In this lesson, students use diagrams to represent situations involving ratios and continue to develop ratio language.

Previously, students used words to describe ratios in collections of objects. Here, they also draw diagrams to represent ratios and interpret statements about ratios. Both the visual and verbal descriptions of ratios demand careful attention to language (MP6).

There is not really a right or wrong way to draw a diagram. What matters is that the diagram accurately represents the quantities, makes sense to the student and others, and can be explained. That said, one goal of this lesson is to help students draw useful diagrams efficiently.

For example, here is a diagram that represents 6 chairs and 3 tables in a room.

When asked to draw diagrams, students may include unnecessary details, for instance, by making each chair look like an actual chair. Examples of very simple diagrams, such as the discrete diagrams shown here, can guide students toward more abstract representations while still offering visual or spatial cues to support reasoning. (Students do not need to know the term “discrete diagrams.”)

Diagrams can also help students see associations between quantities in different ways. For example, we can see that there are 2 chairs for each table by grouping the items as shown.

Students may say “for every 2 chairs there is 1 table,” but for now, we do not suggest writing the association as . Equivalent ratios will be carefully developed in upcoming lessons. 

While the discrete diagrams here reflect the parallel structure of the double number line diagrams that they will see later in the unit, students do not need to draw them this way as long as they can explain their diagrams and interpret those shown in the lesson.