This is the second of two lessons that help students make sense of equivalent ratios through physical experiences.

In this lesson, students mix different numbers of batches of a color mixture and compare the results. In the main activity, they combine blue and yellow water (created ahead of time with food coloring) to see if they produce the same shade of green. They also change the ratio of blue and yellow water to see how doing so changes the result. In an optional activity, students apply their understanding of equivalent ratios to predict the shades of purple mixtures without actually combining red and blue water.

The experiences here reinforce the idea that scaling a recipe up (or down) requires scaling the amount of each ingredient by the same factor (MP7). Students continue to use discrete diagrams as a tool to represent a situation.

A note about seeing color:

For students who do not see color, consider having students make batches of dough with flour and water. Using 1 cup of flour to 5 tablespoons of water makes a very stiff dough, and 1 cup of flour to 6 tablespoons of water makes a soft (but not sticky) dough. In this case, doubling a recipe yields dough with the same tactile properties, just as doubling a colored-water recipe yields a mixture with the same color. The invariant property is stiffness rather than color. The principle that equivalent ratios yield products that are identical in some important way applies to both types of experiments.