Proportions and Graphs

Solve the following problems. Record your solution strategy and then answer the questions that follow the problem set.

Problem 1: Exhausted Examiners: Elke and Faye corrected final exams at the same rate but Elke got a head start. When Elke had completed 12 exams Faye had finished only 4. When Elke had finished 60 exams, how many exams had Faye completed?

Problem 2: A Metric Conversion: If 6 inches is 15.24 cm, 9 inches is how many centimeters?

Problem 3: An Exchange Rate: If 5 Canadian dollars can be exchanged for 4 US dollars, what is 35 Canadian dollars worth in US dollars?

Problem 4: Taken for a Ride: A taxicab charged $1 plus 50 cents a mile. If it costs $3 to go four miles, how much would it cost to go 6 miles?

Of Problems 1-4, which are proportion problems and which are not? Briefly justify your answers.

To distinguish between problems having a direct proportion and nonproportion problems, it can be helpful to record the data in a table and graph it. Draw a line connecting the dots of the graph and if necessary, extend the line so that it intersects the left or bottom side of the graph. Graph Problems 1-4. Graphs of directly proportional relationships have what characteristics? Why do these graphs have these characteristics? In what way are they different from graphs of nonproportional situations?

(Source: Adapted from Fostering Children's Mathematical Power. An Investigative Approach to K-12 Mathematics, Arthur J. Baroody, with Ronald T. Coslick, c. 1998 by Lawrence Erlbaum Associates, Mahwah, NJ.)

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