Making Punch
Student Text
Making Punch
Ratios, Rates, and
Mixture Problems
Workshop Resources • Course 1 • Course 2 • Course 3
Learning Goals
In this lesson, you will:
 Use ratios to make comparisons.
 Use rates and proportions to solve mixture problems.
D
o you like smoothies? Perhaps one of the best things about smoothies is that
you can make one with just about any ingredients. Just throw them in the blender
and turn it on!
Smoothies can be very healthy too. Try this healthy smoothie recipe sometime.
●
1 banana
●
1 cup of vanilla yogurt
●
1 cup of grapes
●
© 2011 Carnegie Learning
Copyright © 2014 Carnegie Learning, Inc.
●
1
__
2
of an apple
2 cups of spinach leaves
If this recipe serves 3 people, how much of each ingredient would you need to
make smoothies your whole class?
1.2
Ratios, Rates, and Mixture Problems
•
15
Course 2
MS_Participant_Handbook.indd 155
155
4/15/14 3:10 PM
Making Punch
Student Text
CONT’D
Problem 1
May the Best Recipe Win
Each year, your class presents its mathematics portfolio to parents and community
members. This year, your homeroom is in charge of the refreshments for the reception that
follows the presentations. Four students in the class give their recipes for punch. The
class wants to analyze the recipes to determine which will make the punch with the
strongest grapefruit flavor, and which will make the strongest lemon-lime soda flavor.
The recipes are shown.
Bobbi’sRecipe
Adam’sRecipe
4 parts lemon-lime soda
3 parts lemon-lime soda
8 parts grapefruit juice
5 parts grapefruit juice
Zeb’sRecipe
Carlos’sRecipe
2 parts lemon-lime soda
1 part lemon-lime soda
3 parts grapefruit juice
4 parts grapefruit juice
1.How many total parts are in each person’s recipe?
2.For each recipe, write a ratio that compares the number of parts of grapefruit juice to
the total number of parts in each recipe. If possible, simplify each rate.
Bobbi’s recipe:
Carlos’s recipe:
16
156
•
Chapter 1
Ratios and Rates
Copyright © 2014 Carnegie Learning, Inc.
Zeb’s recipe:
© 2011 Carnegie Learning
Adam’s recipe:
Course 2
MS_Participant_Handbook.indd 156
4/15/14 3:10 PM
3.Which recipe will make the punch with the strongest grapefruit taste? Explain how
you determined your answer.
Workshop Resources • Course 1 • Course 2 • Course 3
4.For each recipe, write a rate that compares the number of parts of lemon-lime soda to
the total number of parts in each recipe. If possible, simplify each rate.
Adam’s recipe:
Bobbi’s recipe:
Carlos’s recipe:
Zeb’s recipe:
5.Which recipe will make the punch with the strongest lemon-lime soda flavor?
© 2011 Carnegie Learning
Copyright © 2014 Carnegie Learning, Inc.
Explain how you determined your answer.
1.2
Ratios, Rates, and Mixture Problems
•
17
Course 2
MS_Participant_Handbook.indd 157
157
4/15/14 3:10 PM
Making Punch
Student Text
CONT’D
Problem 2
Making the Refreshments
1.You are borrowing glasses from the cafeteria to serve the punch. Each glass holds
6 fluid ounces of punch. Your class expects that 70 students and 90 parents and
community members will attend the reception. You decide to make enough punch so
that every person who attends can have one glass of punch. How many fluid ounces
of punch will you need for the reception?
Previously, you wrote rates to compare parts of each ingredient to total parts of all the
ingredients. Recall that a rate is a ratio in which the units of the parts or the whole being
compared are different.
2.Determine the unit rate for the fluid ounces of punch there would be in one part of the
recipe if your class uses Adam’s recipe.
3.How many fluid ounces of lemon-lime soda and grapefruit juice are needed to make
18
158
•
Chapter 1
Ratios and Rates
Copyright © 2014 Carnegie Learning, Inc.
© 2011 Carnegie Learning
enough punch if your class uses Adam’s recipe? Show all your work.
Course 2
MS_Participant_Handbook.indd 158
4/15/14 3:10 PM
4.How many fluid ounces of lemon-lime soda and grapefruit juice are needed to make
enough punch if your class uses Bobbi’s recipe? Show all your work.
Workshop Resources • Course 1 • Course 2 • Course 3
5.How many fluid ounces of lemon-lime soda and grapefruit juice are needed to make
© 2011 Carnegie Learning
Copyright © 2014 Carnegie Learning, Inc.
enough punch if your class uses Carlos’s recipe? Show all your work.
1.2
Ratios, Rates, and Mixture Problems
•
19
Course 2
MS_Participant_Handbook.indd 159
159
4/15/14 3:10 PM
Making Punch
Student Text
CONT’D
6.How many fluid ounces of lemon-lime soda and grapefruit juice are needed to make
enough punch for the reception if your class uses Zeb’s recipe? Show all your work.
7.Complete the table with the calculations you determined for each person’s recipe.
Amount of
Lemon-Lime
Soda
(fluid ounces)
Amount of
Grapefruit
Juice
(fluid ounces)
Total Amount
of Punch
(fluid ounces)
Adam’s recipe
Carlos’s recipe
Zeb’s recipe
160
•
Chapter 1
Ratios and Rates
Copyright © 2014 Carnegie Learning, Inc.
20
© 2011 Carnegie Learning
Bobbi’s recipe
Course 2
MS_Participant_Handbook.indd 160
4/15/14 3:10 PM
8.In Problem 1, Question 3 you determined which recipe would have the strongest
grapefruit flavor? How does the table confirm your choice?
Workshop Resources • Course 1 • Course 2 • Course 3
9.In Problem 1, Question 5 you determined which recipe would have the strongest
lemon-lime soda flavor? How does the table confirm your choice?
10. If you would use 8-ounce glasses for the reception rather than 6-ounce glasses, how
would that affect the amount of punch you would need to make?
© 2011 Carnegie Learning
Copyright © 2014 Carnegie Learning, Inc.
11. Will the ratio of the parts for any of the recipes change by putting more punch in each
glass? Explain your reasoning.
1.2
Ratios, Rates, and Mixture Problems
•
21
Course 2
MS_Participant_Handbook.indd 161
161
4/15/14 3:10 PM
Making Punch
Student Text
CONT’D
Talk the Talk
1.Explain how ratios and rates helped you solve the problems in this lesson.
22
162
•
Chapter 1
Ratios and Rates
Copyright © 2014 Carnegie Learning, Inc.
© 2011 Carnegie Learning
Be prepared to share your solutions and methods.
Course 2
MS_Participant_Handbook.indd 162
4/15/14 3:10 PM