NAEP NQT v3.0 -- Print Output

Additional Materials (1)

Additional Materials (2)

Additional Materials (3)

Additional Materials (4)

Additional Materials (5)

Additional Material (1)

Question 1 refers to Additional Materials (1)


1.	Which of the following lists the angles shown above in order of measure from smallest to largest?

	A)	1, 2, 3, 4
	B)	2, 3, 4, 1
	C)	3, 2, 1, 4
	D)	3, 1, 4, 2
	E)	4, 2, 1, 3

Question 2 refers to Additional Materials (1)

2.	The weather service reported a tornado 75° south of west. On the figure below, use your protractor to draw an arrow from P in the direction in which the tornado was sighted.

Question 3 refers to Additional Materials (1)


3.	The figure above shows a picture and its frame. In the space below, draw a rectangular picture 2 inches by 3 inches and draw a 1-inch-wide frame around it.


4.	The floor of a room shown in the figure above is to be covered with tiles. One box of floor tiles will cover 25 square feet. Use your ruler to determine how many whole boxes of these tiles must be bought to cover the entire floor.

	________ boxes of tiles. Explain your reasoning in the space below.

Question 5 refers to Additional Materials (5)


5.	What is the area of the shaded figure?

	A)	9 square centimeters
	B)	11 square centimeters
	C)	13 square centimeters
	D)	14 square centimeters

Question 6 refers to Additional Materials (2), and Additional Materials (5)

The following question refers to the additional materials you have been given. Please remove the materials from your packet and put them on your desk.
6.	On the grid below, use piece Q to draw a right triangle. The angles of the right triangle should measure the same as the angles in piece Q. The area of the right triangle should be four times the area of piece Q.

Question 7 refers to Additional Materials (5)

pentagon

a. What is the area, in square units, enclosed by the pentagon above?

b.	On the figure below, draw a different pentagon that has the same area as the one shown. (Be sure the pentagon that you draw does not look like the one shown when it is turned in a different direction.)

8.	A rectangular playground has a perimeter of 390 feet. The width of the playground is 75 feet. What is its length?

	A)	5.2 feet
	B)	97.5 feet
	C)	120 feet
	D)	130 feet
	E)	240 feet


9.	What temperature would be 15° F more than the temperature shown on the thermometer above?


	A)	-20° F
	B)	-10° F
	C)	10° F
	D)	15° F
	E)	20° F


10.	In the figure above, which object is heaviest?

	A)	The metal ball
	B)	The sandwich
	C)	The bag of potato chips
	D)	The puppy

11.	The perimeter of a square is 36 inches. What is the length of one side of the square?

	A)	4 inches
	B)	6 inches
	C)	9 inches
	D)	18 inches

12.

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

Answer:

13.	Length can be measured to within 0.05 centimeter accuracy by using a certain type of measuring instrument. A reading of 3.7 centimeters on this instrument means that the actual length is at least

	A)	3.20 centimeters
	B)	3.65 centimeters
	C)	3.69 centimeters
	D)	3.70 centimeters
	E)	3.75 centimeters


14.	Ted wants to purchase floor covering for the hallway shown above. He knows there are many ways to find the area of the hallway. One way is to divide the hallway into the sections shown below and then add together the area of each section.
	Area of Hallway = Area of Region I + Area of Region II Area = (5 x 10) + (7 x 5) Use the figures below to show 3 other ways that Ted can divide the hallway to find its area. Below each figure explain what numbers and operations Ted could use to calculate the area.

1 mile = 5,280 feet
15.	How many feet are in 15 miles?

	A)	352
	B)	35,200
	C)	79,200
	D)	84,480
	E)	89,760

Did you use the calculator on this question?


16.	According to the indicator on the scale above, what is the weight in ounces of the can of tuna on the scale?
	Answer: _________________________

Did you use the calculator on this question?


17.	Which of the following numerical expressions gives the area of the rectangle above?

	A)	4 × 6
	B)	4 + 6
	C)	2(4 × 6)
	D)	2(4 + 6)
	E)	4 + 6 + 4 + 6

Did you use the calculator on this question?

