# PERSPECTIVES ON GEOMETRY PRE-ASSESSMENT ANSWER SHEET (GEO )

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1 PERSPECTIVES ON GEOMETRY PRE-ASSESSMENT ANSWER SHEET (GEO ) Name Date Site TURN IN BOTH TEST AND ANSWER SHEET TO YOUR INSTRUCTOR WHEN DONE I For office use only I. II. III. AITP(GEO) PP1

2 II. III. AITP(GEO) PP2

3 PERSPECTIVES ON GEOMETRY PRE-ASSESSMENT (GEO ) Ms. Sandeman had just given a quiz to her class. They had been using the 1 formula A = bh to find the area of triangles. She noted that there seemed to be some 2 confusion about what was the height of a triangle. For each of the following figures is the segment labeled h a height of the triangle? Mark YES or NO for each figure. YES NO h h Mr. Maxwell s class was studying cross sections of 3-dimensional objects. The students were trying to determine all the possible shapes that could be created by slicing a cube with a plane. Which of the following are possible cross sections of a cube? Mark YES or NO for each. YES NO 3. A rectangle 4. An equilateral triangle 5. A scalene triangle 6. A hexagon AITP(GEO) PP3

4 7. Ms. Rothko assigned her sixth grade class the following problem from the textbook: Trace Figure I. Move the tracing paper to fit exactly onto Figure II. Use translation, rotation, and reflection to describe the motions used. I II The Teacher s Manual listed only rotation as the answer. Some students gave different responses. Which of the following is correct? Choose ONE response. Rotation works, but so does a translation. Rotation doesn t work, only a reflection. (C) Rotation and reflection both work. (D) The Teacher s Manual is correct: rotation is the only answer. 8. A group of students made a triangle from wooden sticks of length 6, 8, and 10 inches. Another group of students wanted to make a triangle that was similar to this triangle but had longer sides. The group then cut wooden sticks of length 9 and 15 inches. They needed one more stick to complete the triangle. What should the length be so that this new triangle is similar to the original one? Choose ONE answer. 12 inches 16 inches (C) 21 inches (D) It is impossible to determine from the given information. 9. Mr. Powell was considering possible questions to ask students to check their understanding of the number!. He came across the following problem: Which one of the following figures has a perimeter closest to!? (C) (D) AITP(GEO) PP4

5 Ms. Lewis 6th grade class has been working with geoboards (a square grid of pegs at one unit intervals) and finding areas and perimeters of polygons. One of the students, Emilio, creates the following example of a square: Ms. Lewis asks her class to generate strategies for calculating the area of Emilio s example. Which of the following are mathematically acceptable? Mark YES or NO for each. 10. Use the Pythagorean theorem to find the length of one edge, then square this number. YES 11. Just count the number of points inside the square Subtract the areas of four right triangles with legs of lengths 1 and 3 from the area of a square with edge length 4. This square is just a 3.5 by 3.5 that has been rotated, so the area is 3.5 squared. NO Mr. Hsu asks his class to generate statements about squares. The class generates the following list. Mark each one TRUE or FALSE If a quadrilateral has four right angles then it must be a square. If a quadrilateral has opposite sides parallel and all sides congruent then it must be a square If a quadrilateral has at least three congruent angles and at least three congruent sides then it must be a square. TRUE FALSE AITP(GEO) PP5

6 Ms. Zimmer has been studying types of polygons. The students began generating examples, and discussing which of the examples were s. Ms. Zimmer wants to use the definitions form their textbook to help decide. She finds the following definitions in her textbook: Quadrilateral: A closed plane figure made up of four line segments. Trapezoid: A quadrilateral with only one pair of parallel sides. BASED ON THESE DEFINITIONS, how should Ms. Zimmer classify the following figures: Parallel line segments are marked. Choose ONE answer for EACH of the students examples. 17. Quadrilateral Trapezoid (C) Both (D) Neither 18. Quadrilateral Trapezoid (C) Both (D) Neither 19. Quadrilateral Trapezoid (C) Both (D) Neither 20. Quadrilateral Trapezoid (C) Both (D) Neither AITP(GEO) PP6

