Comparing Data
Objective To guide students as they look up and compare
O
numerical data, including geographical measurements.
n
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Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
Key Concepts and Skills
Updating the World Tour
• Read and write large numbers. Math Journal 1, pp. 171–173, 178,
and 179
Student Reference Book, pp. 276,
277, 279–281, 297, 302–305
Math Masters, pp. 419–421 (optional)
Students continue their World Tour
by traveling from Cairo, Egypt, to
Budapest, Hungary. They update their
Route Map and complete the Country
Notes for Hungary. Students who are
keeping a Route Log update it.
[Number and Numeration Goal 1]
• Develop the meaning of percent as per 100. [Number and Numeration Goal 5]
• Compare large numbers. [Number and Numeration Goal 6]
• Use a table of information. [Data and Chance Goal 2]
Key Activities
Students use the World Tour section of
the Student Reference Book to look up
population, area, and climate data for
countries and capitals of Europe. They
identify the maximum and minimum values
for each count or measure. They compare
counts and measures by comparing the
initial digits of the numbers.
Materials
Math Journal 1, p. 134
Student Reference Book, pp. 279–281, 294
(optional), 297, 301, and 304
Study Link 510
Math Masters, p. 426 (optional)
slate
Solving Addition and Subtraction
Number Stories
Math Journal 1, pp. 134A and 134B
Students solve addition and
subtraction number stories.
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Playing Number Top-It
Student Reference Book, p. 255
Math Masters, pp. 492, 493, and 506
per partnership: 4 each of number cards
0–9 (from the Everything Math Deck, if
available) tape
Students practice comparing numbers.
EXTRA PRACTICE
Playing High-Number Toss
Student Reference Book, p. 252
Math Masters, p. 487
per partnership: 1 six-sided die
Students practice comparing numbers.
Math Boxes 5 11
Math Journal 1, p. 135
Students practice and maintain skills
through Math Box problems.
Ongoing Assessment:
Recognizing Student Achievement
Use Math Boxes, Problems 2a–2d. [Number and Numeration Goal 6]
Study Link 5 11
Math Masters, p. 172
Students practice and maintain skills
through Study Link activities.
Advance Preparation
For the optional Readiness activity in Part 3, make a place-value mat by taping together
Math Masters, pages 492 and 493.
Teacher’s Reference Manual, Grades 4–6 pp. 230, 261–264
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Getting Started
Mental Math and Reflexes
Write pairs of numbers on the board. Students record the larger number on their slates. Suggestions:
3,482 and 3,982 3,982
6,005 and 6,500 6,500
8,600 and 8,599 8,600
35,281 and 34,975 35,281
78,004 and 78,400 78,400
238,756 and 209,899 238,756
984,063 and 984,065 984,065
1,239,462 and 1,239,362 1,239,462
5,400,780 and 5,410,780 5,410,780
Math Message
Study Link 5 10 Follow-Up
Find the table listing the tallest mountains on
page 304 in your Student Reference Book.
Which digits tell you that Everest is taller than K-2?
Have students compare their rounded numbers for
the census data. Ask which 20-year span showed
the greatest growth. 1980 to 2000
ten thousands
thousands
hundreds
tens
ones
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
(Student Reference Book, p. 294 (optional); p. 304)
Social Studies Link On the board, draw a unit box like the
one in the margin. Write the names and heights of Everest
and K-2, and underline the digit in the ten-thousands place in
each numeral.
Unit
feet
Everest
K-2
Point out that this digit (2) is the same for both numbers, so it
cannot be used to decide which mountain is higher.
