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Unit 2: Introducing Ratios Lesson 3: Recipes This is the first of two lessons that develop 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. Students see this idea in two contexts, taste and color: In this lesson, 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 powdered drink mix tastes the same as 1 cup of water mixed with 4 teaspoons of powdered drink mix. In the next lesson, a mixture containing two batches of a recipe for colored water will produce the same shade of the color as a mixture containing one batch. For example, 10 ml of blue mixed with 30 ml of yellow produces the same shade of green as 5 ml of blue mixed with 15 ml of yellow. 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 this lesson, students start to use the term equivalent ratios. Students see that scaling a recipe up (or down) requires multiplying the amount of each ingredient by the same factor, e.g., doubling a recipe means doubling the amount of each ingredient (MP7). They also gain more experience using a discrete diagram as a tool to represent a situation.
Material Type: Activity/Lab