Unit 2, Lesson 3
Recipes
Grade 6
Preparation
Lesson Narrative
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. In this lesson, students see this idea in the context of taste.
Here, 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.
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.
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.
- Draw and label a discrete diagram with circled groups to represent multiple batches of a recipe.
- Explain equivalent ratios (orally and in writing) in terms of different-sized batches of the same recipe having the same taste.
- Understand that doubling or tripling a recipe involves multiplying the amount of each ingredient by the same number, yielding something that tastes the same.
Let’s explore how ratios affect the way a recipe tastes.
Required Materials
Required Preparation
For the taste test:
- Create two separate drink mixtures:
- Mixture A: 1 cup of water, 1 teaspoon of powdered drink mix
- Mixture B: 1 cup of water, 4 teaspoons of powdered drink mix
- Stir the mixtures vigorously for a minute or more to ensure all the powder dissolves.
- Prepare six small paper cups. Do not mark the cups. Put a small amount of Mixture A in three of the cups and a small amount of Mixture B in the other three cups. (Keep track of which set contains which mixture. Later, three volunteers will each receive one cup of A and one cup of B.)
- Discard the rest of the mixtures for now.
For the mixing demonstration:
- Prepare three empty mixing containers, each with at least a 2-cup capacity. Label one container A, another B, and the last one C.
- Prepare a supply of water, a supply of drink mix, a measuring cup, and a teaspoon.