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Test Bank for Mathematical Reasoning for Elementary Teachers - Media Update, 7th Edition

Simplify your study sessions with Test Bank for Mathematical Reasoning for Elementary Teachers - Media Update, 7th Edition, an exam guide designed for effective revision and maximum retention.

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Instructorʼs Guide for Activities1Chapter 1Thinking CriticallyActivity 1Box 1: UNDERSTAND THE PROBLEM1.Answers will vary.2.Sample Responses: Shapes are congruent if they have exactly the same shape and size. Shapes arecongruent if they can be made to match exactly by placing one on top of the other.3.a.b. 3 ways4.Answers will vary.5.Answers will vary.Box 2: DEVISE A PLAN1.Squares could be moved around to try to construct the staircases or they could be sketched on graphpaper.2.Simplify the problem, look for a pattern, and make a table3.Answers will vary.Box 4: LOOK BACK3.a.3 waysb.Since the two staircases must fit together to form a rectangle with area 120, find the dimensionsof all rectangles with integral dimensions and an area of 120. The possible dimensions are1×120, 2×60, 3×40, 4×30, 5×24, 6×20, 8×15, 10×12.To form a staircase, both dimensions must be greater than 1, and one dimension must be evenand the other odd. This leaves 3 possibilities, a 3×40 rectangle, a 5×24 rectangle, and an8×15 rectangle.The 3×40 rectangle can be divided into two 3-step staircases. The bottom step is 21 squareslong, the middle step is 20 steps long, and the top step is 19 squares long.The 5×24 rectangle can be divided into two 5-step staircases. The bottom step is 14 squareslong, the next step is 13 squares long, the middle step is 12 steps long, the fourth step is11 squares long and the top step is 10 squares long.The 8×15 rectangle can be divided into two 8-step staircases. The steps are 11, 10, 9, 8, 7, 6,5, and 4 steps long.4.To determine whethernsquares can be used to construct two congruent staircases, find a pair offactors ofn. There is a pair of staircases for each factor pair in which both factors are greater than 1and one factor is odd and the other even.

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Mathematical Reasoning For Elementa...

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