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288 Unit 4 Multiplication and Division

Advance PreparationDisplay maps (see Planning Ahead, page 287). Include the classroom U.S. High/Low Temperatures map.

Cut enough copies of Math Masters, page 109 so that each child has one paper strip (optional). Copy the

Home Link Masters (Math Masters, pages 110 and 111) on two separate pages so that children have the

problems and the maps side-by-side.

Teacher’s Reference Manual, Grades 1–3 p. 184

Key Concepts and Skills• Solve problems involving fractional parts

of regions on a map scale. 

[Number and Numeration Goal 2]

• Fill in missing numbers on number lines. 

[Number and Numeration Goal 6]

• Use multiplication strategies to solve

map-scale problems. 

[Operations and Computation Goal 4]

• Use map scales to estimate the most

direct distance between two places. 

[Measurement and Reference Frames Goal 1]

Key ActivitiesChildren fill in missing numbers on a number

line. Children use map scales to estimate the

most direct distance between two places.

Ongoing Assessment: Recognizing Student Achievement Use the Math Message. [Number and Numeration Goal 6]

Key Vocabularymap scale � as the crow flies � scale factor

MaterialsMath Journal 1, pp. 95 and 96

Home Link 4�8

Math Masters, p. 109 (optional)

map display � straightedge � blank sheet of

paper or tinted transparency � half-sheet

of paper

Areas of RectanglesMath Journal 1, pp. 96A and 96B

Student Reference Book, pp. 154,

155, 156A, and 156B

Children practice multiplying side

lengths to find the areas of rectangles.

Playing Division ArraysStudent Reference Book, p. 282

per group: 1 each of number

cards 6–18 (from the Everything

Math Deck, if available), 18 counters,

1 six-sided die

Children practice basic division facts

as well as recognition of even and

odd numbers.

Math Boxes 4�9Math Journal 1, p. 97

Children practice and maintain skills

through Math Box problems.

Home Link 4�9Math Masters, pp. 110 and 111

Children practice and maintain skills

through Home Link activities.

READINESS

Exploring Scaleper partnership: toy animals, large paper,

crayons, research materials

Children compare the sizes of toy animals

to the actual sizes of real animals.

ENRICHMENTMaking Scale DrawingsMath Masters, p. 112

ruler

Children draw classroom objects to scale.

Teaching the Lesson Ongoing Learning & Practice

132

4

Differentiation Options

Estimating Distanceswith a Map Scale

Objective To introduce the use of a map scale to

estimate distances.e

�������

eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

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Adjusting the Activity

Lesson 4�9 289

0 400

0 1

0 400−100 500200100 300

Number line extended by 100s

0− 1 1 11–

21–4

3–4

1–2

1–4

1–4

−

1–2

Number line extended by 1

_ 4 s

Links to the FutureThe activities in this lesson are an early

exposure to map scales. Using a map

scale to estimate distances is a Grade 4

Goal. Using scales to find distances is a

Grade 5 Goal.

�

Math

Message �

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASSDISCUSSION

Children share their results and their thinking. Then ask them to extend the first number line in both directions and the second number line to the right.

Have children extend the second number line to the left as well as to

the right.

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: Recognizing Student Achievement

Use the Math Message to assess children’s progress toward using number lines

to order whole numbers and fractions. Children are making adequate progress if

they are able to fill in the first number line. Some children may be able to fill in

the second number line.

[Number and Numeration Goal 6]

� Introducing Map Scales WHOLE-CLASS ACTIVITY

Point out the maps on display. Children might notice that the maps do not cover the same areas. For example, a map of a city may be on the same size piece of paper as a map of the United States. Discuss how that is possible with map scales. Explain that a map scale is a tool that helps to estimate real distances between places shown on a map by relating distances on the map to distances in the real world.

ELL

Getting Started

Home Link 4�8 Follow-Up Before turning in their work, have partners share their answers. Have them compare their arrays and answers for Problems 3 and 4.

Math MessageCopy the number lines. Fill in the missing numbers on a half-sheet of paper.

Mental Math and ReflexesPose multiplication facts. Suggestions:

1 × 3 3 2 × 3 6 5 × 3 15 10 × 3 30

6 × 3 18 7 × 3 21 8 × 3 24 9 × 3 27

30 × 1 30 30 × 2 60 30 × 3 90 30 × 4 120

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290 Unit 4 Multiplication and Division

Adjusting the Activity

Adjusting the ActivityName Date Time

One-Inch SegmentsLESSON

4�9

Math Masters, p. 109

Teaching Master

If possible, show children two maps of the same area that have

different scale factors. Another option is to show some different-size school

pictures (2 by 3, 4 by 6, and 8 by 10) of the same person.

