Figure 1

Document Sample

```					Figure 1
FINAL TEST SCORES
Score Number of Students
95     50
90     120
85     170
80     60
75     10

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

2. Peter wrote down a pattern of A's and B's that repeats in groups of 3. Here is the beginning of his
pattern with some of the letters erased. Fill in the missing letters.
3. On the portion of the number line below, a dot shows where 1/2 is. Use another dot to show where
3/4 is.

4. What is the length of the toothpick in the figure above?

5. In the space below, draw an angle that is larger than 90°.

6. On the number line below, shade the part of the line that shows the set of all numbers greater than
or equal to -1 and less than or equal to 3.
7. A box contains 3 chips numbered 1 through 3. One chip will be taken at random from the box and
then put back into the box. Then a second chip will be taken from the box.

In the space provided below, list all possible pairs of chips.

Number on First Chip Number on Second Chip

8. According to the indicator on the scale above, what is the weight in ounces of the can of tuna on the
scale?

9. One store, Price Pleasers, reduces the price each week of a \$100 stereo by 10 percent of the
original price.

Another store, Bargains Plus, reduces the price each week of the same \$100 stereo by 10 percent of
the previous week's price.

After 2 weeks, how will the prices at the two stores compare?

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

10. The table above shows the scores of a group of 11 students on a history test. What is the average
(mean) score of the group to the nearest whole number?

11. A survey is to be taken in a city to determine the most popular sport. Would sampling opinions at a
baseball game be a good way to collect this data? Explain your answer.
12. Divide:

13. Movie tickets cost \$5.25 each. If 100 tickets were sold, how much money was collected?

14. A high school orders 11 buses to transport 418 students. If each bus can seat 35 students, will the
number of buses ordered be enough to provide a seat for each student?

()Yes    ()No

The following question refers to the following information.

Triangles 1, 2, and 3 shown above can be rearranged with no overlap to form either of the following
figures.

15. Draw lines on the figure below to show how triangles 1, 2, and 3 can be rearranged without overlap
to form this parallelogram.

The following question refers to the following information.

Triangles 1, 2, and 3 shown above can be rearranged with no overlap to form either of the following
figures.

16. Draw lines on the figure below to show how triangles 1, 2, and 3 can be rearranged without overlap
to form this rectangle.
17. Two large storage tanks, T and W, contain water. T starts losing water at the same time additional water
starts flowing into W. The graph below shows the amount of water in each tank over a period of hours.

Assume that the rates of water loss and water gain continue as shown. At what number of hours will the
amount of water in T be equal to the amount of water in W ?

On the map below, the rock is located 2 miles west and 1 mile north of the tree. A treasure chest (not
shown) is located 8 miles east and 4 miles north of the rock. Mark the location of the treasure chest on
the map with an X.

18. What is the position of the treasure chest with respect to the tree?

Answer: _____ miles east and _____ miles north of the tree
19. A bag contains two red candies and one yellow candy. Kim takes out one candy and eats it, and
then Jeff takes out one candy. For each sentence below, fill in the oval to indicate whether it is
possible or not possible.

From any vertex of a 4-sided polygon, 1 diagonal can be drawn.
From any vertex of a 5-sided polygon, 2 diagonals can be drawn.
From any vertex of a 6-sided polygon, 3 diagonals can be drawn.
From any vertex of a 7-sided polygon, 4 diagonals can be drawn.

20. How many diagonals can be drawn from any vertex of a 20-sided polygon?

21. Use the unit of length below to estimate the perimeter of the figure shown. Between which two
consecutive whole-number units does the perimeter lie?

22. Jaime knows the following facts about points A, B, and C.

   Points A, B, and C are on the same line, but might not be in that order.
   Point C is twice as far from point A as it is from point B.

Jaime concluded that point C is always between points A and B.
Is Jaime's conclusion correct?

Question 23 refers to Figure 1
With this test booklet, you will receive a packet of 6 pieces: 2 each of shape N, shape P, and shape Q.
You will use these pieces in answering some of the questions. You can turn the pieces in any way or
flip them over. You may use drawings to help explain your answers.

23. Laura was asked to choose 1 of the 3 shapes N, P, and Q that is different from the other 2. Laura
chose shape N. Explain how shape N is different from shapes P and Q.

Question 24 refers to Figure 1

With this test booklet, you will receive a packet of 6 pieces: 2 each of shape N, shape P, and shape Q.
You will use these pieces in answering some of the questions. You can turn the pieces in any way or
flip them over. You may use drawings to help explain your answers.

24. You will need the 2 pieces labeled Q. Please find those 2 pieces now.

Use the 2 pieces labeled Q to make a square. Trace the square and draw the line to show where
the 2 pieces meet.

Question 25 refers to Figure 1

With this test booklet, you will receive a packet of 6 pieces: 2 each of shape N, shape P, and shape Q.
You will use these pieces in answering some of the questions. You can turn the pieces in any way or
flip them over. You may use drawings to help explain your answers.

25. Use the 2 pieces labeled Q to make a 4-sided shape that is not a square. Trace the shape and
draw the line to show where the 2 pieces meet.

Question 26 refers to Figure 1
With this test booklet, you will receive a packet of 6 pieces: 2 each of shape N, shape P, and shape Q.
You will use these pieces in answering some of the questions. You can turn the pieces in any way or
flip them over. You may use drawings to help explain your answers.

26. For this question you will need some of the pieces labeled N, P, and Q.

Use 4 of the 6 pieces labeled N, P, and Q to make the shape shown below. Draw the lines to show
where the pieces meet and label the pieces.

Question 27 refers to Figure 1

With this test booklet, you will receive a packet of 6 pieces: 2 each of shape N, shape P, and shape Q.
You will use these pieces in answering some of the questions. You can turn the pieces in any way or
flip them over. You may use drawings to help explain your answers.

27. Bob, Carmen, and Tyler were comparing the areas of N and P. Bob said that N and P have the
same area. Carmen said that the area of N is larger. Tyler said that the area of P is larger.

Who was correct?____________________

Use words or pictures (or both) to explain why.

Question 28 refers to Figure 1
With this test booklet, you will receive a packet of 6 pieces: 2 each of shape N, shape P, and shape Q.
You will use these pieces in answering some of the questions. You can turn the pieces in any way or
flip them over. You may use drawings to help explain your answers.

28. Which of the shapes N, P, and Q has the longest perimeter (distance around)?

Shape with longest perimeter:____________________

Use words or pictures (or both) to explain why.

Question 29 refers to Figure 1

29. This question refers to pieces N, P, and Q.

In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results.

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:

30. The lowest point of the St. Lawrence River is 294 feet below sea level. The top of Mt. Jacques
Cartier is 1,277 feet above sea level. How many feet higher is the top of Mt. Jacques Cartier than
the lowest point of the St. Lawrence River? Show your work.
31. In 1980, the populations of Town A and Town B were 5,000 and 6,000, respectively. The 1990
populations of Town A and Town B were 8,000 and 9,000, respectively.

Brian claims that from 1980 to 1990 the populations of the two towns grew by the same amount. Use
mathematics to explain how Brian might have justified his claim.

Darlene claims that from 1980 to 1990 the population of Town A had grown more. Use mathematics
to explain how Darlene might have justified her claim.

32. A cereal company packs its oatmeal into cylindrical containers. The height of each container is 10
inches and the radius of the bottom is 3 inches. What is the volume of the box to the nearest cubic
inch? (The formula for the volume of a cylinder is          )

33. Victor's van travels at a rate of 8 miles every 10 minutes. Sharon's sedan travels at a rate of 20
miles every 25 minutes.

