because the student correctly determined the number of tickets the club still needed to sell. |
||
| Incorrect #4 - Student Response |
|
8 |
A club needs to sell 625 tickets. If it has already sold 184 tickets to adults and 80 tickets to children, how many more does it need to sell? | |
 | ||
| Scorer Comments: In this paper, the student answered 104, which was found by subtracting the number of children's tickets already sold from the number of adult tickets already sold. This particular response was coded to gather data on common student errors, but the paper received no credit. |
||
| Incorrect #3 - Student Response |
|
8 |
A club needs to sell 625 tickets. If it has already sold 184 tickets to adults and 80 tickets to children, how many more does it need to sell? | |
 | ||
| Scorer Comments: In this paper, the student answered 889, which is the sum of all three numbers given in the question. This particular response was coded to gather data on common student errors, but the paper received no credit. |
||
| Incorrect #2 - Student Response |
|
8 |
A club needs to sell 625 tickets. If it has already sold 184 tickets to adults and 80 tickets to children, how many more does it need to sell? | |
 | ||
| Scorer Comments: In this paper, the student gave 264 as their answer, which is the sum of the number of adult and children tickets already sold. This particular response was coded to gather data on common student errors, but the paper received no credit. |
||
| Incorrect #1 - Student Response |
|
8 |
A club needs to sell 625 tickets. If it has already sold 184 tickets to adults and 80 tickets to children, how many more does it need to sell? | |
 | ||
| Scorer Comments: Papers scored as incorrect #1 received no credit and represent incorrect responses different than those described under incorrect #4, incorrect #3, and incorrect #2. |
||
| ||||||||||||||||||||||
| Scoring Guide |
|
Score & Description | ||||
| ||||
|
| Correct - Student Response |
|
10 |
Given the information above, write a mathematics word
problem for which  would be the method of solution. |
 | |
| Incorrect - Student Response |
|
10 |
Given the information above, write a mathematics word
problem for which would be the method of solution. |
 | |
| |||||||||||||||||||||||||
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| Scoring Guide |
| Solution: 6 x 3 cards = 18 cards 7 x 1 card = 7 cards This totals 25 cards. 31 - 25 = 6 cards left. Dividing 6 by 2 yields 3. So 3 friends receive exactly 2 cards each. NOTE: Response should contain evidence that student
One or more of these may be implied but not stated explicitly by the presence of the numbers 18, 7, 25, and 31. |
|
Score & Description | ||||
| ||||
| ||||
|
|
|
| Correct - Student Response |
|
14 |
Raynold had 31 baseball cards. He gave the cards to his friends. Six of his friends received 3 cards each. Seven of his friends received 1 card each. The rest received 2 cards each. How many of his friends received exactly 2 cards from Raynold? | |
 | ||
| Scorer Comments: This response received full credit because the student correctly determined the number of cards that each friend will receive and their explanation shows how they arrived at that answer. |
||
| Partial - Student Response |
|
14 |
Raynold had 31 baseball cards. He gave the cards to his friends. Six of his friends received 3 cards each. Seven of his friends received 1 card each. The rest received 2 cards each. How many of his friends received exactly 2 cards from Raynold? | |
 | ||
| Scorer Comments: This response received partial credit because the student had all the correct supporting work, except for dividing by two at the end. |
||
| Incorrect - Student Response |
|
14 |
Raynold had 31 baseball cards. He gave the cards to his friends. Six of his friends received 3 cards each. Seven of his friends received 1 card each. The rest received 2 cards each. How many of his friends received exactly 2 cards from Raynold? | |
 | ||
| Scorer Comments: This response received no credit because the student had incorrect work and an incorrect answer. |
||
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| ||||||||||||||||||||||
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| ||||||||||||||||||||||
| 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 |
|
21 |
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 |
|
21 |
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: A. Cheaper at Price Pleasers At Price Pleasers the stereo would be $80 after 2 weeks. OR Successive 10% reductions of the original price will yield greater savings than successive reductions of 10% of the reduced price. |
|
Score & Description | ||||
| ||||
| ||||
|
| In this question the student was asked to compare the sale price of a stereo, after 3 weeks, based on two different ways for reducing the price. In one store, the price was reduced each week by a fixed amount (10% of $100, or $10). In the other store the price was reduced each week by a varying amount (10% of the current price, which is less each week). To earn full credit, the student needed to indicate that the price would be less at the first store after 3 weeks and explain how the solution was obtained. Students were permitted to use a calculator. |
| Correct - Student Response |
|
25 |
One store, Price Pleasers, reduces the price each
week of a $100 stereo by 10 percent of the original price.
