Teaching the Lesson materials

Key ActivitiesStudents locate and discuss important features of the world globe. They use latitude and longitude to locate places on a globe, a world map, andregional maps.

Key Concepts and Skills• Multiply multidigit numbers to determine miles from the equator.

[Operations and Computation Goal 4]

• 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.

Ongoing Learning & Practice materialsStudents 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 AchievementUse journal page 165. [Operations and Computation Goal 4]

Differentiation Options materials

Students read Sea Clocks:The Story of Longitude.

Students use latitude and longitude to locate places on a map.

� 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

EXTRA PRACTICEENRICHMENT

3

� 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

2

� Math Journal 1, p. 164

� Student Reference Book

� Study Link 6�8

� slate

� globe

� world map

1

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.

Technology Assessment Management SystemMath Boxes, Problem 2

See the iTLG.

Additional InformationAdvance 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).

Lesson 6�9 449

450 Unit 6 Division; Map Reference Frames; Measures of Angles

� Math Message Follow-UpMake one list of things students already know (or think they know)about the world globe and a second list of questions students wouldlike answered. During the discussion that follows, refer to the listswhen facts are reviewed or questions are answered.

Tell students that in this lesson they will explore the coordinategrid system used to locate points on the world globe.

� Studying a World Globe(Student Reference Book, pp. 272 and 273)

Mention that Earth is close to being a perfect sphere; that is, allpoints on Earth’s surface are about the same distance from thecenter of Earth. With the help of the class, locate and discuss someof the important features of the globe.

1. The North Pole and South Pole: Demonstrate how Earthrotates as students share observations:

� Earth rotates about an axis (an imaginary line through itscenter) connecting the two poles. Viewed from above theNorth Pole, Earth rotates counterclockwise.

� All points on the surface of Earth, except the two poles, moveeast as Earth rotates.

2. The equator: Point out that the equator is a circle and thatevery point on it is the same distance from each pole.

3. The prime meridian: Unlike the equator, the prime meridianis a semicircle (half circle). It connects the poles and passesthrough the Royal Observatory at Greenwich, England—nearLondon. It was established when England was the foremostseafaring nation.

WHOLE-CLASS ACTIVITY

WHOLE-CLASS ACTIVITY

1 Teaching the Lesson

Getting Started

Math MessageMake a list of the things that you know about theworld globe. Write down one question that you have about the world globe.

Study Link 6�8 Follow-UpHave students compare answers.

Mental Math and Reflexes Write decimals on the board and have volunteers readthem aloud. Suggestions:

0.1

2.56

14.78

Ask questions such as:

• What digit is in the tenths place?

• What is the value of the digit x?

0.379

50.123

96.478

1.0498

2.0501

11.0063

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 globesand maps to make places easier to find.

LatitudeLines that go east and west around the Earth are called lines oflatitude. The equator is a special line of latitude. Every pointon the equator is the same distance from the North Pole and theSouth Pole. Lines of latitude are called parallels because eachone is a circle that is parallel to the equator.

Latitude is measured in degrees. The symbol for degrees is (̊ ).Lines north of the equator are labeled ˚N. Lines south of theequator are labeled ˚S. The number of degrees tells how farnorth or south of the equator a place is. The area north of theequator is called the Northern Hemisphere. The area south of the equator is called the Southern Hemisphere.

World Tour

ExamplesExamples The latitude of Cairo, Egypt, is 30˚N.We say that Cairo is 30 degrees north of the equator.

The latitude of Durban, South Africa, is 30˚S.Durban is in the Southern Hemisphere.

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.

Parallels(latitude)

Durban

North Pole90°N

South Pole90°S

15°S

30°S

45°S60°S

15°N

30°N

45°N60°N

Equator 0°

Cairo

Northern Hemisphere

Southern Hemisphere

LongitudeA second set of lines runs from north to south. These aresemicircles (half-circles) that connect the poles. They are calledlines of longitude or meridians. The meridians are not parallelsince they meet at the poles.

The prime meridian is the special meridian labeled 0 .̊ Theprime meridian passes through Greenwich, near London, England.Another special meridian falls on, or close to, the InternationalDate Line. This meridian is labeled 180˚ and is exactly oppositethe prime meridian, on the other side of the world.