Student Page
World Tour
Longest Rivers
Largest Oceans and Seas
Area
Average
Name
(sq miles)
Depth (feet)
Name
Length
(miles)
Location
Pacific Ocean
64,186,300
12,925
Nile
Africa
Atlantic Ocean
33,420,000
11,730
Amazon
S. America
4,000
Indian Ocean
28,350,500
12,598
Chang (Yangtze)
Asia
3,964
Arctic Ocean
5,105,700
3,407
Huang (Yellow)
Asia
3,395
South China Sea
4,160
1,148,500
4,802
Ob-Irtysh
Asia
Caribbean Sea
971,400
8,448
Congo
Africa
2,900
Mediterranean Sea
969,100
4,926
Lena
Asia
2,734
4,893
Niger
582,100
5,297
Parana
S. America
2,485
Okhotsk Sea
537,500
3,192
Mississippi
N. America
2,340
873,000
Africa
Location
Area
(sq miles)
Africa
3,500,000
Location
Name
Area
(sq miles)
Superior
N. America
31,700
Gobi
Asia
500,000
Victoria
Africa
26,828
Libyan
Africa
450,000
Huron
N. America
23,000
Sahara
Patagonia
S. America
300,000
Michigan
Rub al Khali
Asia
250,000
Tanganyika
Africa
12,700
Kalahari
Africa
225,000
Baykal
Asia
12,162
N. America
22,300
150,000
Great Bear
N. America
12,096
Great Victoria
Australia
150,000
Malawi (Nyasa)
Africa
11,150
Chihuahua
N. America
140,000
Great Sandy
Australia
Highest/Lowest Elevation Points
Highest/
Elevation
Lowest Point
(feet)
Tallest Mountains
Name
Everest
Location
Nepal–Tibet
Height
(feet)
Continent
29,028
Africa
Mt. Kilimanjaro, Tanzania
Lake Assal, Djibouti
19,340
⫺512
Antarctica
Vinson Massif
Bentley Subglacial Trench
16,864
⫺8,327
Asia
Mt. Everest, Nepal–Tibet
Dead Sea, Israel–Jordan
29,028
⫺1,312
Australia
Mt. Kosciusko, New S. Wales
Lake Eyre, South Australia
Europe
Mt. El’brus, Russia
Caspian Sea, Russia-Azerbaijan
K-2 (Godwin-Austen)
Kashmir
28,250
Kanchenjunga
Nepal–India
28,208
Lhotse I (Everest)
Nepal–Tibet
27,923
Makalu I
Nepal–Tibet
27,824
Lhotse II (Everest)
Nepal–Tibet
27,560
Dhaulagiri I
Nepal
26,810
Manaslu I
Nepal
26,760
Cho Oyu
Nepal–Tibet
26,750
Nanga Parbat
Kashmir
26,660
7,310
⫺52
N. America Mt. McKinley (Denali), Alaska
Death Valley, California
20,320
⫺282
S. America
22,834
⫺131
Mt. Aconcagua, Argentina
Valdés Penninsula, Argentina
29,028
28,250
The remaining 3 digits in each number can be ignored, because
they are in the hundreds or smaller. Only the first 2 digits (the
ten-thousands and thousands digits) are needed to determine that
Everest is higher than K-2.
Repeat this routine by comparing the heights of K-2 and
Kanchenjunga and then the heights of Lhotse I and Makalu I.
K-2
28,250
Lhotse I
27,923
Kanchenjunga
28,208
Makalu I
27,824
18,510
⫺92
Student Reference Book, p. 304
374
Everest
K-2
2,590
Largest Freshwater Lakes
Largest Deserts
Name
Now underline the second digit (thousands) in each numeral. Use
a double underline, because these digits are different. Everest has
one more thousand than K-2. So Everest is higher.
3,362
Gulf of Mexico
Bering Sea
29,028
28,250
tens digit
breaks the tie
hundreds digit
breaks the tie
Unit 5 Big Numbers, Estimation, and Computation
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Student Page
Finally, use the Oceans and Seas table shown on the same page of
the Student Reference Book. Compare the depths of the Indian and
Arctic Oceans. (You need to look only at the ten-thousands place.)
