|
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|
2. |
Amanda wants to paint each face of a cube a different color. How many colors will she need? | |
| A) |
Three | |
| B) |
Four | |
| C) |
Six | |
| D) |
Eight | |
|
| ||
|
5. |
How many of the angles in this triangle are smaller than a right angle? | |
| A) | None | |
| B) |
One | |
| C) |
Two | |
| D) |
Three | |
| ||||||||||
|
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.
| ||
|
8. |
You will need only two of the tiles to answer this question. When the two tiles are partially overlapped, different geometric figures are formed by the overlapping parts. One example is shown below. Which of the following figures cannot be formed by the overlapping parts of the two tiles?
| |
| A) | Triangle | |
| B) | Rectangle | |
| C) | Square | |
| D) | Five-sided figure | |
| E) | Nine-sided figure | |
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|
11. |
The endpoints of a line segment are the points with coordinates (2, 1) and (8, 9). What are the coordinates of the midpoint of this line segment? | |
| A) | (2, 3½) | |
| B) |
(3, 4) | |
| C) | (5, 5) | |
| D) | (4½, 5½) | |
| E) | (10, 10) | |
|
12. |
One of the acute angles in a
right triangle measures 28 degrees. What is the measure, in degrees, of
the other acute angle? | |
| A) | 17° | |
| B) | 28° | |
| C) | 62° | |
| D) | 90° | |
| E) | 152° | |
 | ||
|
14. |
The figure above is shaded on the top side and white on the under side. If the figure were flipped over, its white side could look like which of the following figures? | |
| A) |  | |
| B) |  | |
| C) |  | |
| D) |  | |
|
16. |
Alan says that if a figure has four sides, it must be a rectangle. Gina does not agree. Which of the following figures shows that Gina is correct? | |
| A) |  | |
| B) |  | |
| C) |  | |
| D) |  | |
|
18. |
A triangle that has sides with lengths 6, 6, and 10 is called | |
| A) | acute | |
| B) | right | |
| C) | scalene | |
| D) | isosceles | |
| E) | equilateral | |
 | ||
|
19. |
What is the value of x in the triangle above? | |
| A) | 65° | |
| B) | 82° | |
| C) | 90° | |
| D) | 92° | |
| E) | 98° | |
Did you use the calculator on this question? | ||
 | ||
|
20. |
When the rectangle above is folded along the dotted line, point P will touch which of the lettered points? | |
| A) | A | |
| B) | B | |
| C) | C | |
| D) | D | |
| E) | E | |
| Did you use the calculator on this question? | ||
 | ||
|
21. |
In the figure above, WXYZ is a parallelogram. Which of the following is NOT necessarily true? | |
| A) | Side WX is parallel to side ZY. | |
| B) | Side XY is parallel to side WZ. | |
| C) | The measures of angles W and Y are equal. | |
| D) | The lengths of sides WX and ZY are equal. | |
| E) | The lengths of sides WX and XY are equal. | |
| Did you use the calculator on this question? | ||
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 | ||
|
33. |
The squares in the figure above represent the faces of a cube which has been cut along some edges and flattened. When the original cube was resting on face X, which face was on top? | |
| A) | A | |
| B) | B | |
| C) | C | |
| D) | D | |
 | ||
|
34. |
A sheet of paper is folded once and a piece is cut out as shown above. Which of the following looks like the unfolded paper? | |
| A) |  | |
| B) |  | |
| C) |  | |
| D) |  | |
|
| ||||||
| |||||||||
 | ||
|
38. |
In the rectangle above, the
intersection of  ABC and ADC is which of the
following? | |
| A) | A right angle | |
| B) | A vertex of the rectangle | |
| C) | A diagonal of the rectangle | |
| D) | A pair of parallel sides | |
| E) | A pair of perpendicular sides | |
| Did you use the calculator on this question? | ||
 | ||
|
39. |
The sum of the measures of angles 1 and 2 in the figure above is 90°. What is the measure of the angle formed by the bisectors of these two angles? | |
| A) | 60° | |
| B) | 45° | |
| C) | 30° | |
| D) | 20° | |
| E) | 15° | |
| Did you use the calculator on this question? | ||
| ||
|
40. |
Which of the following constructions at point P in the figure above will produce an angle of 45°? | |
| A) | Constructing only the bisector of  APB | |
| B) | Constructing only a circle with center at P | |
| C) | Constructing one perpendicular line only | |
| D) | Constructing a circle with center at P and a perpendicular line | |
| E) | Constructing a perpendicular line and an angle bisector | |
| ||
|
41. |
