Today in class students worked out the unit rate, or constant of proportionality, from word problems. Once we have a relationship given between two data points, we can use the ratio to figure out the constant that helps us find more data points. For any value x...y = kx and k is the constant, we can solve for y.
Answers to HW: 1.a.Therre is a proportional relationship between weight and the number of sheets of paper because each sheet of paper has the same weight. Multiply the number of sheets in the stack by the weight of 1 sheet of paper (unit rate or constant of proportionality) to find the weight of any stack. b. There is not a proportional relationship between the number of books and the weight of the stack because each different size book has a different weight. You cannot determine the weight of a stack with the different books in it by multiplying the weight of 1 of the books times the total number of books. 2.a. Yes, the constants of proportionality are 2 and 1/2 b. b = 2t and t = 1/2b 3.a. Lin's age Her brother's age 5 2 6 3 15 12 28 25 b. There is no proportional relationship. The ratio of their ages changes each year because they each age 1 year. 4. Hope you disagreed with the student. Dividing by 9 is the same as multiplying by 1/9. We can write y = x/9 or y = 1/9x. Also - y/x = 1/9 is constant for all corresponding values of x and y.
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