If both cars start at the same time, will Sharon's sedan reach point A, 8 miles away, before, at the
same time, or after Victor's van?

If both cars start at the same time, will Sharon's sedan reach point B (at a distance further down the
road) before, at the same time, or after Victor's van?
34. In the space below, use your ruler to draw a square with two of its corners at the points shown.

35. In the space below, draw a rectangle 2 inches wide and 3½ inches long.

Use your centimeter ruler to make the following measurements to the nearest centimeter.

36. What is the length in centimeters of one of the longer sides of the rectangle?

Use your centimeter ruler to make the following measurements to the nearest centimeter.

37. What is the length in centimeters of the diagonal from A to B?

38. Use your protractor to find the degree measure of the angle shown above.

39. On the grid below, draw a rectangle with an area of 12 square units.
40. Jill needs to earn \$45.00 for a class trip. She earns \$2.00 each day on Mondays, Tuesdays, and
Wednesdays, and \$3.00 each day on Thursdays, Fridays, and Saturdays. She does not work on
Sundays. How many weeks will it take her to earn \$45.00?

41. Steve was asked to pick two marbles from a bag of yellow marbles and blue marbles. One possible
result was one yellow marble first and one blue marble second. He wrote this result in the table
below. List all of the other possible results that Steve could get.

y stands for one        First      Second
yellow marble.        Marble      Marble
b stands for one
y            b
blue marble.
42. Each of the cylinders shown below was cut in a different way. The shaded part shows the shape of
the cut. Under each figure, write the name of the shape of the cut.

43.                                              54 < 3 ×
Write two numbers that could be put in the   to make the number sentence above true.

____________________
44. Akira read from a book on Monday, Tuesday, and Wednesday. He read an average of 10 pages
per day. Indicate in the ovals below whether each of the following is possible or not possible.

45. The area of rectangle BCDE shown above is 60 square inches. If the length of AE is 10 inches and
the length of ED is 15 inches, what is the area of trapezoid ABCD, in square inches?

46. The sum of the measures of the 24 angles in a 24-sided regular polygon is 3,960°. What is the
measure in degrees of one of the angles?

47. Tracy said, "I can multiply 6 by another number and get an answer that is smaller than 6."

Pat said, "No, you can't. Multiplying 6 by another number always makes the answer 6 or larger."

48. Raymond must buy enough paper to print 28 copies of a report that contains 64 sheets of paper.
Paper is only available in packages of 500 sheets. How many whole packages of paper will he
need to buy to do the printing?

49. Lynn had only quarters, dimes, and nickels to buy her lunch. She spent all of the money and
received no change. Could she have spent \$1.98?

50. On the grid below, the dot at (4, 4) is circled. Circle two other dots where the first number is equal to
the second number.

51. The length of a dinosaur was reported to have been 80 feet (rounded to the nearest 10 feet). What
length other than 80 feet could have been the actual length of this dinosaur?

52. The pictograph shown above is misleading. Explain why.

The following question refers to the following pattern of dot-figures.

3
54. What is the product of 3.12 and 8 ?

55. The weight of an object on the Moon is 1/6 the weight of that object on the Earth. An object that
weighs 30 pounds on Earth would weigh how many pounds on the Moon?

56. The cost to rent a motorbike is given by the following formula:
Cost = (\$3 × number of hours) + \$2

Fill in the table below.

Time in Hours Cost in Dollars
1              5
4
17

57. If 12 divides a whole number n without a remainder, list all whole numbers greater than 1 and less
than 12 that must also divide n without a remainder.

58. Plot the point (5, 2) on the grid shown below.
HAIR
COLOR
SURVEY
Percentage
RESULTS
Color of
Hair
Blond       17
Brown       50
Black       33
Totals     100

59. The table above shows the results of a survey of hair color. On the circle below, make a circle
graph to illustrate the data in the table. Label each part of the circle graph with the correct hair
color.

60. The Zandalia Zoo uses 214,964 kilograms of meat per year. If the meat costs \$2.53 per kilogram,
how much does the meat cost per week?

1.
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
Use the information in the table above to complete the bar graph below.
Incorrect - Student Response
Use the information in the table above to complete the bar graph below.
2.

Scoring Guide
Solution:

Score & Description
Correct
Correct response

Incorrect
Any incorrect response

In this question the student needed to fill in missing entries in a pattern of the letters "A" and "B." The
student was told that the pattern repeats in groups of 3, and enough information was given for the
student to find the one correct sequence.
Correct - Student Response
Peter wrote down a pattern of A's and B's that repeats in groups of 3. Here is the beginning of his
pattern with some of the letters erased. Fill in the missing letters.

Incorrect - Student Response
Peter wrote down a pattern of A's and B's that repeats in groups of 3. Here is the beginning of his
pattern with some of the letters erased. Fill in the missing letters.
3.

Scoring Guide
Solution:
Dot correctly placed or student labels "3/4" where the dot should be placed

OR

Score & Description
Correct
Correct response

Incorrect
Any incorrect response—includes more than one dot on the number line

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
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
On the portion of the number line below, a dot shows where 1/2 is. Use another dot to show where
3/4 is.
4.

Scoring Guide
Solution:
2 1/2 inches OR 2 1/2" OR 2 1/2 in OR
2 1/2 OR 2.5 OR 10/4
Score & Description
Correct
Correct response

Incorrect #3
10 1/2 or 10.5 inches

Incorrect #2
3 1/2 or 3.5 inches

Incorrect #1
Incorrect response other than those described in 2 and 3

In this question the student needed to determine the length of a toothpick displayed above a portion of
a ruler. One end of the toothpick was above the 8-inch mark on the ruler, and the other end of the
toothpick was located above the 10 1/2-inch mark on the ruler. The student could subtract to find the
length or else count the number of inches from 8 to 10 1/2.

*The use of more than one incorrect category in this question enabled NAEP to gather data on
common student errors. Any response that fell into one of the incorrect categories earned no credit.
Correct - Student Response
What is the length of the toothpick in the figure above?

Incorrect #3 - Student Response
What is the length of the toothpick in the figure above?

Incorrect #2 - Student Response
What is the length of the toothpick in the figure above?
Incorrect #1 - Student Response
What is the length of the toothpick in the figure above?
5.

Scoring Guide
Solution:
Any obtuse angle, such as:

OR

Score & Description
Correct #1
Correct response—any obtuse angle

Correct #2
Any closed figure that contains at least one obtuse angle. The obtuse angle does not need to be
designated

Incorrect
Any incorrect response—includes straight line with no vertex indicated

In this question the student was asked to draw an angle that is larger than 90° (an obtuse angle). Full
credit was earned for a drawing of either an obtuse angle or a closed figure containing an obtuse angle.

*The use of more than one correct category in this question enabled NAEP to gather data on different
ways students responded correctly to this question. Any one of these responses that fell into one of
these correct categories earned full credit.
Correct #1 - Student Response
In the space below, draw an angle that is larger than 90°.

Correct #2 - Student Response
In the space below, draw an angle that is larger than 90°.
Incorrect - Student Response
In the space below, draw an angle that is larger than 90°.
6.

Scoring Guide
Solution:

Score & Description
Correct
Correct response

Incorrect #2
Any of the following:

Incorrect #1
Any incorrect response other than those shown above

In this question the student needed to demonstrate an understanding of the ordering of real numbers
by graphing an interval—not individual points—on the number line.

*The use of more than one incorrect category in this question enabled NAEP to gather data on
common student errors. Any response that fell into one of the incorrect categories earned no credit.
