Objective To introduce latitude and longitude; to provide
practice finding the latitude and longitude of places on a globe
and a map; and to identify places given the latitude and longitude.
1
materials
Teaching the Lesson
Key Activities
Students locate and discuss important features of the world globe. They
use latitude and longitude to locate places on a globe, a world map, and
regional maps.
Key Concepts and Skills
• Multiply multidigit numbers to determine miles from the equator.
[Operations and Computation Goal 4]
Math Journal 1, p. 164
Student Reference Book
Study Link 6 8
slate
globe
world map
• Locate positions on the global coordinate grid system.
[Measurement and Reference Frames Goal 4]
• Describe parallel and intersecting lines in terms of latitude and longitude.
[Geometry Goal 1]
• Identify Earth as a sphere divided into hemispheres. [Geometry Goal 2]
Key Vocabulary sphere • North Pole • South Pole • axis • equator •
prime meridian • hemisphere • latitude (lines) • parallels • longitude (lines) •
meridian bar
Ongoing Assessment: Informing Instruction See page 453.
2
Ongoing Learning & Practice
Students play Over and Up Squares to practice coordinate grid skills.
Students practice and maintain skills through Math Boxes and Study
Link activities.
Ongoing Assessment: Recognizing Student Achievement
Use journal page 165. [Operations and Computation Goal 4]
3
Differentiation Options
ENRICHMENT
Students read Sea Clocks:
The Story of Longitude.
EXTRA PRACTICE
Students use latitude and
longitude to locate places on
a map.
materials
Math Journal 1, p. 165
Student Reference Book, p. 257
Study Link Master (Math Masters, p. 195)
Game Master (Math Masters, p. 494)
colored pencils; 2 dice per partnership
materials
Teaching Master (Math Masters, p. 196)
Teaching Aid Master (Math Masters, p. 388 or 389)
Sea Clocks: The Story of Longitude
per group: flat world political map; 1 penny; scissors
See Advance Preparation
Additional Information
Advance Preparation For the optional Enrichment activity in Part 3, obtain a copy of
Sea Clocks: The Story of Longitude by Louise Bordon (Margaret K. McElderry Books, 2004).
Technology
Assessment Management System
Math Boxes, Problem 2
See the iTLG.
Lesson 6 9
449
Getting Started
Mental Math and Reflexes
Math Message
Write decimals on the board and have volunteers read
them aloud. Suggestions:
Make a list of the things that you know about the
world globe. Write down one question that you have
about the world globe.
0.1
2.56
14.78
0.379
50.123
96.478
1.0498
2.0501
11.0063
Study Link 6 8 Follow-Up
Have students compare answers.
Ask questions such as:
• What digit is in the tenths place?
• What is the value of the digit x?
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
Make one list of things students already know (or think they know)
about the world globe and a second list of questions students would
like answered. During the discussion that follows, refer to the lists
when facts are reviewed or questions are answered.
Tell students that in this lesson they will explore the coordinate
grid system used to locate points on the world globe.
Studying a World Globe
WHOLE-CLASS
ACTIVITY
(Student Reference Book, pp. 272 and 273)
Student Page
Mention that Earth is close to being a perfect sphere; that is, all
points on Earth’s surface are about the same distance from the
center of Earth. With the help of the class, locate and discuss some
of the important features of the globe.
World Tour
Latitude and Longitude
You sometimes use a world globe or a flat map to locate countries,
cities, rivers, and so forth. Reference lines are drawn on globes
and maps to make places easier to find.
Latitude
Lines that go east and west around the Earth are called lines of
latitude. The equator is a special line of latitude. Every point
on the equator is the same distance from the North Pole and the
South Pole. Lines of latitude are called parallels because each
one is a circle that is parallel to the equator.
1. The North Pole and South Pole: Demonstrate how Earth
rotates as students share observations:
Earth rotates about an axis (an imaginary line through its
center) connecting the two poles. Viewed from above the
North Pole, Earth rotates counterclockwise.
Latitude is measured in degrees. The symbol for degrees is (˚).
Lines north of the equator are labeled ˚N. Lines south of the
equator are labeled ˚S. The number of degrees tells how far
north or south of the equator a place is. The area north of the
equator is called the Northern Hemisphere. The area south
of the equator is called the Southern Hemisphere.
Examples The latitude of Cairo, Egypt, is 30 N.
˚
North Pole
90°N
We say that Cairo is 30 degrees north of
the equator.
