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Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

Lesson 6�8 443

Advance PreparationFor Part 1, you may want to use a road atlas of the United States to illustrate the use of indexes and

letter-number grid coordinates.

Teacher’s Reference Manual, Grades 4–6 pp. 249–252

Key Concepts and Skills• Use a map scale.

[Operations and Computation Goal 7]

• Estimate distances on a map.

[Measurement and Reference Frames Goal 1]

• Use ordered number pairs to locate points

on a map.


• Use letter-number pairs to locate points

and regions on a map.


Key ActivitiesStudents use letter-number pairs to find

locations on a map of Ireland. They use

ordered pairs of numbers to identify points,

give directions, and describe routes on a

campground map. Students use a map scale

to estimate distances.

Ongoing Assessment: Recognizing Student Achievement Use a Math Log or Exit Slip (Math Masters, page 388 or 389). [Measurement and Reference Frames

Goal 4]

Key Vocabularyindex of locations � letter-number pair �

ordered number pair � map scale

MaterialsMath Journal 1, pp. 161–163

Study Link 6�7

Math Masters, p. 388 or 389 (optional)

compass (optional) � slate � road atlas

(optional)

Playing Angle TangleStudent Reference Book, p. 230

Math Masters, p. 457

protractor � straightedge

Students practice estimating

the measures of angles and

measuring angles.

Finding Real-Life Angle MeasuresMath Journal 1, pp. 163A and 163B

Students practice finding unknown

angle measures.

Math Boxes 6�8Math Journal 1, p. 160

Students practice and maintain skills

through Math Box problems.

Study Link 6�8Math Masters, p. 194

Students practice and maintain skills

through Study Link activities.

READINESS

Moving on a Coordinate Gridmasking tape and index cards, or rope and

colored tape

Students describe the locations of points and

plot points on a life-size coordinate grid.

ENRICHMENTPlaying Grid SearchStudent Reference Book, pp. 250 and 251


Students practice naming and locating grid

squares and develop search strategies.

EXTRA PRACTICE

Plotting and Naming Points on a Coordinate GridMath Masters, p. 440

Students plot and name points on a

coordinate grid.

Teaching the Lesson Ongoing Learning & Practice

132

4

Differentiation Options

��

Rectangular CoordinateGrids for Maps

Objectives To guide students in the use of letter-number pairs

and ordered pairs of numbers to locate points on a grid; and to

provide practice using a map scale.

a

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

A Map of the Island of IrelandLESSON

6�8Bantry B-1

Belfast F-7

Carlow E-3

Castlebar B-6

Derry E-8

Dublin F-4

Dundalk F-6

Galway C-4

Gort C-4

Kilkee B-3

Lahinch B-4

Larne F-7

Limerick C-3

Mullingar E-5

Navan E-5

Omagh E-7

Tralee B-2

Tuam C-5

Westport B-5

Wicklow F-4

0 50 100 150 200 250 Miles

Tuam

Galway

Lahinch

Ennis

Gort

Loughrea

BallinasloeAthlone

Roscrea

Tarbert

Listowel

Tralee

Dingle

Killarney

Kenmare

Bantry

Skibbereen

Kinsale

Cork

Millstreet

MallowFermoy

Youghal

Dungarvan

Waterford

Wexford

Rosslare Harbor

Macroom

Clifden

Westport

Belmullet

Castlebar

Ballina

Sligo

Bundoran

Killybegs

Donegal

LetterkennyDerry/Londonderry Ballymena

Boyle

Kilkee

Cahersiveen

Clonakilty

New Ross

Dublin

Port Laoise

Clonmel

Cashel

Nenagh

ThurlesKilkenny

Carlow

Bray

Wicklow

Arklow

Enniscorthy

Naas

Tipperary

Rathkeale

Limerick

Ballybofey

Bangor

Belfast

A B C D E F G

A B C D E F G

8

7

6

5

4

3

2

1

8

7

6

5

4

3

2

1

0 50 100 150 200 250 Kilometers

�

Coleraine

Larne

Portadown

DungannonOmagh

Monaghan

Cavan

Longford

Mullingar

NavanDrogheda

Dundalk

NewryNewcastle

DownpatrickArmagh

N

W E

S

Date Time

EM3MJ1_G4_U06_137-169.indd 161 1/13/11 2:24 PM

Math Journal 1, p. 161

Student Page

NOTE The larger part of the island is the

Republic of Ireland. The smaller northern

part is Northern Ireland, a part of the United

Kingdom.