Point O is the center of the circle above. Line segment AC is a diameter of the circle. Line segment BC does not pass through the center of the circle. Which of the following is true? | |
| A) | AC is longer than BC. | |
| B) | BC is longer than AC. | |
| C) | AC and BC are the same length. | |
| D) | BC is twice as long as OA. | |
| E) | The lengths of AC and BC change, depending on how this piece of paper is turned. | |
|
42. |
A straight line segment could NOT be drawn on the surface of which of the following solids? | |
| A) |  | |
| B) |  | |
| C) |  | |
| D) |  | |
| E) |  | |
 | ||
|
43. |
Which of the following shows
the result of flipping the above triangle over the line ? | |
| A) |  | |
| B) |  | |
| C) |  | |
| D) |  | |
| E) |  | |
 | ||
|
44. |
What is the distance between the midpoint of MN and the midpoint of PQ shown above? | |
| A) | 18 cm | |
| B) | 24 cm | |
| C) | 26 cm | |
| D) | 28 cm | |
| E) | 30 cm | |
 | ||
|
45. |
What is the diagonal measurement of the TV screen shown in the figure above? | |
| A) | 25 inches | |
| B) | 35 inches | |
| C) | 50 inches | |
| D) | 70 inches | |
| E) | 1,200 inches | |
|
47. |
In which of the following circles is the line segment a diameter? | |
| A) |  | |
| B) |  | |
| C) |  | |
| D) |  | |
| E) |  | |
| Did you use the calculator on this question? | ||
|
48. |
Which of the following figures has two circular bases? | |
| A) | A pyramid | |
| B) | A sphere | |
| C) | A cube | |
| D) | A cylinder | |
| E) | A cone | |
| Did you use the calculator on this question? | ||
|
49. |
What is the ratio of the length of a side of an equilateral triangle to its perimeter? | |
| A) | 1:1 | |
| B) | 1:2 | |
| C) | 1:3 | |
| D) | 2:1 | |
| E) | 3:1 | |
| Did you use the calculator on this question? | ||
| Scoring Guide |
| Solution: Rectangle or drawing of a rectangle. |
|
Score & Description | ||||
| ||||
| ||||
|
|
*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 |
|
1 |
The paper tube in the figure above is to be cut along the dotted line and opened up. What will be the shape of the flattened piece of paper? | |
 | ||
| Scorer Comments: The student correctly determined the shape of the tube to be a rectangle when flattened. |
||
| Correct #2 - Student Response |
|
1 |
The paper tube in the figure above is to be cut along the dotted line and opened up. What will be the shape of the flattened piece of paper? | |
 | ||
| Scorer Comments: In this paper, the student put square for their answer instead of rectangle. This particular response was coded to gather data on a different way that students could answer the question and still receive full credit. |
||
| Incorrect - Student Response |
|
1 |
The paper tube in the figure above is to be cut along the dotted line and opened up. What will be the shape of the flattened piece of paper? | |
 | ||
| Scorer Comments: This paper received no credit because the student did not put rectangle or square for their answer. |
||
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| Scoring Guide |
| Solution:
|
|
Score & Description | ||||
| ||||
| ||||
|
| Correct - Student Response |
|
6 |
You may use the paper strip from your packet. Place an X in one of the squares below so that if the paper strip were folded along the dotted fold line shown, the square with the X could cover the shaded square. Show your answer on the strip below. | |
 | ||
| Scorer Comments: This response received full credit because the student correctly marked the square that would match up with the shaded square when folded. |
||
| Partial - Student Response |
|
6 |
You may use the paper strip from your packet. Place an X in one of the squares below so that if the paper strip were folded along the dotted fold line shown, the square with the X could cover the shaded square. Show your answer on the strip below. | |
 | ||
| Scorer Comments: This response received partial credit because the student marked the strip of paper to the right of the fold line, but not in the correct box. |
||
| Incorrect - Student Response |
|
6 |
You may use the paper strip from your packet. Place an X in one of the squares below so that if the paper strip were folded along the dotted fold line shown, the square with the X could cover the shaded square. Show your answer on the strip below. | |
 | ||
| Scorer Comments: This response received no credit because the mark is to the left of the fold line. |
||
| Scoring Guide |
| Solution: One possible solution.
