Objective
1
To review customary units of capacity.
materials
Teaching the Lesson
Key Activities
Students review equivalencies between units of capacity. They find the weight of one cup of
uncooked rice and use this information to estimate the weights of an average Thai and
Bangladeshi family’s annual rice consumption.
Key Concepts and Skills
•
•
•
•
Use division to solve conversion problems. [Operations and Computation Goal 4]
Round to the nearest whole number. [Operations and Computation Goal 6]
Estimate weight with and without tools. [Measurement and Reference Frames Goal 1]
Describe relationships among customary units of capacity.
[Measurement and Reference Frames Goal 3]
measuring cup
empty milk cartons (pint, quart,
1
gallon, gallon)
2
1
12 cups rice
1 gallon pourable substance (water,
sand, unpopped popcorn, or light
packing pellets)
scale (accurate to nearest ounce)
slate; chart paper
Key Vocabulary cup • pint • quart • gallon • capacity
2
Math Journal 2, p. 305
Study Link 11 6
materials
Ongoing Learning & Practice
Students create a bar graph to display population data.
Students practice and maintain skills through Math Boxes and Study Link activities.
Math Journal 2, pp. 306 and 307
Student Reference Book, p. 302
Study Link Master (Math Masters,
p. 334)
Ongoing Assessment: Informing Instruction See page 887.
Ongoing Assessment: Recognizing Student Achievement Use journal page 307.
[Measurement and Reference Frames Goal 3]
3
materials
Differentiation Options
READINESS
Students sort
containers according
to capacity.
ENRICHMENT
Students estimate
the number of
containers needed
to hold a quantity
of rice.
EXTRA PRACTICE
Students convert
among customary
units of capacity.
ELL SUPPORT
Students add
capacity to their
Math Word Banks.
Math Journal 2, p. 305
Teaching Aid Master (Math Masters,
p. 389)
Differentiation Handbook
5-Minute Math, p. 132
empty containers of various sizes;
empty copy-paper carton; measuring
cup; pourable substance, such as
sand; and calculator
See Advance Preparation
Additional Information
Advance Preparation For the optional Readiness activity in Part 3, identify several containers
by letter (A, B, C, …), designating a middle-size container as the target capacity.
884
Unit 11 3-D Shapes, Weight, Volume, and Capacity
Technology
Assessment Management System
Math Boxes, Problem 4
See the iTLG.
Getting Started
Mental Math and Reflexes
Have students write the greater of two integers on their slates. Suggestions:
11.5 or –11.2 11.5
–48.5 or 5.3 5.3
–2.98 or –2.89 –2.89
–24 or –240 –24
–103 or –130 –103
–65 or –605 –65
15 or –20 15
–3 or 1 1
45 or –62 45
Math Message
Study Link 11 6 Follow-Up
Fill in the missing numbers in the Math Message
problems at the top of journal page 305.
Have partners compare answers and strategies.
Ask volunteers to share the number sentences
they wrote for Problems 9 and 10.
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
(Math Journal 2, p. 305)
Display the cup, pint, quart, half-gallon, and gallon containers.
Ask students to identify each. Review the answers to the Math
Message. To support English language learners, have students
model the equivalencies by pouring water or another substance
from one container into the other.
Ask: Did anyone figure out the meaning of the picture next to the
Math Message problems? The “frame” is in the shape of the letter
G. It represents the word gallon. Inside the G, there are four Qs.
Each Q represents the word quart. Inside each Q, there are two
Ps. Each P represents the word pint. Inside each P, there are two
Cs. Each C represents the word cup.
Student Page
Date
Time
LESSON
11 7
Explain that cup, pint, quart, and gallon are units of capacity in
the U.S. customary system. Capacity is a measure of the amount
of liquid or other substance a container can hold. Capacity is a
type of volume measure. Tell students that the liter is a unit of
capacity in the metric system. A liter and a quart container will
hold approximately the same amount of liquid.
Converting Measurements
137
Math Message
1 pint 1 quart 1 half-gallon 1 gallon 2
2
2
4
cups
pints
quarts
quarts
Think: How can the picture above help you remember how many cups are in a pint,
how many pints are in a quart, and how many quarts are in a gallon?
Rice Consumption
1. Round your answer to the nearest ounce.
ELL
Adjusting the Activity
One cup of dry (uncooked) rice weighs about
b. 1 quart of rice weighs about
c. 1 gallon of rice weighs about
d. 1 gallon of rice weighs about
16 ounces.
32 ounces.
128 ounces.
