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## Feeding Frenzy

• Lesson
6-8
1

In this activity, students will multiply and divide a recipe to feed groups of various sizes. Students will use unit rates or proportions and think critically about real world applications of a baking problem.

Begin the discussion by asking students if they cook at home. Call on a few students and ask them what they cook and if they follow a recipe. Then ask students if they have ever had to double, triple, or halve a recipe. Explain that most recipes tell how many people they will serve, and if you are cooking for more or fewer people, you may need to adjust the recipe. Ask students how they think they would adjust a recipe. Students will probably suggest multiplying or dividing by a factor, and may bring up ratios and proportions.

Distribute the Feeding Frenzy Activity Sheet to each student. Explain to students that they will be looking at a recipe for chocolate chip cookies, and modifying it to feed different numbers of people. They will be calculating how to prepare 12 cookies for a family meal, 60 cookies for a party, 24 cookies for a class event, and 300 cookies for a bake sale. They need to determine how much of each ingredient they will need.

Before students begin their work, let them know that they should give all the answers as fractions because that is how ingredients are measured. They may choose to first find the amount as a decimal, but must then convert it to a fraction for their answer. For example, they should record rather than 0.75. Also, review the common abbreviations for measurements:

• tsp = teaspoon
• Tbsp = tablespoon
• c = cup

Allow students to begin working. After a few minutes, bring the class together to discuss strategies being used. Put an example of each strategy on the board as students contribute. Students may be using proportions, finding a unit rate, using a diagram to model the situation, or using another method not listed here.

### Proportions

One way to solve the problem is to set up proportions. You may want to guide students to keep their proportions consistent by setting up a sample proportion for the chocolate chips used in the 60-serving recipe as follows:

Remind students to keep the same units in the numerator and in the denominator. Emphasize the labels and the importance of common units. At the same time, let students know they may set it up differently and still be correct. For example:

As long as the units are consistent, a proportion is correct. In the first proportion, both the servings values (original and new) were on the bottom. In the second proportion, both were on the left.

### Unit Rate

Students may also find a unit rate, either by finding the amount of each ingredient used for 1 serving, or by finding the amount for 12 servings, since 12 is the greatest common factor of all the serving amounts. You may want to use the flour measurement as an example on the board:

 = , so each serving should contain  c of flour

For 72 servings: 72 × = c.

### Diagrams

A third method students may use is drawing diagrams to represent the fractions. For example, they may draw 2 full cups and of a cup to represent c flour. Then, to get 24 servings, they can shade of each drawing, since 24 is of 36. This results in the calculation:

+ + = c flour

### Other Methods

Finally, students can use various methods of manipulating the numbers. For example, to get from 36 to 12, students may divide by 3. Then to get from 36 to 24, students may realize it’s as much. In this case, they may double the recipe, then divide by 3, essentially multiplying by in 2 steps.

Since students have already had some time to work on the table, ask volunteers to demonstrate these methods and share with the other students. Make sure students realize that there are many correct methods. Students who have been struggling up to this point will now have multiple starting points. Allow students time to work on the activity sheet individually, while circulating throughout the room to help where needed and informally check that all students are on the right track.

Make measuring cups, sand, and bowls available to student. If you have enough, provide the materials to each student. Otherwise, set up a work station where students can come up and use the manipulatives when they feel they need them. As they work, encourage students to measure out the amount of the ingredient to check the reasonableness of their answers. You may want to have the pre-measured amount of each ingredient at the front of the room for reference. Students can then measure out the amount they calculated for 60 servings, for example, and compare the physical amounts. Since 60 is nearly double 36, they can see that the physical amounts look like approximately double the original. Similarly, their amount for 24 servings should look less than the amount for 36 servings. While this is just an estimation, it can help students visualize their answers and catch mistakes.

Once students have finished, go over the answers as a class. Ask students what methods they used. Discuss as a class how the different methods all led to the same, correct answers. You may wish to challenge students by having them consider why different methods can lead to the same answer, since this may be surprising to some students. Encourage them to bring real-world baking ideas and experiences into their answers. For example, in practice, you don't always double the amounts of all ingredients when you want to double the number of servings.

Review the answers available on the Feeding Frenzy Answer Key. When you discuss Question 2, students should realize that you cannot purchase half a bag of chocolate chips. Therefore, the answers are 3 bags and 13 bags, not bags and bags. For Question 4, talk about the fact that when making such a large number of cookies, you may not have to make exactly that number. You can make more batter and either make the cookies a little bigger, or make extra cookies.

Assessment Options

1. Give students another recipe and ask them to find the amount of each ingredient needed for a different number of servings.
2. Allow students to bring in their own recipes for chocolate chip cookies. If possible, test the conversions by baking the cookies and comparing the results. Ask students to write a journal entry about the way math was applied in this lesson and the other skills that they needed or learned.

Extensions

1. Students could plan an entire dinner party for 12, complete with shopping list. Have students bring in recipes for the dishes they wish to prepare, and then adjust all the recipes to serve 12.
2. Many recipe websites can automatically adjust a recipe to the desired number of servings. Have students explore these recipes, and then write about how the conversions they did in class compare to those on the websites.
3. Have students convert all the units to the simplest form for a particular ingredient. For example, students should have found that tsp of vanilla is needed for 60 servings of chocolate chip cookies. Since 3 tsp =1 Tbsp, it would be easier to measure out 1 Tbsp + tsp of vanilla.
4. Students could convert all measurements into grams and other metric units, which are standard baking units in Europe, and then multiply the recipe for 300 servings. How does the process compare using different units? Which units are easier to calculate? Which units are easier to use when baking?

Questions for Students

1. Did you notice any shortcuts as you worked through the problems?

[Some students may have found that they could repeat their baking soda values for butter (and change the units), and repeat the egg values for vanilla extract. They may also have found that they could multiply their values for baking soda by 2 to get the values for eggs, and so on.]

2. Do you think the calculations would have been easier if you gave your answers in decimals? Why do you think cooking measurements are made in fractions?

[Answers will vary depending on students' comfort with fractions. There is no correct answer for why measurements are made this way—it is just a convention. In fact, in other areas of the world that use the metric system, decimals are used in recipes.]

3. What practical knowledge do you need to bake cookies? Is it enough to calculate the quantities of the ingredients?

[Answers will vary depending on students' knowledge of baking. Most students will easily understand why using of an egg is undesirable, but they may not realize that using a whole egg instead makes little difference in the recipe. Regardless, it should be clear to all students by the end of the lesson that more than math skills are necessary to bake a good batch of cookies.]

Teacher Reflection

• Did students work well on their own? Would they do better in pairs or groups?
• Did students understand the meaning of the proportion?
• Did students have a different way of working out the problem that was not mentioned here?
• Were students encouraged by the problem context? Were students who have no baking background discouraged?

### Learning Objectives

Students will:

• Use ratios and solve proportions.
• Combine math with practical knowledge to analyze a problem.

### NCTM Standards and Expectations

• Select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tools.
• Work flexibly with fractions, decimals, and percents to solve problems.
• Develop and analyze algorithms for computing with fractions, decimals, and integers and develop flue
• Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.