Ratios and Proportions / Connecting Ratios to Graphs

Understanding

The ordered pairs (2a, 3a) represent all the ratios equivalent to 2:3 from a multiplicative perspective.

What to look for

Interpreting the patterns in the ratio table and in the graph of equivalent ratios introduces students to the notion of rate of change—or slope and slope triangles—as well as to similar triangles. Note that the number 0 cannot be used in a ratio. For example, 0:0 does not make sense because equivalent ratios are generated by multiplying or dividing each value in a ratio by the same positive number.

Sample Assessment

Which of the following points will lie on the line that contains points associated with the collection of ratios equivalent to 8:5?
a. (10, 16) b. (2, 1.25) c. (24, 15) d. (14, 11)

Answer: b) (2, 1.25) and c) (24, 15)

The Big Idea

The graph of a collection of equivalent ratios lies on a line through the origin.

What are the students doing?

Students notice patterns that occur - in tables and on a graph - when a collection of equivalent ratios is graphed in a coordinate plane.

What is the teacher doing?

Emphasize the connection of the ordered pairs along a line as “for every 2 over to the right, go up 3” when moving from point to point, using an additive strategy. Moving horizontally first then vertically supports thinking about the horizontal axis as representing the independent variable and the vertical axis as the dependent variable.