Another store, Bargains Plus, reduces the price each week of the
same $100 stereo by 10 percent of the previous week's price.
|
 | |
| Partial - Student Response |
|
25 |
One store, Price Pleasers, reduces the price each
week of a $100 stereo by 10 percent of the original price.
Another store, Bargains Plus, reduces the price each week of the
same $100 stereo by 10 percent of the previous week's price.
|
 | |
| Incorrect - Student Response |
|
25 |
One store, Price Pleasers, reduces the price each
week of a $100 stereo by 10 percent of the original price.
Another store, Bargains Plus, reduces the price each week of the
same $100 stereo by 10 percent of the previous week's price.
|
 | |
| |||||||||||||||||||||||||
| |||||||||||||||||||||||||
| |||||||||||||||||||||||||
| Scoring Guide |
| Solution: 24 |
|
Score & Description | ||||
| ||||
|
| In this question the student needed to solve a long division problem, dividing a 2-digit number into a 3-digit number. |
| Scoring Guide |
| Solution: $525 or 525 |
|
Score & Description | ||||
| ||||
|
| In this question the student needed to apply multiplication to solve a word problem, multiplying $5.25 by 100. |
| Correct - Student Response |
|
30 |
Movie tickets cost $5.25 each. If 100 tickets were sold, how much money was collected? |
 | |
| Incorrect - Student Response |
|
30 |
Movie tickets cost $5.25 each. If 100 tickets were sold, how much money was collected? |
 | |
| Scoring Guide |
| Solution: 418 ÷ 11 = 38 per bus which is 3 more students than 35, or 3 more students would have to fit in each bus OR
OR
OR 11 × 35 is less than 418 |
|
Score & Description | ||||
| ||||
|
| In this question the student needed to apply multiplication or division to solve a word problem, and then interpret the answer in the context of the question. To earn full credit the student needed to explain either that there were not enough seats on 11 buses for 418 students or that 418 students would require more than 11 buses. |
| Correct - Student Response |
|
31 |
A high school orders 11 buses to transport 418 students. If
each bus can seat 35 students, will the number of buses ordered be enough
to provide a seat for each student?
()Yes ()No |
 | |
| Incorrect - Student Response |
|
31 |
A high school orders 11 buses to transport 418 students. If
each bus can seat 35 students, will the number of buses ordered be enough
to provide a seat for each student?
()Yes ()No |
 | |
| |||||||||||||||||||||||||
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| Scoring Guide |
| Solution: Maria will win the game. The following reasons may be given:
Scoring Guide In this question a student needed to use number skills to understand place value and compare numbers. Since Carla placed her number 1 tile in the hundreds place, the greatest number she could have after subtracting would be less than one hundred. Maria could have used the number 2, 3, or 4 tile in the hundreds place and her difference would always be larger than Carla's. For an extended response, the student needed to answer Maria and demonstrate understanding of place value by generalizing a comparison of the possible differences that Carla could obtain to the possible differences that Maria could obtain. ("Generalize" means that the student indicates that since Carla placed her number 1 tile in a place so that she would never win, Maria would always win, no matter how she placed her 2, 3, and 4 tiles.) For a satisfactory response, a student needed to demonstrate understanding that Maria could make a larger top number than Carla, but the response did not generalize Maria's and Carla's possible differences. For a partial response, a student had to provide an explanation that was only partially correct; however, those types of responses did recognize that Maria would have the greater number after determining the difference. A minimal score was earned by responses that indicated that Maria would win, but did not offer an explanation for how Maria would win the game. |
|
Score & Description | ||||
| ||||
| ||||
| ||||
| ||||
|
| Extended - Student Response |
|
37 |
In a game, Carla and Maria are making subtraction problems
using tiles numbered 1 to 5. The player whose subtraction problem gives
the largest answer wins the game.
