Exploring Capacity,
Area, and Measures
Explorations
Objectives To guide children as they explore the capacities of
cylinders,
find the areas of shapes by using inch and centimeter
c
grids, and explore measuring tools and units of measure.
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Common
Core State
Standards
Teaching the Lesson
Key Concepts and Skills
• Identify appropriate units (centimeters and inches) used to make measurements. [Measurement and Reference Frames Goal 1]
• Count unit squares to find the area. [Measurement and Reference Frames Goal 2]
• Identify and create models of cylinders. [Geometry Goal 2]
Key Activities
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Ongoing Learning & Practice
1 2
4 3
Playing Beat the Calculator
Math Journal 2, p. 311
My Reference Book, pp. 124 and 125
1 calculator per child
Ongoing Assessment:
Recognizing Student Achievement
Use an Exit Slip (Math Masters, page 415). Exploration A: Children make two different cylinders from identical sheets
of paper and use macaroni to compare how much each cylinder holds.
Exploration B: Children trace small objects and estimate the areas of shapes
using centimeter and inch grids.
Exploration C: Children explore units of measure and measuring tools
to determine length, weight, volume, and capacity.
[Operations and Computation Goal 1]
Math Boxes 9 6
Math Journal 2, p. 222
Home Link 9 6
Math Masters, p. 281
Key Vocabulary
area square centimeter square inch
Materials
Math Journal 2, p. 221
Home Link 9 5
Fraction Cards
Exploration A: Per group:
Math Masters, pp. 275 and 276
2 sheets of 8_12 " by 11" construction paper 2 squares of cardboard rulers masking tape about 2 pounds of small macaroni
Exploration B: Per group:
Math Masters, pp. 277 and 278; pp. 434 and 440 (at least 2 copies per child)
Everything Math Deck, if available small items such as slates, Pattern-Block
Templates, pattern blocks, and crayon boxes
Differentiation Options
READINESS
Estimating Area
Math Masters, p. 282
centimeter cubes
ENRICHMENT
Building Equal-Capacity Cylinders
Math Masters, p. 415
per group: rulers, masking tape, scissors, macaroni,
cardboard, 2 large sheets of construction paper
Exploration C: Per group:
Math Masters, pp. 279 and 280
measuring tools for finding length, weight, and volume
Advance Preparation
Plan to spend most of your time working with children on Exploration A. Make 1 copy of Math Masters,
pages 275–280 for each small group. For Exploration C, have as many kinds of measuring tools as
possible. For a mathematics and literacy connection, obtain a copy of Millions to Measure by
David Schwartz (Scholastic Inc., 2003).
Teacher’s Reference Manual, Grades 1– 3 pp. 159–161, 165–168
688
Unit 9
Measurement
Mathematical Practices
SMP1, SMP2, SMP4, SMP5, SMP6, SMP8
Content Standards
Getting Started
Mental Math and
Reflexes
Use Fraction Cards. Name a fraction
equivalent to:
3 _
5 _
150
1 _
_
2 6 , 10 , 300 ,
3 _
100
1 _
2 _
_
3 6 , 9 , 300 ,
...
2.OA.2, 2.G.2
Math Message
Home Link 9 5
Follow-Up
Look at the top of journal
page 221. Which shape do
you think is the “biggest” (has
the largest area)? Think about
how you might find out.
This Home Link presents
an opportunity for a Social
Studies connection. Allow
time for a few children to
share their reports.
...
3 _
10 _
25
1 _
_
4 12 , 40 , 100 ,
...
1 Teaching the Lesson
Math Message Follow-Up
(Math Journal 2, p. 221)
WHOLE-CLASS
DISCUSSION
ELL
Discuss answers and children’s strategies for determining which
shape is the “biggest.” Tell children that the activities they do in
this lesson will suggest an answer and that one measure of a
shape is called the area. To support English language learners,
write area on the board and discuss its everyday and
mathematical meanings.
