Mandarin Orange Cake Recipes - Milwaukee Public Schools

HCPSS Worthwhile Math Task

Mandarin Orange Cake Recipes

Common Core Standard

7.RP.2a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table.

The Task

There is a recipe for Mandarin Orange Cake (Mandarin Orange Cake Recipe I) that serves 18 people. How would you modify the recipe in order to serve 72 people? Explain how you found your answer.

Facilitator Notes

1. Ask students the day before to bring in a copy of their favorite dessert recipe (or any recipe). Have students share what information is included on their recipe. Points should include prep/total time, number of servings, ingredients and the amount of each, steps to follow, etc.

2. Ask students how you would adjust a recipe if you are cooking for more or less people than what the original recipe serves. Students may suggest multiplying or dividing by a factor, and may bring up ratios and proportion. If not, ask students if they have ever had to double, triple, or halve a recipe.

3. Introduce the task to the students. Allow students time to read the task and review the Orange Mandarin Cake recipe.

4. Provide students with a variety of materials including but not limited to tables, graph paper, and graphing calculators.

5. Next, have students work in pairs or small groups to solve the problem. Have groups record their strategy.

6. As groups work, circulate to monitor what strategies are being used to solve the problem. Once groups have had an opportunity to solve the task, have groups compare solutions and strategies (either through a gallery walk, a jigsaw, or through group presentations).

7. 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. You may encourage them to set up a ratio chart.

Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

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Follow-Up Questions

1. Mandarin Orange Cake Recipe II serves 144 people. Figure out what the quantities for each ingredient will be if you want to serve 72 people and only 12 people. Explain your answer.

Extension Activity

1. You've decided to use the Mandarin Orange Cake Recipe III to make a cake that will serve 30 people. How much sugar will you need?

2. Choose 2 ingredients that are found in both recipes. Are the two ingredients used in the same ratio in both cakes? Explain.

3. In addition to dessert, students plan an entire dinner to serve 12. Students complete shopping list with all necessary ingredients. Students bring in recipes for the dishes they wish to prepare. Adjust all the recipes to serve 12.

Solutions

Mandarin Orange Cake Recipe I:

Strategy 1: The student may multiply everything by 4.

INGREDIENT

AMOUNT FOR

SERVINGS GIVEN: 18

Yellow cake

1

Eggs

4

Vegetable oil

1

Cans mandarin orange 11 oz

1

Containers frozen whipped

1

(20 ounce) cans crushed

1

pineapple with juice

(3.5 ounce) packages instant

1

vanilla pudding mix

AMOUNT FOR 72 SERVINGS Yellow cake (4) Eggs (16) Vegetable oil (4 cups) Cans mandarin orange 11 oz (4 cans) 4 (8 ounce) containers frozen whipped Topping, thawed 4 (20 ounce) cans crushed pineapple with juice 4 (3.5 ounce) packages instant vanilla pudding mix

Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

HCPSS Worthwhile Math Task

Strategy 2: The student may use a ratio table.

Ingredient Yellow Eggs Vegetable Cans

cake

oil

mandarin

orange 11

oz

New

4

16

4

4

ingredient

Containers frozen whipped

4

(20 ounce) cans crushed pineapple With juice

4

(3.5 ounce) packages instant vanilla Pudding mix

4

Original 1 ingredient

4

1

1

1

1

1

Mandarin Orange Cake Recipe II:

INGREDIENT

AMOUNT FOR SERVINGS GIVEN 144

AMOUNT FOR AMOUNT FOR 9

SERVINGS

SERVINGS

72

cups orange liqueur cups white sugar

3 cups orange liqueur 4 cups white sugar

1.5 orange liqueur 2cups white sugar

3/4cups orange liqueur 1/4cups white sugar

cups water

4 cups water

2 cups water 1/4 cups water

cups vegetable oil

4 cups vegetable oil 2 cups vegetable oil

1/4 cups vegetable oil

(11 ounce) cans mandarin oranges

eggs

12 (11 ounce) cans mandarin oranges

48 eggs

6 (11 ounce) cans mandarin oranges 24 eggs

3/4(11 ounce) cans mandarin oranges

3eggs

(18.25 ounce) packages yellow cake

12 (18.25 ounce)

6(18.25 ounce) 3/4 (18.25 ounce)

packages yellow cake packages yellow packages yellow

cake

cake

Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

HCPSS Worthwhile Math Task

Mandarin Orange Cake Recipe III Extension:

I set up a ratio table. For every 1 cup of sugar, you get 9 servings. I need 30 servings so I saw

that I would need between 3 and 4 cups of sugar. Since 3 cups will give me 27 servings, I need to

figure out how much I need for 3 additional servings. So, I took the original information of 9

servings and 1 cup and divided them by 3. So 3 servings needs 1/3 cup of sugar. 3 cups for 27

servings plus 1/3 cup for 3 servings will mean 3 1/3 cups for 30 servings.

+

=

Servings 9 18 27 36 3 30

Cups of Sugar

1

2

3

4

1/3

3 1/3

Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

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