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASS ACTIVITY

(Math Journal 1, p. 161)

Social Studies Link The map on journal page 161 shows the island of Ireland. Ask students how they found Tralee.

Make sure they know how to use the index of locations. Look up Tralee in the list above the map. It is located in square B-2. Find column B and row 2. The column and row overlap at a square region. Tralee is located in this region.

● Why is this letter-number pair method useful for finding places on a map? It limits the search to a small part of the map.

Have students find other locations on the map.

Point out that in the Math Message students used letter-number pairs to locate regions on a map. In the remainder of the lesson, students will use ordered number pairs to locate specific points on a campground map.

� Using Ordered Pairs to WHOLE-CLASS ACTIVITY

Locate Points on a Map(Math Journal 1, p. 162)

Ask students to look at the campground map and symbols on journal page 162. Tell them that these are standard symbols for United States topographic maps and most conventional road maps. Students should notice that the map has been drawn on a rectangular coordinate grid. Remind them that they can locate points by naming ordered number pairs, such as (0,3) and (7,6).

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Getting Started

Math Message Turn to journal page 161. Find the city of Tralee on the map. Be prepared to explain how you found it.

Study Link 6�7 Follow-Up Students compare answers. The final problem is more difficult because the angle is a reflex angle and the half-circle protractor cannot directly measure angles greater than 180°. Have students share their strategies. One possible strategy: The smaller angle has a measure of 60°. Subtract 60° from 360° to get 300°, which is the measure of the reflex angle.

Mental Math and Reflexes Pose multiplication and division number stories. Suggestions:

3 boxes of beads; 4 beads per box: How many beads in all? 12

12 cups divided equally between 2 trays: How many cups per tray? 6

8 boxes of cupcakes; 6 cupcakes per box: How many cupcakes in all? 48

5 shirts per rack; 45 shirts in all: How many racks? 9

4 crates of tennis balls; 8 cans per crate; 3 balls per can: How many tennis balls in all? 96

180 seats in all; 10 seats per row; 6 rows per section: How many sections? 3

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Adjusting the Activity

Date Time

A Campground MapLESSON

6�8

Camping Area

Picnic Area

Paved Road

Unpaved Road

Trail

River

0 0.2 0.4 0.6 0.8 1 km

SCALE

12

11

10

9

8

7

6

5

4

3

2

1

00 1 2 3 4 5 6 7 8 9 10 11 12

Lake Trail

Gravel Road

County Road

Parking Lot

Ranger Stationand House

Canoe

Rental

Fishing Dock

Camping Area

Picnic AreaBlue Lake

N

W E

S

F

B

C

S

H

144 145


Student Page

Finding Distances on a MapLESSON

6�8Use the campground map on journal page 162 to complete the following:

1. Suppose you hiked along the lake trail from the

fishing dock to the parking lot. Estimate the distance

you hiked. About km

2. The ranger made her hourly check. She started at the

ranger station. She drove northwest and then north

on Gravel Road to County Road. She turned east

onto County Road and drove past the parking lot

and the camping area. After she passed the canoe

rental, she turned right onto Gravel Road and drove

back to the ranger station. About what distance did

she drive? About km

3. Estimate the distance around Blue Lake. About km

4. You are planning to hike from the camping area to

the parking lot. You will stay on the roads or trails.