Exploration A: Discovering
Which Cylinder Holds More
SMALL-GROUP
ACTIVITY
PROBLEM
PRO
PR
P
ROB
RO
SOLVING
S
SO
OLVING
O
(Math Journal 2, p. 221; Math Masters,
pp. 275 and 276)
Student Page
Date
LESSON
Children complete the steps given on Math Masters, pages 275
and 276 to make two cylinders from identical paper rectangles.
Then they predict and verify whether both cylinders hold the same
amount of macaroni or whether one holds more. See the margin on
the following page.
9 6
Time
Math Message
Estimate: Which shape is the “biggest” (has the largest area)? Circle it.
Think: How might you measure the shapes to find out?
NOTE It is recommended that an adult work with each small group to create the
cylinder models. It is important for the children to see that the two cylinders are
created from equal-size sheets of construction paper.
Exploration A: Which Cylinder Holds More?
Which holds more macaroni—the tall and narrow cylinder or the short and
wide cylinder?
My prediction:
Actual result:
Answers vary.
The short and wide cylinder
Exploration B: Measuring Area
Answers vary.
The area of my tracing of the deck of cards is about
centimeters.
square
The area of my tracing of the deck of cards is about
square inches.
I traced
.
It has an area of about
.
(unit)
Using two paper rectangles that are the same size, children
make two cylinders. Then they explore which will hold more.
Math Journal 2, p. 221
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2/10/11 9:34 AM
Lesson 9 6
689
Teaching Master
Name
Date
LESSON
Time
Which Cylinder Holds More?
96
䉬
Exploration B: Measuring
SMALL-GROUP
ACTIVITY
Area with a Centimeter Grid
and an Inch Grid
Work with a small group.
Materials 䊐 Math Journal 2, p. 221
䊐 rulers; masking tape; macaroni
䊐 pieces of cardboard
(Math Journal 2, p. 221; Math Masters, pp. 277, 278, 434, and 440)
䊐 2 sheets of 8 12'' by 11'' construction paper
Directions
Children trace around a deck of cards on centimeter grid paper
and inch grid paper. They count the squares inside their drawings.
Explain that the amount of space inside the borders is called the
area (of that side of the card deck). The number of squares
children count is a measurement of the area in square
centimeters or square inches, respectively. Children then trace
around other objects on grid paper and count squares to find
the areas.
1. Draw a line 1 inch from a long edge
on one construction paper rectangle.
䉬
Roll the rectangle into a long cylinder
and tape the paper along the line.
䉬
Then tape the cylinder to a piece
of cardboard.
2. Draw a line 1 inch from a short edge
on the other rectangle.
䉬
Roll the rectangle into a short cylinder
and tape the paper along the line.
䉬
Then tape the cylinder to a piece
of cardboard.
Adjusting the Activity
ELL
Display Math Masters, page 434 (centimeter grid paper) labeled
“Square Centimeters” and Math Masters, page 440 (inch grid paper) labeled
“Square Inches.” Keep the display up through this lesson and the next.
Math Masters, p. 275
A U D I T O R Y
Name
K I N E S T H E T I C
Date
T A C T I L E
V I S U A L
Time
Centimeter Grid Paper
Teaching Master
Name
LESSON
96
䉬
Date
Which Cylinder Holds More?
Time
continued
3. Talk about these questions with your group.
䉬
Suppose that you fill both containers with macaroni.
Will one of the cylinders hold more macaroni than
the other?
䉬
If so, which one? Why? Record your prediction on
journal page 221.
4. Find out. Fill the tall cylinder with macaroni.
Then carefully pour the macaroni from the tall cylinder into
the short cylinder.
Copyright © Wright Group/McGraw-Hill
Record what happened on journal page 221.
434
Math Masters, p. 276
690
Unit 9 Measurement
Teaching Master
Exploration C: Exploring
Name
SMALL-GROUP
ACTIVITY
Tools and Measures
LESSON
96
䉬
Date
Time
Measuring Area
Work in a small group.
Materials 䊐 centimeter grid paper
(Math Masters, pp. 279 and 280)
䊐 inch grid paper
䊐 Everything Math Deck, if available
Children explore and discuss different types of measuring tools.
