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CurriculumFocal Points

Common Core State Standards

664 Unit 8 Perimeter and Area

Advance PreparationThe grid on journal page 225 accommodates a classroom up to 25 feet by 30 feet. If a larger grid is

needed, make a copy of Math Masters, page 443 for each student to cut out and tape next to the grid on

the journal page. Or, let 1

_ 4 inch represent 2 feet on the journal grid (although this scale is harder to use).

The scale drawing will also be used in Lesson 8�3.

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

Scale DrawingsObjectives To provide practice measuring distance to the

nearest foot; and to provide experience creating a scale drawing

on a grid using measurements and a given scale.

Key Concepts and Skills• Find the median of a data set. 

[Data and Chance Goal 2]

• Make a rough floor plan of the classroom. 

[Operations and Computation Goal 7;

Measurement and Reference Frames Goal 1]

• Make a scale drawing of the classroom.  

[Operations and Computation Goal 7;

Measurement and Reference Frames Goal 1]

• Measure to the nearest foot. 

[Measurement and Reference Frames Goal 1]

Key ActivitiesStudents make a rough floor plan of the

classroom. They use the rough floor plan

to create a scale drawing of the classroom

on grid paper.

Ongoing Assessment: Informing Instruction See page 666.

Key Vocabularyrough floor plan � scale drawing � scale

MaterialsMath Journal 2, pp. 224 and 225

Study Link 8�1

Math Masters, p. 443 (optional)

transparency of Math Masters, p. 443

(optional) � straightedge � per partnership:

1 tape measure � slate

Multiplying a Fraction by a Whole NumberMath Journal 2, pp. 226A and 226B

Students practice multiplying fractions

by whole numbers.

Math Boxes 8�2Math Journal 2, p. 226

Students practice and maintain skills

through Math Box problems.

Ongoing Assessment:Recognizing Student Achievement Use Math Boxes, Problem 1.  [Measurement and Reference Frames Goal 2]

Study Link 8�2Math Masters, p. 250

ruler

Students practice and maintain skills

through Study Link activities.

READINESS

Measuring to the Nearest FootMath Masters, p. 251 and p. 388 or 389

scissors

Students use a “foot-long foot” to measure

objects to the nearest foot.

ENRICHMENTMaking a Scale Drawing of Your BedroomMath Masters, pp. 252 and 253

straightedge � tape measure � scissors �

tape

Students make scale drawings of their

bedrooms and bedroom furniture.

EXTRA PRACTICE

Taking a 50-Facts TestMath Masters, pp. 413 and 414; p. 416

(optional)

pen or colored pencil

Students take a 50-facts test. They use a

line graph to record individual and optional

class scores.

ELL SUPPORTBuilding Background for Mathematics WordsStudents list possible ways of using the

word scale.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

�������

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A Floor Plan of My ClassroomLESSON

8�2

Date Time

When architects design a room or house, they usually make two drawings. The first drawing

is called a rough floor plan. It is not carefully drawn. But the rough floor plan includes all of

the information that is needed to make an accurate drawing. The second drawing is called

a scale drawing. It is drawn on a grid and is very accurate.

Rough floor plan for a bedroom Scale drawing for a bedroom

(1 grid length represents 1 foot.)

1. What information do you need to draw a rough floor plan?

Sample answer: You need the dimensions ofthe walls, windows, and doors. You also needto know the shape of the room.

Architects use these symbols

to show windows and doors:

2. Make a rough floor plan of your classroom in the space below.

window door opening to left door opening to right

Answers vary.

219-247_EMCS_S_MJ2_G4_U08_576426.indd 224 2/1/11 1:47 PM

Math Journal 2, p. 224

Student Page

Lesson 8�2 665

Dimensions of ClassroomLonger Side

(feet)

Shorter Side(feet)

Links to the Future

Getting Started

Math MessageWork with a partner and estimate:

The long side of our classroom is about feet long.The short side is about feet long.

Write your estimates in the table on the board.

Study Link 8�1 Follow-Up Have students compare answers and share the rectangle dimensions they chose for Problems 3 and 4.

Mental Math and ReflexesPose multiplication facts and extended facts. Suggestions:

6 ∗ 7 = 42

8 ∗ 3 = 24

7 ∗ 4 = 28

80 ∗ 7 = 560

90 ∗ 80 = 7,200

500 ∗ 80 = 40,000

400 ∗ 500 = 200,000

5,000 ∗ 60 = 300,000

70 ∗ 300 = 21,000

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASS ACTIVITY

Ask students to find the median of the estimates for the longer and shorter sides. Record them on the board. After students measure the classroom, compare the median estimates with their actual measurements.