Correct - Student Response
On the number line below, shade the part of the line that shows the set of all numbers greater than
or equal to -1 and less than or equal to 3.

Incorrect #2 - Student Response
On the number line below, shade the part of the line that shows the set of all numbers greater than
or equal to -1 and less than or equal to 3.
Incorrect #1 - Student Response
On the number line below, shade the part of the line that shows the set of all numbers greater than
or equal to -1 and less than or equal to 3.
7.

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
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
A box contains 3 chips numbered 1 through 3. One chip will be taken at random from the box and
then put back into the box. Then a second chip will be taken from the box.

In the space provided below, list all possible pairs of chips.

Incorrect #3 - Student Response
A box contains 3 chips numbered 1 through 3. One chip will be taken at random from the box and
then put back into the box. Then a second chip will be taken from the box.

In the space provided below, list all possible pairs of chips.
Incorrect #2 - Student Response
A box contains 3 chips numbered 1 through 3. One chip will be taken at random from the box and
then put back into the box. Then a second chip will be taken from the box.

In the space provided below, list all possible pairs of chips.

Incorrect #1 - Student Response
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.
8.

Scoring Guide
Solution:
6.5 or 6 1/2
Score & Description
Correct
Correct response

Incorrect
Any incorrect response

In this question the student needed to read the weight of a can placed on a scale marked in increments
of 1/2 unit.
Correct - Student Response
According to the indicator on the scale above, what is the weight in ounces of the can of tuna on the
scale?

Incorrect - Student Response
According to the indicator on the scale above, what is the weight in ounces of the can of tuna on the
scale?
9.

Scoring Guide
Solution:

At Price Pleasers the stereo would be \$80 after 2 weeks.
At Bargain Plus, it would cost \$81.

OR

Successive 10% reductions of the original price will yield greater savings than successive reductions of
10% of the reduced price.
Score & Description
Correct
Correct response—cheaper at Price Pleasers with an explanation that compares price at each store
after 2 weeks (\$80 vs. \$81)
OR
Cheaper at Price Pleasers with an explanation that generalizes as described in solution above

NOTE: Score CORRECT if incorrect answer is B or C with a clear statement that Price Pleasers is
cheaper and explanation is correct and complete.

Partial
Cheaper at Price Pleasers with anything less than a complete explanation
OR
Computes the correct amount for at least 2 weeks for either Price Pleasers or Bargain Plus, but
conclusion is missing, incomplete, or incorrect (if the store is not identified the score is still a 2)

Incorrect
Incorrect response

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
One store, Price Pleasers, reduces the price each week of a \$100 stereo by 10 percent of the
original price.

Another store, Bargains Plus, reduces the price each week of the same \$100 stereo by 10 percent
of the previous week's price.

After 2 weeks, how will the prices at the two stores compare?
Partial - Student Response
One store, Price Pleasers, reduces the price each week of a \$100 stereo by 10 percent of the
original price.

Another store, Bargains Plus, reduces the price each week of the same \$100 stereo by 10 percent
of the previous week's price.

After 2 weeks, how will the prices at the two stores compare?

Incorrect - Student Response
One store, Price Pleasers, reduces the price each week of a \$100 stereo by 10 percent of the original price.

Another store, Bargains Plus, reduces the price each week of the same \$100 stereo by 10 percent of the
previous week's price.

After 2 weeks, how will the prices at the two stores compare?
10.

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
The table above shows the scores of a group of 11 students on a history test. What is the average
(mean) score of the group to the nearest whole number?

Incorrect #3 - Student Response
The table above shows the scores of a group of 11 students on a history test. What is the average
(mean) score of the group to the nearest whole number?

Incorrect #2 - Student Response
The table above shows the scores of a group of 11 students on a history test. What is the average
(mean) score of the group to the nearest whole number?

Incorrect #1 - Student Response
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?
11.

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
A survey is to be taken in a city to determine the most popular sport. Would sampling opinions at a
baseball game be a good way to collect this data? Explain your answer.

Incorrect #2 - Student Response
A survey is to be taken in a city to determine the most popular sport. Would sampling opinions at a
baseball game be a good way to collect this data? Explain your answer.

Incorrect #1 - Student Response
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.
12.

Scoring Guide
Solution:
24
Score & Description
Correct
Correct response

Incorrect
Any incorrect response

In this question the student needed to solve a long division problem, dividing a 2-digit number into a 3-
digit number.
Correct - Student Response
Divide:

Incorrect - Student Response
Divide:
13.

Scoring Guide
Solution:
\$525 or 525
Score & Description
Correct
Correct response

Incorrect
Any incorrect response

In this question the student needed to apply multiplication to solve a word problem, multiplying \$5.25 by
100.
Correct - Student Response
Movie tickets cost \$5.25 each. If 100 tickets were sold, how much money was collected?

Incorrect - Student Response
Movie tickets cost \$5.25 each. If 100 tickets were sold, how much money was collected?
14.

Scoring Guide
Solution:
418 ÷ 11 = 38 per bus which is 3 more students than 35, or 3 more students would have to fit in each
bus

OR

is 3 more students than can fit in a bus

OR

buses (must include .9)

OR

11 × 35 is less than 418
Score & Description
Correct
Correct response
Note: Explanation must indicate that 11 buses will only seat 385 students. This may also be
illustrated by an example such as
11 × 35 = 385
OR 418 ÷ 35 = 11 with a remainder of 33
OR needs 33 more seats

Incorrect
Any incorrect or incomplete response
An incorrect response includes an incorrect computation

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
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
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
15.

Scoring Guide
Solution:
Triangles 1 and 2 may be interchanged. Triangles need not be labeled with numbers.

Score & Description
Correct
Correct response

Incorrect
Any incorrect response

In this question the student needed to demonstrate spatial visualization and reasoning skills to show
how to rearrange (touching, but not overlapping) three given triangles to form a parallelogram.
Correct - Student Response
Draw lines on the figure below to show how triangles 1, 2, and 3 can be rearranged without overlap
to form this parallelogram.

Incorrect - Student Response
Draw lines on the figure below to show how triangles 1, 2, and 3 can be rearranged without overlap
to form this parallelogram.
16.

Scoring Guide
Solution:
Triangles 1 and 2 may be interchanged. Triangles need not be labeled with numbers.

Score & Description
Correct
Correct response

Incorrect
Any incorrect response

In this question the student needed to demonstrate spatial visualization and reasoning skills to show
how to rearrange (touching, but not overlapping) three given triangles to form a rectangle.
Correct - Student Response
Draw lines on the figure below to show how triangles 1, 2, and 3 can be rearranged without overlap
to form this rectangle.

Incorrect - Student Response
Draw lines on the figure below to show how triangles 1, 2, and 3 can be rearranged without overlap
to form this rectangle.
17.

Scoring Guide
Solution:
8 hours.
Graphical Solution:
Extend both lines to the right until they intersect. Then read the horizontal coordinate of the point of
intersection.

Note: If lines are extended correctly until they intersect, this will serve as sufficient justification. No
words are required in this situation.

Algebraic Solution:
Equation of lines:
T y = -50x + 900
W y = 25x + 300
Point of intersection (8hrs, 500 gal)
Score & Description
Correct
Correct response

Partial
Number of hours is incorrect, but falls between 6 1/2 and 8 1/2 and a correct procedure is
demonstrated.
OR
Number of hours is correct, but accompanying justification is insufficient or missing

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

Partial - Student Response
Two large storage tanks, T and W, contain water. T starts losing water at the same time additional
water starts flowing into W. The graph below shows the amount of water in each tank over a period
of hours.