Children then make lists of things that can be measured with
linear measuring tools, weighing scales, and containers that
measure capacity. Children write their lists on Math Masters,
page 280. See the margin on the following page. Bring the
children together to discuss how children may have written
the same thing on more than one list. For example, a desk
might appear on all three lists:
The desk’s height, length, and width can be measured with a
tape measure, ruler, yardstick, or meterstick.
䊐 for tracing: slate, Pattern-Block Template,
crayon box, and other objects
䊐 Math Journal 2, p. 221
Directions
1. Place the deck of cards on the centimeter grid paper.
Trace around the deck. The tracing shows the border of
the deck.
2. Count the squares that cover the space inside the border.
䉬
If more than half of a square is inside the border, count
the whole square.
䉬
If less than half of a square is inside the border, do not
count the square at all.
3. The amount of space inside the border is called the area.
The number of squares you counted is a measurement of
the area in square centimeters.
The desk’s weight can be measured with a large scale.
Another possible measure, but a less likely one, is to find the
capacity of a desk drawer. A measuring cup can be used to fill
the drawer with a dry pourable substance (not water!) such as
rice or sand.
Math Masters, p. 277
NOTE Both volume and capacity are measures of the amount of space
something occupies or contains. Common measures of volume and capacity are
cubic units, such as cubic centimeters, cubic inches, cubic feet, quarts, cups,
gallons, and liters.
Teaching Master
Name
LESSON
96
䉬
Date
Measuring Area
Teaching Aid Master
Time
continued
Name
Date
Time
Inch Grid Paper
4. Repeat Steps 1 and 2 using inch grid paper.
5. Find the area of four or five more objects.
You might trace things like …
䉬
a Pattern-Block Template
䉬
pattern blocks
䉬
a crayon box
䉬
objects from the Measures All Around Museum
6. Record the areas you measured on journal page 221.
Follow-Up
Work together as a group. Explain why your results are
estimates and not exact measurements. How are the
units used to measure area different from those used to
measure perimeter?
Math Masters, p. 278
Math Masters, p. 440
Lesson 9 6
691
Teaching Master
Name
Date
LESSON
Time
2 Ongoing Learning & Practice
Things to Measure
96
Work with a small group.
Materials
□ Math Masters, p. 280
Playing Beat the Calculator
□ ruler; tape measure; meterstick; yardstick;
scale; measuring cup; measuring spoon
Directions
(Math Journal 2, p. 311; My Reference Book,
pp. 124 and 125)
1. Explore and discuss how to use each of the measuring
tools.
2. Sort the measuring tools into the following three groups:
linear measures: tools that measure length, width, height,
distance between, distance around (perimeter)
See My Reference Book, pages 124 and 125 for directions. Children
play Beat the Calculator to develop their recall of addition facts.
They should record the facts for which they can beat the calculator
by making a check mark in the box of the corresponding fact.
When they have three check marks next to a particular fact, they
can write the sum in that box to indicate that they know the fact
from memory. The Caller should select problems at random from
the Fact Power Table.
measures of weight: how heavy a thing is; how hard it is
to move
measures of volume and capacity: how much of
something there is; how much a container will hold
g
p
3. Complete Math Masters, page 280. List things you can
measure with tools from each group. Write the unit that
would be used to measure each item.
py g
PARTNER
ACTIVITY
Follow-Up
Discuss other measuring tools you know about.
List them on the back of Math Masters, page 280.
Math Boxes 9 6
INDEPENDENT
ACTIVITY
Math Masters, p. 279
(Math Journal 2, p. 222)
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2/9/11 12:37 PM
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 9-8. The skill in Problem 6
previews Unit 10 content.
Ongoing Assessment: Exit
Recognizing Student Slip
Achievement
Writing/Reasoning Have children draw, write, or
verbalize their answers to the following: Describe how
you determined the perimeter of the rectangle in Problem 4.
Sample answer: I added the lengths of all the sides.
Use an Exit Slip (Math Masters, page 415)
to have children record the facts in the boxes
for which they have at least one check mark.
Children are making adequate progress if they
record most of the facts in the Fact Power
Table. Some children may record all the facts.
