Ratios and Proportions / Ratios and Fractions

Understanding

Students associate the “value” of a ratio with a fraction and connect the unit rate associated with a ratio to a fraction.

What to look for

The language “part to part” and “part to whole” is deliberately avoided as this language is constraining and limits student thinking as they continue to work with ratios in situations such as those involving slope and similarity.

Sample Assessment

The ratio of people over 45 years of age to those 45 years old and under in a certain region is 3:2. What fraction of the population in the region is 45 years or younger?

Answer: $\frac{2}{5}$

The Big Idea

A ratio is a pair of non-negative numbers, a:b, which are not both 0. As one of the numbers changes, the other changes by the corresponding multiplier. A ratio may be associated with a value; the value of a ratio a:b is the quotient, $\frac{a}{b}$, (if b is not 0).

What are the students doing?

Students consider different ways to use ratios to describe a situation, basically thinking about the ratio of two different parts of a group or of a part of a group to the whole group.

What is the teacher doing?

If students are struggling, have them recall the concepts of equivalent fractions and equivalent ratios. It may be helpful to complete a ratio table to illustrate the difference between the two.