Student Reference Book, p. 272

Student Page

4. The hemispheres: Demonstrate how the equator and theprime meridian each partition Earth into half-spheres, orhemispheres.

� The Northern Hemisphere is the half-sphere north of theequator. The Southern Hemisphere is the half-sphere southof the equator.

� The Western Hemisphere is the half-sphere west of theprime meridian. The Eastern Hemisphere is the half-sphereeast of the prime meridian.

5. The latitude and longitude lines: Point out the grid thatcircles the globe.

� The latitude lines are circles above and below the equator.Because these circles are parallel to the equator, they areoften called parallels.

� The longitude lines are semicircles that connect the poles.The semicircles of longitude are not parallel, since they meetat the poles.

Be sure to emphasize that longitude is represented by semicirclesand latitude by full circles.

� Introducing the System for Locating Places on the Globe

Social Studies Link Emphasize that all latitude andlongitude readings must have two parts: a number of

degrees and a direction with reference to the equator or primemeridian. The only exceptions are 0° latitude and either 0° or180° longitude; the direction is not included because it is notneeded.

Point out that degrees are printed on, or near, the latitude andlongitude lines on the globe. But the directions (N, S, E, and W)are not printed on the globe, and students must attach a directionto each latitude and longitude reading they make.

� Latitudes north of the equator (Northern Hemisphere) arelabeled °N or °North.

� Latitudes south of the equator (Southern Hemisphere) arelabeled °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.

Then demonstrate how to locate a point on the globe in relation to the prime meridian and the equator. On the globe, the degreeseast and west of the prime meridian are shown along the equator.Most globes have a meridian bar that shows degrees north andsouth of the equator.

WHOLE-CLASS ACTIVITY

Lesson 6�9 451

Adjusting the ActivityStudents 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

When both latitude and longitude lines are shown on a globe ormap, they form a pattern of crossing lines called a grid. Thegrid can help you locate places on the globe or map. Any placeon the map can be located by naming its latitude and longitude.

Check Your UnderstandingCheck Your Understanding

Use the grid below to find the approximate latitude and longitude for the cities shownon the map. For example, Denver, Colorado, is about 40˚ North and 105˚ West.

Check your answers on page 347.

Longitude is measured in degrees. Lines west of the primemeridian are labeled ˚W. Lines east of the prime meridian arelabeled ˚E. The number of degrees tells how far west or east ofthe prime meridian a place is located. The area west of theprime meridian is called the Western Hemisphere. The areaeast of the prime meridian is called the Eastern Hemisphere.

World Tour

ExamplesExamples The longitude of London is 0˚ becauseLondon lies close to the prime meridian.

The longitude of Durban, South Africa, is 30˚E.Durban is in the Eastern Hemisphere.

The longitude of Gambia (a small country inAfrica) is about 15˚W. We say that Gambia is 15 degrees west of the prime meridian.

Meridians

(longitude)

60

°W4

5°W

30

°W

15

°W

15

°E

30

°E

45

°E6

0°E

Prim

e M

erid

ian

0°

Ea

ste

rn

H

em

is

ph

ere

We

ste

rn

H

em

is

ph

ere

GAMBIA

Durban

Student Reference Book, p. 273

Student Page

452 Unit 6 Division; Map Reference Frames; Measures of Angles

164

Locating Places on Regional MapsLESSON

6�9

Date Time

Use the maps on pages 282–293 in the Student Reference Book to answer Problems 1–3.

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)

2. Find the approximate latitude and longitude of each city. Record the degrees

and circle the correct direction. Answers vary. Allow 5° variance.

a. Pretoria, South Africa latitude N or S ; longitude E or W

b. London, England latitude N or S; longitude E or W

c. La Paz, Bolivia latitude N or S ; longitude E or W

d. Dhaka, Bangladesh latitude N or S; longitude E or W

e. Washington, D.C., USA latitude N or S; longitude E or W

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 miles

b. London, England About miles

c. La Paz, Bolivia About miles

d. Dhaka, Bangladesh About miles

e. Washington, D.C., USA About miles2,660

1,610

1,120

3,570

1,750

7738

9023

6816

051

2825

North America

Asia

South America

Europe

Africa

272 273

Answers will vary based on answers to Problem 2.