|
|
Score & Description | ||||
| ||||
| ||||
|
| Correct - Student Response |
|
7 |
Shade five more squares on the grid below so that if your completed figure were folded along the fold line both sides would match. | |
 | ||
| Scorer Comments: This response received full credit because the student correctly shaded five more squares to make a symmetric figure with respect to the given fold line. |
||
| Partial - Student Response |
|
7 |
Shade five more squares on the grid below so that if your completed figure were folded along the fold line both sides would match. | |
 | ||
| Scorer Comments: This response received partial credit because the student made a symmetric figure with respect to the given fold line, but they did not use a total of eight squares. |
||
| Incorrect - Student Response |
|
7 |
Shade five more squares on the grid below so that if your completed figure were folded along the fold line both sides would match. | |
 | ||
| Scorer Comments: This response received no credit because the figure the student made is not symmetric with respect to the given fold line. |
||
| |||||||||||||||||||||||||
| Scoring Guide |
| Solution: One solution. 
|
|
Score & Description | ||||
| ||||
| ||||
|
|
NOTE: All squares must be counted unless some indicator (marked “open”– or numbered squares 1, 2, 3) is given |
| Correct - Student Response |
|
9 |
Five tiles are arranged on the work mat above to make a design. Then the work mat is turned. Notice that after the turn, the design looks the same as it did before the turn. Place your work mat so that the word “Bottom” is closest to you. Place two tiles on the mat as shown on the next page. Now add three new tiles to your design so that when you turn the work mat, the new design will look different from the design before the turn. Draw your designs on the next two pages. | |
 | ||
| Scorer Comments: This response received full credit because the student correctly drew two designs that each contain five squares, including the two given squares, and it looks different when rotated 90 degrees. |
||
| Partial - Student Response |
|
9 |
Five tiles are arranged on the work mat above to make a design. Then the work mat is turned. Notice that after the turn, the design looks the same as it did before the turn. Place your work mat so that the word “Bottom” is closest to you. Place two tiles on the mat as shown on the next page. Now add three new tiles to your design so that when you turn the work mat, the new design will look different from the design before the turn. Draw your designs on the next two pages. | |
 | ||
| Scorer Comments: This response received partial credit because the student correctly drew two designs that each contain five squares, including the two given squares, but the second design is not drawn correctly after being rotated 90 degrees. |
||
| Incorrect - Student Response |
|
9 |
Five tiles are arranged on the work mat above to make a design. Then the work mat is turned. Notice that after the turn, the design looks the same as it did before the turn. Place your work mat so that the word “Bottom” is closest to you. Place two tiles on the mat as shown on the next page. Now add three new tiles to your design so that when you turn the work mat, the new design will look different from the design before the turn. Draw your designs on the next two pages. | |
 | ||
| Scorer Comments: This response received no credit because the design the student gave is just a repeat of the given example. |
||
| Scoring Guide |
| Solution: Response shows Figure A correctly reflected through the vertical line. |
|
Score & Description | ||||
| ||||
|
| Correct - Student Response |
|
10 |
In the space above, draw the image of Figure A after it is reflected (flipped) across the dotted line. |
 | |
| Incorrect - Student Response |
|
10 |
In the space above, draw the image of Figure A after it is reflected (flipped) across the dotted line. |
 | |
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| Scoring Guide |
| Solution: Any obtuse angle, such as:
OR
|
|
Score & Description | ||||
| ||||
| ||||
|
| 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 |
|
17 |
In the space below, draw an angle that is larger than 90°. |
 | |
| Correct #2 - Student Response |
|
17 |
In the space below, draw an angle that is larger than 90°. |
 | |
| Incorrect - Student Response |
|
17 |
In the space below, draw an angle that is larger than 90°. |
 | |
| |||||||||||||||||||||||||
| |||||||||||||||||||||||||
| |||||||||||||||||||||||||
| Scoring Guide |
| Solution: Triangles 1 and 2 may be interchanged. Triangles need not be labeled with numbers.