Look at where each girl placed two of her tiles. |
 | |
|
37 |
In a game, Carla and Maria are making subtraction problems
using tiles numbered 1 to 5. The player whose subtraction problem gives
the largest answer wins the game.
Look at where each girl placed two of her tiles. |
 | |
| Satisfactory - Student Response |
|
37 |
In a game, Carla and Maria are making subtraction problems
using tiles numbered 1 to 5. The player whose subtraction problem gives
the largest answer wins the game.
Look at where each girl placed two of her tiles. |
 | |
|
37 |
In a game, Carla and Maria are making subtraction problems
using tiles numbered 1 to 5. The player whose subtraction problem gives
the largest answer wins the game.
Look at where each girl placed two of her tiles. |
 | |
| Partial - Student Response |
|
37 |
In a game, Carla and Maria are making subtraction problems
using tiles numbered 1 to 5. The player whose subtraction problem gives
the largest answer wins the game.
Look at where each girl placed two of her tiles. |
 | |
|
37 |
In a game, Carla and Maria are making subtraction problems
using tiles numbered 1 to 5. The player whose subtraction problem gives
the largest answer wins the game.
Look at where each girl placed two of her tiles. |
 | |
| Minimal - Student Response |
|
37 |
In a game, Carla and Maria are making subtraction problems
using tiles numbered 1 to 5. The player whose subtraction problem gives
the largest answer wins the game.
Look at where each girl placed two of her tiles. |
 | |
|
37 |
In a game, Carla and Maria are making subtraction problems
using tiles numbered 1 to 5. The player whose subtraction problem gives
the largest answer wins the game.
Look at where each girl placed two of her tiles. |
 | |
| Incorrect - Student Response |
|
37 |
In a game, Carla and Maria are making subtraction problems
using tiles numbered 1 to 5. The player whose subtraction problem gives
the largest answer wins the game.
Look at where each girl placed two of her tiles. |
 | |
|
37 |
In a game, Carla and Maria are making subtraction problems
using tiles numbered 1 to 5. The player whose subtraction problem gives
the largest answer wins the game.
Look at where each girl placed two of her tiles. |
 | |
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| Scoring Guide |
| Solution: Brian (constant difference)
Scoring Guide In this question, a student has to use mathematical reasoning to construct different justifications that support Darlene’s and Brian’s claims. In this real-world problem, students have to construct an appropriate method for supporting each claim in the question. One such method uses proportional thinking as well as percentages to explain how a conclusion could be reached, while the other involves comparing differences in growth by subtraction. Partial credit is earned if a student just gives a correct justification for Brian’s or Darlene’s claim, but not both, or shows a limited understanding of how to proceed with the problem. |
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Score & Description | ||||
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| Correct - Student Response |
|
40 |
In 1980, the populations of Town A and Town B were 5,000 and
6,000, respectively. The 1990 populations of Town A and Town B were 8,000
and 9,000, respectively.
Brian claims that from 1980 to 1990 the populations of the two towns grew by the same amount. Use mathematics to explain how Brian might have justified his claim. Darlene claims that from 1980 to 1990 the population of Town A had grown more. Use mathematics to explain how Darlene might have justified her claim. |
 | |
| Partial - Student Response |
|
40 |
In 1980, the populations of Town A and Town B were 5,000 and
6,000, respectively. The 1990 populations of Town A and Town B were 8,000
and 9,000, respectively.