You want to hike at least 5 kilometers.

a. Plan your route. Then draw it on the map with a

colored pencil or crayon.

b. Estimate the distance. About km

5. Use the ordered number pairs to locate each item on the map. Mark a dot

at the location. Next to the dot, write the letter given for the feature.

2.5–3.5

6.5–7.5

2–3

Answersvary.

Sample answers:

Campground Features ChartLocation Letter

parked car (5,9) C

boat (3�12

�,8) B

swing set (8,11) S

hikers (10.5,6.5) H

farmhouse (�12

�,7) F

Date Time

144 145


Student Page

Lesson 6�8 445

To review the concept that the order of the numbers in an ordered pair is important, ask students which ordered pair—(3,7) or (7,3)—names a point in Blue Lake. To find point (3,7), start at 0, go 3 to the right, and then go up 7. To find point (7,3), start at 0, go 7 to the right, and then go up 3. The ordered pair (3,7) names a point in Blue Lake; (7,3) does not.

Then ask students to name an ordered pair that describes the location of the ranger station. Some students may name (6,1), but point out that (5 1 _ 2 , 1 1 _ 2 ) is a better answer because the station is located in the middle of a grid square.

Practice naming ordered pairs with other examples, including points that are between grid lines.

A “ladder” metaphor may help some students plot ordered number

pairs. The first number tells where to put the ladder. The second tells how high

to climb. Or have students locate points by making heel-to-toe steps from the

origin (0,0) to named points (x,y). Students chant “over” as they move to the

x-coordinate and then “up” as they move to the y-coordinate.

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

Ongoing Assessment: Math Log

or Exit SlipRecognizing Student Achievement

Use a Math Log or an Exit Slip (Math Masters, page 388 or 389) to assess

students’ understanding of coordinate grid systems. Ask students to compare

the grid system on the map of Ireland to the one on the campground map.

Students are making adequate progress if they mention the following:

� The grid of the map of Ireland identifies square regions using letter-number

pairs.

� The grid of the campground map identifies points using ordered pairs of

numbers.

� The order in a letter-number pair is not important, but the order of the

numbers in an ordered number pair is important.


� Estimating Distances PARTNER ACTIVITY

on a Map(Math Journal 1, pp. 162 and 163)

Point out the map scale on journal page 162. To support English language learners, write map scale on the board and explain that the scale tells the relationship between the measured distance on the map and the actual distance. Students should notice that each side of a grid square represents 0.2 kilometers.

ELL

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Adjusting the Activity


Using a compass to estimate the distance around

an irregular shape

0 0.2 0.80.4 0.6 1 km

Date Time

Dartboard AnglesLESSON

6�8

A regulation dartboard is made up of 20 equal sectors. The measure of each sector’s

angle is 18 degrees.

20

3 17

12

2

9

15

14

10

11 6

8

13

16

4

7

18

19

15

18°

Solve Problems 1–3 without using your protractor. After you have solved each

problem, write a number model with a letter for the unknown to show how you found

your answer.

1. Draw ∠ABC around sectors 14, 9, 12, 5, 20, and 1. What is the measure of ∠ABC ?

20

3 17

12

2

9

15

14

10

11 6

8

13

16

4

7

18

19

15

A

C

B

Measure of ∠ABC = 108 °

Number model with unknown: 18 + 18 + 18 + 18 + 18 + 18 = mSample answer:

137-169_EMCS_S_MJ1_G4_U06_576361.indd 163A 2/15/11 5:52 PM

Math Journal 1, p. 163A

Student Page

Ask students to estimate the distance along Lake Trail from the fishing dock to the parking lot and to record it on journal page 163. Have students compare estimates and strategies:

� Count the number of squares the trail passes through. 15 Each side of a grid square represents a distance of 0.2 kilometers, so the length of the trail is about 3 kilometers.

� Make a mark on the edge of a sheet of paper. Place that mark at the beginning point of the trail with the edge of the paper along the trail. When the trail turns, make a mark on the edge and turn the paper so the edge follows the trail. When you reach the end of the trail, make a final mark. Measure the distance between the first and last marks on the paper. Then use the map scale to estimate the actual distance.