[Operations and Computation Goal 1]
Student Page
Teaching Master
Name
LESSON
96
Date
Things to Measure
Time
Date
Time
LESSON
9 6
continued
1. List 4 things you can measure with a ruler, a tape
measure, a meterstick, or a yardstick. Write the unit that
you would use to make each measurement.
Object
Unit
Example: Math Journal
Inches
Math Boxes
1. Write 5 names in the 90-box.
2. Fill in the
missing
numbers.
90
Sample answers:
89 + 1, 9 × 10,
30 + 30 + 30,
100 - 10, 45 + 45
Answers vary.
5
2
98
100
95
94
92
97
98 99
16
3. Solve. Show your work.
2. List 4 things you can weigh with a scale.
Object
Answers vary.
3 cm
4.
27
+ 56
Unit
2 cm
2 cm
3 cm
83
Perimeter =
10
cm
68
5. Write a number model for a
3. List 4 things you can measure with a measuring cup,
a measuring spoon, or some other container.
Object
Unit
6. The total cost is 60¢.
ballpark estimate. Then solve.
You pay with a $1 bill.
Ballpark estimate:
How much change do you get?
70 + 30 = 100
Answers vary.
40¢
Show the change using
‰, Í, and Â.
68
+ 34
102
30
Math Journal 2, p. 222
Math Masters, p. 280
252-292_EMCS_B_MM_G2_U09_576949.indd 280
692
Unit 9 Measurement
Sample answer:
‰ÍÂ
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Home Link 9 6
Home Link Master
Name
INDEPENDENT
ACTIVITY
(Math Masters, p. 281)
Date
HOME LINK
96
䉬
Family
Note
Home Connection Children explore capacity as they
predict and then check whether one glass of water holds
more than another. They also count squares to find areas.
Time
Capacity and Area
Today your child explored the ideas of capacity and area. Before your child is exposed to
formal work with these measures (such as equivalent units of capacity or formulas for finding
area), it is important that he or she have an informal understanding of these measures.
In Problem 1, help your child see that although the glasses may have different dimensions,
they can still hold about the same amount of water. In Problem 2, the number of squares
that your child counts is the area in square centimeters.
69 70
Please return this Home Link to school tomorrow.
1. Find two different glasses at home that you think
hold about the same amount of water. Test your
prediction by pouring water from one glass into the
other. Do they hold about the same amount of
water? Does one glass hold more than the other?
Explain to someone at home how you know.
2. Count squares to find the area of each figure.
3 Differentiation Options
READINESS
Estimating Area
INDEPENDENT
ACTIVITY
359
350
50
4. 594 200 6.
400
To provide experience with area, have children estimate the number
of centimeter cubes needed to cover a 5 cm × 5 cm square and an
8 cm × 8 cm square. They check their estimates by covering the
squares with the cubes.
Building Equal-Capacity
Practice
5.
8
square centimeters
3. 459 100 5–15 Min
(Math Masters, p. 282)
ENRICHMENT
15
square centimeters
794
460
59
401
Math Masters, p. 281
SMALL-GROUP
ACTIVITY
15–30 Min
Cylinders
(Math Masters, p. 415)
To further explore cylinders, have children build two different
cylinders that will hold about the same amount of macaroni. After
completing Exploration A, the children work together to plan how
to make two cylinders with different dimensions that will hold
about the same amount of macaroni. They experiment with the
materials and record their results on an Exit Slip (Math Masters,
page 415).
Planning Ahead
Bring a checkerboard to class for children to use when solving the
Try This problems in the optional Part 3 Extra Practice activity
in Lesson 9-7.
Teaching Master
Name
LESSON
96
䉬
Date
Time
Area
Guess how many cubes are needed to cover each square with
no gaps or overlaps. Cover each square with cubes to check
your guess.
1. I think it will take
cubes to
cover this square.
It took 25 cubes
to cover this square.
2. I think it will take
cubes to
cover this square.
It took 64 cubes
to cover this square.
Math Masters, p. 282
Lesson 9 6
693