Brian claims that from 1980 to 1990 the populations of the two towns grew by the same amount. Use mathematics to explain how Brian might have justified his claim. Darlene claims that from 1980 to 1990 the population of Town A had grown more. Use mathematics to explain how Darlene might have justified her claim. |
 | |
|
40 |
In 1980, the populations of Town A and Town B were 5,000 and
6,000, respectively. The 1990 populations of Town A and Town B were 8,000
and 9,000, respectively.
Brian claims that from 1980 to 1990 the populations of the two towns grew by the same amount. Use mathematics to explain how Brian might have justified his claim. Darlene claims that from 1980 to 1990 the population of Town A had grown more. Use mathematics to explain how Darlene might have justified her claim. |
 | |
| Incorrect - Student Response |
|
40 |
In 1980, the populations of Town A and Town B were 5,000 and
6,000, respectively. The 1990 populations of Town A and Town B were 8,000
and 9,000, respectively.
Brian claims that from 1980 to 1990 the populations of the two towns grew by the same amount. Use mathematics to explain how Brian might have justified his claim. Darlene claims that from 1980 to 1990 the population of Town A had grown more. Use mathematics to explain how Darlene might have justified her claim. |
 | |
| Scoring Guide |
| Solution: They will both reach points A and B at the same time because their rates are equal. Scoring Guide In this question, a student needed to use proportional thinking to solve this problem. The student should have reasoned that both Victor’s rate and Sharon’s rate are equal. To earn full credit the student needed to answer both parts of the question correctly with the correct justification for each. To earn partial credit, a student could have just answered one part correctly with the correct justification or answered both parts with no justification or incorrect justifications. |
|
Score & Description | ||||
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| ||||
|
| Correct - Student Response |
|
41 |
Victor's van travels at a rate of 8 miles every 10 minutes.
Sharon's sedan travels at a rate of 20 miles every 25 minutes.
If both cars start at the same time, will Sharon's sedan reach point A, 8 miles away, before, at the same time, or after Victor's van? Explain your reasoning. |
 | |
|
41 |
Victor's van travels at a rate of 8 miles every 10 minutes.
Sharon's sedan travels at a rate of 20 miles every 25 minutes.
If both cars start at the same time, will Sharon's sedan reach point A, 8 miles away, before, at the same time, or after Victor's van? Explain your reasoning. |
 | |
| Partial - Student Response |
|
41 |
Victor's van travels at a rate of 8 miles every 10 minutes.
Sharon's sedan travels at a rate of 20 miles every 25 minutes.
If both cars start at the same time, will Sharon's sedan reach point A, 8 miles away, before, at the same time, or after Victor's van? Explain your reasoning. |
 | |
|
41 |
Victor's van travels at a rate of 8 miles every 10 minutes.
Sharon's sedan travels at a rate of 20 miles every 25 minutes.
If both cars start at the same time, will Sharon's sedan reach point A, 8 miles away, before, at the same time, or after Victor's van? Explain your reasoning. |
 | |
| Incorrect - Student Response |
|
41 |
Victor's van travels at a rate of 8 miles every 10 minutes.
Sharon's sedan travels at a rate of 20 miles every 25 minutes.
If both cars start at the same time, will Sharon's sedan reach point A, 8 miles away, before, at the same time, or after Victor's van? Explain your reasoning. |
 | |
|
41 |
Victor's van travels at a rate of 8 miles every 10 minutes.
Sharon's sedan travels at a rate of 20 miles every 25 minutes.