Math Journal 1, p. 164

Student PageTo 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.

Examples:

� 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. Youshould end up just off the southern tip of Greenland.

� Find the city of Durban in South Africa. It is near the 30° Southparallel. Move up the longitude semicircle to the equator. Thisshows that Durban is about 30° East of the prime meridian.Thus, the location of Durban is about 30° South, 30° East.

� Find the place at 36° North and 140° East. Use the degreescale 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 ofTokyo is about 36° North, 140° East.

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 MapHave the class gather around a wall map of the world. Repeat theroutine that you followed above using the globe.

Name several well-known places. Ask volunteers to identify theseon the map and then find the latitude and longitude for each.

Specify several places by giving the latitude and longitude foreach. Ask volunteers to locate and name each place.

� Locating Places on Regional Maps(Math Journal 1, p. 164; Student Reference Book, pp. 282–293)

Have students use the continent maps on pages 282–293 in theStudent Reference Book to locate cities and find the approximatelatitude and longitude of each city. Find the answers for Pretoriain 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 andlongitude. In such cases, students must estimate the degrees oflatitude and longitude. Allow a 5-degree variance in their answers,but expect that generally they should not be off by more than adegree or two.

PARTNER ACTIVITY

WHOLE-CLASS ACTIVITY

Figure 1

Player 1 rolls a 3 and a 6.The point (6,3) is markedon the grid.

Over and Up Squares

Materials 1 Over and Up Squares Gameboard and Record Sheet (Math Masters, p. 494)

1 colored pencil per player (different colors) 2 six-sided dice

Players 2 Skill Plotting ordered pairs; developing a

winning game strategyObject 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 iton the grid with his or her colored pencil (See Figure 1.)

2. Player 1 records the ordered pair and the score in the firsttable. 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 orderedpair. If both possible ordered pairs are already marked onthe grid, the player rolls the dice again. (Variation: If bothpossible ordered pairs are already marked, the player canchange one or both of the numbers to 0.)

4. Player 2 uses the other colored pencil to mark the ordered pairand records the ordered pair and score in the second table.

5. Players take turns rolling the dice, marking ordered pairs onthe grid, and recording the results. On a player’s turn, if 2marked grid points are next to each other on the same sideof one of the grid squares, the player connects them with aline segment he or she makes. Sometimes more than 1 linesegment may be drawn in a single turn. (See Figure 2.) Aplayer scores 10 points for each line segment drawn.

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 playercolors in the square and earns 50 points. (See Figure 3.)

7. The player with more points after 10 rounds wins.

Games

Figure 3

Player 1 marks (1,2) andscores 10 points. Player 1draws 2 line segments andscores 20 points. The linesegments complete asquare. Player 1 colors inthe square and scores 50points. The score for theround is 80 points.

Figure 2

Player 1 marks (6,4) andscores 10 points. Player 1draws 2 line segments andscores 20 points. The scorefor the round is 30 points.

1 2 3 4 5 6

1

2

4

3

5

6

y

00

x

1 2 3 4 5 6

1

2

4

3

5

6

00

y

x

1 2 3 4 5 6

1

2

4

3

5

6

00

y

x

Student Reference Book, p. 257

Student Page

Adjusting the Activity

165

Math Boxes LESSON

6�9

Date Time

1. Cindy received $40 from her aunt and uncle. She drew a circle graph to show how she will

use the money.

a. How much will she save?

b. How much will be spent on clothes?

c. On movies?

$10

$20

$10

2. Mrs. Moy’s students are folding paper

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?

Number model:

Answer: paper cranes 405

27 � 15 � 405

3. Divide with a paper-and-pencil algorithm.

Write the remainder as a fraction.

598 / 3 �

18 19 22 23179

Clothes

Savings

Cindy's Money

Movies

199 �13

�

red

yellow

orange

5. For this spinner, which color would you be

least likely to land on?

red

80 84

4. Which number sentence is true?

Circle the best answer.

A. 33,000,000 33,000

B. 5,200,000 � 9 million

C. 104 � 10,000

D. six hundred thousand � 106

5 6

�

Math Journal 1, p. 165

Student Page

Lesson 6�9 453

Ongoing Assessment: Informing InstructionWatch 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).