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

If the scale is not given on a map, make an approximate scale. The distance from coast to coast in the United States, for example, from New York to Los Angeles, is about 2,500 miles as the crow flies. To support English language learners, take a moment to discuss the meaning of the expression, as the crow flies. Measure that distance on the map to make an approximate scale of miles per inch, rounded off to an easy number.

Cartographers (mapmakers) scale down large areas of land and space to represent them on paper. Places that are actually thousands of miles apart appear only inches apart on a map. People then estimate real distances using map scales.

Different maps use different scale factors. On one map, 1 inch may represent 10 miles; on another map, 1 inch may represent 100 miles. To support English language learners, write scale factor on the board along with some examples of scale factors using available maps.

Have children imagine that they are drawing a floor plan of their kitchen

on notebook paper. Their drawings will have to be scaled down in order to fit on

the paper.

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

� Estimating Distances WHOLE-CLASS ACTIVITY

on a U.S. MapTalk about as-the-crow-flies distances—the most direct route from point to point on a map. Actual road distances are longer than these direct paths. Point out the scale information for the classroom map.

Ask children how they might estimate the distance between the cities with the highest and lowest temperatures for the current week. Discuss, try, and compare some of their ideas. Model the following methods in your discussion.

Estimating DistancesLESSON

4�9

Date Time

1

9

10

7

2

3

4

5

6

8

Map S

cale

0300 m

iles

1 inch r

epre

sents

300 m

iles

1.

Mo

un

t S

t. H

ele

ns

6

. C

ivil

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hts

Me

mo

ria

l

2.

Sa

nta

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oo

7

. S

tatu

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f L

ibe

rty

3.

Ye

llow

sto

ne

Na

tio

na

l P

ark

8

. W

hite

Ho

use

4.

Pik

es P

ea

k

9

. C

ow

bo

y H

all

of

Fa

me

5.

Se

ars

To

we

r 1

0.

Sp

ace

Sh

utt

le L

au

nch

Site

,

Ca

pe

Ca

na

ve

ral

Loca

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ns

to V

isit

9

EM3MJ1_G3_U04_79-101.indd 95 12/20/10 6:23 PM

Math Journal 1, p. 95

Student Page

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Adjusting the Activity

Lesson 4�9 291

1

9

10

7

2

3

4

5

6

8

N

EW

SMap Scale

0 300 miles

1

9

10

7

2

3

4

5

6

8

N

EW

SMap Scale

0 300 miles

1

9

10

7

2

3

4

5

6

8

N

EW

SMap Scale

0 300 miles

1

9

10

7

2

3

4

5

6

8

N

EW

SMap Scale

0 300 miles

A Pretend TripLESSON

4�9

Date Time

Pretend that you want to take a trip to see some of the sights in the

United States. Find out about how far it is between locations.

1. Yellowstone National Park is number .

The Cowboy Hall of Fame is number .

The distance between them is about inches on the map.

That is about miles.

2. Pikes Peak is number .

The White House is number .

The distance between them is about inches on the map.

That is about miles.

3. The Civil Rights Memorial is number .

Santa Ana Zoo is number .

The distance between them is about inches on the map.

That is about miles.

4. The Statue of Liberty is number .

The Sears Tower is number .

The distance between them is about

inches on the map.

That is about miles.

5. Make up one of your own.

is number .

is number .

The distance between them is about

inches on the map.

That is about miles.

Try This

93

3

9004

85

62

6

7

5

14

3 1

_ 2

2 1

_ 2

750

1,050

1,800

1,500

Mount St. Helens

Pikes Peak

Sample answers:

79-101_EMCS_S_SMJ_G3_U04_576353.indd 96 1/26/11 9:11 AM

Math Journal 1, p. 96

Student Page

Date Time

96A

Areas of RectanglesLESSON

4�9

1.

This is a -by- rectangle.

Area = square units

Number model: × =

2.

This is a -by- rectangle.

Area = square units

Number model: × =

Fill in the blanks.

3.

This is a -by- rectangle.

Area = square units

Number model: × =

4.

This is a -by- rectangle.

