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Objectives
To demonstrate how to estimate the area of a
surface having a curved boundary; and to provide practice
converting from one square unit to another.
1
materials
Teaching the Lesson
Key Activities
Students estimate the area of the front of their hand by tracing it on a 1-inch grid and counting
squares. Then they use a rule of thumb to estimate their total skin area. Students convert
measurements from square inches to square feet and from square feet to square yards.
Math Journal 2, pp. 230 and 231
Study Link 8 3
Key Concepts and Skills
Teaching Aid Masters (Math Masters,
p. 388 or 389; and p. 444)
calculator
• Use the terms estimate and guess. [Operations and Computation Goal 6]
• Use an estimate to judge the reasonableness of a solution.
scissors
tape
[Operations and Computation Goal 6]
• Count squares and partial squares or use a formula to estimate area.
See Advance Preparation
[Measurement and Reference Frames Goal 2]
• Convert between square inches and square feet. [Measurement and Reference Frames Goal 3]
Ongoing Assessment: Recognizing Student Achievement Use a Math Log or Exit Slip.
[Measurement and Reference Frames Goal 2]
2
Ongoing Learning & Practice
Students resume the World Tour in South America.
Students practice and maintain skills through Math Boxes and Study Link activities.
materials
Math Journal 2, pp. 229, 329
(optional), 330, 331, 334, and 335
Student Reference Book
Study Link Master (Math Masters,
p. 255)
Teaching Aid Masters (Math Masters,
pp. 419 and 420, optional)
3
materials
Differentiation Options
READINESS
Students use square stick-on notes to
determine the area of an irregular region.
EXTRA PRACTICE
Students place objects on a grid, trace their
outlines, and count grid squares to estimate
their areas.
Additional Information
Advance Preparation For Part 1, make 3 copies of 1-inch grid paper (Math Masters,
page 444) for each student. Place copies near the Math Message.
Teaching Aid Masters (Math Masters,
p. 388 or 389; and p. 444)
objects with flat irregular surfaces
masking tape; square stick-on notes
Technology
Assessment Management System
Math Log or Exit Slip
See the iTLG.
Lesson 8 4
675
Getting Started
Mental Math and Reflexes
Math Message
Pose mental subtraction problems. Suggestions:
Take 3 sheets of grid paper. Cut and tape the grids
to make a square with sides that measure 1 foot (12 inches).
How many square inches are there in 1 square foot?
80 – 50 30
86 – 41 45
64 – 45 19
120 – 30 90
149 – 42 107
203 – 150 53
250 – 60 190
278 – 73 205
671 – 80 591
370 – 90 280
357 – 122 235
417 – 60 357
Study Link 8 3 Follow-Up
Have students share their conclusions about the
area of their new shapes. Confirm with the class
that shapes that look different can have the same area.
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
(Math Journal 2, p. 230)
Each student should have made a square consisting of 12 rows
with 12 one-inch squares in each row.
Since 12 12 144, there are 144 square inches in
1 square foot.
Students record this equivalency in Problem 1 on journal
page 230. Tell students that in this lesson they will use the
1-foot square to estimate the area of their skin.
Estimating the Area
Student Page
Date
8 4
of Your Skin
Time
LESSON
What Is the Total Area of My Skin?
Follow your teacher’s directions to complete this page.
1. There are
144
square inches in 1 square foot.
(Math Journal 2, pp. 230 and 231)
Answers vary for
Problems 2–5 and 6b.
1 ft
2. My guess is that the total
area of my skin is about
PARTNER
ACTIVITY
square feet.
Rule of Thumb: The total area of your skin is about
100 times the area of the outline of your hand.
1 ft
Ask students to guess the total area of their skin in square feet
and record it in Problem 2 on journal page 230. Have them refer
to their 1-foot square to help them with their guess.
1 square foot
Follow these steps to estimate the total area of your skin:
Ask your partner to trace the outline of your hand on the grid on page 231.
