Ratios and Proportions / Ratios and Rational Numbers

Understanding

Any line that contains the graph of a collection of equivalent ratios goes through the point (0, 0); however, the point (0, 0) is not a member of the collection.

What to look for

Unit rates are suggested in some of the questions as good strategies for solving problems. Students should remember that adding two columns in a ratio table produces another ratio equivalent to those added.

Sample Assessment

Mark and Steve bike at the same rate. If it takes Steve $\frac{1}{4}$ hour to bike 6 miles, how long will it take Mark to bike 8 miles?

Answer: $\frac{1}{3}$ hour

The Big Idea

The points associated with collections of equivalent ratios lie on the graph of the same straight line.

What are the students doing?

Students build tables of ratios using pairs of rational number entries to find associated unit rates. Students then graph lines with different unit rates to compare the ratios and slopes of the lines.

What is the teacher doing?

Have students name some points that lie along the ray. Guide students in a discussion of to remind them that the points are on the same ray because they are associated with a collection of equivalent ratios.