Geometry Test Prep
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Feb 20, 2024
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Geometry Test Preparation Questions Week 8
Mr. Bass is working on defining quadrilaterals with his students. He notices that many students are focused on the number of sides, saying things like “a quadrilateral is a shape with four sides.” Which two of the following figures are most likely to support students in refining their definition of quadrilaterals? % pe (B) ; %\ Problem 1
Problem 2 A rectangular message board in Aleyah's dormitory room has a length of 30 inches and a perimeter of 108 inches. A rectangular bulletin board in the hallway outside Aleyah’s room is twice as long and twice as wide as the message board. Which of the following statements about the bulletin board is true? @The bulletin board has a width of 48 inches. OThe bulletin board has a length of 96 inches. O The area of the bulletin board is twice the area of the message board. O The perimeter of the bulletin board is four times the perimeter of the message board.
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Problem 3 Mr. Varela asked his students to define a square in terms of other two-dimensional geometric figures. Which two of the following student definitions precisely define a square? [x] A square is a rectangle that has 4 sides of equal length. [ ] A square is a parallelogram that has 4 angles of equal measure. [ ] A square is a parallelogram that has 4 sides of equal length. [x] A square is a rhombus that is also a rectangle. [ ] A square is a rectangle that is not a rhombus.
Problem 4 A student answered two elapsed-time problems using the same method, as represented in the work shown. The student’s answer to the first problem was correct, but the student’s answer to the second problem was incorrect. 1. Determine the elapsed time from 2. Determine the elapsed time from 7:05 AM. to 1:45 pM. 11:45 pm. to 3:20 AM. T-1=6 l-3=8 45 - 5 = 40 45 - a0 = 25 6 hours 40 minutes passed 8 hours 25 minutes passed If the student continues to use the same method, for which two of the following time intervals will the student give the correct elapsed time? [[]645AM to 315AM. [] 10:10 AM. to 3:35 PM. [x] 2:30 P.M. to 7:50 P.M. []8:55PM. to4:20 AM. x] 11:25PM. to 5:30 AM.
Ms. Palmeri has worked with her students on the concepts of area and perimeter of rectangles. She is concerned that students may have confused the concepts because both concepts were taught in the same unit and lessons for both included drawing rectangles on grid paper. She wants to assess students on only the concept of perimeter at this time. To do this, she will show her students pictures of rectangles drawn on grids and then have students find the perimeters of the rectangles and write their final answers on individual marker boards so that she can check them quickly. Which of the following pictures would be LEAST useful for Ms. Palmeri to show as she assesses her students’ understanding of perimeter of rectangles in this way? © Problem 5
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Problem 6 Ms. Chamberlain’s students are discussing the following quadrilaterals and their diagonals. Ms. Chamberlain asks her students what they notice about the diagonals in the quadrilaterals. One student says, “I noticed that the diagonals of the quadrilaterals always cross at a right angle.” Of the following sets of quadrilaterals, for which set is the student’s conjecture always true? O Quadrilaterals with one pair of congruent opposite angles O Quadrilaterals with one pair of parallel opposite sides @ Quadrilaterals with two pairs of congruent adjacent sides (O Quadrilaterals with two pairs of parallel opposite sides
Ms. Stockton and her students are working on naming different polygons using their geometric attributes. She finds a suggestion online to use pattern blocks for this work. A set of pattern blocks is N A Which two of the following statements describe limitations of using pattern blocks for the purpose of naming polygons based on their attributes? [X] The blocks could support the conclusion that all polygons are convex. [C] The blocks do not clearly show how polygons can be composed of other polygons. [] The blocks could support the conclusion that all polygons can be composed of equilateral triangles. [] The blocks do not show which polygons have the defining attribute of having at least one set of parallel lines. [X] The blocks could support the conclusion that an attribute of polygons is that they must have at least two sides of equal length. Problem 7
Problem 8 Ms. Shaughnessy is working with her class on measuring area using nonstandard units. While the students are finding the area of the surface of their desks using rectangular note cards, one student says, ‘I can just measure the long side of the desk with the long side of the card, then measure the short side of the desk with the short side of the card, and multiply them.” Which of the following best describes the validity of the student's strategy? The strategy is not valid because the same unit must be used to measure each side of the desk. O The strategy is valid only if the note cards are squares. O The strategy is valid and the unit of measurement is square units. @ The strategy is valid and the unit of measurement is note cards.
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Problem 9 18. At the close of a lesson on reflection symmetry in polygons, Ms. White gave her students several problems to do. She collected their answers and read through them after class. For the problem below, several of her students answered that the figure has two lines of symmetry and several answered that it has four. How many lines of symmetry does this figure have? L/ Which of the following is the most likely reason for these incorrect answers? (Circle ONE answer.) (@ Students were not taught the definition of reflection symmetry. b) Students were not taught the definition of a parallelogram. c) Students confused lines of symmetry with edges of the polygon. d) Students confused lines of symmetry with rotating half the figure onto the other half.
Problem 10 24. Ms. Miller wants her students to write or find a definition for triangle, and then improve their definition by testing it on different shapes. To help them, she wants to give them some shapes they can use to test their definition. She goes to the store to look for a visual aid to help with this lesson. Which of the following is most likely to help students improve their definitions? (Circle ONE answer.) a) b) d) Shapes Shapes @ Triangles Triangles A )/ N AL v A triangle has 3 corners, 1 on the top and 2 on the bottom. square triangle A triangle is a polygon. A clown'’s hat is like a triangle. circle rectangle %
Problem 11 25. Ms. Donaldson’s class was working on an assignment where they had to find the measures of unknown angles in triangles. One student consistently found the measures of unknown angles in right triangles by subtracting the known angle from 90. For example: 90 -62=28 xz28 B Ms. Donaldson was concerned that this student might run into difficulty when trying to find the measures of unknown angles in more general triangles. Which of the following questions would be best to ask the student in order to help clarify this issue? (Circle ONE answer.) a) “What do you get when you add 90 + 62 + 28?” “"Why does subtracting 62 from 90 give you the measure of the unknown angle?” ¢) “How could you find the missing angle in an isosceles triangle?” d) “How did you know that this was a right triangle?” e) “What if this angle measured 17° instead of 62°?”
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