If both cars start at the same time, will Sharon's sedan reach point A, 8 miles away, before, at the same time, or after Victor's van? Explain your reasoning. |
 | |
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| 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 |
|
52 |
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? |
 | |
|
52 |
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 |
|
52 |
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? |
 | |
|
52 |
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 |
|
52 |
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? |
 | |
|
52 |
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 |
|
52 |
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? |
 | |
|
52 |
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? |
 | |
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| 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 |
|
57 |
Tracy said, "I can multiply 6 by another number and get an
answer that is smaller than 6." Pat said, "No, you can't. Multiplying 6 by another number always makes the answer 6 or larger." Who is correct? Give a reason for your answer. |
 | |
|
57 |
Tracy said, "I can multiply 6 by another number and get an
answer that is smaller than 6." Pat said, "No, you can't. Multiplying 6 by another number always makes the answer 6 or larger." Who is correct? Give a reason for your answer. |
 | |
| Correct #2 - Student Response |
|
57 |
Tracy said, "I can multiply 6 by another number and get an
answer that is smaller than 6." Pat said, "No, you can't. Multiplying 6 by another number always makes the answer 6 or larger." Who is correct? Give a reason for your answer. |
 | |
|
57 |
Tracy said, "I can multiply 6 by another number and get an
answer that is smaller than 6." Pat said, "No, you can't. Multiplying 6 by another number always makes the answer 6 or larger." Who is correct? Give a reason for your answer. |
 | |
| Incorrect #2 - Student Response |
|
57 |
Tracy said, "I can multiply 6 by another number and get an
answer that is smaller than 6." Pat said, "No, you can't. Multiplying 6 by another number always makes the answer 6 or larger." Who is correct? Give a reason for your answer. |
 | |
|
57 |
Tracy said, "I can multiply 6 by another number and get an
answer that is smaller than 6." Pat said, "No, you can't. Multiplying 6 by another number always makes the answer 6 or larger." Who is correct? Give a reason for your answer. |
 | |
| Incorrect #1 - Student Response |
|
57 |
Tracy said, "I can multiply 6 by another number and get an
answer that is smaller than 6." Pat said, "No, you can't. Multiplying 6 by another number always makes the answer 6 or larger." Who is correct? Give a reason for your answer. |
 | |
|
57 |
Tracy said, "I can multiply 6 by another number and get an
answer that is smaller than 6." Pat said, "No, you can't. Multiplying 6 by another number always makes the answer 6 or larger." Who is correct? Give a reason for your answer. |
 | |
| Scoring Guide |
|
Score & Description | ||||
| ||||
| ||||
| ||||
| ||||
|
| *The use of more than one correct category in this
question enabled NAEP to gather data on different ways students responded
correctly to this question. Any one of these responses that fell into one
of these correct categories earned full credit.
*The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. |
| Correct #1 - Student Response |
|
58 |
Raymond must buy enough paper to print 28 copies of a report that contains 64 sheets of paper. Paper is only available in packages of 500 sheets. How many whole packages of paper will he need to buy to do the printing? |
 | |
|
58 |
Raymond must buy enough paper to print 28 copies of a report that contains 64 sheets of paper. Paper is only available in packages of 500 sheets. How many whole packages of paper will he need to buy to do the printing? |
 | |
| Correct #2 - Student Response |
|
58 |
Raymond must buy enough paper to print 28 copies of a report that contains 64 sheets of paper. Paper is only available in packages of 500 sheets. How many whole packages of paper will he need to buy to do the printing? |
 | |
|
58 |
Raymond must buy enough paper to print 28 copies of a report that contains 64 sheets of paper. Paper is only available in packages of 500 sheets. How many whole packages of paper will he need to buy to do the printing? |
 | |
| Incorrect #3 - Student Response |
|
58 |
Raymond must buy enough paper to print 28 copies of a report that contains 64 sheets of paper. Paper is only available in packages of 500 sheets. How many whole packages of paper will he need to buy to do the printing? |
 | |
|
58 |
