Capacity: Liter, Milliliter, and Cubic Centimeter

Capacity: Liter, Milliliter,
and Cubic Centimeter
Objective To reinforce the relationships among the liter,
milliliter, and cubic centimeter.
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Teaching the Lesson
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 Activities
Students 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.
Family
Letters
Assessment
Management
Common
Core State
Standards
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
Students practice and maintain skills
through Math Box problems.
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Comparing the Capacity of Containers
per 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
Study Link 9 10
Reading a Story about Volume
Math Masters, p. 289
Students practice and maintain skills
through Study Link activities.
Room for Ripley
Students explain how they would calculate
the volume of water needed to fill a fish tank.
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.
ELL SUPPORT
Using Metric Prefix Multipliers
Student Reference Book, p. 396
Students use metric prefix multipliers
to name quantities.
Key Vocabulary
liter (L) capacity quart (qt) cup (c) milliliter (mL) cubic centimeter volume of
a container
Materials
Math 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
Advance Preparation
For 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
760
Unit 9
Coordinates, Area, Volume, and Capacity
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Getting Started
Mental Math and Reflexes
Math Message
Have students record measurement equivalencies for units of
capacity and volume on their slates. Suggestions:
Which holds more, a 1-quart bottle or a
1-liter bottle? Be prepared to explain your answer.
3 gallons equals how many pints? 24 pints
1
gallons
40 cups equals how many gallons? 2_
2
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
Study Link 9 9 Follow-Up
Have partners compare their answers and
resolve any differences.
1 Teaching the Lesson
▶ Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
ELL
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
Equals 1,000 Milliliters
WHOLE-CLASS
DISCUSSION
ELL
Liquids 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.
Lesson 9 10
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Student Page
Date
Time
LESSON
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.
Units of Volume and Capacity
9 10
䉬
In the metric system, units of length, volume, capacity, and weight are related.
3
䉬 The cubic centimeter (cm ) is a metric unit of volume.
䉬 The liter (L) and milliliter (mL) are units of capacity.
1.
Complete.
1 liter (L) b.
There are
c.
2.
Since 4 ∗ 250 mL = 1,000 mL, then 1 liter = 1,000 milliliters.
1,000 milliliters (mL).
1,000 cubic centimeters (cm ) in 1 liter.
1 mL.
So 1 cm a.
3
3
The cube in the diagram has sides
5 cm long.
3. a.
What is the volume of the rectangular
prism in the drawing?
500
▶ Demonstrating That 1 Liter
Equals 1,000 cm3
cm3
5 cm
5 cm
WHOLE-CLASS
DISCUSSION
5 cm
10 cm
a.
What is the volume of the cube?
125
cm3
Model the relationship between 1 liter and 1,000 cubic centimeters:
5 cm
10 cm
b.
If the cube were filled with water,
how many milliliters would it hold?
125
b.
mL
500
c.
mL
That is what fraction of a liter?
1
2
L
Complete.
4.
2L
2,000mL
5.
350 cm3 350
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.
If the prism were filled with water,
how many milliliters would it hold?
mL
6.
1,500 mL 112
L
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
Math Journal 2, p. 327
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.
Student Page
Date
Time
LESSON
9 10
䉬
7.
Units of Volume and Capacity
continued
One liter of water weighs about 1 kilogram (kg).
50 cm
20 cm
40 cm
If the tank in the diagram above is filled with
water, about how much will the water weigh? About
40
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.
䉬 1 cup (c) 8 fluid ounces (fl oz)
䉬 1 pint (pt) 2 cups (c)
䉬 1 quart (qt) 2 pints (pt)
䉬 1 gallon (gal) 4 quarts (qt)
8. a.
1 gallon b.
1 gallon 9. a.
2 quarts b.
2 quarts 10.
4
8
4
64
quarts
pints
pints
fluid ounces
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?
Less than
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 liter
1 mL = _
1,000
1 L = 1,000 cm3
1 mL = 1 cm3
328
Math Journal 2, p. 328
762
Unit 9
Coordinates, Area, Volume, and Capacity
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Student Page
▶ Solving Problems about
INDEPENDENT
ACTIVITY
Volume and Capacity
Date
Time
LESSON
9 10
Open Boxes
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?
(Math Journal 2, pp. 327 and 328)
1.
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:
Recognizing Student Achievement
Exit Slip
[Measurement and Reference Frames Goal 3]
Height of box
Length of base
Width of base
Volume of box
1 cm
20 cm
14 cm
2 cm
18 cm
16 cm
14 cm
12 cm
10 cm
8 cm
12 cm
10 cm
8 cm
6 cm
4 cm
2 cm
280 cm3
432 cm3
480 cm3
448 cm3
360 cm3
240 cm3
112 cm3
3 cm
4
5
6
7
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.
Use centimeter grid paper to experiment until you discover a pattern. Record your
results in the table below.
2.
cm
cm
cm
cm
What are the dimensions of the box with the greatest volume?