Incorrect - Student Response
Two large storage tanks, T and W, contain water. T starts losing water at the same time additional
water starts flowing into W. The graph below shows the amount of water in each tank over a period
of hours.
18.

Scoring Guide
Solution:

6 miles east and 5 miles north of the tree
Score & Description
Correct #1
Treasure marked "X" at (6,5) on map (any X within the small squares that surround (6,5)) and fill-ins
are correct

Correct #2
Treasure located incorrectly but both fill-ins are correct

Incorrect
Any incorrect response

In this question, presented in context, the student needed to determine the effect of horizontal and
vertical translations on a point in a coordinate plane.

*The use of more than one correct category in this question enabled NAEP to gather data on different
ways students responded correctly to this question. Any one of these responses that fell into one of
these correct categories earned full credit.
Correct #1 - Student Response
What is the position of the treasure chest with respect to the tree?
Correct #2 - Student Response
What is the position of the treasure chest with respect to the tree?
Incorrect - Student Response
What is the position of the treasure chest with respect to the tree?
19.

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.

Score & Description
4 Right

3 Right

2 Right

1 Right

0 Right

4 Right - Student Response
A bag contains two red candies and one yellow candy. Kim takes out one candy and eats it, and
then Jeff takes out one candy. For each sentence below, fill in the oval to indicate whether it is
possible or not possible.
3 Right - Student Response
A bag contains two red candies and one yellow candy. Kim takes out one candy and eats it, and
then Jeff takes out one candy. For each sentence below, fill in the oval to indicate whether it is
possible or not possible.

2 Right - Student Response
A bag contains two red candies and one yellow candy. Kim takes out one candy and eats it, and
then Jeff takes out one candy. For each sentence below, fill in the oval to indicate whether it is
possible or not possible.

1 Right - Student Response
A bag contains two red candies and one yellow candy. Kim takes out one candy and eats it, and
then Jeff takes out one candy. For each sentence below, fill in the oval to indicate whether it is
possible or not possible.

0 Right - Student Response
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.
20.

Scoring Guide
Solution:

17

Scoring Guide

In this question a student needed to demonstrate an understanding of diagonals of polygons. A
diagonal of a polygon is a segment that joins two nonadjacent vertices.(A vertex is a common endpoint
of two sides of the polygon). To answer the question it was expected that a student would observe that
the number of diagonals from any vertex is 3 less than the number of sides. That is, from any vertex of
a convex polygon a diagonal can be drawn to any of the other vertices of that polygon except the two
adjacent vertices. For a 20-sided polygon, the answer is 20 - 3 = 17.
Score & Description
Correct
Correct response

Incorrect
Any incorrect response

Correct - Student Response
How many diagonals can be drawn from any vertex of a 20-sided polygon?

Incorrect - Student Response
How many diagonals can be drawn from any vertex of a 20-sided polygon?
21.

Scoring Guide
Solution:

Between 6 and 7
Must have both 6 and 7 in answer to be counted as correct.

Between 7 and 6 is also a correct answer.

Scoring Guide

This question involved the use of estimation skills by using a given unit of length to find the perimeter
(distance around) of the 4-sided figure. The correct answer is between 6 and 7 (or 7 and 6). There are
different types of incorrect responses. If a student overestimated the perimeter as between 7 and 8,
then a score of incorrect # 3 is earned. If a student underestimated the perimeter as between 5 and 6,
then a score of incorrect # 2 is earned. Any other response is an incorrect # 1.
Score & Description
Correct
Correct response.

Incorrect #3
Between 7 and 8.

Incorrect #2
Between 5 and 6.

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
Use the unit of length below to estimate the perimeter of the figure shown. Between which two
consecutive whole-number units does the perimeter lie?

Incorrect #3 - Student Response
Use the unit of length below to estimate the perimeter of the figure shown. Between which two
consecutive whole-number units does the perimeter lie?

Incorrect #2 - Student Response
Use the unit of length below to estimate the perimeter of the figure shown. Between which two
consecutive whole-number units does the perimeter lie?

Incorrect #1 - Student Response
Use the unit of length below to estimate the perimeter of the figure shown. Between which two
consecutive whole-number units does the perimeter lie?
22.

Scoring Guide
Solution:
The explanation must include either one of the following diagrams;

The diagram should include or illustrate the idea that B is halfway between A and C.
Note: Points need to be indicated by some mark, such as a dot or tic mark. A response in which points
are indicated by letters only is incorrect.

Scoring Guide

In this question a student needed to reason about the possible positions of points on a line and present
the conclusion in the form of a diagram. A correct response needed to show that B is halfway between
A and C (or C and A).
Score & Description
Correct
Correct response including correct diagram

Incorrect #2
B is placed between A and C but is not the midpoint.

Incorrect #1
Any incorrect diagram

* 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
Jaime knows the following facts about points A, B, and C.

   Points A, B, and C are on the same line, but might not be in that order.
   Point C is twice as far from point A as it is from point B.

Jaime concluded that point C is always between points A and B.
Is Jaime's conclusion correct?
.    Jaime knows the following facts about points A, B, and C.

    Points A, B, and C are on the same line, but might not be in that order.
    Point C is twice as far from point A as it is from point B.

Jaime concluded that point C is always between points A and B.
Is Jaime's conclusion correct?

Incorrect #2 - Student Response
Jaime knows the following facts about points A, B, and C.

    Points A, B, and C are on the same line, but might not be in that order.
    Point C is twice as far from point A as it is from point B.

Jaime concluded that point C is always between points A and B.
Is Jaime's conclusion correct?

Incorrect #1 - Student Response
Jaime knows the following facts about points A, B, and C.
   Points A, B, and C are on the same line, but might not be in that order.
   Point C is twice as far from point A as it is from point B.

Jaime concluded that point C is always between points A and B.
Is Jaime's conclusion correct?

.   Jaime knows the following facts about points A, B, and C.

   Points A, B, and C are on the same line, but might not be in that order.
   Point C is twice as far from point A as it is from point B.

Jaime concluded that point C is always between points A and B.
Is Jaime's conclusion correct?
23.

Scoring Guide
Solution:

N is a square (but P and Q are triangles.)

OR N has four sides, (or vertices or points or angles), (but P and Q each have 3).

OR All the sides of N are =, (but not so with P and Q).

OR All the angles of N are = (or, all right angles), (not so with P and Q.)

Must mention both P and Q or neither P nor Q plus N is a square or give other characteristics of N.
Score & Description
Correct
Correct responses

Incorrect #2
Response refers to the letters (N, P, or Q), rather than to the shape.

Incorrect #1
Any incorrect response other than as described above.
Not acceptable: N is bigger or N is prettier

Note to scorers:

   Areas of N, P, Q are equal
   "It" or "they" is assumed to refer to N.
   Use of the word box instead of square is not acceptable

*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
Laura was asked to choose 1 of the 3 shapes N, P, and Q that is different from the other 2. Laura
chose shape N. Explain how shape N is different from shapes P and Q.

.     Laura was asked to choose 1 of the 3 shapes N, P, and Q that is different from the other 2. Laura
chose shape N. Explain how shape N is different from shapes P and Q.
Incorrect #2 - Student Response
Laura was asked to choose 1 of the 3 shapes N, P, and Q that is different from the other 2. Laura
chose shape N. Explain how shape N is different from shapes P and Q.

.    Laura was asked to choose 1 of the 3 shapes N, P, and Q that is different from the other 2. Laura
chose shape N. Explain how shape N is different from shapes P and Q.

Incorrect #1 - Student Response
Laura was asked to choose 1 of the 3 shapes N, P, and Q that is different from the other 2. Laura
chose shape N. Explain how shape N is different from shapes P and Q.