Compare the depths of the Arctic Ocean and the South China Sea.
(You need to look only at the thousands place.)
Date
5 11
䉬
1.
Which country in Region 2 has
b.
c.
d.
K I N E S T H E T I C
T A C T I L E
2.
V I S U A L
c.
d.
INDEPENDENT
ACTIVITY
PROBLEM
PRO
P
RO
R
OB
BLE
BL
LE
L
LEM
EM
SO
S
SOLVING
OL
O
LV
LV
VING
VI
VIN
IIN
NG
(Math Journal 1, p. 134; Student Reference Book,
pp. 279–281, 297, and 301; Math Masters, p. 426)
the largest area?
the smallest area?
60,424,000
country
population
Iceland
294,000
country
population
France
211,200 sq mi.
country
area
Netherlands
16,000 sq mi.
country
area
the warmest weather?
the coolest weather?
the greatest amount of rain?
the least amount of rain?
Athens
Greece
capital
country
temperatures
Oslo
Norway
32/20°F
capital
country
temperatures
Rome
56/45°F
Italy
3.3
capital
country
inches rainfall
Warsaw
Poland
1.2
capital
country
inches rainfall
Use the Population Data table on page 301.
3.
Which country in Region 2 has
a.
about the Countries in Europe
the smallest population?
France
From December to February, which capital in Region 2 has
b.
Looking Up and Comparing Data
the largest population?
Use the Climate and Elevation of Capital Cities table on page 297.
a.
280
297 301
Use the World Tour section of your Student Reference Book to answer the questions.
Adjusting the Activity
A U D I T O R Y
Traveling to Europe
It is time to leave Africa. Your destination is Region 2—the continent of Europe. You
and your classmates will fly from Cairo, Egypt to Budapest, Hungary. Before exploring
Hungary, you will collect information about the countries in Region 2. You may even
decide to visit another country in Europe after your stay in Budapest.
a.
Refer students to Student Reference Book, page 294 for more information
about how geographical measurements such as heights of mountains, depths of
oceans, and lengths of rivers are obtained.
Time
LESSON
b.
the greatest percent of population ages 0 –14?
Iceland
23
country
percent
the smallest percent of population ages 0 –14?
Italy
14
country
percent
Math Journal 1, p. 134
Social Studies Link Students complete journal page 134
by looking up the information in the World Tour section of
the Student Reference Book.
Country population and area data are listed in the Country
Profiles on pages 279–281.
Temperature data are listed in the Climate and Elevation of
Capital Cities table on page 297.
Percent of a country’s population that is 0–14 years old is listed
in the Population Data table on page 301.
Adjusting the Activity
ELL
Have students shade 10-by-10 grids to interpret the Percent of
Population Ages 0–14 data in the table on Student Reference Book, page 301.
For example:
The percent of population ages 0–14 for Ethiopia is 47. This means that
47 out of every 100 Ethiopians are 14 years old or younger. Have students
shade 47 squares on a 10-by-10 grid (Math Masters, page 426). The
47
shaded squares,_
, represent the percent of the Ethiopian population that is
100
14 years old or younger.
The percent of population ages 0–14 for the United States is 21. Have
students shade 21 squares on a 10-by-10 grid (Math Masters, page 426).
21
The shaded squares, _
, represent the percent of the U.S. population that is
100
14 years old or younger.
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
Links to the Future
In Unit 9 of Fourth Grade Everyday Mathematics, students will rename fourths,
fifths, tenths, and hundredths as decimals and percents.
Lesson 5 11
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Student Page
Date
LESSON
5 11
Time
2 Ongoing Learning & Practice
Water, Water Everywhere
Solve each problem below. Record a number model for the problem using a letter for
the unknown. You may want to use two number models for some of the problems.
Then write a summary number model with your answer in place of the letter.
178A
178B
Updating the World Tour
Sample number models are given.
