capacity: liter, milliliter, and cubic centimeter - login · pdf filecapacity: liter,...

www.everydaymathonline.com

eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

760 Unit 9 Coordinates, Area, Volume, and Capacity

Advance PreparationFor Part 1, you will need a 1-liter cube, a water-tight liter box, a 1-liter pitcher, and a measuring cup that shows 1 cup and 250 mL. Gather

a 1-liter bottle and other containers labeled with metric units of capacity. Make 2–4 copies of Math Masters, page 436 for each partnership.

For the optional Extra Practice activity in Part 3, obtain a copy of Room for Ripley by Stuart J. Murphy (HarperCollins, 1999).

Teacher’s Reference Manual, Grades 4–6 pp. 216 –218, 222–225

Key Concepts and Skills• Explore relationships between units of

length and units of capacity. Investigate

relationships and conversions between units

of capacity and volume. Describe patterns in

relationships between the dimensions and

volume of rectangular prisms.

[Measurement and Reference Frames Goal 3]

Key ActivitiesStudents verify that 1 L = 1,000 mL, a 1 L box

actually holds 1 L, and 1 L = 1,000 cm3.

They convert among units of volume and

capacity and relate the dimensions of a prism

to its volume.

Ongoing Assessment: Recognizing Student Achievement Use an Exit Slip (Math Masters, p. 414). [Measurement and Reference Frames Goal 3]

Ongoing Assessment: Informing Instruction See page 763.

Key Vocabularyliter (L) � capacity � quart (qt) � cup (c) �

milliliter (mL) � cubic centimeter � volume of

a container

MaterialsMath Journal 2, pp. 327–329

Study Link 9 �9

Student Reference Book, pp. 196 and 197

Math Masters, pp. 414 and 436

Class Data Pad (optional) � scissors �

transparent tape � slate � for demonstration:

1-liter cube, water-tight liter box, 1-liter pitcher,

measuring cup, base-10 flats or longs

Finding Areas of Rectangles with Fractional MeasuresMath Journal 2, p. 330

Students find the areas of rectangles

with fractional side lengths.

Math Boxes 9�10Math Journal 2, p. 331

Students practice and maintain skills

through Math Box problems.

Study Link 9�10Math Masters, p. 289

Students practice and maintain skills

through Study Link activities.

READINESS

Comparing the Capacity of Containersper group: 5 different-sized containers;

5 volume-measuring tools; macaroni,

centimeter cubes, or other small items

to fill containers

Students explore the concept of capacity

by comparing five different-sized containers.

EXTRA PRACTICE

Reading a Story about VolumeRoom for Ripley

Students explain how they would calculate

the volume of water needed to fill a fish tank.

ELL SUPPORT

Using Metric Prefix MultipliersStudent Reference Book, p. 396

Students use metric prefix multipliers

to name quantities.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

Capacity: Liter, Milliliter,and Cubic Centimeter

Objective To reinforce the relationships among the liter,

milliliter, and cubic centimeter.

��

Common Core State Standards

760_EMCS_T_TLG2_G5_U09_L10_576914.indd 760760_EMCS_T_TLG2_G5_U09_L10_576914.indd 760 3/23/11 2:50 PM3/23/11 2:50 PM

Lesson 9�10 761

Getting Started

1 Teaching the Lesson

▶ Math Message Follow-Up WHOLE-CLASSDISCUSSION

Survey students for their answers to the Math Message problem. Ask volunteers to explain their solution strategies. Then show students the 1-liter bottle, and remind them that the liter (L) is a metric unit of capacity. Ask volunteers to define capacity. Capacity is the amount a container can hold. Demonstrate that 1 liter is a little more than 1 quart (qt):

� Remind students that 1 quart equals 4 cups (c).

� Measure 1 cup of water with a measuring cup and pour it into the 1-liter pitcher. Do this four times. Show students that 4 cups or 1 quart of water does not reach the 1-liter level.

To support English language learners and students new to the United States who might not be familiar with the U.S. customary units of capacity, show the appropriate containers as these units are discussed.