.    Laura was asked to choose 1 of the 3 shapes N, P, and Q that is different from the other 2. Laura
chose shape N. Explain how shape N is different from shapes P and Q.
24.

Scoring Guide
Solution:

The square may be tilted.
Diagonal must be shown.
Pieces may or may not be labeled.

Space between is acceptable.
Freehand drawings are acceptable.

Scoring Guide

In this question, a student needed to visualize how to form a square using two isosceles right triangles.
Score & Description
Correct
Correct response

Incorrect
Any incorrect response

Correct - Student Response
You will need the 2 pieces labeled Q. Please find those 2 pieces now.

Use the 2 pieces labeled Q to make a square. Trace the square and draw the line to show where
the 2 pieces meet.

.    You will need the 2 pieces labeled Q. Please find those 2 pieces now.

Use the 2 pieces labeled Q to make a square. Trace the square and draw the line to show where
the 2 pieces meet.

Incorrect - Student Response
You will need the 2 pieces labeled Q. Please find those 2 pieces now.

Use the 2 pieces labeled Q to make a square. Trace the square and draw the line to show where
the 2 pieces meet.

.    You will need the 2 pieces labeled Q. Please find those 2 pieces now.

Use the 2 pieces labeled Q to make a square. Trace the square and draw the line to show where
the 2 pieces meet.
25.

Scoring Guide
Solution:
Examples of correct response #1 (see note below score & description)

Examples of correct response #2 (see note below score & description)

Space between pieces is acceptable.
Freehand drawings are acceptable.

Scoring Guide

In this question, a student needed to take 2 isosceles triangles and construct a 4-sided figure that was
not a square or a rhombus. A student had to manipulate 2 figures, form a shape other than a square or
rhombus, and draw a line of separation in order to earn a score of correct #1. To earn a correct #2, a
student had to manipulate 2 figures with some overlapping possible, form a shape that was not a
square or rhombus, but did not have to drawn a line of separation.
Score & Description
Correct #1
Correct response (The figure may be tilted. Pieces may or may not be labeled. Line of seperation
must be shown.)

Correct #2
A correct shape without the line of separation shown. (Figure is not a rhombus.)
OR
A 4-sided shape (that is not a square) that results when part of two Q shapes overlap.
Incorrect
Any incorrect response

* The use of more than one correct category in this question enabled NAEP to gather data on different
ways in which students responded correctly to this question. Any response that fell into one of these
correct categories earned full credit.
Correct #1 - Student Response
Use the 2 pieces labeled Q to make a 4-sided shape that is not a square. Trace the shape and
draw the line to show where the 2 pieces meet.

.    Use the 2 pieces labeled Q to make a 4-sided shape that is not a square. Trace the shape and
draw the line to show where the 2 pieces meet.

Correct #2 - Student Response
Use the 2 pieces labeled Q to make a 4-sided shape that is not a square. Trace the shape and
draw the line to show where the 2 pieces meet.
.    Use the 2 pieces labeled Q to make a 4-sided shape that is not a square. Trace the shape and
draw the line to show where the 2 pieces meet.

Incorrect - Student Response
Use the 2 pieces labeled Q to make a 4-sided shape that is not a square. Trace the shape and
draw the line to show where the 2 pieces meet.

.    Use the 2 pieces labeled Q to make a 4-sided shape that is not a square. Trace the shape and
draw the line to show where the 2 pieces meet.
26.

Scoring Guide
Solution:

Scoring Guide

In this question, a student needed to visualize where to place 4 of the 6 given shapes (2 squares, 2
isosceles triangles, and 2 right triangles) so that they formed a 6-sided shape that was already given to
the student.
Score & Description
Correct #1
Correct response (The second figure may be reversed left to right. Pieces must be labeled
correctly. Accept even if there is space between pieces.)

Correct #2
Lines are drawn correctly but lables are incorrect or missing.

Incorrect
Any incorrect response.

* The use of more than one correct category in this question enabled NAEP to gather data on different
ways in which students responded correctly to this question. Any response that fell into one of these
correct categories earned full credit.
Correct #1 - Student Response
For this question you will need some of the pieces labeled N, P, and Q.

Use 4 of the 6 pieces labeled N, P, and Q to make the shape shown below. Draw the lines to show
where the pieces meet and label the pieces.
.    For this question you will need some of the pieces labeled N, P, and Q.

Use 4 of the 6 pieces labeled N, P, and Q to make the shape shown below. Draw the lines to show
where the pieces meet and label the pieces.

Correct #2 - Student Response
For this question you will need some of the pieces labeled N, P, and Q.

Use 4 of the 6 pieces labeled N, P, and Q to make the shape shown below. Draw the lines to show
where the pieces meet and label the pieces.
.    For this question you will need some of the pieces labeled N, P, and Q.

Use 4 of the 6 pieces labeled N, P, and Q to make the shape shown below. Draw the lines to show
where the pieces meet and label the pieces.

Incorrect - Student Response
For this question you will need some of the pieces labeled N, P, and Q.

Use 4 of the 6 pieces labeled N, P, and Q to make the shape shown below. Draw the lines to show
where the pieces meet and label the pieces.
.   For this question you will need some of the pieces labeled N, P, and Q.

Use 4 of the 6 pieces labeled N, P, and Q to make the shape shown below. Draw the lines to show
where the pieces meet and label the pieces.
27.

Scoring Guide
Solution:

An adequate explanation with or without Bob.
May say "neither" or "both".

Parts of P overlaps N, and part sticks out. The sticking out part is equal to the left out part of N.

OR

Two P's match two N's therefore they have the same area. (Therefore, one N has the same area as
one P.)

OR

Areas are equal because height of P is the same as the height of N, and the base of P is twice the
base of N.

OR

Either of these two figures alone are acceptable.
Scoring Guide

In this question, a student has to compare two given shapes with respect to their area. A student
needed to realize that area meant the amount of surface a shape covers. They also needed to know
how to compare the areas of the shapes. Using pictures and words to make the comparison between
the areas of N and P, a student could have given a variety of explanations such as two shape P's
match with two shape N's; therefore, one N has the same area as one P. They also could have used
the geometric shapes placed one on top of the other to see how their areas compared.
Score & Description
Correct
Correct response

Incorrect #2
Bob was correct, but explanation not given or inadequate.

Incorrect #1
Any response that answers Carmen or Tyler to "Who was correct?"
OR
Omits the name and gives no satisfactory explanation.

* 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
Bob, Carmen, and Tyler were comparing the areas of N and P. Bob said that N and P have the
same area. Carmen said that the area of N is larger. Tyler said that the area of P is larger.
.    Bob, Carmen, and Tyler were comparing the areas of N and P. Bob said that N and P have the
same area. Carmen said that the area of N is larger. Tyler said that the area of P is larger.

Incorrect #2 - Student Response
Bob, Carmen, and Tyler were comparing the areas of N and P. Bob said that N and P have the
same area. Carmen said that the area of N is larger. Tyler said that the area of P is larger.

.    Bob, Carmen, and Tyler were comparing the areas of N and P. Bob said that N and P have the
same area. Carmen said that the area of N is larger. Tyler said that the area of P is larger.
Incorrect #1 - Student Response
Bob, Carmen, and Tyler were comparing the areas of N and P. Bob said that N and P have the
same area. Carmen said that the area of N is larger. Tyler said that the area of P is larger.

.    Bob, Carmen, and Tyler were comparing the areas of N and P. Bob said that N and P have the
same area. Carmen said that the area of N is larger. Tyler said that the area of P is larger.
28.