� Use a traditional compass. On the map scale, set the opening of the compass to represent 0.2 kilometers. Place the anchor point at the fishing dock and swing the pencil point, marking off about 0.2 km along the trail. Place the anchor point on this mark and swing the pencil point, marking off the next 0.2 km along the trail. Continue to the end of the trail. Count the number of compass swings and estimate the distance. 11 or 12 compass swings, or about 2.2 to 2.4 km

Ask: Why are the estimates obtained by the last two methods above probably less than the actual length? Each segment on the paper’s edge or each compass swing measures the path as though it were made up of straight pieces. Such a path would be a little shorter than the actual curved path.

Have partnerships complete the journal page and share results.

2 Ongoing Learning & Practice

� Playing Angle Tangle PARTNER ACTIVITY

(Student Reference Book, p. 230; Math Masters, p. 457)

Students play Angle Tangle to practice estimating and measuring angles.

Use this game variation as appropriate: Have students draw and

measure reflex angles. Their drawings should include the directional arc in the

appropriate place.

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

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STUDY LINK

6

�8 Coordinate Grids

144

Name Date Time

1. Plot and label each point on the coordinate grid. A (1,7)

B (6,6)

C (10,1)

D (4,3)

E (8,6)

F (2,9)

G (9,1)

H (10,4)1

2

4

3

5

6

7

8

9

10

01 2 3 4 5 6 7 8 9 100

B

C

D

EA

F

G

H

2. Write the ordered number pair for each point plotted on the coordinate grid.

I ( , )

J ( , )

K ( , )

L ( , )

M ( , )

N ( , )

O ( , )

P ( , )

Q ( , )

R ( , ) 10321048268151077842735

1

2

4

3

5

6

7

8

9

10

01 2 3 4 5 6 7 8 9 100

I

J

K

L

M

N

O

P

Q

R

3. 28 ∗ 7 = 4. 304 ∗ 5 =

5. = 52 ∗ 89 6. = 43 ∗ 361,5484,6281,520196

Practice

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Study Link Master

Lesson 6�8 447

Date Time

Dartboard Angles continuedLESSON

6�8

2. The measure of angle DFE = 54° and the measure of angle DFG = 252°. What is the

measure of reflex angle EFG?

20

3 17

12

2

9

15

14

10

11 6

8

13

16

4

7

18

19

15

G

E

F

D

Measure of reflex angle EFG = 198 °

Number model with unknown: 54 + a = 252

3. Angle RST is a right angle. Use your straightedge to draw ray SM so that the measure of

∠MST = 54° and ∠RSM is an acute angle. Then find the measure of ∠RSM.

20

3 17

12

2

9

15

14

10

11 6

8

13

16

4

7

18

19

15R

M

T

S

Measure of ∠RSM = 36 °

Number model with unknown: 90 - 54 = dSample answer:

Sample answer:

137-169_EMCS_S_MJ1_G4_U06_576361.indd 163B 2/15/11 5:52 PM

Math Journal 1, p. 163B

Student Page

Date Time

Math Boxes LESSON

6�8

5. Round to the nearest hundred-thousand.

a. 9,540,234 9,500,000 b. 37,609,034 37,600,000 c. 78,291,554 78,300,000 d. 290,696,332 290,700,000

6. Fill in the missing fractions on the number line.

1. Name the ordered number pair for each point plotted on the coordinate grid.

A ( 2 , 5 )

B ( 4 , 4 )

C ( 1 , 3 )

D ( 2 , 2 )

E ( 4 , 1 )

3. ∠EDF is acute (acute or obtuse).

Measure of ∠EDF = 80 °.

