Lesson 2

Variables in Proportion

Est. Class Sessions: 2–3

Summarizing the Lesson

Upon completion, discuss students' responses to several of Check-In: Questions 17–21. Refer to the Super Ball Graph that accompanies the questions.

Ask:

X
  • How do you know whether variables are in proportion? (Possible responses: The lines graphing variable proportions will be straight. They will begin at (0, 0) on the graph. If the ratios are equivalent, the variables are in proportion.)
  • Are the variables for the Super Ball Graph in proportion (Question 19)? How do you know? (Possible response: Since the graph is a straight line going through (0, 0) the variables D and B are in proportion. Since the ratio for B/D reduce to the same fraction, 3/4, the variables D and B are in proportion.)
  • Did you use interpolation or extrapolation to predict the height of the bounces in Question 17? Question 20? Question 21? (interpolation; extrapolation; extrapolation)
  • If John drops the ball at 100 cm and it bounces 75 cm, how can you use multiplication to find the bounce height if he drops the ball at 200 cm? (Because the variables are in proportion, if the drop height is doubled, you can multiply the bounce height by 2. 75 cm × 2 = 150 cm.)
  • Describe the relationship between these variables in words. (The ratio of the bounce height to drop height is 3 cm to 4 cm, or 150 cm to 200 cm.)
  • Write the ratio of bounce height to drop height as a fraction. (150 cm/200 cm or 3 cm/4 cm)
  • Write this ratio using a colon. (150 : 200 or 3 : 4)
  • Write the proportion that describes this situation.
    (B/D = 75 cm/100 cm = 150 cm/200 cm)
  • Explain how you predicted the bounce height with a drop height of 150 cm (Question 21). (Possible response: I knew the ratio was 3 cm/4 cm, so I thought about 3/4 = ?/150 to find a fraction that was close to equivalent. If I multiply the denominator 4 times a number to get 150, I have to multiply the numerator 3 times the same number. 4 × 30 = 120 and 4 × 40 = 160. A drop height of 150 would be in between 120 − 160, closer to 160. So I multiplied both the numerator and denominator by a number in between 30 and 40, closer to 40: 38. 3 × 38 = 114, the bounce height, and 4 × 38 = 152, which was close to the drop height. I predict the bounce height is about 114 cm.)
  • Did anyone use a different strategy to solve this problem? Explain. (Possible response: I extended the graph and used it to extrapolate.)
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