Unit 2, Lesson 3
Recipes
Grade 6
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The purpose of this Warm-up is to quickly remind students of different ways to write ratios. They also have an opportunity to multiply the number of each type of shape by 2 to make two copies of the flower, which previews the process introduced in this lesson for making a double batch of a recipe.
Arrange students in groups of 2. Ensure that students understand that there are 6 hexagons, 2 trapezoids, and 9 triangles in the picture, and that their job is to write ratios about the numbers of shapes. Give 2 minutes of quiet work time and then invite students to share their sentences with their partner. Follow up with a whole-class discussion.
This flower is made up of yellow hexagons, red trapezoids, and green triangles.
Students might get off track by attending to the area that each shape covers. Clarify that this task is concerned only with the number of each shape and not with the area covered.
Invite a student to share a sentence that describes the ratio of two shapes in the picture. Ask if any students described the same relationship in a different way. For example, three ways to describe the same ratio are: The ratio of hexagons to trapezoids is
Ask a student to describe why two copies of the picture would have 12 hexagons, 4 trapezoids, and 18 triangles. If no student brings it up, be sure to point out that each number in one copy of the picture can be multiplied by 2 to find the number of each shape in two copies.
MLR8: Discussion Supports
This is the first of several activities that help students develop an intuition for equivalent ratios. First, a few volunteers taste two drink mixtures and consider diagrams that could represent the ratios of ingredients. Next, the class observes a demonstration of the creation of the two mixtures, a change to one mixture, and the creation of a third mixture. Students then consider how the three mixtures would taste and whether multiple batches of a recipe would taste the same as one batch.
Students see that combining two things that taste the same will produce a mixture that tastes the same. They should also note that each ingredient was doubled in the mixture.
Display the diagram for all to see:
Taste test: Recruit three volunteers for a taste test. Give each volunteer two unmarked cups—one each of a small amount of Mixture A and Mixture B. Explain that their job is to take a tiny sip of each sample, match the diagrams to the samples, and explain their matches.
Demonstration: Conduct a dramatic demonstration of mixing powdered drink mix and water. Start with two empty containers labeled A and B. To Container A, add 1 cup of water and 1 teaspoon of drink mix. To Container B, add 1 cup of water and 4 teaspoons of drink mix. Mix them both thoroughly. The first diagram should still be displayed.
Discuss:
Add 3 more teaspoons of drink mix to Container A. Display a new diagram to represent the situation:
Discuss:
Pour the contents of both Container A and Container B into a larger container labeled ContainerC and mix them thoroughly.
Discuss:
Following this demonstration, students individually interpret the drink mixture diagrams. The work in the task will reiterate what happened in the demonstration.
Mixing 1 cup of water with 4 teaspoons of powdered drink mix makes a mixture that tastes exactly the same as mixing 2 cups of water with 8 teaspoons of powdered drink mix. We say that the ratios
A recipe for fizzy juice says, “Mix 5 cups of cranberry juice with 2 cups of soda water.”
To double this recipe, we would use 10 cups of cranberry juice with 4 cups of soda water. To triple this recipe, we would use 15 cups of cranberry juice with 6 cups of soda water.
This diagram shows a single batch of the recipe, a double batch, and a triple batch:
We say that the ratios
Help us improve by sharing suggestions or reporting issues.
Here are diagrams representing three mixtures of powdered drink mix and water:
Use the diagrams to complete each statement:
Mixture B uses
The ratio of cups of water to teaspoons of drink mix in Mixture B is
Mixture C uses
The ratio of cups of water to teaspoons of drink mix in Mixture C is
Students may not initially realize that Mixtures C and B taste the same. Consider asking them to imagine ordering a smoothie from a takeout window. Would a small size smoothie taste the same as a size that is double that amount? If we double the amount of each ingredient, the mixture tastes the same.
A recipe for one batch of cookies calls for 5 cups of flour and 2 teaspoons of vanilla.
Draw a diagram that shows the amount of flour and vanilla needed for two batches of cookies.
Whether the ratio of cups of flour to teaspoons of vanilla is
Find another ratio of cups of flour to teaspoons of vanilla that is equivalent to these ratios.
How many batches can you make using this new ratio of ingredients?
For the fourth question, students may not multiply both the amount of flour and the amount of vanilla by the same number. If this happens, refer students to the previous questions in noting that the amount of each ingredient was changed in the same way.
Building Toward
Building Toward