In this activity, students continue to draw connections between a diagram and the ratios it represents. Students discuss with a partner different ways to use ratio language to describe discrete diagrams. They first identify statements that would correctly describe a given diagram. Then they create both a diagram and corresponding statements to represent a new situation involving ratio. 

Monitor for the different kinds of diagrams that students create and the different statements that they write to describe the play clay recipe. Here are some ways in which students may create diagrams, from more elaborate to more simple:

• Draw literal drawings of cups and pints.
• Draw rectangles, circles, or other shapes.
• Use letters or other symbols.

They may write statements that:

• Use the given values, such as: “the ratio of cups of corn flour to pints of glue is 8 to 2.”
• Regroup the quantities, such as: “for every 4 cups of corn flour, Jada used 1 cup of glue.”
• Use equivalent ratios, even though these have not been explicitly taught, such as: “the ratio of cups of corn flour to pints of glue is .” While this is correct and we have regrouped quantities and used language, such as “for every 4 of something, there is 1 of another thing,” we have not yet asserted that the ratio can be written as . The idea of equivalent ratios is sophisticated and will be developed over the next several lessons.
• Include fractions, such as: “for every 1 cup of corn flour, Jada used pint of glue.” Although students are not expected to work with fractions in this lesson, responses involving fractions are fine.

Invite previously selected students to share. Sequence the diagrams in the order listed in the Activity Narrative.

Connect the various ways in which the quantities in the play clay can be represented and described. For example, ask questions such as:

• “How can all the drawings—of objects, shapes, and letters— represent the same situation?” (They all show the ratio of corn flour to glue but with different levels of detail.)
• “How can we keep track of what each drawing or each mark represents?” (Labels can help us keep track of the quantities.)
• “Does it matter the order in which we draw the quantities or name them in a sentence?” (No, we can draw or name the items in different orders, but the numbers must match the ratio in the situation.)
• “How might we decide whether to create detailed drawings or draw diagrams?” (It might depend on the quantities or situation. In this case, a discrete diagram is a more efficient way of showing the recipe.) 

Writing and using ratio language requires attention to detail. This activity further develops students’ ability to describe ratio situations precisely by attending carefully to the quantities, their units, and their order in the ratio.

Students are given a set of cards showing discrete diagrams and statements that represent ratios of objects in pencil cases. They work with a partner to find diagrams and statements that represent the same ratio. Students take turns making a match and explaining their reasoning. In doing so, they practice constructing viable arguments and critiquing the reasoning of others (MP3).

This is the first Card Sort activity of the course. An important aspect of this routine is to allow students time at the start to sort the cards into categories of their choosing. This step gives students the opportunity to familiarize themselves with the content of the cards without the additional pressure of organizing them in a specific fashion. It also provides insight into the aspects of each card students attend to and the language they have to describe their observations.

After all groups have completed the matching, discuss the following: 

• Which matches were tricky? Explain why.
• Did any groups need to make adjustments in their matches? What might have caused an error? What adjustments were made?