|
|
Score & Description | ||||
| ||||
|
| 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 |
|
22 |
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 |
|
22 |
Draw lines on the figure below to show how triangles 1, 2, and 3 can be rearranged without overlap to form this parallelogram. |
 | |
| Scoring Guide |
| Solution: Triangles 1 and 2 may be interchanged. Triangles need not be labeled with numbers.  |
|
Score & Description | ||||
| ||||
|
| 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 |
|
23 |
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 |
|
23 |
Draw lines on the figure below to show how triangles 1, 2, and 3 can be rearranged without overlap to form this rectangle. |
 | |
| Scoring Guide |
| Solution: Possible dimensions of boxes are 1×1×8 2×2×2 2×4×1 |
|
Score & Description | ||||
| ||||
| ||||
| ||||
| ||||
|
| In this question the student was asked to demonstrate two- and three-dimensional visualization skills by drawing two different figures (two-dimensional) that will fold up into a box (three-dimensional) of given volume. This question required students to know and apply the formula for volume in a non-standard situation and to draw a model of the flattened box with correct dimensions. |
| Extended - Student Response |
|
25 |
On the grid on the next page, draw two flattened boxes that will fold up into different open boxes. Each box should have a volume of 8 cubic units. Be sure to label your drawings with numbers that show the length, width, and height for each box. Each square on the grid has a side of length 1 unit. |
 | |
| Satisfactory - Student Response |
|
25 |
On the grid on the next page, draw two flattened boxes that will fold up into different open boxes. Each box should have a volume of 8 cubic units. Be sure to label your drawings with numbers that show the length, width, and height for each box. Each square on the grid has a side of length 1 unit. |
 | |
| Partial - Student Response |
|
25 |
On the grid on the next page, draw two flattened boxes that will fold up into different open boxes. Each box should have a volume of 8 cubic units. Be sure to label your drawings with numbers that show the length, width, and height for each box. Each square on the grid has a side of length 1 unit. |
 | |
| Minimal - Student Response |
|
25 |
On the grid on the next page, draw two flattened boxes that will fold up into different open boxes. Each box should have a volume of 8 cubic units. Be sure to label your drawings with numbers that show the length, width, and height for each box. Each square on the grid has a side of length 1 unit. |
 | |
| Incorrect - Student Response |
|
25 |
On the grid on the next page, draw two flattened boxes that will fold up into different open boxes. Each box should have a volume of 8 cubic units. Be sure to label your drawings with numbers that show the length, width, and height for each box. Each square on the grid has a side of length 1 unit. |
 | |
| 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. 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 - Student Response |
|
26 |
Jaime knows the following facts about points A, B,
and C.
Is Jaime's conclusion correct? |
 | |
|
26 |
Jaime knows the following facts about points A, B,
and C.
Is Jaime's conclusion correct? |
 | |
| Incorrect - Student Response |
|
26 |
Jaime knows the following facts about points A, B,
and C.
Is Jaime's conclusion correct? |
 | |
|
26 |
Jaime knows the following facts about points A, B,
and C.
Is Jaime's conclusion correct? |
 | |
| 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 | ||||
| ||||
| ||||
|
Note to scorers:
*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 |
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. |
 | |
|
27 |
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 |
|
27 |
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. |
 | |
|
27 |
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 |
|
27 |
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. |
 | |
|
27 |
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. |
 | |
| Scoring Guide |
| Solution: The square may be tilted.
Space between is acceptable.
Scoring Guide In this question, a student needed to visualize how to form a square using two isosceles right triangles. |
|
Score & Description | ||||
| ||||
|
| Correct - Student Response |
|
28 |
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. |
 | |
|
28 |
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 |
|
28 |
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. |
 | |
|
28 |
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. |
 | |
| 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. 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 | ||||
| ||||
| ||||
|
|
* 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 |
|
29 |
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. |
 | |
|
29 |
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 |
|
29 |
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. |
 | |
|
29 |
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 |
|
29 |
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. |
 | |
|
29 |
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. |
 | |
| 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 | ||||
| ||||
| ||||
|
|
* 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 |
|
30 |
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. |
 | |
|
30 |
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 |
|
30 |
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. |
 | |
|
30 |
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 |
|
30 |
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. |
 | |
|
30 |
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. |
 | |
| Scoring Guide |
|
Score & Description | ||||
| ||||
| ||||
|
| 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 |
|
31 |
In the space below, use your ruler to draw a square with two of its corners at the points shown. |
 | |
|
31 |
In the space below, use your ruler to draw a square with two of its corners at the points shown. |
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| Correct #2 - Student Response |
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31 |
In the space below, use your ruler to draw a square with two of its corners at the points shown. |
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| Incorrect - Student Response |
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31 |
In the space below, use your ruler to draw a square with two of its corners at the points shown. |
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| Scoring Guide |
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Score & Description | ||||
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| *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 |
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32 |
In the space below, draw a rectangle 2 inches wide and 3½ inches long. |
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| Incorrect #4 - Student Response |
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32 |
In the space below, draw a rectangle 2 inches wide and 3½ inches long. |
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| Incorrect #3 - Student Response |
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32 |
In the space below, draw a rectangle 2 inches wide and 3½ inches long. |
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|
32 |
In the space below, draw a rectangle 2 inches wide and 3½ inches long. |
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| Incorrect #2 - Student Response |
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32 |
In the space below, draw a rectangle 2 inches wide and 3½ inches long. |
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| Incorrect #1 - Student Response |
|
32 |
In the space below, draw a rectangle 2 inches wide and 3½ inches long. |
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| Scoring Guide |
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Score & Description | ||||||||||||||||||||||
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| *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 |
|
35 |
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. |
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|
35 |
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. |
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| Incorrect #3 - Student Response |
|
35 |
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. |
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|
35 |
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. |
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| Incorrect #2 - Student Response |
|
35 |
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. |
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|
35 |
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. |
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| Incorrect #1 - Student Response |
|
35 |
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. |
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|
35 |
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. |
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| Scoring Guide |
| Solution: There is a 75 mile part of Highway 7 that is within both broadcast areas. It starts 75 miles outside Math City and ends 150 miles outside Math City.