18.	The cruise ship Titanic was 882 feet long. Which of the following is closest to that length?

	A)	Two moving-van lengths
	B)	Fifty car lengths
	C)	One hundred skateboard lengths
	D)	Five hundred school-bus lengths
	E)	One thousand bicycle lengths


19.	The following steps are used to read the electric meter shown above. (1) On each dial, the pointer moves in the direction of the arrow for that dial. (2) On each dial, the number that the pointer has just passed is that dial's reading. (3) To obtain the meter reading, the dials are read from left to right. What is the reading on the meter?

	A)	2,975 kwh
	B)	3,086 kwh
	C)	5,792 kwh
	D)	5,803 kwh
	E)	6,803 kwh

20.	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?
	Answer: Between __________ and __________

Question 21 refers to Additional Material (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.
21.	Bob, Carmen, and Tyler were comparing the areas of N and P. Bob said that N and P have the same area. Carmen said that the area of N is larger. Tyler said that the area of P is larger.
	Who was correct?____________________ Use words or pictures (or both) to explain why.

Question 22 refers to Additional Material (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.
22.	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.

23.	Of the following, which is the best unit to use when measuring the growth of a plant every other day during a 2-week period?

	A)	Centimeter
	B)	Meter
	C)	Kilometer
	D)	Foot
	E)	Yard

Did you use the calculator on this question?

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

Did you use the calculator on this question?

25.	A car odometer registered 41,256.9 miles when a highway sign warned of a detour 1,200 feet ahead. What will the odometer read when the car reaches the detour? (5, 280 feet = 1 mile)

	A)	42,456.9
	B)	41,279.9
	C)	41,261.3
	D)	41,259.2
	E)	41,257.1

Did you use the calculator on this question?


26.	The weights of three objects were compared using a pan balance. Two comparisons were made as shown in the figure above. Which object is the heaviest?

	A)	A
	B)	B
	C)	C
	D)	Not enough information is given.

Use your centimeter ruler to make the following measurements to the nearest centimeter.
27.	What is the length in centimeters of one of the longer sides of the rectangle?
	Answer:____________________

Use your centimeter ruler to make the following measurements to the nearest centimeter.
28.	What is the length in centimeters of the diagonal from A to B?
	Answer:____________________

29.	A rectangular carpet is 9 feet long and 6 feet wide. What is the area of the carpet in square feet?

	A)	15
	B)	27
	C)	30
	D)	54


30.	Use your protractor to find the degree measure of the angle shown above.
	Answer:____________________

31.	On the grid below, draw a rectangle with an area of 12 square units.


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

Did you use the calculator on this question?


33.	In the figure above, a circle with center O and radius of length 3 is inscribed in a square. What is the area of the shaded region?

	A)	3.86
	B)	7.73
	C)	28.27
	D)	32.86
	E)	36.00

Did you use the calculator on this question?


34.	Chris wishes to carpet the rectangular room shown above. To the nearest square yard, how many square yards of carpet are needed to carpet the floor of the room if the closet floor will not be carpeted? (1 square yard = 9 square feet)

	A)	8
	B)	10
	C)	11
	D)	19
	E)	22

Did you use the calculator on this question?


35.	Which figure has the least area?

	A)	A
	B)	B
	C)	C
	D)	D


36.	What is the weight shown on the scale?

	A)	6 pounds
	B)	7 pounds
	C)	51 pounds
	D)	60 pounds

37.	The length of a trail that Pat hiked in one day could have been

	A)	5 milliliters
	B)	5 centimeters
	C)	5 meters
	D)	5 kilometers

38.	Lynn had only quarters, dimes, and nickels to buy her lunch. She spent all of the money and received no change. Could she have spent $1.98?
	Give a reason for your answer.