No
rth
ern
Hemi
60°N
45°N
30°N
The latitude of Durban, South Africa, is 30˚S.
Durban is in the Southern Hemisphere.
sph
er
e
Cairo
15°N
Parallels
(latitude)
The latitude of the North Pole is 90˚N.
The latitude of the South Pole is 90˚S.
The poles are the points farthest north and
farthest south on Earth.
Equator 0°
All points on the surface of Earth, except the two poles, move
east as Earth rotates.
15°S
Durban
30°S
So
uth
Longitude
A second set of lines runs from north to south. These are
semicircles (half-circles) that connect the poles. They are called
lines of longitude or meridians. The meridians are not parallel
since they meet at the poles.
The prime meridian is the special meridian labeled 0˚. The
prime meridian passes through Greenwich, near London, England.
Another special meridian falls on, or close to, the International
Date Line. This meridian is labeled 180˚ and is exactly opposite
the prime meridian, on the other side of the world.
45°S
60°S
ern
Hemi
South Pole
90°S
sph
er
e
2. The equator: Point out that the equator is a circle and that
every point on it is the same distance from each pole.
3. The prime meridian: Unlike the equator, the prime meridian
is a semicircle (half circle). It connects the poles and passes
through the Royal Observatory at Greenwich, England—near
London. It was established when England was the foremost
seafaring nation.
Student Reference Book, p. 272
450
Unit 6 Division; Map Reference Frames; Measures of Angles
Student Page
5. The latitude and longitude lines: Point out the grid that
circles the globe.
The latitude lines are circles above and below the equator.
Because these circles are parallel to the equator, they are
often called parallels.
Introducing the System for
30°E
45°E
e
60°E
er
rn Hemisph
as
te
15°E
Durban
E
15°W
30°W
GAMBIA
er
The longitude of Gambia (a small country in
Africa) is about 15˚W. We say that Gambia is
15 degrees west of the prime meridian.
Prime Meridian 0°
n Hemisph
er
60°W
e
45°W
The longitude of Durban, South Africa, is 30˚E.
Durban is in the Eastern Hemisphere.
When both latitude and longitude lines are shown on a globe or
map, they form a pattern of crossing lines called a grid. The
grid can help you locate places on the globe or map. Any place
on the map can be located by naming its latitude and longitude.
Check Your Understanding
Use the grid below to find the approximate latitude and longitude for the cities shown
on the map. For example, Denver, Colorado, is about 40˚ North and 105˚ West.
The longitude lines are semicircles that connect the poles.
The semicircles of longitude are not parallel, since they meet
at the poles.
Be sure to emphasize that longitude is represented by semicircles
and latitude by full circles.
Meridians
(longitude)
London lies close to the prime meridian.
st
The Western Hemisphere is the half-sphere west of the
prime meridian. The Eastern Hemisphere is the half-sphere
east of the prime meridian.
Examples The longitude of London is 0 because
˚
e
The Northern Hemisphere is the half-sphere north of the
equator. The Southern Hemisphere is the half-sphere south
of the equator.
World Tour
Longitude is measured in degrees. Lines west of the prime
meridian are labeled ˚W. Lines east of the prime meridian are
labeled ˚E. The number of degrees tells how far west or east of
the prime meridian a place is located. The area west of the
prime meridian is called the Western Hemisphere. The area
east of the prime meridian is called the Eastern Hemisphere.
W
4. The hemispheres: Demonstrate how the equator and the
prime meridian each partition Earth into half-spheres, or
hemispheres.
Check your answers on page 347.
Student Reference Book, p. 273
WHOLE-CLASS
ACTIVITY
Locating Places on the Globe
Social Studies Link Emphasize that all latitude and
longitude readings must have two parts: a number of
degrees and a direction with reference to the equator or prime
meridian. The only exceptions are 0° latitude and either 0° or
180° longitude; the direction is not included because it is not
needed.
Point out that degrees are printed on, or near, the latitude and
longitude lines on the globe. But the directions (N, S, E, and W)
are not printed on the globe, and students must attach a direction
to each latitude and longitude reading they make.
Latitudes north of the equator (Northern Hemisphere) are
labeled °N or °North.
Latitudes south of the equator (Southern Hemisphere) are
labeled °S or °South.
Longitudes west of the prime meridian (Western Hemisphere)
are labeled °W or °West.
Longitudes east of the prime meridian (Eastern Hemisphere)
are labeled °E or °East.