� Playing Over and Up Squares(Student Reference Book, p. 257; Math Masters, p. 494)

Students play Over and Up Squares to practice locating points and plotting points on a coordinate grid.

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 � V I S U A L

� Math Boxes 6�9(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 5previews Unit 7 content.

Ongoing Assessment:Recognizing Student Achievement

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]

� Study Link 6�9(Math Masters, p. 195)

Home Connection Using a picture of the globe, studentslabel important parts of the global grid system.

INDEPENDENTACTIVITY

Math Boxes

Problem 2 �

INDEPENDENTACTIVITY

PARTNER ACTIVITY

2 Ongoing Learning & Practice

STUDY LINK

6�9 Latitude and Longitude

272 273

Name Date Time

Use your Student Reference Book to help you complete this Study Link.

Read the examples and study the figures on pages 272 and 273.

1. Do the following on the picture of the world globe.

a. 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

Hemisphere and also in the Eastern

Hemisphere. Label the point A.

g. Mark a point that is in the Northern

Hemisphere and also in the Western

Hemisphere. Label the point B.

2. The entire continent of Africa is shown in the figure above. Is Africa

mostly in the Western Hemisphere or in the Eastern Hemisphere?

3. Do the equator and prime meridian meet over water or over land? water

Eastern Hemisphere

South Pole

North Pole

line o

f lo

ngitude

equator

line of latitude

prim

e m

erid

ianB

A

Practice

4. � 47 / 3 5. 7��9�8�

6. 217 � 5 � 7. � 804 / 6 13443 R2

1415 R2

Math Masters, p. 195

Study Link Master

454 Unit 6 Division; Map Reference Frames; Measures of Angles

� Using Time to Determine Longitude (Math Masters, p. 388 or 389)

Literature Link To apply students’ understanding oflongitude, 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 accuratesea clock, allowing sailors to know more accurately their locationat sea by giving them the correct home port time.

Have students explain, in a Math Log or on an Exit Slip, whyknowing the correct home port and sea time helped sailorsdetermine longitude at sea. Each hour is marked by exactly15 degrees of longitude. If it is noon on a ship sailing west and3 P.M. at the home port, the ship is 45° west of home port. If aclock on a ship sailing east reads 3 P.M. and the home port time is noon, the ship is 45° east of home port.

� Locating Places with Latitude and Longitude(Math Masters, p. 196)

To practice locating places using latitude and longitude, havesmall groups use a world political map, a penny, and the Latitudeand Longitude Cards cut from Math Masters, page 196.

1. Have students shuffle the Latitude and Longitude Cardsseparately and put them facedown in two piles.

2. Team 1 draws a Latitude Degree Card and then flips a pennyto find whether it is north (heads) or south (tails). The latitudeand direction are recorded, and the card is returned facedownto the bottom of the pile.

3. Team 1 now draws a Longitude Card and flips the penny tofind whether it is east (heads) or west (tails). The longitudeand direction are recorded, and the card is returned to thebottom of the pile.

4. The team uses the information to locate and record thecountry 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.

5–15 Min

SMALL-GROUP ACTIVITYEXTRA PRACTICE

30+ Min

PARTNER ACTIVITY

ENRICHMENT

3 Differentiation Options

Longitude140

E or W

Longitude90

E or W

Longitude40

E or W

Latitude90

N or S

LESSON

6�9

Name Date Time

Latitude and Longitude Cards

Latitude0

Equator

Latitude10

N or S

Latitude20

N or S

Latitude30

N or S

Latitude40

N or S

Latitude50

N or S

Latitude60

N or S

Latitude70

N or S

Latitude80

N or S

Longitude0

PrimeMeridian

Longitude10

E or W

Longitude20

E or W

Longitude30

E or W

Longitude50

E or W

Longitude60

E or W

Longitude70

E or W

Longitude80

E or W

Longitude100

E or W

Longitude110

E or W

Longitude120

E or W

Longitude130

E or W

Longitude150

E or W

Longitude160

E or W

Longitude170

E or W

Longitude180

InternationalDate Line

LongitudePLAYER’SCHOICE

Math Masters, p. 196

Teaching Master