39.	If the area of the shaded triangle shown above is 4 square inches, what is the area of the entire square?

	A)	4 square inches
	B)	8 square inches
	C)	12 square inches
	D)	16 square inches
	E)	Not enough information given

40.	For each figure below, the lengths of 3 sides are given. Which figure could have a perimeter of 28?

	A)
	B)
	C)
	D)
	E)

41.

How many hours are equal to 150 minutes?

1	1
	2

2	1
	4

2	1
	3

2	1
	2

2	5
	6


42.	In the figure above, the tube was filled to the 0 mark at the start. How much liquid has been let out?

	A)	10 milliliters
	B)	15 milliliters
	C)	25 milliliters
	D)	40 milliliters
	E)	50 milliliters

43.	If a measurement of a rectangular box is given as 48 cubic inches, then the measurement represents the

	A)	distance around the top of the box
	B)	length of an edge of the box
	C)	surface area of the box
	D)	volume of the box

44.

In the model town that a class is building, a car 15 feet long is represented by a scale model 3 inches long. If the same scale is used, a house 35 feet high would be represented by a scale model how many inches high?

Did you use the calculator on this question?


45.	A certain rectangle has area equal to the sum of the areas of the four rectangles shown above. If its length is 4, what is its width?

	A)	2
	B)	2¼
	C)	2½
	D)	3
	E)	3½

Did you use the calculator on this question?

Question 1

Key


1.	Which of the following lists the angles shown above in order of measure from smallest to largest?

	A)	1, 2, 3, 4
	B)	2, 3, 4, 1
	C)	3, 2, 1, 4
	D)	3, 1, 4, 2
	E)	4, 2, 1, 3

Question 2

Scoring Guide

Solution:

Score & Description

	Correct
	Correct response (acceptable range 68º- 78º)

Partial

Arrow is located at 75° with respect to x-axis, but in the wrong direction

Arrow direction is correct, but angle measure is not.

	Incorrect
	Incorrect response

Correct - Student Response

2	The weather service reported a tornado 75° south of west. On the figure below, use your protractor to draw an arrow from P in the direction in which the tornado was sighted.

	Scorer Comments: This response received full credit because the student drew an arrow in the correct direction and at the correct angle.

Partial - Student Response

2	The weather service reported a tornado 75° south of west. On the figure below, use your protractor to draw an arrow from P in the direction in which the tornado was sighted.

	Scorer Comments: This response received partial credit because the student drew the arrow in the correct direction, but with an incorrect angle measure.

Incorrect - Student Response

2	The weather service reported a tornado 75° south of west. On the figure below, use your protractor to draw an arrow from P in the direction in which the tornado was sighted.

	Scorer Comments: This response received no credit because the arrow is drawn in the wrong direction and the angle measure is incorrect.

Question 3

Scoring Guide

Solution:

Tolerance of inch on all measurements.

picture frame

Score & Description

	Correct
	Correct response, which will include a picture and frame drawn with the correct dimensions.

Partial

Response shows a rectangular picture with correct dimensions and incorrect frame dimensions

A rectangular picture with incorrect dimensions but one-inch frame is drawn correctly

(if picture is drawn inside - score 2)

	Incorrect
	Incorrect response (i.e., one rectangle only drawn)

Correct - Student Response

3	The figure above shows a picture and its frame. In the space below, draw a rectangular picture 2 inches by 3 inches and draw a 1-inch-wide frame around it.

	Scorer Comments: This response received full credit because both the picture and the frame were drawn with the correct dimensions.

Partial - Student Response

3	The figure above shows a picture and its frame. In the space below, draw a rectangular picture 2 inches by 3 inches and draw a 1-inch-wide frame around it.

	Scorer Comments: This response received partial credit because the picture was drawn correctly, but the frame was not drawn correctly.

Incorrect - Student Response

3	The figure above shows a picture and its frame. In the space below, draw a rectangular picture 2 inches by 3 inches and draw a 1-inch-wide frame around it.

	Scorer Comments: This response received no credit because both the picture and the frame were drawn incorrectly.

