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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.