▶ Demonstrating That 1 Liter WHOLE-CLASSDISCUSSION

Equals 1,000 MillilitersLiquids such as water, soft drinks, and fuel are often measured in liters. Smaller amounts of liquids are often measured in milliliters. Show students several containers whose labels give the capacity in milliliters (mL). Review the symbols for liter (L) and milliliter (mL). To support English language learners, distinguish between the use of a single letter to indicate a unit such as L for liter and the use of a single letter as a variable, such as in the formula A = l ∗ w.

ELL

ELL

Mental Math and Reflexes Have students record measurement equivalencies for units of capacity and volume on their slates. Suggestions:

3 gallons equals how many pints? 24 pints

40 cups equals how many gallons? 2 1

_ 2 gallons

3 quarts equals how many fluid ounces? 96 fluid ounces

5 liters equals how many milliliters? 5,000 milliliters

700 cm3 equals how many milliliters? 700 milliliters

650 milliliters equals how many cubic centimeters? 650 cm3

Math Message Which holds more, a 1-quart bottle or a 1-liter bottle? Be prepared to explain your answer.

Study Link 9�9 Follow-Up Have partners compare their answers and resolve any differences.

761-765_EMCS_T_TLG1_G5_U09_L10_576914.indd 761761-765_EMCS_T_TLG1_G5_U09_L10_576914.indd 761 2/15/11 7:01 PM2/15/11 7:01 PM

Math Journal 2, p. 327

Student Page


Student Page

Units of Volume and CapacityLESSON

9 �10

Date Time

In the metric system, units of length, volume, capacity, and weight are related.

� The cubic centimeter (cm3) is a metric unit of volume.

� The liter (L) and milliliter (mL) are units of capacity.

1. Complete.

a. 1 liter (L) � milliliters (mL).

b. There are cubic centimeters (cm3) in 1 liter.

c. So 1 cm3 � mL.

2. The cube in the diagram has sides

5 cm long.

a. What is the volume of the cube?

cm3

b. If the cube were filled with water,

how many milliliters would it hold?

mL

Complete.

4. 2 L � mL 5. 350 cm3 � mL 6. 1,500 mL � L

3. a. What is the volume of the rectangular

prism in the drawing?

cm3

b. If the prism were filled with water,

how many milliliters would it hold?

mL

c. That is what fraction of a liter?

L

10 cm

10 cm

5 cm

5 cm

5 cm

5 cm

1,000

1,000

1

125

125

2,000 350 1�12

�

500

500

�12

�

328

Units of Volume and Capacity continuedLESSON

9 �10

Date Time

7. One liter of water weighs about 1 kilogram (kg).

If the tank in the diagram above is filled with

water, about how much will the water weigh? About kg

In the U.S. customary system, units of length and capacity are not closely related.

Larger units of capacity are multiples of smaller units.

� 1 cup (c) � 8 fluid ounces (fl oz)

� 1 pint (pt) � 2 cups (c)

� 1 quart (qt) � 2 pints (pt)

� 1 gallon (gal) � 4 quarts (qt)

8. a. 1 gallon � quarts

b. 1 gallon � pints

9. a. 2 quarts � pints

b. 2 quarts � fluid ounces

10. Sometimes it is helpful to know that 1 liter is a little more than 1 quart. In the

United States, gasoline is sold by the gallon. If you travel in other parts of the

world, you will find that gasoline is sold by the liter. Is 1 gallon of gasoline more or

less than 4 liters of gasoline?

40 cm

50 cm

20 cm

40

48

464

Less than


� Demonstrate that there are 1,000 milliliters in 1 liter. Measure 250 milliliters of water with a measuring cup, and pour it into the 1-liter pitcher. Do this four times. Show students that the water reaches the 1-liter level.

Since 4 ∗ 250 mL = 1,000 mL, then 1 liter = 1,000 milliliters.

▶ Demonstrating That 1 Liter WHOLE-CLASSDISCUSSION

Equals 1,000 cm3

Model the relationship between 1 liter and 1,000 cubic centimeters:

� Demonstrate that a liter box actually holds 1 liter. Fill the 1-liter pitcher with water to the 1-liter level, and pour this into the liter box. Show students that the water is level with the top edge of the liter box. The liter box holds 1 liter of liquid.