Raymond must buy enough paper to print 28 copies of a report that contains 64 sheets of paper. Paper is only available in packages of 500 sheets. How many whole packages of paper will he need to buy to do the printing? |
 | |
| Incorrect #2 - Student Response |
|
58 |
Raymond must buy enough paper to print 28 copies of a report that contains 64 sheets of paper. Paper is only available in packages of 500 sheets. How many whole packages of paper will he need to buy to do the printing? |
 | |
|
58 |
Raymond must buy enough paper to print 28 copies of a report that contains 64 sheets of paper. Paper is only available in packages of 500 sheets. How many whole packages of paper will he need to buy to do the printing? |
 | |
| Incorrect #1 - Student Response |
|
58 |
Raymond must buy enough paper to print 28 copies of a report that contains 64 sheets of paper. Paper is only available in packages of 500 sheets. How many whole packages of paper will he need to buy to do the printing? |
 | |
|
58 |
Raymond must buy enough paper to print 28 copies of a report that contains 64 sheets of paper. Paper is only available in packages of 500 sheets. How many whole packages of paper will he need to buy to do the printing? |
 | |
| Scoring Guide |
| Solution: Treena's fixed expenses will be 7 × 45 = $315 for the 7 days. Therefore, she has 1000 - 315 = 685 to spend for instruction and travel. The group plan will cost 7 × 40 = 280 while the individual plan will cost 7 × 60 = 420. Treena has three options: Group and Train: 280 + 125 = 405
(720)---$280 left She cannot choose the individual plan and travel by plane because her total expenses would be $1,070 which is greater than the allotted scholarship. (This can be considered as a valid conclusion but can only be counted in a score of Minimal or Partial.) Any full credit response clearly communicates that Treena has three options, what the three options are, and how the student arrived at the three options. |
|
Score & Description | ||||
| ||||
| ||||
| ||||
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|
| Extended - Student Response |
|
59 |
Treena won a 7-day scholarship worth $1,000 to the Pro Shot Basketball Camp. Round-trip travel expenses to the camp are $335 by air or $125 by train. At the camp she must choose between a week of individual instruction at $60 per day or a week of group instruction at $40 per day. Treena's food and other expenses are fixed at $45 per day. If she does not plan to spend any money other than the scholarship, what are all choices of travel and instruction plans that she could afford to make? Explain your reasoning. |
 | |
| Satisfactory - Student Response |
|
59 |
Treena won a 7-day scholarship worth $1,000 to the Pro Shot Basketball Camp. Round-trip travel expenses to the camp are $335 by air or $125 by train. At the camp she must choose between a week of individual instruction at $60 per day or a week of group instruction at $40 per day. Treena's food and other expenses are fixed at $45 per day. If she does not plan to spend any money other than the scholarship, what are all choices of travel and instruction plans that she could afford to make? Explain your reasoning. |
 | |
| Partial - Student Response |
|
59 |
Treena won a 7-day scholarship worth $1,000 to the Pro Shot Basketball Camp. Round-trip travel expenses to the camp are $335 by air or $125 by train. At the camp she must choose between a week of individual instruction at $60 per day or a week of group instruction at $40 per day. Treena's food and other expenses are fixed at $45 per day. If she does not plan to spend any money other than the scholarship, what are all choices of travel and instruction plans that she could afford to make? Explain your reasoning. |
 | |
| Minimal - Student Response |
|
59 |
Treena won a 7-day scholarship worth $1,000 to the Pro Shot Basketball Camp. Round-trip travel expenses to the camp are $335 by air or $125 by train. At the camp she must choose between a week of individual instruction at $60 per day or a week of group instruction at $40 per day. Treena's food and other expenses are fixed at $45 per day. If she does not plan to spend any money other than the scholarship, what are all choices of travel and instruction plans that she could afford to make? Explain your reasoning. |
 | |
|
59 |
Treena won a 7-day scholarship worth $1,000 to the Pro Shot Basketball Camp. Round-trip travel expenses to the camp are $335 by air or $125 by train. At the camp she must choose between a week of individual instruction at $60 per day or a week of group instruction at $40 per day. Treena's food and other expenses are fixed at $45 per day. If she does not plan to spend any money other than the scholarship, what are all choices of travel and instruction plans that she could afford to make? Explain your reasoning. |