Question 4

Scoring Guide

Solution:

7 boxes

Correct process for solution includes evidence of each of the following (may be implied or explicit):

a) measuring dimensions correctly (getting 2 ½ " and 4") (If cm. is used the measure must be exact)

b) converting to feet correctly (getting 10' and 16’)

c) finding the area (160 sq. ft.)

d) dividing by 25 to find the number of boxes (6.4)

(Note: Steps b and c may be interchanged; if done, this would yield 10 sq. in. and 160 sq. ft., respectively.)

Score & Description

	Extended
	Correct response

	Satisfactory
	Response contains correct complete process as outlined above (a through d) but has a minor error (such as only the dimensions, in inches, are measured incorrectly OR the answer to the scale conversion is incorrect OR one other minor computational error OR does not round).

	Partial
	7 with no explanation OR response contains correct complete process as outlined above (a through d) but has a major conceptual error (such as use of incorrect conversion factor or use of perimeter, 52, instead of area) OR perceives the floor as a square and performs all 4 steps.

Minimal

6.4 with no explanation

Measures 2" and 4" correctly and gets 10-sq. in. for area

Measures 2" and 4" correctly and converts correctly to 10' and 16' (may also indicate area is 160 sq. ft.)

	Incorrect
	Incorrect response

Extended - Student Response

4	The floor of a room shown in the figure above is to be covered with tiles. One box of floor tiles will cover 25 square feet. Use your ruler to determine how many whole boxes of these tiles must be bought to cover the entire floor.

	Scorer Comments: This response received full credit because the number of boxes of tiles was correctly determined and all work was shown. First, the area of the floor was determined by measuring the scaled drawing and converting to square feet. Next, the area of the floor was divided by the area that one box of tiles would cover, which the student then correctly rounded to a whole number.

Satisfactory - Student Response

4	The floor of a room shown in the figure above is to be covered with tiles. One box of floor tiles will cover 25 square feet. Use your ruler to determine how many whole boxes of these tiles must be bought to cover the entire floor.

	Scorer Comments: This response received a satisfactory score. The student correctly converted the scaled dimensions into feet, calculated the area of the room, and divided by 25, but they did not round the final answer to a whole number.

Partial - Student Response

4	The floor of a room shown in the figure above is to be covered with tiles. One box of floor tiles will cover 25 square feet. Use your ruler to determine how many whole boxes of these tiles must be bought to cover the entire floor.

	Scorer Comments: This response received partial credit. The student calculated the area of the room using the scaled dimensions, but did not convert that area into square feet. They knew to divide by 25 and round the answer, but the number is not correct since they were using different units.

Minimal - Student Response

4	The floor of a room shown in the figure above is to be covered with tiles. One box of floor tiles will cover 25 square feet. Use your ruler to determine how many whole boxes of these tiles must be bought to cover the entire floor.

	Scorer Comments: This response received minimal credit because the student correctly determined the area of the room from the scaled drawing.

Incorrect - Student Response

4	The floor of a room shown in the figure above is to be covered with tiles. One box of floor tiles will cover 25 square feet. Use your ruler to determine how many whole boxes of these tiles must be bought to cover the entire floor.

	Scorer Comments: This response received no credit because the answer given is incorrect and there is no relevant supporting work.

Question 5

Key


5.	What is the area of the shaded figure?

	A)	9 square centimeters
	B)	11 square centimeters
	C)	13 square centimeters
	D)	14 square centimeters

Question 6

Scoring Guide

Solution:

right triangle on grid

Tolerance

tolerance scale

Note: Both sides should be the same measure

Score & Description

Correct

Correct response.

Note: In addition to the usual correct responses, watch for correct responses in which the isosceles right triangle is drawn with the right angle pointing toward the top of the grid and either the right or left base angle “sticks out” a little beyond the side of the grid. In this instance, if the length of the horizontal side opposite the right angle is 19 blocks, or close to it, this will be a correct response, as well.

Partial

Response is a right triangle other than Q with incorrect area.

