Geometry -
ANSWER KEY
DAY 1
1. D.
2.
Solution:
4 blocks north and 3 blocks east.
Score & Description
Correct
Correct response.
Incorrect
Incorrect response.
3.
Solution:
Some acceptable reasons for why the figures are alike are listed below.
a.
b.
c.
d.
e.
f.
They both have 4 sides (or 4 corners or 4 angles).
They both have parallel sides.
They both have two sets of sides that are the same length.
They have the same area.
They have the same length (base).
They have the same height.
Notes: 4 sides and 4 angles are not considered different reasons. Indicating that both figures have lines that are
straight is not a reason for why they are alike.
Some acceptable reasons for why the figures are different are listed below.
g.
h.
i.
j.
One has 4 equal angles and the other does not.
One has right angles or perpendicular lines and the other does not. (Students don’t need to make the
comparisons; i.e., they can just say, "one has 4 equal angles".)
One is "slantier" than the other (or one takes up full squares and the other does not).
They have different perimeters.
Note: Indicating that both figures are not the same shape is not acceptable.
Score & Description
Extended
Student gives at least two reasons why they are alike and at least two reasons why they are different.
Satisfactory
Student gives two reasons why the figures are alike and one reason why they are different
OR
One reason why they are alike and two reasons why they are different.
Partial
Student gives one correct reason alike and one correct reason different
OR
Two reasons why they are alike
OR
Two reasons why they are different
Minimal
A nonspecific response, i.e., the one on the right is skinnier
OR
Only one correct reason (alike or different).
Incorrect
Incorrect response
Geometry -
ANSWER KEY
DAY 2
1. D.
2.
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.
3.
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.
Geometry -
ANSWER KEY
1. A.
2.
Score & Description
Correct
Line may be dotted, or have arrowheads.
Minimum length of line:
Incorrect
Incorrect answer
3.
Solution:
Any three of these.
(freehand drawings acceptable)
Score & Description
DAY 3
Extended
Gets 3 correct. Must have lines drawn separating squares. (Disregard incorrect attempts.)
Satisfactory
Gets 2 correct. Must have lines drawn separating squares. (Disregard incorrect attempts.)
Partial
Gets 1 figure correct. Must have separation lines. (Disregard incorrect attempts.)
OR
Draws 2 of the figures given with a translation (must be translations or flips of two different figures)
Minimal
Makes an attempt with five squares but shows no examples of a different way to arrange the
squares. (e.g., repeats one or more of the examples.)
OR
Makes an arrangement with 5 squares that fails to meet criteria, such as
Incorrect
Incorrect response.
Geometry -
ANSWER KEY
DAY 4
1. D.
2.
Solution:
Examples of correct response #1 (see note below score & description)
Examples of a 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
3. D.
Geometry -
ANSWER KEY
DAY 5
1. B.
2.
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.
3.
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 equal (but not so with P and Q).
OR
All the angles of N are equal (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.
Scoring Guide:
In this question, a student needed to compare the shapes with respect to a common attribute such as
number of sides or angles or vertices. The student could choose which attribute he or she wished to
use.
Score & Description
Correct
Correct response
Incorrect #2
Response refers to the shape of the letters (N, P, or Q), rather than to the geometric shapes
Incorrect #1
Any incorrect response other than as described above.
Not acceptable: N is bigger or N is prettier
Geometry -
ANSWER KEY
1. B.
2. B.
3.
Solution:
Any four-sided shape EXCEPT a rectangle or a square. For example,
Note: A figure in which the interior is shaded should be counted as correct.
Score & Description
Correct
Correct response
Incorrect 1
Figure is a rectangle or a square
Incorrect 2
Figure that is not four-sided
DAY 6
Geometry -
ANSWER KEY
DAY 7
1. D.
2. 10
3.
Solution:
A different-sized triangle in each figure. It does not matter which figure has which size triangle. For
example, any three of the following four sizes:
Note: A figure in which the interior is shaded should be counted as correct.
Score & Description
Correct
Correct response
Incorrect 1
Only two correct triangles drawn - other drawings may be repeats, missing, or incorrect.
Incorrect 2
Only one correct triangle drawn - other drawings may be repeats, missing or incorrect.
Incorrect 3
Any incorrect response other than those described above.
Geometry -
ANSWER KEY
DAY 8
1. B.
2.
Solution:
Figure must be closed and have 5 sides and 2 or more right angles.
Right angles do not have to be marked, but should appear to be right angles. Two right angles must be
on the inside of the figure.
Score & Description
Correct
Correct response.
Incorrect #3
Figure drawn is a five-pointed star with a pentagon shown in the interior. The pentagon may or may
not have right angles.
Incorrect #2
Figure has 5 sides and only 1 right angle.
Incorrect #1
No right angles in the figure drawn.
OR
Figure is not 5-sided or is not closed.
In this question the student needed to show geometric understanding by drawing a closed figure with 5
sides and at least 2 right angles. Students did not have a ruler or protractor.
3.
Solution:
Score & Description
Correct
Correct response
Partial
Puts “X” to the right of the fold line, but not in the correct box.
Incorrect
Incorrect response (i.e., “X” on the fold line).
Geometry -
ANSWER KEY
DAY 9
1. C.
2. C.
3.
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.
Geometry -
ANSWER KEY
DAY 10
1. C.
2. B.
3.
Solution:
A different-sized square in each figure. It does not matter which figure has which size square. For
example, any three of the following four sizes:
Note: A figure in which the interior is shaded should be counted as correct.
Score & Description
Correct
Correct response
Incorrect 1
Only two correct squares drawn - other drawings may be repeats, missing, or incorrect.
Incorrect 2
Only one correct square drawn - other drawings may be repeats, missing or incorrect.
Incorrect 3
Any incorrect response other than those described above.