8 pounds. (1 pound 16 ounces)
3. On average, a family of 4 in Bangladesh eats about 170 pounds of rice per month.
a. That is about how many pounds per year?
A U D I T O R Y
K I N E S T H E T I C
T A C T I L E
V I S U A L
ounces.
2. Use the answer in Problem 1 to complete the following:
a. 1 pint of rice weighs about
Have students create a poster of the gallon frame shown on journal
page 305 and display it as a reminder of equivalent capacities in the U.S.
customary system.
8
Answers vary
for Problem 1.
Answers for
Problems 2–5
assume that the
answer for
Problem 1 is
8 ounces.
b. How many gallons?
2,040
255
gallons
15
gallons
pounds
4. On average, a family of 4 in the United States
eats about 120 pounds of rice per year.
That is about how many gallons per year?
5. On average, a family of 4 in Thailand eats about
a. That is about how many gallons per year?
b. How many pounds?
1
3 2
gallons of rice per week.
182
1,456
gallons
pounds
305
Math Journal 2, p. 305
Lesson 11 7
885
Student Page
Date
Time
LESSON
Largest Cities by Population
11 7
76 302
1. Use the data in the Largest Cities by Population table at the top of Student Reference Book,
page 302 to complete the bar graph. Round each figure to the nearest million.
Finding the Weight
WHOLE-CLASS
ACTIVITY
of a Cup of Rice
(Math Journal 2, p. 305)
Largest Cities by Population
36
34
Number of People (in millions)
32
Tell students that in this lesson they will apply their knowledge
of capacity and weight to compare the consumption of rice in
Bangladesh, the United States, and Thailand. Ask:
30
28
26
24
22
20
18
16
14
12
●
How would you measure rice if you needed a certain amount
for a recipe? Probably with a measuring cup
●
How would you find the weight of one cup of uncooked rice?
Sample answer: Weigh an empty measuring cup. Fill it with
rice to the 1-cup level. Weigh the filled cup. Subtract the weight
of the empty cup from the weight of the cup containing rice.
●
About how many ounces do you think a cup of uncooked rice
weighs? (Record a few estimates on the board.)
10
Tokyo
Mexico
City
New York
City
São
Paulo
Mumbai
(Bombay)
Calcutta
Shanghai
Cities
2. Make three statements comparing the cities in the bar graph.
Example:
A bout 21 million more people live in Tokyo than in Shanghai.
Sample answers: About the same number of
people live in Mexico City and New York City;
about 1 million more people live in São Paulo
than Mumbai; about twice as many people live in
Tokyo as São Paulo.
Ask two students to weigh 1 cup of rice as accurately as they can.
1
1
Expect a range of 72 to 82 ounces for 1 cup. Have the class round
the result to the nearest ounce and record it in Problem 1 on
journal page 305.
306
Math Journal 2, p. 306
Solving Problems Involving
PARTNER
ACTIVITY
Units of Weight and Capacity
(Math Journal 2, p. 305)
Students use the weight of 1 cup of rice to solve Problems 2–5
on journal page 305. These problems involve conversions between
gallons and pounds. After a few minutes, bring the class together
to go over the answers.
Student Page
World Tour
Fascinating Facts
Smallest Countries by Population
Country
Area (sq miles)
Population
Vatican City
0.17
900
Largest Cities by Population
City, Country
Population
Tokyo, Japan
34,450,000
Tuvalu
10
11,000
Mexico City, Mexico
Nauru
8
13,000
New York City, U.S.
17,846,000
Palau
177
20,000
Sao Paulo, Brazil
17,099,000
24
28,000
Mumbai (Bombay), India
32,000
Calcutta, India
13,058,000
33,000
Shanghai, China
12,887,000
San Marino
Monaco
0.75
Liechtenstein
62
18,066,000
16,086,000
Languages with the Most Speakers
Speakers
Language
(in millions)
Countries
Chinese
873
Spanish
322
43
English
309
107
180
17
Hindi
16
Portuguese
177
Bengali
171
9
Russian
145
31
Japanese
122
25
Country
Taiwan
33
Cellular Telephone Use
Number of Cellular
Telephone Subscriptions
(in millions)
25.1
Luxembourg
Italy
Iceland
1
110.8
0.5
106.1
101.8
96.6
6.3
95.5
Spain
37.5
91.6
United Kingdom
49.7
84.1
Greece
8.9
78.0
Japan
86.7
68.0
Canada
Turkey
South Africa
World
Problem 5: A family of 4 in Thailand eats about 32 gallons of
rice per week. That is equivalent to 182 gallons per year. To find
the weight of the rice consumed, multiply 182 by 8. 1,456 pounds
Subscriptions
per 100 People
Israel
United States
Problem 3: A family of 4 in Bangladesh eats about 170 pounds
of rice per month. That is equivalent to 2,040 pounds per year.