Area = square units

Number model: × =

5.

This is a -by- rectangle.

Area = square units

Number model:

× =

6.

This is a -by- rectangle.

Area = square units

Number model:

× =

10 units

5 units

7 units

4 units

9 units

6 units

6 units

7 units

5 units

4 units

2 units

3 units

7

28

4 7 50

5 10

50

5 1028

4

6

42

7 6 54

6 9

54

6 942

7

2

6

3 2 20

4 5

20

4 56

3

79-101_EMCS_S_SMJ_G3_U04_576353.indd 96A 1/26/11 9:11 AM

Math Journal 1, p. 96A

Student Page

Method 1

Lay a piece of paper or a tinted transparency between the two cities, mark the distance on the paper, and then mark off the measured piece along the map scale while counting the miles as indicated on the scale.

Method 2

Mark off the scale repeatedly on the edge of a strip of paper and then use that strip of paper to read the distances directly.

Have children estimate partial distances between the marked

increments. For example, children estimate about two and a half 100-mile

increments as 250 miles.

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

� Estimating Mileage PARTNER ACTIVITY

on a U.S. Map(Math Journal 1, p. 95; Math Masters, p. 109)

Point out the scale for the map on the journal page. This scale shows that approximately 300 miles are represented by 1 inch on the map. Choose two locations on the map, such as the Santa Ana Zoo and Mount St. Helens, and measure the distance between them. You may want to have the class try one or both of the following methods.

Method 1

Partners use the edge of a piece of paper to mark the distance between the points as described in the previous activity.

Method 2

Children use the paper strips from Math Masters, page 109, marked off in 1-inch segments, to read the distance.

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NOTE You may want to tell children that

on Math Journal 1, page 95, the Sears

Tower has been renamed Willis Tower, but

many people continue to refer to it as the

Sears Tower.

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292 Unit 4 Multiplication and Division

5. Ages of 9 grandfathers:

60, 54, 79, 80, 65, 74, 70, 65, 81

mode = 65

median = 70

3. Complete.

Date Time

2. Complete the Fact Triangle and

write the fact family.

7 × 4 = 28

4 × 7 = 28

28 ÷ 4 = 7

28 ÷ 7 = 4

4. Draw an array of 28 Xs arranged

in 4 rows.

How many Xs in each row? 7 Xs

Write a number model for the array.

4 × 7 = 28 or 28 ÷ 4 = 7

1. Write <, >, or 5.

5 × 5 > 4 × 4

1 × 9 > 7 × 1

6 × 2 < 2 × 8

3 × 7 = 7 × 3

Math BoxesLESSON

4�9

64 65

80 81

in out

9 3

15 5

21 7

30 10

Answers vary.

52203–204

13 56 55

6. Fill in the empty

frames.

200 201

Rule

in

out

÷3

•

7 4

28×,÷

Rule

�1,000

6,670

7,6708,6709,670

10,670

5,6704,670

79-101_EMCS_S_SMJ_G3_U04_576353.indd 97 2/4/11 10:24 AM

Math Journal 1, p. 97

Student Page

NOTE Have children who are unfamiliar

with these locations do some research on

the Internet to determine if they would be

interested in visiting them.

Date Time

Areas of Rectangles continuedLESSON

4�9

Follow these steps to find the area of the shape shown below. Show

your work.

1. Divide the shape below into rectangles.

2. Use your ruler to measure the sides of each rectangle in centimeters.

Label the sides of the rectangles with the measures.

3. Find the area of each rectangle.

4. How can the area of each rectangle help you find the area of the shape?

Sample answer: The rectangles are parts of

the whole shape. If I find the area of each

part and then add the areas together, I can

cm8

cm2

cm4 cm4

cm4

cm3 cm3

cm4

Total area of shape = 40 square cm

find the area of the whole shape.

79-101_EMCS_S_SMJ_G3_U04_576353.indd 96B 2/10/11 2:49 PM

Math Journal 1, p. 96B

Student PageCirculate and help as needed. Bring the class together to share the results and discuss strategies. Come to a consensus for the estimate. About 900 miles between the Santa Ana Zoo and Mount St. Helens Have children use a straightedge to draw a line segment between the two locations and label it with the estimated mileage.

Point out that this measurement is an as-the-crow-flies estimate to the nearest 50 or 100 miles. Explain that such estimates provide useful information about the relative distances between locations.