Scoring Guide
Solution:

P has the longest perimeter.

e.g. hold pieces up to each other, moving edges around to match up,
see which piece has some edge left over.

OR

Copy the sides of each piece in a line as shown below, and compare lengths

Scoring Guide

In this question, a student has to estimate the perimeter of each shape and then compare perimeters to
see which shape has the longest perimeter. This question requires a student to come up with some
method to determine the perimeter of the shapes without the use of a ruler and to explain why he or
she selected the shape.
Score & Description
Correct
Correct responses

Incorrect #2
P has the longest perimeter but explanation not given or inadequate.

Incorrect #1
Any response that gives Q or N as having the longest perimeter.
OR
Does not indicate that P has longest perimeter.

* 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
Which of the shapes N, P, and Q has the longest perimeter (distance around)?
.    Which of the shapes N, P, and Q has the longest perimeter (distance around)?

Incorrect #2 - Student Response
Which of the shapes N, P, and Q has the longest perimeter (distance around)?
.    Which of the shapes N, P, and Q has the longest perimeter (distance around)?

Incorrect #1 - Student Response
Which of the shapes N, P, and Q has the longest perimeter (distance around)?

.    Which of the shapes N, P, and Q has the longest perimeter (distance around)?
29.

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
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.

.     This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results.

Incorrect #3 - Student Response
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.

.    This question refers to pieces N, P, and Q.

In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results.

Incorrect #2 - Student Response
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.

.    This question refers to pieces N, P, and Q.
In Mr. Bell's classes, the students voted for their favorite shape for a symbol. Here are the results.

Incorrect #1 - Student Response
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.

.    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.
30.

Scoring Guide
Solution:
1571

Scoring Guide

In this question, a student needed to interpret that the lowest point of the St. Lawrence River is a
negative number and the highest point of Mt. Jacques Cartier is a positive number (both with respect to
sea level). To find the difference between the highest point and the lowest point and to earn full credit,
a student needed to subtract the two numbers. To earn partial credit, a student would have had to show
the correct procedure using positive and negative numbers, but made a computation error.
Score & Description
Correct
Correct response

Partial
Shows correct procedure (addition) but does not answer 1571. Correct procedure means either
1277-(-294) or 1277 + 294, but not 1277 - 294.

Incorrect
Incorrect response

Correct - Student Response
The lowest point of the St. Lawrence River is 294 feet below sea level. The top of Mt. Jacques
Cartier is 1,277 feet above sea level. How many feet higher is the top of Mt. Jacques Cartier than
the lowest point of the St. Lawrence River? Show your work.

.     The lowest point of the St. Lawrence River is 294 feet below sea level. The top of Mt. Jacques
Cartier is 1,277 feet above sea level. How many feet higher is the top of Mt. Jacques Cartier than
the lowest point of the St. Lawrence River? Show your work.

Partial - Student Response
The lowest point of the St. Lawrence River is 294 feet below sea level. The top of Mt. Jacques
Cartier is 1,277 feet above sea level. How many feet higher is the top of Mt. Jacques Cartier than
the lowest point of the St. Lawrence River? Show your work.

.    The lowest point of the St. Lawrence River is 294 feet below sea level. The top of Mt. Jacques
Cartier is 1,277 feet above sea level. How many feet higher is the top of Mt. Jacques Cartier than
the lowest point of the St. Lawrence River? Show your work.

Incorrect - Student Response
The lowest point of the St. Lawrence River is 294 feet below sea level. The top of Mt. Jacques
Cartier is 1,277 feet above sea level. How many feet higher is the top of Mt. Jacques Cartier than
the lowest point of the St. Lawrence River? Show your work.

.    The lowest point of the St. Lawrence River is 294 feet below sea level. The top of Mt. Jacques
Cartier is 1,277 feet above sea level. How many feet higher is the top of Mt. Jacques Cartier than
the lowest point of the St. Lawrence River? Show your work.
31.

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.
Score & Description
Correct
Correct response

Partial
Gives correct reason for Brian or Darlene but not both. (Reason must include mathematics
illustrated in above solution or an appropriate reason using proportion.)
OR
uses 1000 or 3000 (without additional mathematics) for Brian's claim and uses 60% and 50% (or
their equivalents) without additional mathematics for Darlene's claim

Incorrect
Incorrect response

Correct - Student Response
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
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.
.    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
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.
32.

Scoring Guide
Solution:
283

Scoring Guide

In this question, a student is given the formula for the volume of a cylinder. To earn full credit, a student
needed to give an answer of 283 (with or without work) which has been rounded to the nearest cubic
inch. To earn partial credit, the correct substitutions would have been made but the student did not
round his or her answer correctly.
Score & Description
Correct
Correct response

Partial
Response shows correct substitutions into the formula but does not round answer correctly to get
283
OR
282.74334 with no work (uses key)
OR
282.6 with no work (uses 3.14)
OR
282.8571 with no work (uses 22/7)

Incorrect
Incorrect response

Correct - Student Response
A cereal company packs its oatmeal into cylindrical containers. The height of each container is 10
inches and the radius of the bottom is 3 inches. What is the volume of the box to the nearest cubic
inch? (The formula for the volume of a cylinder is          )
.    A cereal company packs its oatmeal into cylindrical containers. The height of each container is 10
inches and the radius of the bottom is 3 inches. What is the volume of the box to the nearest cubic
inch? (The formula for the volume of a cylinder is          )

Partial - Student Response
A cereal company packs its oatmeal into cylindrical containers. The height of each container is 10
inches and the radius of the bottom is 3 inches. What is the volume of the box to the nearest cubic
inch? (The formula for the volume of a cylinder is          )

Incorrect - Student Response
A cereal company packs its oatmeal into cylindrical containers. The height of each container is 10
inches and the radius of the bottom is 3 inches. What is the volume of the box to the nearest cubic
inch? (The formula for the volume of a cylinder is          )

.    A cereal company packs its oatmeal into cylindrical containers. The height of each container is 10
inches and the radius of the bottom is 3 inches. What is the volume of the box to the nearest cubic
inch? (The formula for the volume of a cylinder is          )
33.

Scoring Guide
Solution:
They will both reach points A and B at the same time because their rates are equal.

Scoring Guide

In this question, a student needed to use proportional thinking to solve this problem. The student
should have reasoned that both Victor’s rate and Sharon’s rate are equal. To earn full credit the student
needed to answer both parts of the question correctly with the correct justification for each. To earn
partial credit, a student could have just answered one part correctly with the correct justification or
answered both parts with no justification or incorrect justifications.
Score & Description
Correct
Correct response

Partial
Answers either part with correct justification.
OR
Answers both parts correctly with no justification

Incorrect
Incorrect response

Correct - Student Response
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?

.     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?

Partial - Student Response
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?

.     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?

Incorrect - Student Response
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?

.     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?

34.

Scoring Guide

Score & Description
Correct #1
A square with the two dots as adjacent vertices:

Correct #2
The two dots are end points of a diagonal:

Incorrect
Any incorrect response.

NOTE: All correct answers must contain at least three equal sides and the figure must appear to be a
square.

*The use of more than one correct category in this question enabled NAEP to gather data on different
ways students responded correctly to this question. Any one of these responses that fell into one of
these correct categories earned full credit.
Correct #1 - Student Response
In the space below, use your ruler to draw a square with two of its corners at the points shown.

.     In the space below, use your ruler to draw a square with two of its corners at the points shown.
Correct #2 - Student Response
In the space below, use your ruler to draw a square with two of its corners at the points shown.

Incorrect - Student Response
In the space below, use your ruler to draw a square with two of its corners at the points shown.