To find the number of gallons, divide the total weight by 8.
2,040 8 255 gallons
Problem 4: 120 8 15 gallons
55.9
0.3
Problem 2: Assuming that 1 cup of uncooked rice weighs about
8 ounces, then 1 pint weighs about 16 ounces; 1 quart about
32 ounces; and 1 gallon about 128 ounces. Because there are
16 ounces in 1 pound, 128 ounces is equivalent to 8 pounds
(128 16 8). You can use the same procedure if 1 cup of rice
is found to weigh about 7 ounces. Then 1 gallon would weigh
about 7 pounds.
158.7
54.3
13.2
41.7
27.9
40.8
16.9
36.4
1,340.7
21.9
Taiwan has the highest
subscription rate for
cellular telephone use
of all countries.
Student Reference Book, p. 302
886
Unit 11 3-D Shapes, Weight, Volume, and Capacity
Student Page
Date
2 Ongoing Learning & Practice
Time
LESSON
Math Boxes
11 7
1. What is the total number of cubes needed
2. Calculate the volume.
to completely fill the box?
96
Creating a Bar Graph
2 cm
cubes
5 cm
INDEPENDENT
ACTIVITY
9 cm
Number model:
(Math Journal 2, p. 306; Student Reference Book, p. 302)
(9 5) 2 90
90
Volume cm3
138
Students create a bar graph to display population data.
3. When you roll a 10-sided die, about what
fraction of the time would you expect a
multiple of 3 to come up?
138
4. Complete.
b. 56 cm c.
Use a probability term to describe the
likelihood of this event.
Ongoing Assessment: Informing Instruction
d.
unlikely
e.
Watch for students who make incorrect statements for Problem 2, such as
“About twice as many people live in New York City as Calcutta.” Point out that
the vertical scale for the number of people in each city begins at 10 million. The
bar for New York City may be twice the height of the bar for Calcutta, but the
population of New York City is approximately 18 million, and the population of
Calcutta is approximately 13 million.
f.
81
5. Add.
a.
b.
3.21 m
560 mm
172 in.
14 ft 4 in. 2 mi 10,560 ft
5.3 km 5,300 m
4
mi 7,040 yd
a. 321 cm 3
10
129
6. If you travel at an average speed
26
41
23 (18) of 50 miles per hour, how far will
you travel in
46 20 16
c.
150 miles
25 miles
hours? 125 miles
hours? 280 miles
a. 3 hours?
1
b. 2 hour?
33 (17)
d.
$21.27 $36.54 ($57.81)
1
c. 2 2
e.
$131.09 ($76.98) $208.07
3
d. 5 5
47
307
Math Boxes 11 7
INDEPENDENT
ACTIVITY
Math Journal 2, p. 307
(Math Journal 2, p. 307)
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 11-5. The skill in Problem 6
previews Unit 12 content.
Ongoing Assessment:
Recognizing Student Achievement
Math Boxes
Problem 4
Use Math Boxes, Problem 4 to assess students’ ability to describe the
relationships among U.S. customary units of length and among metric units
of length. Students are making adequate progress if they are able to complete
the equivalencies correctly. Some students may include number models to
explain their work.
[Measurement and Reference Frames Goal 3]
Study Link Master
Name
Date
STUDY LINK
Time
Capacity
11 7
Find at least one container that holds each of the amounts listed below.
Describe each container and record all the capacity measurements on the label.
Study Link 11 7
1.
INDEPENDENT
ACTIVITY
Less than 1 Pint
137
Answers vary.
Container
Capacity Measurements on Label
bottle of hot chili sesame oil
5 fl oz, 148 mL
(Math Masters, p. 334)
2.
Home Connection Students find containers that hold
less than 1 pint, 1 pint, 1 quart, and more than 1 quart.
They solve problems about equivalent capacities.
3.
4.
1 Pint
Container
Capacity Measurements on Label
bottle of cooking oil
16 fl oz, 473 mL
1 Quart
Container
Capacity Measurements on Label
More than 1 Quart
Container
Capacity Measurements on Label
Complete.
5.
2 quarts 7.
2
9.
6 pints 4
pints
pints 4 cups
3
quarts
6.