Height of box =
Width of base =
3
10
cm
Length of base =
cm
Volume of box =
16
480
cm
cm3
Math Journal 2, p. 329
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▶ Exploring Volume
2/22/11 5:19 PM
PARTNER
ACTIVITY
(Math Journal 2, p. 329; Student Reference Book,
pp. 196 and 197; Math Masters, p. 436)
PROBLEM
PR
PRO
P
RO
R
OBL
BLE
B
L
LE
LEM
EM
SO
S
SOLVING
OL
O
L
LV
VIN
V
ING
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.
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.
Lesson 9 10
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Student Page
Date
Time
LESSON
2 Ongoing Learning & Practice
Areas of Rectangles with Fractional Side Lengths
9 10
1.
Imagine that you are going to tile the rectangle below with this unit square.
3
2
▶ Finding Areas of Rectangles
1
0
0
a.
1
2
3
4
5
6
2
unit square
21
unit squares
by the tile at the right?
b.
with Fractional Measures
_1
What fraction of a unit square is represented
How many unit squares are needed to tile the
large rectangle?
c.
What are the dimensions of the large rectangle?
d.
Find the area of the rectangle by using the area formula.
(Math Journal 2, p. 330)
6 units by 3_12 units
6 ∗ 3_12 = 21
Students find the areas of rectangles with fractional side lengths.
square units
Find the area of each rectangle.
2.
3
4
3.
in.
4.
20 cm
▶ Math Boxes 9 10
7
5 10
ft
2 12 cm
3
4
in.
3 13 ft
9
_
2
16 in
2
INDEPENDENT
ACTIVITY
(Math Journal 2, p. 331)
2
50 cm
(unit)
5.
INDEPENDENT
ACTIVITY
19 ft
(unit)
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.
(unit)
Which has a larger area: A square that is 10 meters long on a side, or a rectangle
1
1
_
that is 10_
2 meters long and 9 2 meters wide? Explain.
The square has a larger area. The area of the
square is 100 m2; the area of the rectangle
399
_3 2
is _
4 , or 99 4 m .
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).
Math Journal 2, p. 330
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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
INDEPENDENT
ACTIVITY
(Math Masters, p. 289)
Home Connection Students complete a page that reviews
plotting points and calculating area.
Student Page
Date
Time
LESSON
Math Boxes
9 10
1.
2.
Solve.
a.
309.017
c.
b.
40.017
+ 269.000
d.
377.33
÷8
590.32
- 465.75
124.57
34–36
3.
231 232
4.
Monroe said that the least common
5
_2
denominator for _
20 and 3 was 60.
Is he correct?
in
Rule
30.003
402.03
- 24.70
Yes
Rename the fractions using
the least common denominator.
15
40
_
_
60
60
and
out
40
5
80
10
72
64
8
56
7
9
▶ Comparing the Capacity
Mon
Tue
Wed
Thur
Fri
35
25
30
24
24
What was the total number
of days of outside recess?
To 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.
24
median: 25
mean: 27.6
119
September
65
Days of
Outside Recess
Number of Days
b.
15–30 Min
of Containers
mode:
65
Use the graph to answer the questions.
Which month had the
most days of outside recess?
SMALL-GROUP
ACTIVITY
Find the following landmarks for this data.
24
maximum: 35
range: 11
a.
READINESS
The table below shows the student
attendance for after school clubs at
Lincoln Elementary School.
minimum:
5.
3 Differentiation Options
Complete the “What’s My Rule?” table,
and state the rule.
24.303
+ 5.700
30
25
20
15
10
5
0
Sep Oct Nov Dec
Month
124
Math Journal 2, p. 331
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Unit 9
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Coordinates, Area, Volume, and Capacity
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Study Link Master
EXTRA PRACTICE
▶ Reading a Story about Volume
WHOLE-CLASS
ACTIVITY
Name
5–15 Min
1.
Date
STUDY LINK
9 10
Time
Unit 9 Review
Plot 6 points on the grid below and connect them to form a hexagon.
List the coordinates of the points you plotted. Sample answers:
5
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.
-5 , -3 )
-4 , 4 )
( 1 , 5 )
( 1 , 2 )
( 4 , -2 )
( 0 , -5 )
4
(
3
(
2
1
⫺5 ⫺4 ⫺3 ⫺2 ⫺1 0
⫺1
192 193
208
1
2
3
4
5
⫺2
⫺3
⫺4
⫺5
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.
Find the area of the figures shown below.
Write the number model you used to
find the area.
Area of a rectangle: A = b ∗ h
Area of a parallelogram: A = b ∗ h
1
Area of a triangle: A = _2 ∗ b ∗ h
3.
7
Perimeter = 36 in.
Number model:
5–15 Min
Multipliers
(Student Reference Book, p. 396)
in.
cm
▶ Using Metric Prefix
10
6
ELL SUPPORT
6 in.
cm
2.
SMALL-GROUP
ACTIVITY
Area:
=
A
_1
2
∗7∗6
2
21 cm
Number model:
Area:
(unit)
4.
A
=
8∗6
48 in2
(unit)
On the back of this page, explain how you solved Problem 3.
Answers vary.
Math Masters, p. 289
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 liter
_
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1,000
Encourage students to look for the prefixes in number names.
Consider having students illustrate some of the words and prefixes
that they discuss.
Lesson 9 10
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