Note: If an isosceles right triangle is drawn with the right angle pointing toward the top of the grid and the length of the horizontal side opposite the right angle is between 9 and 10 blocks, this will be piece Q, since the equal sides of that triangle are close to 1 inch in length. This earns a score of 1.

A non-right triangle with a correct area. (In this case, the area of the triangle must be exactly 2 square inches. This can be determined by using the measuring tool to find the base length in inches and the height in inches and then multiplying them together. If the result is exactly 4, then the area will be exactly 2.)

	Incorrect
	Incorrect response.

Correct - Student Response

6	On the grid below, use piece Q to draw a right triangle. The angles of the right triangle should measure the same as the angles in piece Q. The area of the right triangle should be four times the area of piece Q.

	Scorer Comments: This response received full credit because the student correctly drew a right triangle that has an area four times that of piece Q, also a right triangle.

Partial - Student Response

6	On the grid below, use piece Q to draw a right triangle. The angles of the right triangle should measure the same as the angles in piece Q. The area of the right triangle should be four times the area of piece Q.

	Scorer Comments: This response received partial credit because the student drew a right triangle, but its area is not four times the area of piece Q.

Incorrect - Student Response

6	On the grid below, use piece Q to draw a right triangle. The angles of the right triangle should measure the same as the angles in piece Q. The area of the right triangle should be four times the area of piece Q.

	Scorer Comments: This response received no credit because all the student did was trace piece Q once, so they did not create a right triangle with an area four times that of piece Q.

Question 7

Scoring Guide

Solution:

a. 16 square units

b. Here are some of the possible correct responses

petagons

Score & Description

	Correct
	Correct response

	Partial
	Part a or part b correct

	Incorrect
	Incorrect response

Correct - Student Response

7	a. What is the area, in square units, enclosed by the pentagon above?

	Scorer Comments: This response received full credit because the student correctly determined the area of the given pentagon and drew another, different pentagon with the same area.

Partial - Student Response

7	a. What is the area, in square units, enclosed by the pentagon above?

	Scorer Comments: This response received partial credit because the student correctly determined the area of the given pentagon, but they did not answer part b.

Incorrect - Student Response

7	a. What is the area, in square units, enclosed by the pentagon above?

	Scorer Comments: This response received no credit because part a is incorrect and the pentagon they drew in part b is the same as the one given, but in a different direction.

Question 8

Key


8.	A rectangular playground has a perimeter of 390 feet. The width of the playground is 75 feet. What is its length?

	A)	5.2 feet
	B)	97.5 feet
	C)	120 feet
	D)	130 feet
	E)	240 feet

Question 9

Key


9.	What temperature would be 15° F more than the temperature shown on the thermometer above?

	A)	-20° F
	B)	-10° F
	C)	10° F
	D)	15° F
	E)	20° F

Question 10

Key


10.	In the figure above, which object is heaviest?

	A)	The metal ball
	B)	The sandwich
	C)	The bag of potato chips
	D)	The puppy

Question 11

Key


11.	The perimeter of a square is 36 inches. What is the length of one side of the square?

	A)	4 inches
	B)	6 inches
	C)	9 inches
	D)	18 inches

Question 12

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

12	What is the length of the toothpick in the figure above?

Incorrect #3 - Student Response

12	What is the length of the toothpick in the figure above?

Incorrect #2 - Student Response

12	What is the length of the toothpick in the figure above?

Incorrect #1 - Student Response

12	What is the length of the toothpick in the figure above?

Question 13

Key


13.	Length can be measured to within 0.05 centimeter accuracy by using a certain type of measuring instrument. A reading of 3.7 centimeters on this instrument means that the actual length is at least

	A)	3.20 centimeters
	B)	3.65 centimeters
	C)	3.69 centimeters
	D)	3.70 centimeters
	E)	3.75 centimeters

Question 14

Scoring Guide

Solution:
Possible correct answers include:

Area = (5 × 5) + (5 × 12)
Area = (5 × 5) + (5 × 5) + (7 × 5)

Area =
Area = (10 × 12) ? (7 × 5)
For this method the missing piece must be indicated