35.

Scoring Guide

Score & Description
Correct
Any 2 inch (±1/8") by 3 1/2 inch (±1/8") rectangle is acceptable. Sides should be reasonably straight
and angles should be about 90°.

Incorrect #4
Drawing is a rectangle, but dimensions are incorrect. (3 or more right angles)

Incorrect #3
Drawing is a four-sided figure, but is not a rectangle. (Less than 3 right angles.)

Incorrect #2
Drawing is a triangle.

Incorrect #1
Drawing is neither four-sided nor a triangle.

*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
In the space below, draw a rectangle 2 inches wide and 3½ inches long.

Incorrect #4 - Student Response
In the space below, draw a rectangle 2 inches wide and 3½ inches long.
Incorrect #3 - Student Response
In the space below, draw a rectangle 2 inches wide and 3½ inches long.

.    In the space below, draw a rectangle 2 inches wide and 3½ inches long.

Incorrect #2 - Student Response
In the space below, draw a rectangle 2 inches wide and 3½ inches long.

Incorrect #1 - Student Response
In the space below, draw a rectangle 2 inches wide and 3½ inches long.
36.

Scoring Guide

Score & Description
Correct
8 or 8 centimeters or 8 cm.

Any number between 7.9 and 8.1 inclusive is acceptable.

Incorrect #2
6 cm (the measurement of the shorter side).

Incorrect #1
Any incorrect response other than as described in Incorrect #2.

*The use of more than one incorrect category in this question enabled NAEP to gather data on
common student errors. Any response that fell into one of the incorrect categories earned no credit.
Correct - Student Response
What is the length in centimeters of one of the longer sides of the rectangle?

.     What is the length in centimeters of one of the longer sides of the rectangle?

Incorrect #2 - Student Response
What is the length in centimeters of one of the longer sides of the rectangle?

Incorrect #1 - Student Response
What is the length in centimeters of one of the longer sides of the rectangle?
37.

Scoring Guide

Score & Description
Correct
10 or 10 centimeters or 10cm

Any number between 9.9 and 10.1 inclusive is acceptable.

Incorrect
Any incorrect response.

Correct - Student Response
What is the length in centimeters of the diagonal from A to B?

.     What is the length in centimeters of the diagonal from A to B?

Incorrect - Student Response
What is the length in centimeters of the diagonal from A to B?
38.

Scoring Guide

Score & Description
Correct
128°

Any answer in the range 124° - 130° will be accepted as correct.

Incorrect
Any incorrect response.

Note: Answer need not have the degree symbol.
Correct - Student Response
Use your protractor to find the degree measure of the angle shown above.

Incorrect - Student Response
Use your protractor to find the degree measure of the angle shown above.
39.

Scoring Guide

Score & Description
Correct
Any rectangle with an area of 12.

e.g. 1 by 12
2 by 6
3 by 4

Incorrect #2
Any rectangle with a perimeter of 12.

e.g. 1 by 5
3 by 3
2 by 4

Incorrect #1
Any incorrect response other than as described in Incorrect #2.

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

Incorrect #2 - Student Response
On the grid below, draw a rectangle with an area of 12 square units.
Incorrect #1 - Student Response
On the grid below, draw a rectangle with an area of 12 square units.
40.

Scoring Guide

Score & Description
Correct #1
3 or 3 weeks.

Correct #2
18 days or 21 days.

Incorrect #2
9 or 9 weeks.

Incorrect #1
Any incorrect response other than as described in Incorrect #2.

*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
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?

.     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
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?

.    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
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?

.    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
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?

.    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?
41.

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
Steve was asked to pick two marbles from a bag of yellow marbles and blue marbles. One possible
result was one yellow marble first and one blue marble second. He wrote this result in the table
below. List all of the other possible results that Steve could get.
Incorrect #3 - Student Response
Steve was asked to pick two marbles from a bag of yellow marbles and blue marbles. One possible
result was one yellow marble first and one blue marble second. He wrote this result in the table
below. List all of the other possible results that Steve could get.

Incorrect #2 - Student Response
Steve was asked to pick two marbles from a bag of yellow marbles and blue marbles. One possible
result was one yellow marble first and one blue marble second. He wrote this result in the table
below. List all of the other possible results that Steve could get.

Incorrect #1 - Student Response
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.
42.

Scoring Guide

Score & Description
Correct
Circle:            Rectangle:            Oval:
or                 or
Parallelogram         Ellipse
or

Incorrect #3

Incorrect #2

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
Each of the cylinders shown below was cut in a different way. The shaded part shows the shape of
the cut. Under each figure, write the name of the shape of the cut.

.     Each of the cylinders shown below was cut in a different way. The shaded part shows the shape of
the cut. Under each figure, write the name of the shape of the cut.

Incorrect #3 - Student Response
Each of the cylinders shown below was cut in a different way. The shaded part shows the shape of
the cut. Under each figure, write the name of the shape of the cut.

.    Each of the cylinders shown below was cut in a different way. The shaded part shows the shape of
the cut. Under each figure, write the name of the shape of the cut.

Incorrect #2 - Student Response
Each of the cylinders shown below was cut in a different way. The shaded part shows the shape of
the cut. Under each figure, write the name of the shape of the cut.

.    Each of the cylinders shown below was cut in a different way. The shaded part shows the shape of
the cut. Under each figure, write the name of the shape of the cut.

Incorrect #1 - Student Response
Each of the cylinders shown below was cut in a different way. The shaded part shows the shape of
the cut. Under each figure, write the name of the shape of the cut.
.   Each of the cylinders shown below was cut in a different way. The shaded part shows the shape of
the cut. Under each figure, write the name of the shape of the cut.
43.

Scoring Guide

Score & Description
Correct
Any two different numbers greater than 18.

OR

A general statement such as "Any number greater than 18."

Incorrect #3
Only one correct response and the other response is "18".

Incorrect #2
Only one correct response and the other response is not "18" or is missing.

Incorrect #1
Both responses are incorrect.

*The use of more than one incorrect category in this question enabled NAEP to gather data on
common student errors. Any response that fell into one of the incorrect categories earned no credit.
Correct - Student Response
54 < 3 ×
Write two numbers that could be put in the  to make the number sentence above true.

.                                                  54 < 3 ×
Write two numbers that could be put in the    to make the number sentence above true.

Incorrect #3 - Student Response
54 < 3 ×
Write two numbers that could be put in the    to make the number sentence above true.

Incorrect #2 - Student Response
54 < 3 ×
Write two numbers that could be put in the    to make the number sentence above true.

.                                                 54 < 3 ×
Write two numbers that could be put in the    to make the number sentence above true.

Incorrect #1 - Student Response
54 < 3 ×
Write two numbers that could be put in the    to make the number sentence above true.

.                                                 54 < 3 ×
Write two numbers that could be put in the    to make the number sentence above true.
44.

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.

Score & Description
4 Right

3 Right

2 Right

1 Right

0 Right

4 Right - Student Response
Akira read from a book on Monday, Tuesday, and Wednesday. He read an average of 10 pages per
day. Indicate in the ovals below whether each of the following is possible or not possible.
3 Right - Student Response
Akira read from a book on Monday, Tuesday, and Wednesday. He read an average of 10 pages per
day. Indicate in the ovals below whether each of the following is possible or not possible.

2 Right - Student Response
Akira read from a book on Monday, Tuesday, and Wednesday. He read an average of 10 pages per
day. Indicate in the ovals below whether each of the following is possible or not possible.