 | |
| Incorrect/Off Task - Student Response |
|
59 |
Treena won a 7-day scholarship worth $1,000 to the Pro Shot Basketball Camp. Round-trip travel expenses to the camp are $335 by air or $125 by train. At the camp she must choose between a week of individual instruction at $60 per day or a week of group instruction at $40 per day. Treena's food and other expenses are fixed at $45 per day. If she does not plan to spend any money other than the scholarship, what are all choices of travel and instruction plans that she could afford to make? Explain your reasoning. |
 | |
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| Scoring Guide |
|
Score & Description | ||||
| ||||
| ||||
| ||||
|
| Note: 85 is acceptable since not all students are taught to round numbers in the same way. *The use of more than one correct category in this question enabled NAEP to gather data on different ways students responded correctly to this question. Any one of these responses that fell into one of these correct categories earned full credit. *The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. |
| Correct #1 - Student Response |
|
63 |
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? |
 | |
|
63 |
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 |
|
63 |
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 |
|
63 |
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? |
 | |
|
63 |
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 |
|
63 |
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? |
 | |
|
63 |
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? |
 | |
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| 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 |
|
69 |
What is the product of 3.12 and 83? |
 | |
|
69 |
What is the product of 3.12 and 83? |
 | |
| Incorrect #1 - Student Response |
|
69 |
What is the product of 3.12 and 83? |
 | |
| Incorrect #2 - Student Response |
|
69 |
What is the product of 3.12 and 83? |
 | |
|
69 |
What is the product of 3.12 and 83? |
| Scoring Guide |
|
Score & Description | ||||
| ||||
|
| Correct - Student Response |
|
70 |
The weight of an object on the Moon is 1/6 the weight of that object on the Earth. An object that weighs 30 pounds on Earth would weigh how many pounds on the Moon? |
 | |
| Incorrect - Student Response |
|
70 |
The weight of an object on the Moon is 1/6 the weight of that object on the Earth. An object that weighs 30 pounds on Earth would weigh how many pounds on the Moon? |
 | |
| |||||||||||||||||||||||||
| Scoring Guide |
|
Score & Description | ||||
| ||||
| ||||
|
| *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 |
|
72 |
If 12 divides a whole number n without a remainder,
list all whole numbers greater than 1 and less than 12 that must also
divide n without a remainder. |
 | |
| Incorrect #1 - Student Response |
|
72 |
If 12 divides a whole number n without a remainder,
list all whole numbers greater than 1 and less than 12 that must also
divide n without a remainder. |
 | |
| Incorrect #2 - Student Response |
|
72 |
If 12 divides a whole number n without a remainder,
list all whole numbers greater than 1 and less than 12 that must also
divide n without a remainder. |
 | |
| |||||||||||||||||||||||||
| Scoring Guide |
|
Score & Description | ||||
| ||||
| ||||
| ||||
| ||||
|
| *The use of more than one incorrect category in this question enabled NAEP to gather data on common student errors. Any response that fell into one of the incorrect categories earned no credit. |
| Correct #1 - Student Response |
|
74 |
The Zandalia Zoo uses 214,964 kilograms of meat per year. If the meat costs $2.53 per kilogram, how much does the meat cost per week? |
 | |
| Correct #2 - Student Response |
|
74 |
The Zandalia Zoo uses 214,964 kilograms of meat per year. If the meat costs $2.53 per kilogram, how much does the meat cost per week? |
| Incorrect #1 - Student Response |
|
74 |
The Zandalia Zoo uses 214,964 kilograms of meat per year. If the meat costs $2.53 per kilogram, how much does the meat cost per week? |
 | |
| Incorrect #2 - Student Response |
|
74 |
The Zandalia Zoo uses 214,964 kilograms of meat per year. If the meat costs $2.53 per kilogram, how much does the meat cost per week? |
 | |
| Incorrect #3 - Student Response |
|
74 |
The Zandalia Zoo uses 214,964 kilograms of meat per year. If the meat costs $2.53 per kilogram, how much does the meat cost per week? |
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of the rectangle below.
pineapple
The price will be cheaper at Price
Pleasers.
The price will be the same
at both stores.
The price will be cheaper at
Bargains Plus.
is 3 more
students than can fit in a bus
buses (must
include .9)