Adjusting the Activity
Students and adults often confuse
the words latitude (parallels) and longitude
(meridians). Suggest and sketch visuals such
as “latitudes are like rungs on a ladder to
climb north or south of the equator,” and
“longitude lines are long half-circle paths to
the poles.”
AUDITORY
KINESTHETIC
TACTILE
VISUAL
Then demonstrate how to locate a point on the globe in relation
to the prime meridian and the equator. On the globe, the degrees
east and west of the prime meridian are shown along the equator.
Most globes have a meridian bar that shows degrees north and
south of the equator.
Lesson 6 9
451
Student Page
Date
Time
LESSON
6 9
To make it easier to read latitude, you can rotate the globe so
that the meridian bar is close to the place you want to locate.
Locating Places on Regional Maps
Use the maps on pages 282–293 in the Student Reference Book to answer Problems 1–3.
272 273
Examples:
1. Record the continent in which each city is located.
a. Pretoria, South Africa (Region 1)
b. London, England (Region 2)
c. La Paz, Bolivia (Region 3)
d. Dhaka, Bangladesh (Region 4)
e. Washington, D.C., USA (Region 5)
Africa
Europe
South America
Asia
North America
Start at the point where the equator and prime meridian meet.
Then move along the equator 45° West of the prime meridian.
Next move 60° North along the 45° West semicircle. You
should end up just off the southern tip of Greenland.
2. Find the approximate latitude and longitude of each city. Record the degrees
and circle the correct direction.
a. Pretoria, South Africa
Answers vary. Allow 5° variance.
Find the city of Durban in South Africa. It is near the 30° South
parallel. Move up the longitude semicircle to the equator. This
shows that Durban is about 30° East of the prime meridian.
Thus, the location of Durban is about 30° South, 30° East.
25 N or S ; longitude 28 E or W
51 N or S; longitude 0 E or W
latitude 16 N or S ; longitude 68 E or W
latitude 23 N or S; longitude 90 E or W
latitude 38 N or S; longitude 77 E or W
latitude
b. London, England
latitude
c. La Paz, Bolivia
d. Dhaka, Bangladesh
e. Washington, D.C., USA
Find the place at 36° North and 140° East. Use the degree
scale along the equator to find 140° East of the prime meridian.
Rotate the globe so that the meridian bar is next to 140° East.
Use the meridian bar to find 36° North latitude. Tokyo, Japan,
is adjacent to the meridian bar at this latitude. The location of
Tokyo is about 36° North, 140° East.
3. Each degree of latitude that you travel north or south from the equator is equal
to about 70 miles. About how many miles from the equator is each city?
a. Pretoria, South Africa
About
b. London, England
About
c. La Paz, Bolivia
About
d. Dhaka, Bangladesh
About
e. Washington, D.C., USA
About
1,750
3,570
1,120
1,610
2,660
miles
miles
miles
miles
miles
Answers will vary based on answers to Problem 2.
164
Math Journal 1, p. 164
NOTE The words latitude and longitude need not be used when naming
locations. Also, the words North, South, East, and West can be abbreviated.
Thus, the location of Durban, for example, can be written as about 30°S and
30°E. The north or south location is always named first, followed by the east
or west location.
Locating Places on a World Map
WHOLE-CLASS
ACTIVITY
Have the class gather around a wall map of the world. Repeat the
routine that you followed above using the globe.
Name several well-known places. Ask volunteers to identify these
on the map and then find the latitude and longitude for each.
Student Page
Games
Over and Up Squares
Materials 1 Over and Up Squares Gameboard
and Record Sheet (Math Masters, p. 494)
y
4
3
1
2
Skill
Plotting ordered pairs; developing a
winning game strategy
Object of the game To score more points by connecting
ordered pairs on a coordinate grid.
Directions
1. Player 1 rolls 2 dice and uses the numbers to make an
ordered pair. Either number can be used to name the
x-coordinate (over) of the ordered pair. The other number
is used to name the y-coordinate (up) of the ordered pair.
After deciding which ordered pair to use, the player marks it
on the grid with his or her colored pencil (See Figure 1.)
2. Player 1 records the ordered pair and the score in the first
table. A player earns 10 points each time an ordered pair
is marked correctly.
3. Player 2 rolls the dice and decides how to make an ordered
pair. If both possible ordered pairs are already marked on
the grid, the player rolls the dice again. (Variation: If both
possible ordered pairs are already marked, the player can
change one or both of the numbers to 0.)