1 Right - Student Response
Akira read from a book on Monday, Tuesday, and Wednesday. He read an average of 10 pages per
day. Indicate in the ovals below whether each of the following is possible or not possible.

0 Right - Student Response
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.
45.

Scoring Guide

Score & Description
Correct
80

BE =      = 4, and Area   ABE = ½ • 4 • 10 = 20 so, 60 + 20 = 80

Incorrect
Any incorrect response.

Correct - Student Response
The area of rectangle BCDE shown above is 60 square inches. If the length of AE is 10 inches and
the length of ED is 15 inches, what is the area of trapezoid ABCD, in square inches?

.     The area of rectangle BCDE shown above is 60 square inches. If the length of AE is 10 inches and
the length of ED is 15 inches, what is the area of trapezoid ABCD, in square inches?

Incorrect - Student Response
The area of rectangle BCDE shown above is 60 square inches. If the length of AE is 10 inches and
the length of ED is 15 inches, what is the area of trapezoid ABCD, in square inches?

.     The area of rectangle BCDE shown above is 60 square inches. If the length of AE is 10 inches and
the length of ED is 15 inches, what is the area of trapezoid ABCD, in square inches?
46.

Scoring Guide

Score & Description
Correct
165 or 165°

Incorrect
Any incorrect response.

Correct - Student Response
The sum of the measures of the 24 angles in a 24-sided regular polygon is 3,960°. What is the
measure in degrees of one of the angles?

.     The sum of the measures of the 24 angles in a 24-sided regular polygon is 3,960°. What is the
measure in degrees of one of the angles?

Incorrect - Student Response
The sum of the measures of the 24 angles in a 24-sided regular polygon is 3,960°. What is the
measure in degrees of one of the angles?

.     The sum of the measures of the 24 angles in a 24-sided regular polygon is 3,960°. What is the
measure in degrees of one of the angles?
47.

Scoring Guide

Score & Description
Correct #1
Tracy, with correct reason given.
Examples of correct reasons:
 If you multiply by a number smaller than 1 the result is less than 6.
 6×0=0
 6 × 1/2 = 3
 6 × -1 = -6

Correct #2
No name stated but reason given is correct.

Incorrect #2
Tracy, with no reason or an incorrect reason.

Incorrect #1
Any response that states that Pat is correct

OR

No name stated and reason given is incorrect.

*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
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."

.     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."

Correct #2 - Student Response
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."

.    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."

Incorrect #2 - Student Response
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."

.    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."

Incorrect #1 - Student Response
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."

.   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."

48.

Scoring Guide

Score & Description
Correct #1
4

Correct #2
4 with incorrect units, e.g., "4 pages."

Incorrect #3
3.5 to 3.6 or "about 4."

Incorrect #2
3

Incorrect #1
Any incorrect response other than those described in Incorrect #2, Incorrect #3.

*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
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?

.     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
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?

.    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
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?

.    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
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?

.    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
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?

.    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?
49.

Scoring Guide

Score & Description
Correct
Correct reason

There must be some mention of not having any pennies, or not having 3 pennies, or needing 3
pennies, or some pennies

OR

a statement that indicates the amount she spent must be divisible by 5.

For example,

   "With the coins she had, she could have only had 1.95 or 2.00."
   "She has no pennies."

Incorrect
Any incorrect or incomplete response.
For example,

   "She has no pennies because she spent them all."

Correct - Student Response
Lynn had only quarters, dimes, and nickels to buy her lunch. She spent all of the money and
received no change. Could she have spent \$1.98?

Incorrect - Student Response
Lynn had only quarters, dimes, and nickels to buy her lunch. She spent all of the money and
received no change. Could she have spent \$1.98?
50.

Scoring Guide

Score & Description
Correct
Any two (or more) of the correct dots should be circled, and no others.

This kind of circling is acceptable.

Incorrect #2
One correct dot circled and no incorrect dots circled.

Incorrect #1
Any incorrect response other than as described in Incorrect #2.

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

Incorrect #2 - Student Response
On the grid below, the dot at (4, 4) is circled. Circle two other dots where the first number is equal to
the second number.
Incorrect #1 - Student Response
On the grid below, the dot at (4, 4) is circled. Circle two other dots where the first number is equal to
the second number.

.     On the grid below, the dot at (4, 4) is circled. Circle two other dots where the first number is equal to
the second number.
51.

Scoring Guide

Score & Description
Correct #1
A correct response that n = 80 and 75 < n < 85.

Accept more than one response as long as all fit 75< n < 85.

Correct #2
85

Incorrect #2
90

Incorrect #1
Any incorrect response other than as described in Incorrect #2.

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
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?

.     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
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
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?

.    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
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?

.    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?
52.

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
The pictograph shown above is misleading. Explain why.

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

.     The pictograph shown above is misleading. Explain why.
53.

Scoring Guide

Score & Description
Correct
An explanation that leads to 201, such as:

   Multiply the position of the figure by 2, then add 1 to that answer.
   It is the 101st odd number.
   2x 100 + 1
   Any statements equivalent to the previous ones.
   Extended the pattern and counted the dots.

Incorrect #1 & 2
Incorrect #1
Incorrect answer to #16 and an explanation given.

Incorrect #2
Correct answer to #16 but incorrect explanation given.

Includes: I guessed.

Correct - Student Response

Incorrect #1 & 2 - Student Response

54.

Scoring Guide

Score & Description
Correct
1597.44    or   1597.4

Incorrect #1

Includes : 1597.5

Incorrect #2
515.12

Correct - Student Response
3
What is the product of 3.12 and 8 ?

3
.     What is the product of 3.12 and 8 ?

Incorrect #1 - Student Response
3
What is the product of 3.12 and 8 ?

Incorrect #2 - Student Response
3
What is the product of 3.12 and 8 ?
55.

Scoring Guide

Score & Description
Correct
5 or 5 pounds

Incorrect

Correct - Student Response
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
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?
56.

Scoring Guide

Score & Description
Correct
Time in Hours Cost in Dollars
1              5
4                    14
5                    17

Incorrect

Includes: one correct entry (either 5 or 14)

Correct - Student Response
The cost to rent a motorbike is given by the following formula:
Cost = (\$3 × number of hours) + \$2

Fill in the table below.

.     The cost to rent a motorbike is given by the following formula:
Cost = (\$3 × number of hours) + \$2

Fill in the table below.

Incorrect - Student Response
The cost to rent a motorbike is given by the following formula:
Cost = (\$3 × number of hours) + \$2

Fill in the table below.
57.

Scoring Guide

Score & Description
Correct
All of the following: 2, 3, 4, 6
1 and 12 may also be included. They are not to be counted as incorrect factors.

Incorrect #1
One or more incorrect factors

Incorrect #2
An incomplete list of correct factors
May include 1 and 12

Correct - Student Response
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
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
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.
58.

Scoring Guide

Score & Description
Correct
Correct answer (with or without label):

Label can be P or P(5,2) or (5,2)

Incorrect #1

Incorrect #2
(2,5)

Correct - Student Response
Plot the point (5, 2) on the grid shown below.

Incorrect #1 - Student Response
Plot the point (5, 2) on the grid shown below.
Incorrect #2 - Student Response
Plot the point (5, 2) on the grid shown below.
59.

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.

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

Incorrect

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

.     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.
60.

Scoring Guide

Score & Description
Correct
\$10,458.83     or   10,458.83   or   10,458.825

Incorrect #1

Incorrect #2
543,858.92

Correct - Student Response
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
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
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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