Estimate the area of the outline of your hand by counting squares on the grid.
Record your estimate in Problem 3 below.
Use the rule of thumb to estimate the total area of your skin (area of skin 100 area of hand). Record your estimate in Problem 4 below.
3. I estimate that the area of the outline of my hand is about
square inches.
5. I estimate that the total area of my skin is about
square feet.
9
Rule of Thumb: The total area of your skin is about 100 times the
area of the outline of your hand.
square inches.
4. I estimate that the total area of my skin is about
6. a. There are
Tell them to use the following to check their guess.
Then have partners follow these steps:
1. Trace the outline of your partner’s hand on the grid on your
partner’s journal page 231.
square feet
in 1 square yard.
b. I estimate that the total area of my
2. Estimate the area of your own hand by counting grid squares
(square inches) inside the tracing of your hand.
square yards.
3 ft
skin is about
3 ft
1 square yard
230
Math Journal 2, p. 230
676
Unit 8 Perimeter and Area
3. Use the rule of thumb to estimate the total area of your skin
(area of skin 100 area of hand).
Students record the results in Problems 3 and 4.
A student’s fingers should be closed when his or
her partner traces the hand outline on journal
page 231.
Ongoing Assessment:
Recognizing Student Achievement
Math Log
or Exit Slip
Use a Math Log or an Exit Slip to assess students’ ability to count unit squares
and fractions of unit squares to estimate the area of an irregular figure. Have
students explain how they found the area of their hands. Students are making
adequate progress if their strategy includes counting whole squares and
combining partial squares to approximate whole squares. Some students may
describe a strategy in which they find the area of a rectangular region within the
hand tracing by multiplying its length and width.
[Measurement and Reference Frames Goal 2]
Sharing the Results of
WHOLE-CLASS
ACTIVITY
the Experiment
(Math Journal 2, pp. 230 and 231)
Review the information students have obtained so far.
In Problem 2, they guessed the total area of their skin in
square feet.
In Problem 4, they estimated the total area of their skin in
square inches.
Remind students about the difference between a guess and an
estimate—an estimate is more systematic and usually more
accurate than a guess.
Ask students to compare how close the guesses they made in
Problem 2 are to their estimates in Problem 4.
The guess and the estimate cannot be immediately compared
because the guess is in square feet and the estimate is in
square inches.
Lesson 8 4
677
Help students convert their square-inch estimates to square
feet. Have them record the square-foot estimates in Problem 5.
Example: Guess is 15 square feet. Estimate is 1,512 square
inches. Convert 1,512 square inches to square feet. Use the fact
that 144 square inches equals 1 square foot. You want to know
how many 144s there are in 1,512. Since 1,512 144 10.5,
it follows that 1,512 square inches equals 10.5 square feet.
ELL
Adjusting the Activity
Have students use their 1-foot squares to model the conversion of a
volunteer’s skin estimate in square inches to square feet. Ask students to come
to the board, one at a time, with 1-foot squares and tape them onto the board.
Have a student with a calculator add 144 each time a 1-foot square is added.
Students should tape the first nine 1-foot squares in three rows with three
squares in each row. Call attention to the fact that 9 square feet is equal to
1 square yard.
Have students tape 1-foot squares until the total is equal to or greater than the
estimated area. Discuss how to use the taped squares to find the approximate
area in square feet. For example, 1,500 square inches is between 10 square feet
(10 144 1,440) and 11 square feet (11 144 1,584).
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
Now ask students to convert their estimates to an approximate
number of square yards (probably between 1 and 2) and record it
in Problem 6. To convert to square yards, students divide the
number of square feet by 9.
2 Ongoing Learning & Practice
World Tour Option:
SMALL-GROUP
ACTIVITY
Visiting South America
(Math Journal 2, pp. 329–331, 334, and 335; Student Reference Book )
Social Studies Link If you have chosen to extend the scope
of the World Tour for your class, have small groups visit a
second country in South America. You may let them choose which
countries to visit, or you may assign a country to each group.
