This is the first of several activities that help students develop an intuition for equivalent ratios. First, a few volunteers taste two drink mixtures and consider diagrams that could represent the ratios of ingredients. Next, the class observes a demonstration of the creation of the two mixtures, a change to one mixture, and the creation of a third mixture. Students then consider how the three mixtures would taste and whether multiple batches of a recipe would taste the same as one batch. 

Students see that combining two things that taste the same will produce a mixture that tastes the same. They should also note that each ingredient was doubled in the mixture.

Mixing 1 cup of water with 4 teaspoons of powdered drink mix makes a mixture that tastes exactly the same as mixing 2 cups of water with 8 teaspoons of powdered drink mix. We say that the ratios and are equivalent. Ask students to discuss what they think it means for the ratios to be “equivalent.” Students might say:

• The ratios make the mixtures taste the same.
• If there is twice as much of one ingredient, there is also twice as much of another ingredient, so the result still tastes the same. 

Students continue to use diagrams to represent the ratio of ingredients in a recipe as well as mixtures that contain multiple batches. They come to understand that a change in the number of batches changes the quantities of the ingredients, but the end product tastes the same. They then use this observation to come up with a working definition for equivalent ratios.

For the fourth question, students may not multiply both the amount of flour and the amount of vanilla by the same number. If this happens, refer students to the previous questions in noting that the amount of each ingredient was changed in the same way.

Invite a few students to share their responses and diagrams with the class. A key point to emphasize during discussion is that when we double (or triple) a recipe, we also have to double (or triple) each ingredient. Record a working (but not final) definition for equivalent ratio that can be displayed for at least the next several lessons. Here is an example: “Cups of flour and teaspoons of vanilla in the ratio , , or are equivalent ratios because they describe different numbers of batches of the same recipe.” Include a diagram in this display.

Students revisit color mixing—this time by producing purple-colored water—to further understand equivalent ratios. They recall that doubling, tripling, or halving a recipe for colored water yields the same resulting color, and that equivalent ratios can represent different numbers of batches of the same recipe. 

As students work, monitor for students who use different representations to answer both questions, as well as students who come up with different ratios for the second question.

Select students to share their answers to the questions.

• For the first question, emphasize that not only did Jada triple each amount of red and blue, but this means that the amount of each color is being multiplied by the same value, in this case, 3.
• For the second question, list (for all to see) all of the different ratios that students brought up. Discuss how each ratio differed from that for the original mixture. Point out that as long as both terms are multiplied by the same quantity, the resulting ratio will be equivalent and will yield the same shade of purple.

If time permits, use Critique, Correct, Clarify to give students an opportunity to improve a sample response by correcting errors, clarifying meaning, and adding details. 

• Display and read: “Andre says, ‘Mixing 18 ml of blue water with 13 ml of red water would result in the same shade of purple. This is because the same amount, 10 ml of each color, is added to the recipe.’”
• Ask, “What parts of this response are unclear, incorrect, or incomplete?” As students respond, annotate the display with 2–3 ideas to indicate the parts of the writing that could use improvement.
• Give students 2–4 minutes to work with a partner to revise the first draft. Ask them to use complete sentences and include diagrams and labels if helpful for clarifying their thinking.
• Select 1–2 students or groups to read their revised draft aloud, slowly enough to record for all to see. Scribe as each student shares, then invite the whole class to contribute additional language and edits to make the final draft even more clear and convincing.