� Demonstrate that a liter box holds 1,000 cubic centimeters. Count out and stack 10 flats (each 10 cm by 10 cm by 1 cm), or combine available flats with groups of 10 longs (each 10 cm by 1 cm by 1 cm) equivalent to 10 flats. Ask: What is the volume of the cube structure? 1,000 cm3 Next, fill the 1-liter box with the cube structure. Ask: How much does the 1-liter box hold? 1,000 cm3

Clarify that volume is the amount of space that a 3-dimensional object takes up. The volume of a container is a measure of how much the container will hold. The volume of a container that is filled with a liquid or a solid that can be poured is often called its capacity.

Capacity is usually measured in units such as gallons, quarts, pints, cups, fluid ounces, liters, and milliliters. These units of capacity are not cubic units, but liters and milliliters easily convert to cubic units.

Use questions similar to the following to summarize the discussions:

● 1 liter is equivalent to how many cubic centimeters? 1,000 cm3

● 1 liter is equivalent to how many milliliters? 1,000 milliliters

● What is the relationship between milliliters and cubic centimeters? 1 milliliter is equivalent to 1 cubic centimeter.

Write the following equivalencies on the board or on the Class Data Pad:

1 L = 1,000 mL

1 mL = 1 _ 1,000 liter

1 L = 1,000 cm3

1 mL = 1 cm3



Student Page

What are the dimensions of an open box—having the greatest possible volume—that

can be made out of a single sheet of centimeter grid paper?

1. Use centimeter grid paper to experiment until you discover a pattern. Record your

results in the table below.

2. What are the dimensions of the box with the greatest volume?

Height of box = cm Length of base = cm

Width of base = cm Volume of box = cm3

Open BoxesLESSON

9 �10

Date Time

Height of box Length of base Width of base Volume of box

1 cm 20 cm 14 cm 2 cm

3 cm

18 cm

16 cm

14 cm

12 cm

10 cm

8 cm

4 cm

5 cm

6 cm

7 cm

12 cm

10 cm

8 cm

6 cm

4 cm

2 cm

432 cm3

480 cm3

448 cm3

360 cm3

240 cm3

112 cm3

280 cm3

3

10

16

480

292-332_EMCS_S_G5_MJ2_U09_576434.indd 329 2/22/11 5:19 PM

Lesson 9�10 763

▶ Solving Problems about

INDEPENDENT ACTIVITY

Volume and Capacity(Math Journal 2, pp. 327 and 328)

Assign journal pages 327 and 328. Students convert between metric units of volume and capacity and between U.S. customary units of capacity.

Ongoing Assessment: Exit Slip �Recognizing Student Achievement

Use an Exit Slip (Math Masters, page 414) to assess students’ understanding of

the distinction between volume and capacity. Have students explain the difference

between volume and capacity, and have them list several examples of things that

would be measured in cubic centimeters and several examples of things that

would be measured in milliliters. Students are making adequate progress if they

reference liquids that can be poured as being measured in milliliters, or a unit of

capacity, and cubic centimeters as the measure of nonliquids, or the measure of

how much space is taken up or enclosed.

[Measurement and Reference Frames Goal 3]

▶ Exploring Volume PARTNER ACTIVITY

(Math Journal 2, p. 329; Student Reference Book,

pp. 196 and 197; Math Masters, p. 436)

Ask students to refer to the formulas for finding the volumes of rectangular prisms on pages 196 and 197 of the Student Reference Book, as needed. Ask volunteers to record the two formulas for finding the volume of a rectangular prism on the board.

V = l ∗ w ∗ h

V = B ∗ h

Pass out several copies of Math Masters, page 436 (1 cm Grid Paper) to each partnership. Partners first cut out a 16 cm by 22 cm section of grid paper. Then on journal page 329 they try to find the dimensions of the open box with the greatest possible volume that can be made out of that section of grid paper. Remind students of the open-box patterns they used on Activity Sheet 8 in Lesson 9-8 and the nets they made in the Part 3 activities of Lesson 9-9. Finally, they record their discovery in Problem 2.

PROBLEMBBBBBBBBBBBOOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBBBB MMMMMEEEMMBLEBLLELBLLLLBLEBLEBLEBLEBLEBLEBLEEEEMMMMMMMMMMMMMOOOOOOOOOOBBBBBLBLBLBLBLBLBLLLLLPROPROPROPROPROPROPROPROPROPROPROPRPRPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPRORORORROROROOOPPPPPPP MMMMMMMMMMMMMMMMMMMMMEEEEEEEEEEEEEEEELELELELEEEEEEEELLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRRPROBLEMSOLVING

BBBBBBBBBBBBBBBBBBB EEELEMMMMMMMMOOOOOOOOOBBBLBLBLBLBLBBBOOOOROROROROROROROROROO LELELELEEEEEELEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRGGGLLLLLLLLLLLLLVINVINVINVINNNNVINVINNVINVINVINVINVINVV GGGGGGGGGGGOOOOLOLOOLOOLOO VINVINVVLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVINNGGGGGGGGGGOOOLOLOLOLOLOLOOO VVLLLLLLLLLLVVVVVVVVOOSOSOOSOSOSOSOSOSOSOOSOSOSOSOOOSOOOSOSOSOSOSOSOSOOSOSOSOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVVVLLLLLLLVVVVVVVVVLVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSSSOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIIISOLVING

Ongoing Assessment: Informing Instruction

Watch for students who have difficulty

deciding how to cut the grid paper correctly to

make boxes. Suggest that they cut a 1 cm by

1 cm square out of each of the four corners

of the grid to make a pattern for an open box

that is 1 centimeter in height, then cut a 2 cm

by 2 cm square at each corner to make a

pattern for an open box that is 2 cm in height,

and so on.

Students use Math Masters, page 436 to find

the greatest possible volume of an open box.

761-765_EMCS_T_TLG2_G5_U09_L10_576914.indd 763761-765_EMCS_T_TLG2_G5_U09_L10_576914.indd 763 4/7/11 9:31 AM4/7/11 9:31 AM


Student Page

Areas of Rectangles with Fractional Side LengthsLESSON

9 � 10

Date Time

1. Imagine that you are going to tile the rectangle below with this unit square.

0 1 2 3 4 5 60

1

2

3

a. What fraction of a unit square is represented

by the tile at the right? unit square

b. How many unit squares are needed to tile the

large rectangle? unit squares

c. What are the dimensions of the large rectangle?

d. Find the area of the rectangle by using the area formula.

square units

Find the area of each rectangle.

2. 3. 4.

(unit) (unit) (unit)

5. Which has a larger area: A square that is 10 meters long on a side, or a rectangle

that is 10 1 _ 2 meters long and 9 1

_ 2 meters wide? Explain.

12 cm2

20 cm

13 ft3

710 ft5

34 in.

34 in.

1 _ 2

21

6 units by 3 1 _ 2 units

6 ∗ 3 1 _ 2 = 21

9 _ 16 in2 50 cm2 19 ft2

The square has a larger area. The area of the

square is 100 m2; the area of the rectangle

is 399

_ 4 , or 99 3 _ 4 m2.

292-332_EMCS_S_MJ2_G5_U09_576434.indd 330 4/6/11 11:01 AM

Math Boxes LESSON

9�10

Date Time

5. Use the graph to answer the questions.

a. Which month had the

most days of outside recess?

b. What was the total number

of days of outside recess?

1. Solve.

a. b.

c. d.

3. Monroe said that the least common

denominator for 5

_ 20 and 2

_ 3 was 60.

Is he correct?

Rename the fractions using

the least common denominator.

and

2. Complete the “What’s My Rule?” table,

and state the rule.

309.017

124.57

30.003Rule

÷8

in out

40 5 80 10

72 9

64 8

56 7

40.017

+ 269.000

377.33

402.03

- 24.70

590.32

- 465.75

24.303

+ 5.700

Sep Oct Nov DecMonth

Days ofOutside Recess

05

1015202530

Nu

mb

er

of

Da

ys

34–36

124

231 232

65

4. The table below shows the student

attendance for after school clubs at

Lincoln Elementary School.