Remind students to update their Route Log (if they are keeping
one) and Route Map and to complete Country Notes for the
country they visit.
Adjusting the Activity
Have students determine the latitude and longitude of the capital city of
the country they visit.
A U D I T O R Y
678
Unit 8 Perimeter and Area
K I N E S T H E T I C
T A C T I L E
V I S U A L
Student Page
Math Boxes 8 4
INDEPENDENT
ACTIVITY
(Math Journal 2, p. 229)
Date
Time
LESSON
Math Boxes
8 4
1. Measure the sides of the figure to the
2. If you tossed a coin onto the grid below,
nearest centimeter. Then find its
perimeter.
3 cm
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 8-2. The skill in Problem 6
previews Unit 9 content.
Writing/Reasoning Have students write a response to the
following: Describe the strategy you used to estimate the product
in Problem 4. Sample answer: I used 200 instead of 192, and 50
instead of 49, because they are “close-but-easier” numbers.
200 50 10,000
1
2
4
cm
8
,
16
2
cm
15
Perimeter cm
2
INDEPENDENT
ACTIVITY
P
E
P
E
R
O
P
E
R
E
R
O
P
45 84
cm
Fraction
1
10
20
100
0.1
0.20
0.8
0
4
5
0
3
4. Which number is closest to the product
100
B
1,000
C
10,000
D
100,000
181
18
6. Shade more than but less than
100
3
of the grid.
10
notation.
105
a. 100,000 A
61
5. Write each number in exponential
O
of 192 and 49? Circle the best answer.
Decimal
c.
R
O
131
whole number.
b.
1
2
cm
3. Write an equivalent fraction, decimal, or
a.
or
cm
cm
1
d.
Study Link 8 4
about what fraction of the time would you
expect it to land on a vowel?
Sample answer:
1
(Math Masters, p. 255)
b. 10 10
107
109
1,000,000,000 c. 10,000,000 Home Connection Students estimate the area of São
Paulo State and Rio de Janeiro State in Brazil.
d.
5
27
229
Math Journal 2, p. 229
Study Link Master
Name
Date
STUDY LINK
8 4
1.
Below is a map of São Paulo State in Brazil. Each grid square represents
2,500 square miles. Estimate the area of São Paulo State.
I counted about
The area is about
2.
Time
Areas of Irregular Figures
133
35 grid squares.
87,500 square miles.
To the right is a map of Rio de Janeiro State in Brazil.
Each grid square represents 2,500 square miles.
Estimate the area of Rio de Janeiro State.
I counted about
The area is about
7 grid squares.
17,500 square miles.
Practice
3.
88.71
5.
386.174
73.04 15.67
4.
86.05 27.97 312.11 74.064
6.
57.1 39.002 58.08
18.098
Math Masters, p. 255
Lesson 8 4
679
3 Differentiation Options
READINESS
Counting Squares to Find Area
PARTNER
ACTIVITY
5–15 Min
(Math Masters, p. 388 or 389)
To explore the concept of area as the number of unit squares and
fractions of unit squares needed to cover a surface without gaps or
overlaps, have students use square stick-on notes to cover an
irregular region.
Using masking tape, create (or have students create) a large figure
on the floor. Students first estimate the area and then cover the
figure with stick-on notes. They count stick-on notes and partial
areas not covered by stick-on notes to refine their estimates.
In a Math Log or on an Exit Slip, have students describe how they
determined the area of the irregular region.
Students use square stick-on notes to estimate
the area of an irregular region.
EXTRA PRACTICE
Estimating Areas of
INDEPENDENT
ACTIVITY
5–15 Min
Irregular Regions
(Math Masters, p. 444)
To practice finding the area of irregular regions, have students
place objects that have flat, irregular surfaces on a grid and trace
their outlines. Then have students count grid squares and partial
grid squares to estimate the areas.
Students estimate areas of irregular regions on
Math Masters, page 444.
680
Unit 8 Perimeter and Area