This lesson develops the idea of equivalent ratios through physical experiences. A key understanding is that if we scale a recipe up (or down) to make multiple batches (or a fraction of a batch), the result will still be “the same” in some meaningful way. In this lesson, students see this idea in two contexts, taste and color.

• A mixture containing two batches of a recipe tastes the same as a mixture containing one batch. For example, 2 cups of water mixed thoroughly with 8 teaspoons of a powdered drink mix tastes the same as 1 cup of water mixed with 4 teaspoons of the powdered drink mix.
• A mixture containing two batches of a color mixture will produce the same shade of the color as a mixture containing one batch. For example, 10 ml of blue water mixed with 30 ml of yellow water produces the same shade of green water as 5 ml of blue water mixed with 15 ml of yellow water.

The fact that two equivalent ratios yield the same taste or produce the same color is a physical manifestation of the equivalence of the ratios. 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.

Students notice structure when they see that scaling a recipe up (or down) requires multiplying the amount of each ingredient by the same factor (MP7). For instance, doubling a recipe means doubling the amount of each ingredient. They also gain more experience using a discrete diagram as a tool to represent a situation.