IES Award# R324A110262 2014 ASPM, Iowa State University, University of Missouri

Proportional Reasoning Form A Page 1

For every foot of fence built (q), a carpenter needs a consistent number of nails (n). What does the equation n = 12q + 24 tell you? A. You need 36 nails and boards. B. The number of nails increases by 12 for every foot of fence. C. The number of nails increases 12 times for every foot of fence. D. The number of nails increases by 24 for every foot of fence. Answer ______Do these ratios represent the same relationship? 3:4 and A. No, because one is written like a fraction. B. No, because they are different numbers. C. Yes, because they are written like a ratio and ratios show relationships. D. Yes, because they both represent the unit rate of 0.75:1. Answer ______In the expression 2h – 8, the value of h increases by . What is the effect on the value of the expression? A. The value of 2h – 8 increases by . C. The value of 2h – 8 decreases by . B. The value of 2h – 8 increases by 1. D. The value of 2h – 8 decreases by 8. Answer ______Given the ratio of 6 miles every 4 hours, which of the following is an equivalent ratio? A. 12 miles every 8 hours C. 4 miles every 6 hours B. 8 miles every 6 hours D. 2 miles every 3 hours Answer ______Which of the following is the value of n closest to? A. 2.8 C. 8.2 B. 6.2 D. 10.1 Answer ______Consider each statement below. Then, write agree (A) or disagree (D) in the blank. _____ 3:5 and 6:8 are equivalent because 3 + 2 = 5 and 6 + 2 = 8. _____ 3:5 and 6:8 are equivalent because 3 + 3 = 6 and 5 + 3 = 8. _____ 3:5 and 6:8 are NOT equivalent because the unit rate for 6:8 is larger than the unit rate for 3:5. _____ 3:5 and 6:8 are NOT equivalent because odd numbers cannot be equivalent to even numbers. Kerry made lemonade by adding 2 cups of lemon juice for every 3 cups of water. Jon made lemonade by adding 4 cups of lemon juice for every 7 cups of water. Whose lemonade had a stronger lemon flavor? A. Kerry’s lemonade had a stronger lemon flavor. B. Jon’s lemonade had a stronger lemon flavor. C. Both lemonades had the same flavor. D. You cannot tell by the information given. Answer ______Consider each statement below. Then, write <, >, = or cannot tell (CT) in the blank. If a and b are greater than 0 but less than 1, then _____ a + b. If a and b are equal to 1, then _____ a + b. If a and b are greater than 1, then _____ a + b. If a and b are less than 0, then _____ a + b. A band will play for school events for a flat rate of $750 and an additional $325 for each hour (y) they play. What does the 325y represent in the equation m = 325y + 750? A. The band charges $750 for an event. B. The cost of the band increases by $325 each hour. IES Award# R324A110262 © 2014 ASPM, Iowa State University, University of Missouri Proportional Reasoning A Page 2 C. The cost of the band increases $325 times each hour. D. The cost of the band increases by $750 each hour. Answer ______In the expression 4a – 1, the value of a increases by 5. What is the effect on the value of the expression? A. The value of 4a – 1 decreases by 1. B. The value of 4a – 1 decreases by 5. C. The value of 4a – 1 increases by 5. D. The value of 4a – 1 increases by 20. Answer ______The y-intercept of a line is at the point (0, –3). As the value of x increases by 1, the y value increases by 4. Which of the following is the slope of the line? A. 1 C. 5 B. 4 D. You cannot tell by the information given. Answer ______Serena and Jeff have the same number of candies. Serena has 2 green candies for every 3 red candies. Jeff has 4 green candies out of every 7 candies. Which of the following describes the colors of their candies? A. Serena and Jeff have equal numbers of red candies. B. Serena has more red candies than Jeff. C. Jeff has more red candies than Serena. D. You cannot tell because you don’t know how much candy mix they made. Answer ______Find the value of p: =

A. p = 2 C. p = 40 B. p = 25 D. p = 1000 Answer ______Using the ratios , 3:4, and , which of the following describes their relationship? A. > 3:4 > C. > > 3:4 B. 3:4 > > D. > 3:4 > Answer ______Line h has a slope of –7. Line p has a slope of 4. Which of the following is true? A. Line h has a steeper slope than line p. B. Line p has a steeper slope than line h. C. Both lines have the same steepness. D. You cannot tell by the information given. Answer ______Are these ratios equivalent? and A. Yes, because is multiplied by . B. Yes, because can be simplified to . C. No, because the ratios do not have a common scale factor. D. No, because ratios that have a squared term can never be equivalent. Answer ______Sam made punch by adding 6 cups of powdered mix for every 25 cups of water. Tom made punch by adding 5 cups of powdered mix for every 19 cups of water. Whose punch had the stronger flavor?

IES Award# R324A110262 © 2014 ASPM, Iowa State University, University of Missouri Proportional Reasoning A Page 3 A. Sam’s punch flavor was stronger. B. Tom’s punch flavor was stronger. C. Their punch flavors were the same. D. You cannot tell by the information given. Answer ______The ratio of each term to the next term is the same. Find the next term in the sequence. 14 42 126

Answer ______Marcus drew a line such that as the value of x increased by 5, the y-value increased by 3. Marika drew a line such that as the value of x increased by 7, the y-value increased by 4. Whose line is steeper? A. Marika’s line is steeper. B. Marcus’ line is steeper. C. The two lines are equally steep. D. You cannot tell by the information given. Answer ______