Find the following landmarks for this data.

minimum: mode:

maximum: median:

range: mean:

119

Mon Tue Wed Thur Fri

35 25 30 24 24

24

Yes

24

25

27.6

35

September

65

11

15

_ 60

40

_ 60

292-332_EMCS_S_G5_MJ2_U09_576434.indd 331 2/22/11 5:19 PM


Student Page


2 Ongoing Learning & Practice

▶ Finding Areas of Rectangles


with Fractional Measures(Math Journal 2, p. 330)

Students find the areas of rectangles with fractional side lengths.

▶ Math Boxes 9�10


(Math Journal 2, p. 331)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 9-8. The skills in Problems 2 and 5 preview Unit 10 content.

Writing/Reasoning Have students write a response to the following: Explain how you found the least common denominator for Problem 3. Sample answer: I wrote the

multiples for 20 (20, 40, 60, and so on) until I found a number that was divisible by 3 (60).

Writing/Reasoning Have students write a response to the following: Explain the strategy you used to solve Problem 1d and the reasoning used. Answers vary.

▶ Study Link 9�10


(Math Masters, p. 289)

Home Connection Students complete a page that reviews plotting points and calculating area.

3 Differentiation Options

READINESS

SMALL-GROUP ACTIVITY

▶ Comparing the Capacity 15–30 Min

of ContainersTo explore the concept of capacity, have students compare the capacity of five different-sized containers. Ask students to predict which containers have the largest and smallest capacities. Then have students use fill material (macaroni, centimeter cubes) to compare the capacities of the five containers and to determine if their predictions were correct. Encourage students to continue to develop their personal references as they make and check their predictions.

761-765_EMCS_T_TLG2_G5_U09_L10_576914.indd 764761-765_EMCS_T_TLG2_G5_U09_L10_576914.indd 764 4/7/11 9:31 AM4/7/11 9:31 AM

STUDY LINK

9�10 Unit 9 Review

192 193208

Name Date Time

1. Plot 6 points on the grid below and connect them to form a hexagon.

List the coordinates of the points you plotted.

Find the area of the figures shown below.

Write the number model you used to

find the area.

2. 3.

Number model: Number model:

Area: Area:

(unit) (unit)

4. On the back of this page, explain how you solved Problem 3.

Answers vary.

�1�2�3�4�5 1 2 3 4 5

1

�1

�2

�3

�4

�5

2

4

3

5

0

7 cm

6 cm

A = 1

_ 2 ∗ 7 ∗ 6 A = 8 ∗ 6

21 cm2 48 in2

( , )

( , )

( , )

( , )

( , )

( , )0

4-5

-2

21

1 5

4-4

-3-5

Area of a rectangle: A = b ∗ h

Area of a parallelogram: A = b ∗ h

Area of a triangle: A = 1

_ 2 ∗ b ∗ h

Sample answers:

10 in.6 in

.

Perimeter = 36 in.

254-293_497_EMCS_B_MM_G5_U09_576973.indd 289 2/22/11 6:06 PM

Math Masters, p. 289

Study Link Master

Lesson 9�10 765

EXTRA PRACTICE

WHOLE-CLASS ACTIVITY

▶ Reading a Story about Volume 5–15 Min

Literature Link To explore volume, read the following book to the class. Explore the following question: How much water

does the fish tank hold? Discuss how students would calculate the volume of water in the fish tank.

Room for Ripley

Summary: This book follows a boy’s adventure to buy a fish and figure out how much water is needed in the fish tank.

ELL SUPPORT

SMALL-GROUP ACTIVITY

▶ Using Metric Prefix 5–15 Min

Multipliers(Student Reference Book, p. 396)

To support language development for metric measurement, have students look at the prefixes table on Student Reference Book, page 396. Ask questions similar to the following:

● If a cycle is a wheel, how many wheels does a unicycle have? A bicycle? A tricycle? One wheel; two wheels; three wheels

● How many angles does a quadrangle have? four

● How many sides does a pentagon have? A hexagon? A heptagon? A nonagon? 5 sides; 6 sides; 7 sides; 9 sides

● How many liters are in a kiloliter? A milliliter? 1,000 liters; 1 _ 1,000 liter

Encourage students to look for the prefixes in number names. Consider having students illustrate some of the words and prefixes that they discuss.


capacity: liter, milliliter, and cubic centimeter - login · pdf filecapacity: liter,...

Documents