Score & Description

	Extended
	Three figures divided correctly with no incorrect labels and three correct expressions for area

	Satisfactory
	Three figures divided correctly with no incorrect labels and two correct expressions for area

	Partial
	Two figures divided correctly with no incorrect labels and one or two correct expressions for area of those figures OR Three figures divided correctly with no incorrect labels and one correct expression for area

	Minimal
	One figure divided correctly with no incorrect labels and correct expression for area of that figure OR Two or three figures divided correctly with no incorrect labels and no correct (or missing) expressions for area of figures

	Incorrect
	Incorrect response

In this question the student was asked to draw and explain three different ways to divide an L-shaped region to determine the area. The student was also required to give an expression representing the area for each of the different divisions of the region (however, the student was not asked to calculate the area of the region). There are many possible ways to do this, but to earn full credit the student needed to show three different divisions of the region, label the lengths in each figure correctly, and write an expression for the area consistent with each figure. This question requires visualization and knowledge of one or more formulas for finding area.

Notes: Any division of the figures into rectangles, triangles, trapezoids, or parallelograms is acceptable. Student either needs to show (5 × 5) + (5 × 12), for example OR label all appropriate dimensions in the figure to give credit for 25 + 60. However, "25+60" is not acceptable if dimensions are not labeled.

Extended - Student Response

14	Ted wants to purchase floor covering for the hallway shown above. He knows there are many ways to find the area of the hallway. One way is to divide the hallway into the sections shown below and then add together the area of each section.

Satisfactory - Student Response

14	Ted wants to purchase floor covering for the hallway shown above. He knows there are many ways to find the area of the hallway. One way is to divide the hallway into the sections shown below and then add together the area of each section.

Partial - Student Response

14	Ted wants to purchase floor covering for the hallway shown above. He knows there are many ways to find the area of the hallway. One way is to divide the hallway into the sections shown below and then add together the area of each section.

Minimal - Student Response

14	Ted wants to purchase floor covering for the hallway shown above. He knows there are many ways to find the area of the hallway. One way is to divide the hallway into the sections shown below and then add together the area of each section.

Incorrect - Student Response

14	Ted wants to purchase floor covering for the hallway shown above. He knows there are many ways to find the area of the hallway. One way is to divide the hallway into the sections shown below and then add together the area of each section.

Question 15

Key


15.	How many feet are in 15 miles?

	A)	352
	B)	35,200
	C)	79,200
	D)	84,480
	E)	89,760

Question 16

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

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

Incorrect - Student Response

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

Question 17

Key


17.	Which of the following numerical expressions gives the area of the rectangle above?

	A)	4 × 6
	B)	4 + 6
	C)	2(4 × 6)
	D)	2(4 + 6)
	E)	4 + 6 + 4 + 6

Question 18

Key


18.	The cruise ship Titanic was 882 feet long. Which of the following is closest to that length?

	A)	Two moving-van lengths
	B)	Fifty car lengths
	C)	One hundred skateboard lengths
	D)	Five hundred school-bus lengths
	E)	One thousand bicycle lengths

Question 19

Key


19.	The following steps are used to read the electric meter shown above. (1) On each dial, the pointer moves in the direction of the arrow for that dial. (2) On each dial, the number that the pointer has just passed is that dial's reading. (3) To obtain the meter reading, the dials are read from left to right. What is the reading on the meter?

	A)	2,975 kwh
	B)	3,086 kwh
	C)	5,792 kwh
	D)	5,803 kwh
	E)	6,803 kwh

Question 20

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

20	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

20	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

20	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

20	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?

Question 21

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.

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

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.

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

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


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

Incorrect #2 - Student Response

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


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

Incorrect #1 - Student Response

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


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

Question 22

Scoring Guide

Solution:

P has the longest perimeter.

Adequate explanation

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

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

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


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

Incorrect #2 - Student Response

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


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

Incorrect #1 - Student Response

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


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

Question 23

Key


23.	Of the following, which is the best unit to use when measuring the growth of a plant every other day during a 2-week period?