2
0
x
0
1
2
3
4
5
6
Player 1 rolls a 3 and a 6.
The point (6,3) is marked
on the grid.
Figure 2
y
6
5
4
3
2
1
0
x
0
1
2
3
4
5
6
Player 1 marks (6,4) and
scores 10 points. Player 1
draws 2 line segments and
scores 20 points. The score
for the round is 30 points.
Figure 3
y
6
5
4. Player 2 uses the other colored pencil to mark the ordered pair
and records the ordered pair and score in the second table.
4
5. Players take turns rolling the dice, marking ordered pairs on
the grid, and recording the results. On a player’s turn, if 2
marked grid points are next to each other on the same side
of one of the grid squares, the player connects them with a
line segment he or she makes. Sometimes more than 1 line
segment may be drawn in a single turn. (See Figure 2.) A
player scores 10 points for each line segment drawn.
1
6. If a player draws a line segment that completes a grid square,
(so that all 4 sides of the square are now drawn), that player
colors in the square and earns 50 points. (See Figure 3.)
Locating Places on Regional Maps
5
2 six-sided dice
Players
Figure 1
6
1 colored pencil per player (different colors)
Specify several places by giving the latitude and longitude for
each. Ask volunteers to locate and name each place.
3
2
0
x
0
1
2
3
4
5
6
Player 1 marks (1,2) and
scores 10 points. Player 1
draws 2 line segments and
scores 20 points. The line
segments complete a
square. Player 1 colors in
the square and scores 50
points. The score for the
round is 80 points.
(Math Journal 1, p. 164; Student Reference Book, pp. 282–293)
Have students use the continent maps on pages 282–293 in the
Student Reference Book to locate cities and find the approximate
latitude and longitude of each city. Find the answers for Pretoria
in Problems 1–3 with the class. Then have partnerships complete
the rest of the problems.
Most locations do not fall exactly on the lines of latitude and
longitude. In such cases, students must estimate the degrees of
latitude and longitude. Allow a 5-degree variance in their answers,
but expect that generally they should not be off by more than a
degree or two.
7. The player with more points after 10 rounds wins.
Student Reference Book, p. 257
452
PARTNER
ACTIVITY
Unit 6 Division; Map Reference Frames; Measures of Angles
Student Page
Date
Time
LESSON
Math Boxes
69
Ongoing Assessment: Informing Instruction
1. Cindy received $40 from her aunt and uncle. She drew a circle graph to show how she will
use the money.
Watch for students who have difficulty using the continent maps, because only
a portion of the world is shown on each map. Remind them that the lines of
latitude and longitude on the continent maps are labeled to show both a number
of degrees and a direction (N, S, E, or W).
Cindy's Money
a. How much will she save?
$10
Savings
b. How much will be spent on clothes?
$20
Clothes
Movies
c. On movies?
$10
2. Mrs. Moy’s students are folding paper
3. Divide with a paper-and-pencil algorithm.
cranes for an art project. Each of her 27
students is assigned to make at least 15
paper cranes. What is the least number of
cranes the class will have for the project?
2 Ongoing Learning & Practice
Playing Over and Up Squares
PARTNER
ACTIVITY
1
598 / 3 405
paper cranes
22 23
179
18 19
4. Which number sentence is true?
5. For this spinner, which color would you be
least likely to land on?
Circle the best answer.
(Student Reference Book, p. 257; Math Masters, p. 494)
199 3
27 15 405
Number model:
Answer:
Write the remainder as a fraction.
red
A. 33,000,000 33,000
yellow
B. 5,200,000 9 million
red
C. 10 10,000
Students play Over and Up Squares to practice locating points
and plotting points on a coordinate grid.
4
orange
D. six hundred thousand 10
6
5 6
80 84
165
Math Journal 1, p. 165
Adjusting the Activity
Use these game variations as appropriate:
Have students play the game in teams to share strategies and skills or
eliminate the line segment and square aspects of the game.
Have students choose and name their own points, thus emphasizing the
importance of strategy.
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
Math Boxes 6 9
V I S U A L
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 165)
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 6-6. The skill in Problem 5
previews Unit 7 content.
Study Link Master
Name
Date
STUDY LINK
69
Time
Latitude and Longitude
Use your Student Reference Book to help you complete this Study Link.
Read the examples and study the figures on pages 272 and 273.