3 gallons 3
10
8.
10.
Practice
11.
13.
3 7 40
4
40 (80)
14.
cups
1
quarts 2 2 gallons
4
12.
48
quarts 12 cups
3 (7)
60 (60) 120
Math Masters, p. 334
Lesson 11 7
887
3 Differentiation Options
READINESS
Estimating Capacity
SMALL-GROUP
ACTIVITY
5–15 Min
(Math Masters, p. 389)
To explore capacity, have students sort empty containers
(identified by letter) according to whether they will hold more
than, less than, or about the same as a target container. Ask
students to label three columns on an Exit Slip (Math Masters,
page 389) more than, less than, and about the same. Have them
sort the containers according to the categories.
Provide students with a pourable substance such as sand, rice,
pasta, or beans to check their estimates. Have students rearrange
the groups as necessary.
ENRICHMENT
Modeling the Capacity of
SMALL-GROUP
ACTIVITY
30+ Min
Annual Rice Consumption
(Math Journal 2, p. 305)
To apply students’ understanding of capacity, have them
estimate how many empty copy-paper cartons would be
needed to hold a year’s supply of rice for an average
Thai family of four. A family of four eats about 182 gallons, or
1,456 pounds, of uncooked rice per year, assuming that 1 gallon
of rice weighs about 8 pounds.
Display an empty copy-paper carton. Ask students to estimate
about how many cartons of this size would be needed to store all
of the rice.
Student Page
Date
Time
LESSON
11 7
Converting Measurements
137
Write students’ estimates on the board. Then ask students to
propose a method for checking their estimates.
Math Message
1 pint 1 quart 1 half-gallon 1 gallon 2
2
2
4
cups
pints
quarts
quarts
Think: How can the picture above help you remember how many cups are in a pint,
how many pints are in a quart, and how many quarts are in a gallon?
Rice Consumption
1. Round your answer to the nearest ounce.
One cup of dry (uncooked) rice weighs about
8
ounces.
2. Use the answer in Problem 1 to complete the following:
a. 1 pint of rice weighs about
b. 1 quart of rice weighs about
c. 1 gallon of rice weighs about
d. 1 gallon of rice weighs about
Answers vary
for Problem 1.
Answers for
Problems 2–5
assume that the
answer for
Problem 1 is
8 ounces.
16 ounces.
32 ounces.
128 ounces.
8 pounds. (1 pound 16 ounces)
3. On average, a family of 4 in Bangladesh eats about 170 pounds of rice per month.
a. That is about how many pounds per year?
b. How many gallons?
2,040
255
gallons
15
gallons
pounds
4. On average, a family of 4 in the United States
eats about 120 pounds of rice per year.
That is about how many gallons per year?
5. On average, a family of 4 in Thailand eats about
a. That is about how many gallons per year?
b. How many pounds?
1
3 2
The most obvious approach is to find about how many pounds
a copy-paper carton of rice weighs and divide the number of
pounds of rice consumed in a year by the weight of a carton of
rice. But this is not practical, because you would need a large
quantity of rice to fill the carton.
Another way is to find about how many gallons a copy-paper
carton holds. Then divide the number of gallons of rice
consumed in a year by the number of gallons a carton holds.
1
Use any pourable substance to fill the carton to about 6 of
its height, measure the material with a measuring cup, and
multiply the result by 6. Divide by 16 to convert the answer
to gallons.
gallons of rice per week.
182
1,456
gallons
pounds
305
Math Journal 2, p. 305
888
Unit 11 3-D Shapes, Weight, Volume, and Capacity
Once the capacity of a carton has been determined, encourage
students to estimate the number of cartons needed to hold the
total yearly consumption of rice. Students can check their
estimates on their calculators. Have students present their
strategies and solutions in a brief report. Sample answer: The
1
capacity of a carton of copy paper is about 72 gallons. This means
that 4 cartons hold about 30 gallons and that 24 cartons hold
about 180 gallons.
EXTRA PRACTICE
5-Minute Math
SMALL-GROUP
ACTIVITY
5–15 Min
To offer students more experience with units of capacity, see
5-Minute Math, page 132.
ELL SUPPORT
Building a Math Word Bank
SMALL-GROUP
ACTIVITY
5–15 Min
(Differentiation Handbook)
To provide language support for capacity, have students use the
Word Bank Template found in the Differentiation Handbook. Ask
students to write the term capacity, draw pictures relating to the
term, and write other related words. See the Differentiation
Handbook for more information.
Lesson 11 7
889