1. The world’s largest lake is the Caspian Sea, with an area of about 143,200 square
miles. The second largest lake, Lake Superior, has an area of about 31,320 square
miles. What is the approximate total area of both lakes?
INDEPENDENT
ACTIVITY
(Math Journal 1, pp. 171–173, 178, and 179; Student Reference Book,
pp. 276, 277, 279–281, 297, and 302–305; Math Masters, pp. 419–421)
174,520 square miles
143,200 + 31,320 = t
Answer: About
(number model with unknown)
143,200 + 31,320 = 174,520
Social Studies Link Students follow the established World
Tour routine.
(number model with answer)
2. The Nile River in Egypt is about 4,132 miles long. The longest river in the United
States, the Missouri River, stretches about 2,540 miles. How much longer is the
Nile River than the Missouri River?
1,592 miles
4,132 – 2,540 = m
They update the Route Map by drawing a line segment to
connect Cairo, Egypt, and Budapest, Hungary.
Answer: About
(number model with unknown)
4,132 – 2,540 = 1,592
They use the World Tour section of the Student Reference Book
to locate facts about Hungary and Budapest and fill in the
Country Notes pages for this country and capital.
(number model with answer)
3. To grow a single orange, it takes about 13.8 gallons of water. A tomato is made of
95% water, but takes only 3 gallons of water to grow it. How much more water is
needed to grow an orange than a tomato?
10.8 gallons
13.8 – 3 = m
Answer: About
If students are using a Route Log, they update it.
(number model with unknown)
13.8 – 3 = 10.8
(number model with answer)
134A
Math Journal 1, p. 134A
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Solving Addition and Subtraction
PARTNER
ACTIVITY
Number Stories
(Math Journal 1, pp. 134A and 134B)
Students solve addition and subtraction number stories about
water. They find the answer, record a number model with an
unknown, and then record a summary number model.
Math Boxes 5 11
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 135)
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 5-9. The skill in Problem 6 previews
Unit 6 content.
Student Page
Date
LESSON
5 11
4.
Time
Water, Water Everywhere
continued
The average depth of the ocean is 4,267 meters. The deepest spot, Challenger Deep in the
Mariana Trench near Guam, is about 11,030 meters below the surface. How much deeper is
Challenger Deep than the average depth of the ocean?
Ongoing Assessment:
Recognizing Student Achievement
Sample number
6,763 meters
models are given.
11,030 - 4,267 = d
Answer: About
(number model with unknown)
11,030 - 4,267 = 6,763
The total annual rainfall for the three wettest inhabited places in the world is 1,416 inches. In the
wettest place, Cherrapunji, India, it rains about 498 inches per year. In the second wettest place,
Mawsynram, India, it rains about 467 inches per year. About how many inches per year does it rain
in the third wettest place, Waialeale, Hawaii?
Answer: About
451
Use Math Boxes, Problems 2a–2d to assess students’ ability to compare
numbers up to 1 billion. Students are making adequate progress if they can
insert > and < symbols to make true number sentences. Some students may be
able to solve Problem 2e, which involves exponential notation for powers of 10.
(number model with answer)
5.
Math Boxes
Problems
2a–2d
[Number and Numeration Goal 6]
in.
1416 – 498 – 467 = r
(number model(s) with unknown)
1416 – 498 – 467 = 451
(number model(s) with answer)
6.
Alaska, the biggest state in the United States, has more miles of rivers and streams than any other
state. The next four highest ranked states are California with 211,513 miles; Texas with 191,228
miles; Montana with 176,750 miles; and Nevada with 143,750 miles. The top five states have
1,088,241 miles of rivers and streams. How many miles of rivers and streams does Alaska have?
Study Link 5 11
365,000 miles
211,513 + 191,228 + 176,750 + 143,750 = 723,241;
1,088,241 - 723,241 = m
Answer: About
(number model(s) with unknown)
211,513 + 191,228 + 176,750 + 143,750 = 723,241;
1,088,241 - 723,241 = 365,000
INDEPENDENT
ACTIVITY
(Math Masters, p. 172)
Home Connection Students compare numerical data.