Use Math Boxes, Problem 2 to assess students’ ability to solve multidigit
multiplication number stories. Students are making adequate progress if they are
able to perform the computation correctly. Some students may make a ballpark
estimate or use the relationship between multiplication and division to check
their answers.
[Operations and Computation Goal 4]
North Pole
Label the North and South Poles.
b.
Draw and label the equator.
c.
Label the prime meridian.
d.
Draw and label a line of latitude that is north
of the equator.
e.
Draw and label a line of longitude that is
west of the prime meridian.
f.
Mark a point that is in the Southern
2.
INDEPENDENT
ACTIVITY
A
South Pole
The entire continent of Africa is shown in the figure above. Is Africa
mostly in the Western Hemisphere or in the Eastern Hemisphere?
Eastern Hemisphere
3.
(Math Masters, p. 195)
Home Connection Using a picture of the globe, students
label important parts of the global grid system.
equator
Mark a point that is in the Northern
Hemisphere and also in the Western
Hemisphere. Label the point B.
line of latitude
Hemisphere and also in the Eastern
Hemisphere. Label the point A.
g.
Study Link 6 9
B
prime meridian
Ongoing Assessment:
Recognizing Student Achievement
Do the following on the picture of the world globe.
a.
line of longitude
1.
Math Boxes
Problem 2
272 273
Do the equator and prime meridian meet over water or over land?
water
Practice
4.
6.
15 R2 47 / 3
43 R2
217 5 5.
7冄苶9
苶8
苶
7.
14
134
804 / 6
Math Masters, p. 195
Lesson 6 9
453
3 Differentiation Options
PARTNER
ACTIVITY
ENRICHMENT
Using Time to Determine Longitude
30+ Min
(Math Masters, p. 388 or 389)
Literature Link To apply students’ understanding of
longitude, have them read Sea Clocks: The Story of
Longitude by Louise Bordon (Margaret K. McElderry Books;
2004). The book tells how John Harrison created the first accurate
sea clock, allowing sailors to know more accurately their location
at sea by giving them the correct home port time.
Have students explain, in a Math Log or on an Exit Slip, why
knowing the correct home port and sea time helped sailors
determine longitude at sea. Each hour is marked by exactly
15 degrees of longitude. If it is noon on a ship sailing west and
3 P.M. at the home port, the ship is 45° west of home port. If a
clock on a ship sailing east reads 3 P.M. and the home port time
is noon, the ship is 45° east of home port.
EXTRA PRACTICE
Locating Places with Latitude
SMALL-GROUP
ACTIVITY
5–15 Min
and Longitude
(Math Masters, p. 196)
To practice locating places using latitude and longitude, have
small groups use a world political map, a penny, and the Latitude
and Longitude Cards cut from Math Masters, page 196.
Teaching Master
Name
LESSON
69
Date
Time
Latitude and Longitude Cards
Latitude
0
Equator
Latitude
10
N or S
Latitude
20
N or S
Latitude
30
N or S
Latitude
40
N or S
Latitude
50
N or S
Latitude
60
N or S
Latitude
70
N or S
Latitude
80
N or S
Latitude
90
N or S
Longitude
0
Prime
Meridian
Longitude
10
E or W
Longitude
20
E or W
Longitude
30
E or W
Longitude
40
E or W
Longitude
50
E or W
Longitude
60
E or W
Longitude
70
E or W
Longitude
80
E or W
Longitude
90
E or W
Longitude
100
E or W
Longitude
110
E or W
Longitude
120
E or W
Longitude
130
E or W
Longitude
140
E or W
Longitude
150
E or W
Longitude
160
E or W
Longitude
170
E or W
Longitude
180
International
Date Line
Longitude
PLAYER’S
CHOICE
1. Have students shuffle the Latitude and Longitude Cards
separately and put them facedown in two piles.
2. Team 1 draws a Latitude Degree Card and then flips a penny
to find whether it is north (heads) or south (tails). The latitude
and direction are recorded, and the card is returned facedown
to the bottom of the pile.
3. Team 1 now draws a Longitude Card and flips the penny to
find whether it is east (heads) or west (tails). The longitude
and direction are recorded, and the card is returned to the
bottom of the pile.
4. The team uses the information to locate and record the
country or body of water indicated by the coordinates.
5. Teams take turns until each team has located 10 places.
The team with the most land locations is the winner.
Math Masters, p. 196
454
Unit 6 Division; Map Reference Frames; Measures of Angles