7 21. Ms. Braxton s class was studying symmetry. She asked the students to determine what would happen to the shaded figure if it were reflected across the line Y. X Y The students came up with a variety of responses. Which of the following is correct? Choose ONE. X X X X Y (C) (D) 22. The class is painting cubes. Two jars of paint exactly covers the surface of a cube. How many jars of paint are needed to cover the surface of a cube with edges twice as long. Choose ONE answer. 4 jars 8 jars (C) 12 jars (D) 16 jars Y Y Y AITP(GEO) PP7

8 23. Ms. Darbaux s class was studying sums of angles in polygons. The class knew that the sum of the angles in a triangle was 180º. They then went on to investigate the sum of the angles in a hexagon. Which of the following statements is correct? Choose ONE answer. (C) (D) A hexagon has six angles. 360/6 = 60, so each angle is 60º. Thus, the sum is The sum of the angles doubles each time the number of sides in a polygon increases by one. Triangles sum to 180º; quadrilaterals sum to 360º; pentagons sum to 720º, and so hexagons sum to 1440º. A hexagon can be cut up into four triangles. Each triangle s angles sum to 180º, so the hexagon s angles sum to Based on the diagram: it is clear that each of the six vertices of the hexagon has three angles totaling 180º, thus the sum of the angles is A B C A farmer has a square field. He wants to install a sprinkler system to water the field. Each sprinkler waters a circular region of a fixed radius. Which configuration covers the greatest proportion of the field? Choose ONE answer. Configuration A Configuration B (C) Configuration C (D) They cover the same proportion AITP(GEO) PP8

9 25. The students in Mr. Taylor s fourth grade class were studying three-dimensional objects. The state standards indicated that his students should be able to interpret two-dimensional representations for three-dimensional solids. Which of the following best describes the solid formed by cutting out the above pattern and folding it into a solid? Choose ONE answer. Tetrahedron Triangular Pyramid (C) Triangular Prism (D) Square Pyramid 26. Cassandra is building with cubes. She makes the following building: Now Cassandra wants to make a new building of the same shape. She wants it to have double all the dimensions of the original. How many cubes will Cassandra need? 10 cubes 16 cubes (C) 20 cubes (D) 40 cubes AITP(GEO) PP9

10 Mr. Johnson wanted his sixth grade class to study some properties and vocabulary related to circles. He generated the following questions. Which of the following statements are correct? Mark TRUE or FALSE for each statement. TRUE FALSE 27. All circles are similar. 28. A chord is a line segment that connects any two points on the circle. 29. A radius is a chord. 30. Triangle A has an area of 18 square centimeters. Which of the following could NOT be triangle A's height? 2.25 cm 3 cm (C) 4 cm (D) 24 cm (E) Any of the above choices could be the height of triangle A. Students in Ms. Lopez class were studying area and perimeter. She gave them the following arrangement of square tiles: The side length of each tile is 1 unit, so the class correctly determined that the area was 5 square units and the perimeter was 12 units. Ms. Lopez asked the class the question: If another square tile is added anywhere to the arrangement, as long as it shares at least one complete side with another tile, what can happen to the perimeter? The class generated several responses. Which of the following possibilities can occur? Mark YES or NO for each response. YES NO 31. The perimeter increases. 32. The perimeter decreases. 33. The perimeter stays the same. AITP(GEO) PP10

11 Free Response Using Tools Complete in space provided on the answer sheet. I. Use a protractor and ruler to draw a quadrilateral with one pair of opposite sides each measuring 2 inches, one pair of opposite sides each measuring 1 inch, and no right angles. Label the shape with its mathematical name. II. Using a compass and straightedge only, construct a square. Do not use a ruler to make measurements. III. Give a mathematical explanation to support your construction of the square AITP(GEO) PP11

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