� Making a Rough Floor Plan PARTNER ACTIVITY

of the Classroom(Math Journal 2, p. 224)

Tell students that they are going to make a rough floor plan of the classroom. They will then use the rough plan to make a very accurate drawing of the classroom called a scale drawing.

This is an introduction to scale drawing. Students will do additional work with

scales in Fifth and Sixth Grade Everyday Mathematics.

Ask students to look at the two drawings on journal page 224.

� The first drawing is a rough floor plan of a room. It is not carefully drawn, but it does include all of the information needed to make an accurate drawing.

� The second drawing is a scale drawing for the same room. It is drawn on a grid and is very accurate.

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666 Unit 8 Perimeter and Area

A Floor Plan of My Classroom continuedLESSON

8 �2

Date Time

3. Make a scale drawing of your classroom. Scale: inch represents foot.

Each side of a small square in the grid below is �1

4� inch long.

For use in Lesson 8-3: The area of my classroom is about square feet.

1�14

�

Answers vary.

Math Journal 2, p. 225

Student Page

windows

door

Figure 1

windows

door

Figure 2

windows

door

6'

20'

6'

12'

4'

3'

5'

3 '2 '3 '

Figure 3

Have students discuss with their partners the information needed to make a rough floor plan of the classroom. They list this information in Problem 1 on journal page 224 and then sketch a rough outline of the classroom in Problem 2.

With students’ help, draw a simple, rough floor plan of the classroom on the board. Students should add refinements to their own sketches as you add them to yours.

1. Draw the walls and show the doors and windows. (See Figure 1.)

2. Show the symbols commonly used to represent doors and windows and add them to the sketch. (See Figure 2.)

doorswindow

3. Give a measurement assignment to each partnership. For example, one pair of students measures the total length of a wall; another, the width of a window or door opening; another, the distance from a corner to a door or window; and so on. Ask students to make their measurements accurate to the nearest foot and to record them on the board sketch using two-headed arrows. (See Figure 3.)

4. With the class, check the reported measurements:

� The sum of the lengths of wall sections, windows, and door openings along each wall should be close to the total length of that wall.

� Opposite walls should have nearly equal lengths (assuming the floor is rectangular).

Ongoing Assessment: Informing Instruction

Watch for students who note that the opposite walls of their rectangular

classroom do not have the same length due to rounding to the nearest foot.

Have students revise one of the measurements so that they have equal lengths.

� Making the Scale Drawing WHOLE-CLASS ACTIVITY

(Math Journal 2, pp. 224 and 225;

Math Masters, p. 443)

Have students examine the grid on journal page 225. Explain that accurate floor plans are often drawn on this kind of grid. Ask:

● What is the length of the side of a small square? 1 _ 4 inch How many small square sides make up 1 inch? 4

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Date Time

Solving Number StoriesLESSON

8�2 58

The students in the teen living class at Eagle Ridge Middle School are sewing

baggy shorts for a fundraiser. They plan to sell each pair for $7.50. Use the

information in the table to solve the number stories.

1. a. How much fabric will Kent need if he wants to sew 4 pairs of S shorts?

yards Equation:

b. Kent needs between yards of fabric. Circle the best answer.

1 and 2 2 and 3 3 and 4

2. a. Monique wants to sew 3 pairs of XXL shorts. How much fabric will she need?

yards Equation:

b. Monique needs between yards of fabric. Circle the best answer.

1 and 2 2 and 3 3 and 4

3. a. Omar wants to sew 2 pairs of shorts that will fit a person with a 38-inch waist.

How much fabric will he need?

yards Equation:

b. Omar needs between yards of fabric. Circle the best answer.

1 and 2 2 and 3 3 and 4

4. If Olivia has 21

_ 8 yards of fabric, how many pairs of S shorts will she be able to sew?

3 pairs

5. Ryan sewed $30.00 worth of XXL shorts. How many yards of fabric did he use?

20

__

4 , or 5 yards

4 ∗ 7

_ 8 =

28

__ 8

3 ∗ 5

_ 4 =

15

__ 4

2 ∗ 9

_ 8 =

18

__ 8

Size Waist (in.) Fabric (yd)

S 24–30 7 _ 8

M 31–33 1

L 34–36 1

XL 37–40 9 _ 8

XXL 41–45 5 _ 4

Sample

equations

are given.

