In this activity, students mix different numbers of batches of a color recipe to obtain a certain shade of green. They observe how multiple batches of the same recipe produce the same shade of green as a single batch produces, which suggests that the ratios of blue to yellow for the two situations are equivalent. They also come up with a ratio that is not equivalent which will produce a mixture that is a different shade of green.

As students make the mixtures, ensure that they measure accurately so they will get accurate outcomes. As students work, note the different diagrams that students use to represent their recipes. Select a few examples that could be highlighted in discussion later.

In the digital version of the activity, students use an applet to mix different amounts of blue and yellow. The applet allows students to add each color in increments of 1 or 5 units and to start over as needed. Consider using the digital version if there isn’t enough available physical equipment for students to experiment in small groups, or if time is limited and students can access the applet readily on devices.

After each group has completed the task, have the students rotate through each group’s workspace to observe the mixtures and diagrams. As students circulate, pose some guiding questions. (For students using the digital version, these questions refer to the mixtures on their computers.)

• “Are each group’s results of the first two experiments the same shade of green? How do you know?”
• “In the first two experiments, are the ratios of blue water to yellow water equivalent?”
• “Is each group’s result of the third experiment the same shade of green as the first two?”
• “Is the ratio of blue water to yellow water in the third experiment equivalent to the ratios in the first two? How do you know?”
• “What are some different diagrams created to represent the ratios?”

Highlight the idea that a ratio is equivalent to another if the two ratios describe different numbers of batches of the same recipe.

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.

At a quick glance, students may think that because Andre is mixing a multiple of 8 with a multiple of 3, it will also result in Perfect Purple Water. If this happens, ask them to take a closer look at how the values are related or to draw a diagram showing batches.

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.