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Score & Description | ||||
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| Note: A student's map must include enough information concerning the lengths given in the question to justify that 75 miles is the common broadcast area. If pertinent information concerning lengths is missing, the maximum score that can be awarded is Partial. |
| Extended - Student Response |
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36 |
Radio station KMAT in Math City is 200 miles from radio station KGEO in Geometry City. Highway 7, a straight road, connects the two cities. KMAT broadcasts can be received up to 150 miles in all directions from the station and KGEO broadcasts can be received up to 125 miles in all directions. Radio waves travel from each radio station through the air, as represented below. 
Be sure to label the distances along the highway and the length in miles of the part of the highway where both stations can be received. |
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| Satisfactory - Student Response |
|
36 |
Radio station KMAT in Math City is 200 miles from radio station KGEO in Geometry City. Highway 7, a straight road, connects the two cities. KMAT broadcasts can be received up to 150 miles in all directions from the station and KGEO broadcasts can be received up to 125 miles in all directions. Radio waves travel from each radio station through the air, as represented below.
Be sure to label the distances along the highway and the length in miles of the part of the highway where both stations can be received. |
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|
36 |
Radio station KMAT in Math City is 200 miles from radio station KGEO in Geometry City. Highway 7, a straight road, connects the two cities. KMAT broadcasts can be received up to 150 miles in all directions from the station and KGEO broadcasts can be received up to 125 miles in all directions. Radio waves travel from each radio station through the air, as represented below.
Be sure to label the distances along the highway and the length in miles of the part of the highway where both stations can be received. |
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| Partial - Student Response |
|
36 |
Radio station KMAT in Math City is 200 miles from radio station KGEO in Geometry City. Highway 7, a straight road, connects the two cities. KMAT broadcasts can be received up to 150 miles in all directions from the station and KGEO broadcasts can be received up to 125 miles in all directions. Radio waves travel from each radio station through the air, as represented below.
Be sure to label the distances along the highway and the length in miles of the part of the highway where both stations can be received. |
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|
36 |
Radio station KMAT in Math City is 200 miles from radio station KGEO in Geometry City. Highway 7, a straight road, connects the two cities. KMAT broadcasts can be received up to 150 miles in all directions from the station and KGEO broadcasts can be received up to 125 miles in all directions. Radio waves travel from each radio station through the air, as represented below.
Be sure to label the distances along the highway and the length in miles of the part of the highway where both stations can be received. |
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| Minimal - Student Response |
|
36 |
Radio station KMAT in Math City is 200 miles from radio station KGEO in Geometry City. Highway 7, a straight road, connects the two cities. KMAT broadcasts can be received up to 150 miles in all directions from the station and KGEO broadcasts can be received up to 125 miles in all directions. Radio waves travel from each radio station through the air, as represented below.
Be sure to label the distances along the highway and the length in miles of the part of the highway where both stations can be received. |
 | |
| Incorrect/Off Task - Student Response |
|
36 |
Radio station KMAT in Math City is 200 miles from radio station KGEO in Geometry City. Highway 7, a straight road, connects the two cities. KMAT broadcasts can be received up to 150 miles in all directions from the station and KGEO broadcasts can be received up to 125 miles in all directions. Radio waves travel from each radio station through the air, as represented below.
Be sure to label the distances along the highway and the length in miles of the part of the highway where both stations can be received. |
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| Scoring Guide |
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Score & Description | ||||
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| Correct - Student Response |
|
37 |
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? |
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|
37 |
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? |
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| Incorrect - Student Response |
|
37 |
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? |
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|
37 |
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? |
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