4. Cross off the names that do not belong in the name-collection box below.

93142 143 149

182 183 316

2. Complete the “What’s My Rule?” table and state the rule.

54321

5

4

3

2

1

00

C

A

D

B

E

162–166144

Rule

-1.5 in out

3.6 2.1

10 8.5

7.2 5.7 6.4 4.9

E

DF

32

81 - 49

9 ∗ 4

(5 ∗ 6) + 2

98 ÷ 3

10 + 15 + 7

0 112

14

34��

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Student Page

� Finding Real-Life Angle INDEPENDENTACTIVITY

Measures(Math Journal 1, pp. 163A and 163B)

Students practice finding unknown angle measures using real-life examples. Using addition and subtraction, students find missing measures on a dartboard.

� Math Boxes 6�8 INDEPENDENTACTIVITY

(Math Journal 1, p. 160)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 6-10. The skill in Problem 6 previews Unit 7 content.

Writing/Reasoning Have students write a response to the following: Explain how to use the in and out numbers in Problem 2 to determine the rule. Sample answer: The first

two rows have both the in and out numbers. The out numbers are smaller than the in numbers, so I thought the rule might involve subtraction. I subtracted the out number from the in number in both rows and got 1.5 for an answer, so I knew the rule was –1.5.

� Study Link 6�8 INDEPENDENTACTIVITY

(Math Masters, p. 194)

Home Connection Students plot and label points on a coordinate grid. They write the ordered number pair for each point.

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Grid Search

Materials � 1 sheet of Grid Search Grids for each player (Math Masters, p. 486)

Players 2Skill Deduction; developing a search strategy Object of the game To locate the opponent’s queen on a coordinate grid in the fewest turns possible. DirectionsPlayers sit so that they cannot see what the other player isdoing. Each player uses 2 grids like those shown at the right.

Advance Preparation Before the start of the game, each playersecretly decides where to place a queen and 6 knights on theirGrid 1. They write the letter Q to record the location of thequeen and the letter K to record the location of each knight.

♦ The queen may be placed on any square.♦ The knights may also be placed on any squares, as long

as the queen and the knights can all be connected withoutskipping squares.

These are acceptable arrangements of the pieces:

Games

My Pieces(Grid 1)

Opponent’s Pieces(Grid 2)

These are not acceptable arrangements because the piecescannot be connected without skipping squares.

Student Reference Book, p. 250

Student Page

The book is located at blue 3, red 5.

1 2 3 4 5 6

1

2

3

4

5

6

I LoveMath

3 Differentiation Options

READINESS SMALL-GROUP ACTIVITY

� Moving on a Coordinate Grid 15–30 Min

To provide experience locating ordered pairs, create or have students help you create a life-size 6-by-6 coordinate grid on the floor. Suggestions:

� Use masking tape to mark off the x-axis and y-axis on carpet or a tile floor. Use index card “tents” (two colors) to mark the points on each axis.

� Tie two ropes together to create the x-axis and y-axis. Use two colors of electrical tape at regular intervals to mark the points on each axis. (See margin.)

Place objects on the coordinate grid. Have students describe their location.

Give directions for students to follow to “plot” themselves on the grid. For example, Walk over 3 blue steps. Now walk up 5 red steps.

ENRICHMENT PARTNER ACTIVITY

� Playing Grid Search 15–30 Min

(Student Reference Book, pp. 250 and 251;

Math Masters, p. 486)

To apply students’ understanding of coordinate grids, have them play Grid Search. Expect students to develop strategies for zeroing in on the area where the queen has been hidden. They may also invent variations—add more knights, add a king worth 7 points, and so on.

EXTRA PRACTICE INDEPENDENTACTIVITY

� Plotting and Naming Points 5–15 Min

on a Coordinate Grid(Math Masters, p. 440)

To practice plotting and labeling points (including those between grid lines) on a coordinate grid, have students complete Math Masters, page 440. Fill in the page to create a new set of problems for students each time they use the master or have students create and solve their own problems.

Planning Ahead

In Part 1 of Lesson 6-9, you will need a world globe and a wall map.


rectangular coordinate grids for maps - everyday math coordinate grids for maps objectives to guide...

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