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.
HCPSS Worthwhile Math Task
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
pineapple with juice
1
(3.5 ounce) packages instant
vanilla pudding mix
1
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
Containers (20 ounce)
cans
cake
oil
mandarin frozen
crushed
orange 11 whipped
pineapple
oz
With juice
(3.5
ounce)
packages
instant
vanilla
Pudding
mix
New
ingredient
4
16
4
4
4
4
4
Original
ingredient
1
4
1
1
1
1
1
Mandarin Orange Cake Recipe II:
INGREDIENT
AMOUNT FOR
SERVINGS
GIVEN 144
AMOUNT FOR
SERVINGS
72
AMOUNT FOR 9
SERVINGS
cups orange liqueur
3 cups orange liqueur
cups white sugar
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
12 (11 ounce) cans
mandarin oranges
3/4(11 ounce) cans
mandarin oranges
eggs
48 eggs
6 (11 ounce)
cans mandarin
oranges
24 eggs
(18.25 ounce)
packages yellow cake
12 (18.25 ounce)
packages yellow cake
3eggs
6(18.25 ounce)
3/4 (18.25 ounce)
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.