Have the class repeat the procedure with other locations. Use the map scale to find the distance; draw a line segment between the locations, and then label it with the distance. Suggestions:

� Cowboy Hall of Fame and Civil Rights Memorial About 600 miles

� Statue of Liberty and Santa Ana Zoo About 2,250 miles

� Willis Tower (formerly Sears Tower) and Space Shuttle Launch Site, Cape Canaveral About 975 miles

� Taking a Pretend Trip PARTNER ACTIVITY

(Math Journal 1, pp. 95 and 96)

Children work with partners or in small groups to answer questions about a pretend trip. Circulate among the groups to offer assistance. Bring the class together to share their strategies for estimating distances between locations.

2 Ongoing Learning & Practice

� Areas of Rectangles PARTNER ACTIVITY

(Math Journal 1, pp. 96A and 96B; Student Reference Book,

pp. 154, 155, 156A, and 156B)

Children practice multiplying side lengths of rectangles on journal page 96A to find the areas. They find the area of a rectilinear figure on journal page 96B. If necessary, have children read Student Reference Book, pages 154, 155, 156A, and 156B.

� Playing Division Arrays SMALL-GROUP ACTIVITY

(Student Reference Book, p. 282)

Children practice basic division facts as well as recognition of even and odd numbers by playing Division Arrays. If necessary, review the game directions on page 282 in the Student Reference Book.

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Lesson 4�9 293

Name Date Time

LESSON

4�9 Scale Drawings

Measure the length and width of your Math Journal in cm. Draw your

journal to scale on the grid. 1 cm represents 10 cm.

Scale: 1 cm represents 10 cm

1. Math Journal

length: about cm

width: about cm

Choose 1 more object. Record the length and width in cm. Draw the

object to scale on the cm grid.

2. Object:

length: about cm

width: about cm

21�12

�

27�12

�

Scale

1 cm : 10 cm

Answers vary.

Math Masters, p. 112

Teaching Master

Name Date Time

Family Note text

Please return this Home Link to school tomorrow.

000 000

Using a Map ScaleHOME LINK

4�9

Your child is just learning how to use a map scale. He or she should use the scale to measurean as-the-crow-flies estimate for each problem. This expression refers to the most direct routebetween two points, disregarding road distance. Actual road distances are longerthan these direct paths.

Please return this Home Link to school tomorrow.

For each question, circle all reasonable answers. (There may be more

than one reasonable answer.) All distances are as the crow flies. Be

sure to use the map scale on the next page.

1. About how many miles is it from New York to Los Angeles?

about 1,000 miles

more than the distance from Chicago to Dallas

about 2,400 miles

2. About how many miles is it from Chicago to Atlanta?

about 600 miles

more than the distance from Chicago to Seattle

less than the distance from Chicago to Denver

3. About how many miles is it from Seattle to Dallas?

about 2,600 miles

about 5,000 miles

more than the distance from New York to Chicago

4. About how many miles is it from New York to Atlanta?

less than the distance from Denver to Atlanta

more than the distance from New York to Portland

about 750 miles

FamilyNote

Math Masters, p. 110

Home Link Master

� Math Boxes 4�9 INDEPENDENTACTIVITY

(Math Journal 1, p. 97)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 4-6. The skill in Problem 6 previews Unit 5 content.

Writing/Reasoning Have children write an answer to the following: Explain how you figured out the number you wrote in the first empty frame of Problem 6. Sample

answer: I subtracted 1,000 from the number in the second frame.

� Home Link 4�9 INDEPENDENTACTIVITY

(Math Masters, pp. 110 and 111)

Home Connection Children estimate distances between U.S. cities on a map.

3 Differentiation Options

READINESS PARTNER ACTIVITY

� Exploring Scale 15–30 Min

To explore scale using concrete models, have children bring in toy animals and compare them to the animals’ actual size. Children bring a toy animal from home. They research the actual dimensions of the animal—either on the Internet or in a book. On large-size paper, children draw a rectangle for the animal’s approximate size. They display their toy animals next to the rectangle representing the animal’s actual size. If possible, provide some models that are scaled up, for example, an insect that is smaller than its scale model. Briefly discuss why toy animals are usually scale models.

ENRICHMENT PARTNER ACTIVITY

� Making Scale Drawings 5–15 Min

(Math Masters, p. 112)

To apply children’s understanding of scale, have them make scale drawings of classroom objects. Children follow directions on Math Masters, page 112.

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