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Common Core State Standards

884 Unit 11 3-D Shapes, Weight, Volume, and Capacity

Advance PreparationIn preparation for the Liter and Milliliter Museum in Part 1, gather containers of various capacities. See

page 886 for more information.

For Part 1, you will also need a 1-liter pitcher filled with water, a milliliter of water held in an eyedropper

(20 drops), and 5 additional containers of varying capacities (under 2 liters).

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.

Teacher’s Reference Manual, Grades 4–6 pp. 13, 44–46, 216–218, 222–225, 233 –237

Key Concepts and Skills• Use division to solve conversion problems. 

[Operations and Computation Goal 4]

• Describe relationships among units

of capacity. 

[Measurement and Reference Frames Goal 3]

Key ActivitiesStudents review equivalencies between units

of capacity. They start a classroom Liter and

Milliliter Museum. Students compare

capacities by measuring.

Key Vocabularycup � pint � quart � gallon � capacity � liter �

milliliter

MaterialsMath Journal 2, pp. 305, 305A, and 305B

Student Reference Book, p. 137

Study Link 11�6

measuring cup � empty milk cartons (pint,

quart, 1

_ 2 gallon, gallon) � chart paper

(optional) � per group: 1 eyedropper,

1 liter pitcher, 1 graduated beaker, 2 liters of

water � slate � index cards � containers of

various capacities

Creating a Bar GraphMath Journal 2, p. 306

Student Reference Book, p. 302

Students create a bar graph to display

population data.

Ongoing Assessment: Informing Instruction See page 887.

Math Boxes 11�7Math Journal 2, p. 307

Students practice and maintain skills

through Math Box problems.

Ongoing Assessment: Recognizing Student Achievement Use Math Boxes, Problem 4. [Measurement and Reference Frames

Goal 3]

Study Link 11�7Math Masters, p. 334

Students practice and maintain skills

through Study Link activities.

READINESS

Estimating CapacityMath Masters, p. 389

empty containers of various sizes � pourable

substance, such as sand

Students sort containers according

to capacity.

EXTRA PRACTICE

5-Minute Math5-Minute Math™, p. 132

Students convert among customary units

of capacity.

ELL SUPPORT

Building a Math Word BankDifferentiation Handbook, p. 140

Students add the term capacity to their

Math Word Banks.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

� Capacity Objective To review units of capacity.

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Measuring CapacityLESSON

11� 7

Date Time

137

Math Message

1 pint = 2 cups

1 quart = 2 pints

1 half-gallon = 2 quarts

1 gallon = 4 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?

Units of Capacity

1. Circle the unit you would use to measure each amount.

A large jug of milk milliliters or liters

Water in a thimble milliliters or liters

A glass of juice milliliters or liters

Water in a water cooler milliliters or liters

Water in a fish tank milliliters or liters

Liquid in a paper cup milliliters or liters

A tank of gas milliliters or liters

A spoonful of oil milliliters or liters

A large bottle of water milliliters or liters

A can of soup milliliters or liters

2. Explain how you decided which unit to use for a can of soup.

Sample answer: I chose milliliters because most cans hold less than a liter.

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Math Journal 2, p. 305

Student Page

Lesson 11�7 885

Getting Started

10 ∗ 1

_ 2 = 5

18 ∗ 1

_ 6 = 3

36 ∗ 1

_ 9 = 4

10 ∗ 7

_ 10

= 7

12 ∗ 3

_ 4 = 9

24 ∗ 3

_ 8 = 9

7 ∗ 1

_ 2 = 3

1

_ 2

12 ∗ 1

_ 5 = 2

2

_ 5

6 ∗ 3

_ 8 = 2

1

_ 4

Mental Math and ReflexesPose problems involving the multiplication of a fraction by a whole number. Have students find each product in simplest form. Suggestions:

Adjusting the Activity

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASSDISCUSSION

(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.

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.

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.

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

ELL

ELL

Math Message Fill in the missing numbers in the Math Message problems at the top of journal page 305.

Study Link 11�6 Follow-Up Have partners compare answers and strategies. Ask volunteers to share the number sentences they wrote for Problems 9 and 10.

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886 Unit 11 3-D Shapes, Weight, Volume, and Capacity

Comparing CapacitiesLESSON

11�7

Date Time

1. Shade in the appropriate amount to show the capacity of each of your containers.

a. 2 L

1 L

Container

b. 2 L

1 L

Container

c.