	A)	Centimeter
	B)	Meter
	C)	Kilometer
	D)	Foot
	E)	Yard

Question 24

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

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


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

Partial - Student Response

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

Incorrect - Student Response

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


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

Question 25

Key


25.	A car odometer registered 41,256.9 miles when a highway sign warned of a detour 1,200 feet ahead. What will the odometer read when the car reaches the detour? (5, 280 feet = 1 mile)

	A)	42,456.9
	B)	41,279.9
	C)	41,261.3
	D)	41,259.2
	E)	41,257.1

Question 26

Key


26.	The weights of three objects were compared using a pan balance. Two comparisons were made as shown in the figure above. Which object is the heaviest?

	A)	A
	B)	B
	C)	C
	D)	Not enough information is given.

Question 27

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

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


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

Incorrect #2 - Student Response

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

Incorrect #1 - Student Response

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

Question 28

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

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


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

Incorrect - Student Response

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

Question 29

Key


29.	A rectangular carpet is 9 feet long and 6 feet wide. What is the area of the carpet in square feet?

	A)	15
	B)	27
	C)	30
	D)	54

Question 30

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

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

Incorrect - Student Response

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

Question 31

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

31	On the grid below, draw a rectangle with an area of 12 square units.

Incorrect #2 - Student Response

31	On the grid below, draw a rectangle with an area of 12 square units.

Incorrect #1 - Student Response

31	On the grid below, draw a rectangle with an area of 12 square units.

Question 32

Scoring Guide

Score & Description

Correct

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

	Incorrect
	Any incorrect response.

Correct - Student Response

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


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

Incorrect - Student Response

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


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

Question 33

Key


33.	In the figure above, a circle with center O and radius of length 3 is inscribed in a square. What is the area of the shaded region?

	A)	3.86
	B)	7.73
	C)	28.27
	D)	32.86
	E)	36.00

Question 34

Key


34.	Chris wishes to carpet the rectangular room shown above. To the nearest square yard, how many square yards of carpet are needed to carpet the floor of the room if the closet floor will not be carpeted? (1 square yard = 9 square feet)

	A)	8
	B)	10
	C)	11
	D)	19
	E)	22

Question 35

Key


35.	Which figure has the least area?

	A)	A
	B)	B
	C)	C
	D)	D

Question 36

Key


36.	What is the weight shown on the scale?

	A)	6 pounds
	B)	7 pounds
	C)	51 pounds
	D)	60 pounds

Question 37

Key


37.	The length of a trail that Pat hiked in one day could have been

	A)	5 milliliters
	B)	5 centimeters
	C)	5 meters
	D)	5 kilometers

Question 38

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

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

"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

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

Incorrect - Student Response

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

Question 39

Key


39.	If the area of the shaded triangle shown above is 4 square inches, what is the area of the entire square?

	A)	4 square inches
	B)	8 square inches
	C)	12 square inches
	D)	16 square inches
	E)	Not enough information given

Question 40

Key


40.	For each figure below, the lengths of 3 sides are given. Which figure could have a perimeter of 28?

	A)
	B)
	C)
	D)
	E)

Question 41

Key

41.

How many hours are equal to 150 minutes?

1	1
	2

2	1
	4

2	1
	3

2	1
	2

2	5
	6

Question 42

Key


42.	In the figure above, the tube was filled to the 0 mark at the start. How much liquid has been let out?

	A)	10 milliliters
	B)	15 milliliters
	C)	25 milliliters
	D)	40 milliliters
	E)	50 milliliters

Question 43

Key


43.	If a measurement of a rectangular box is given as 48 cubic inches, then the measurement represents the

	A)	distance around the top of the box
	B)	length of an edge of the box
	C)	surface area of the box
	D)	volume of the box

Question 44

Key

44.

Question 45

Key


45.	A certain rectangle has area equal to the sum of the areas of the four rectangles shown above. If its length is 4, what is its width?

	A)	2
	B)	2¼
	C)	2½
	D)	3
	E)	3½