Ratios and Proportions / Comparing Ratios

Understanding

When comparing ratios, students should be able to use more than one strategy for drawing conclusions.

What to look for

As students explore the activity, they should compare two ratios by looking at tables of equivalent ratios for each given ratio. They will also compare the ratios by identifying common values for the same quantity in the two labels.

Sample Assessment

Which company has the smallest ratio of defective bolts to non-defective bolts? Company A, which produces 2 defective bolts for every 300 non-defective bolts, or Company B, which produces 3 defective bolts for every 420 non-defective bolts?

Answer: Company A is 2:300, equivalent to 1:150 and Company B is 3:420, equivalent to 1:140. Company A has the smallest ratio of defective to non-defective because they produce 1 defective for every 150 good ones, while Company B produces 1 defective for every 140 good ones.

The Big Idea

When comparing ratios students should be aware that the rows (or columns) of a ratio table are multiples of each other.

What are the students doing?

As students explore the activity, they should compare two ratios by looking at tables of equivalent ratios for each given ratio. They will also compare the ratios by identifying common values for the same quantity in the two labels.

What is the teacher doing?

A common error when comparing ratios is to make additive comparisons. Be sure students are thinking multiplicatively when comparing ratios.