2 L

1 L

Container

d. 2 L

1 L

Container

e.

2 L

1 L

Container

2. Use the conversion table above to solve the problems.

a. 6 qt = 12 pt b. 8000 mL = 8 L

c. 3 pt = 48 fl oz d. 6,450 mL = 6.450 L

e. 10 qt = 2 1 _

2 gal f. 500 mL = 0.500 L

g. 4 gal = 64 c h. 32 mL = 0.032 L

Answers vary.

Units of Capacity U.S. Customary Metric

1 gallon (gal) = 4 quarts (qt) 1,000 milliliter (mL) = 1 liter (L)

1 quart (qt) = 2 pints (pt) 1 milliliter (mL) = 1_1,000 liter (L)

1 pint (pt) = 2 cups (c)

1 pint (pt) = 16 fluid ounces (fl oz)

f. Circle the container

with the largest

capacity. Was your

prediction accurate?

305A-305B_EMCS_S_MJ2_G4_U11_576426.indd 305A 3/16/11 11:14 AM

Math Journal 2, p. 305A

Student Page

Date Time

Solve. You may draw pictures to help you.

1. Adaline filled her watering can with 1,250 mL of water.

After watering her plants she had 485 mL left.

How much water did she use?

2. Betty and Don spent the morning squeezing oranges

for juice. Betty squeezed 1 2 _ 4 L and Don squeezed 1

3

_ 4 L.

What is the total amount of juice?

3. There are 450 mL of syrup in 1 can. What is the

total amount of syrup in 6 cans?

4. Dimitra poured 2 _ 5 liter of water into a fish tank. William

poured 4 _ 5 liter of water into the fish tank.

a. How much more water did William pour? 2 _ 5 L

b. How many milliliters is that? 400 mL

5. Raina brought a 1,500 mL jug of water to the school

picnic. Her water jug has enough water to fill 5 glasses.

How much does each glass hold?

6. The teacher set out 24 bowls of glue for the students

to use for an art project. Each bowl holds 75 mL of glue.

How much glue did the teacher need to fill all the bowls?

Solving Capacity ProblemsLESSON

11�7 175

765 mL

L3 1 _ 4 or 3.250

2,700 mL

300 mL

1,800 mL

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Math Journal 2, p. 305B

Student Page

� Measuring Capacity in WHOLE-CLASS ACTIVITY

Metric Units(Math Journal 2, p. 305; Student Reference Book, p. 137)

Tell students that a liter is a metric unit of capacity. Liquids such as water, soft drinks, and fuel are often measured in liters. Smaller amounts of liquid are often measured in milliliters. Have students read Student Reference Book, page 137 and discuss the essay with a partner.

Review the relationship between liters and milliliters (1 liter = 1,000 milliliters). Show students the eyedropper and explain that it holds 20 drops of water, which is equivalent to 1 milliliter. Then show them the 1-liter pitcher and explain that this is 1 liter, or 1,000 milliliters. Explain that 1,000 eyedroppers full of water are needed to fill the 1-liter pitcher. Record the following number sentence on the board to illustrate the relationship between these two metric units:

1 liter (L) = 1,000 milliliters (mL)

Now have students complete journal page 305 to practice determining the appropriate unit for measuring capacity.

� Setting up a Liter and WHOLE-CLASS ACTIVITY

Milliliter MuseumIntroduce a project to explore a museum of objects that have different capacities measured in milliliters and liters. Use index cards to label objects in the museum with their capacities. The measuring tools available will determine the range of capacities. Keep a variety of measuring tools near the Liter and Milliliter Museum (for example, an eyedropper, liter pitcher, a measuring cup with a scale in mL, and graduated cylinders of various sizes) so students can measure a wide range of capacities.

Discuss the goals for the collection, the kinds of objects to be collected, and the procedures for adding objects to the museum.

The procedure for adding items should probably be managed by students. Ask students to bring in objects for the museum over the next week or two. This project will continue into the next unit. To ensure accuracy and to assess students’ skill in finding the capacity of different objects, require that every item added to the museum be measured by two or three students working independently.

This project will be revisited in Lesson 12-7.