They practice reading numbers in the billions.
(number model(s) with answer)
Math Journal, p. 134B
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Unit 5 Big Numbers, Estimation, and Computation
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Student Page
Date
3 Differentiation Options
Time
LESSON
1.
Playing Number Top-It
PARTNER
ACTIVITY
(Student Reference Book, p. 255; Math Masters,
pp. 492, 493, and 506)
2.
799 + 11,304 + 48,609
4,382 + 6,911 + 7,035
c.
4,000 + 7,000 + 7,000 = 18,000
d.
e.
3. a.
4.
Draw a pair of parallel line segments.
5,293,881
b.
> 354,999
< 67,000,000
62 million > 9,700,000
105,000,000 > 15,500,000
> 1,000
10
356,789
670,000
4
Draw a pair of perpendicular line segments.
Sample answer:
out
6.46
6.58
3.08
3.20
11.22
11.34
25.25
25.37
99.98
5.
6.
1,456
7 ∗ 208 =
The millions digits are the same; their value is 5,000,000
each.
100.1
63.09
95
Multiply. Use a paper-and-pencil algorithm.
6
+0.12
in
94
5
Complete.
Rule:
Sample answer:
5,274,906
b.
Number model:
181
To explore comparing large numbers, have students play Number
Top-It. Players make a place-value mat by taping together Math
Masters, pages 492 and 493. Students compare two numbers by
seeing them, one under the other, with the same-place digits
aligned. Students compare the values of the aligned pairs of digits,
starting on the left. For example:
Write <, >, or = to make each number
sentence true.
a.
Number model: Sample answers:
800 + 11,000 + 49,000 = 60,800
b.
5–15 Min
Estimate the sum. Write a number model
to show how you estimated.
a.
READINESS
Math Boxes
5 11
63.21
162–166
Which of the angles below has a measure
less than 90 degrees? Circle it.
93
18 19
Math Journal 1, p. 135
The hundred-thousands digits are the same; their
value is 200,000 each.
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The ten-thousands digits are not the same; 90,000
is greater than 70,000, so 5,293,881 is greater than
5,274,906.
Have students record a few rounds of play on Math Masters,
page 506 and then choose one of the rounds to explain how
they knew which number was greater.
EXTRA PRACTICE
Playing High-Number Toss
PARTNER
ACTIVITY
5–15 Min
(Student Reference Book, p. 252; Math Masters, p. 487)
Study Link Master
Name
Date
STUDY LINK
To practice comparing numbers, have students play High-Number
Toss. See Lesson 2-7 for additional information.
Time
Comparing Data
5 11
This table shows the number
of pounds of fruit produced by the
top 10 fruit-producing countries in
2001. Read each of these numbers
to a friend or a family member.
Country
Pounds of Fruit
Brazil
77,268,294,000
China
167,046,420,000
France
1.
Which country produced the
most fruit?
2.
Which country produced the
least fruit?
China
France
3.
4.
4
26,823,740,000
India
118,036,194,000
Iran
28,599,912,000
Italy
44,410,538,000
Mexico
34,549,912,000
Philippines
27,028,556,000
Spain
36,260,392,000
United States
73,148,598,000
For each pair, circle the country that produced more fruit.
a.
India
Mexico
b.
United States
c.
Brazil
Philippines
d.
Spain
Iran
Italy
Which two countries together produced about as much fruit as India?
Italy and the United States
Practice
Sample answers:
700 + 900 = 1,600
2,409 + 1,196 + 1,327 2,400 + 1,200 + 1,300 = 4,900
11,899 + 35,201 12,000 + 35,000 = 47,000
Estimate the sum. Write a number model.
5.
6.
7.
687 + 935
Math Masters, p. 172
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