# More: In-Depth Discussion of the Reasoning Activities in "Teaching Fractions and Ratios for Understanding"

By Susan J. Lamon | Go to book overview

Chapter 13
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 a. 4:6 b. 2:3 c. 2:3, 4:4, and 8:12 are equivalent because the shaded and unshaded areas of the rectangle never changed. We merely renamed them by thinking of different-sized chunks. d. Click for a larger version e. From any point on the line, draw a vertical line to the x axis and a horizontal line to the y axis to read its coordinates. Some that are easy to read from the graph are (3,4.5), (5,7.5), (6,9), (7,10.5) f. The ratio of shaded to unshaded is the ratio of the y coordinate to the x coordinate. The ratios 7:3 and 1 1/2:3/4 are both greater than 1. 4:6 is on the line and 64:96 is on the line. g. h. The constant is .667 (2 ÷ 3). h. i. The slope of the line is the vertical change compared to the horizontal change between any tow point on the line. Using the points (3,2) and (6,4), we get Click for a larger version.

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