� Comparing Capacity Using SMALL-GROUP ACTIVITY

Metric Measures(Math Journal 2, p. 305A)

Have students compare the capacity of 5 different size containers. Ask students to predict which containers have the largest and

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Ongoing Assessment: Recognizing Student Achievement

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]

Math Boxes

Problem 4 �

Math Boxes LESSON

11�7

Date Time

5. Add.

a. -46 + 20 =

b. -23 + (-18) =

c. 16 = 33 + (-17)

d. = $36.54 + (-$57.81)

e. -$131.09 + (-$76.98) =

6. If you travel at an average speed

of 50 miles per hour, how far will

you travel in

a. 3 hours? 150 miles

b. 1

_

2 hour? 25 miles

c. 2 1

_

2 hours? 125 miles

d. 5 3

_ 5 hours? 280 miles

1. What is the total number of cubes needed

to completely fill the box?

96 cubes

3. When you roll a 10-sided die, about what

fraction of the time would you expect a

multiple of 3 to come up?

3

_ 10

Use a probability term to describe the

likelihood of this event.

unlikely

81 129

47

2. Calculate the volume.

Number model:

Volume = 90 cm3

138138

9 cm

5 cm

2 cm

�

(9 ∗ 5) ∗ 2 = 90

4. Complete.

a. 321 cm = 3.21 m

b. 56 cm = 560 mm

c. 14 ft 4 in. = 172 in.

d. 2 mi = 10,560 ft

e. 5.3 km = 5,300 m

f. 4 mi = 7,040 yd

-26

-41

-$21.27

-$208.07

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Math Journal 2, p. 307

Student Page

Lesson 11�7 887

smallest capacities. Then have the students use various measuring tools and water to find and compare the capacities of the five containers and to determine if their predictions were correct. Students shade in the pitchers on journal page 305A to record the capacities. Encourage students to develop personal references for units of capacity as they make and check their predictions.

� Solving Capacity Number Stories PARTNER ACTIVITY

(Math Journal 2, p. 305B)

Have students solve the capacity number stories on journal page 305B.

2 Ongoing Learning & Practice

� Creating a Bar Graph INDEPENDENTACTIVITY

(Math Journal 2, p. 306; Student Reference Book, p. 302)

Students create a bar graph to display population data.

Ongoing Assessment: Informing Instruction

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.

� Math Boxes 11�7 INDEPENDENTACTIVITY

(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.

Largest Cities by PopulationLESSON

11�7

Date Time

10

12

14

16

18

20

22

24

26

28

30

32

34

36

Nu

mb

er

of

Pe

op

le (

in m

illio

ns)

Largest Cities by Population

Cities

Tokyo Mexico

City

New York

City

São

Paulo

Mumbai

(Bombay)

Calcutta Shanghai

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.

2. Make three statements comparing the cities in the bar graph.

Example: About 21 million more people live in Tokyo than in Shanghai.Sample answers: About the same number ofpeople 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 inTokyo as São Paulo.

76 302

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Math Journal 2, p. 306

Student Page

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888 Unit 11 3-D Shapes, Weight, Volume, and Capacity

� Study Link 11�7 INDEPENDENTACTIVITY

(Math Masters, p. 334)

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 Differentiation Options

READINESS SMALL-GROUP ACTIVITY

� Estimating Capacity 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.

11. -3 + 7 = 12. = 3 + (-7)

13. = 40 + (-80) 14. -60 + (-60) =

STUDY LINK

11�7 Capacity

137

Name Date Time

Container Capacity Measurements on Label

bottle of hot chili sesame oil 5 fl oz, 148 mL

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.

1. Less than 1 Pint Answers vary.

Complete.

5. 2 quarts = pints 6. 3 gallons = cups

7. pints = 4 cups 8. quarts = 12 cups

9. 6 pints = quarts 10. quarts = 2 1 _ 2 gallons103

48

32

4

2. 1 Pint

3. 1 Quart

4. More than 1 Quart

-120-40-44

Practice

Container Capacity Measurements on Label

bottle of cooking oil 16 fl oz, 473 mL

Container Capacity Measurements on Label

Container Capacity Measurements on Label

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Math Masters, p. 334

Study Link Master

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EXTRA PRACTICE SMALL-GROUP ACTIVITY

� 5-Minute Math 5–15 Min

To offer students more experience with units of capacity, see 5-Minute Math, page 132.

ELL SUPPORT SMALL-GROUP ACTIVITY

� Building a Math Word Bank 5–15 Min

(Differentiation Handbook, p. 140)

To provide language support for capacity, have students use the Word Bank Template found on Differentiation Handbook, page 140. 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

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