28

__

8 , or 3 4

_ 8 , or 3

1

_ 2

15

__ 4 , or 3

3

_ 4

18

__ 8 , or 2

2

_ 8 , or 2

1

_ 4

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Math Journal 2, p. 226B

Student Page

Date Time

Multiplying Fractions by Whole NumbersLESSON

8�2 58

Write an equation to describe each number line.

1.

4 ∗ 1

_ 6 =

4

_ 6 , or

2

_ 3

2.

2 ∗ 3

_ 2 =

6

_ 2 , or 3

Use number lines to help you solve the problems.

3. = 2 ∗

3

_ 5

4. 3 ∗ 2 _ 7 =

6

_ 7

Solve. You may use a visual fraction model such as a number line or any other method.

5. 7 ∗ 1 _ 12 =

7

__ 12

7. = 3 ∗ 4

_ 7

360 1

16

16

16

16

0 1 2 3 4

32

32

1050

55

35

35

770

27

27

27

6. = 5 ∗

3

_ 10

8. 2 ∗ 5

_ 9 = 10

__

9 , or 1 1

_ 9

6

_ 5 , or 1

1

_ 5

15

__

10 , or 1 5

__ 10 ,

or 1 1

_ 2

12

__

7 , or 1 5

_ 7

226A-226B_EMCS_S_MJ2_G4_U08_576426.indd 226A 3/31/11 11:09 AM

Math Journal 2, p. 226A

Student Page

Lesson 8�2 667

Write “Scale: 1 _ 4 inch represents 1 foot” on the board, and ask students to copy this onto the journal page. Tell them that this is the scale they will use in their scale drawings. Ask:

● How many small square sides are needed to represent a 6-foot wall? 6 A 2 1 _ 2 -foot door opening? 2 1 _ 2

● On the scale drawing, what would be the length of a 14-foot wall? 14 small square sides, or 3 1 _ 2 inches

The class now has all the information needed to make the scale drawing. If you wish, use a transparency of a 1 _ 4 -inch grid (Math Masters, page 443) to make the scale drawing of the classroom as students follow your lead on journal page 225. Remind students that the length of 1 grid square ( 1 _ 4 inch) represents 1 foot of actual length.

After students have completed both the rough floor plan and the scale drawing of the classroom, ask the following questions:

● When would someone want to make just a rough floor plan of a room? Sample answer: shopping for furniture

● When would someone need to make a more accurate scale drawing? Sample answer: remodeling a room

2 Ongoing Learning & Practice

� Multiplying a Fraction by a Whole Number(Math Journal 2, pp. 226A and 226B)

Students practice multiplying fractions by whole numbers.

� Math Boxes 8�2 INDEPENDENTACTIVITY

(Math Journal 2, p. 226)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 8-4. The skill in Problem 6 previews Unit 9 content.

PARTNER ACTIVITY

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668 Unit 8 Perimeter and Area

Name Date Time

STUDY LINK

8� 2 Scale

1. If 1 inch on a map represents

13 miles, then

a. 4 inches represent miles.

b. 9 inches represent miles.

c. 2 1

_ 2 inches represent miles.

d. 13 1

_ 2 inches represent miles.

2. The scale for a drawing is

1 centimeter : 5 meters.

Make a scale drawing of a

rectangle that measures

20 meters by 15 meters.

4 cm

3 cm

3. Scale: 1

_ 4 inch represents 6 feet. Measure the height of each rectangle

to the nearest 1

_ 4 inch. Complete the table.

A

BC

D

E

Try This

Rectangle Height in Drawing Actual Height

A 1

_ 2 in. 12 ft

B 1 1

_ 4 in. 30 ft

C 2 in. 48 ft

D 1 3

_ 4 in. 42 ft

E 1 in. 24 ft

145

175 1

_ 2

32 1

_ 2

117

52

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Math Masters, p. 250

Study Link Master

226

Math Boxes LESSON

8�2

Date Time

2. If you tossed a coin onto the grid below,

about what fraction of the time would you

expect it to land on R?

4

__ 16 , or

1

_ 4 R O P E

O P E R

P E R O

E R O P

131 45 84

4. Which number is closest to the product

of 510 and 18? Circle the best answer.

A 100

B 1,000

C 10,000

D 100,000

3. Write an equivalent fraction, decimal, or

whole number.

Decimal Fraction

a. 0.8 8

__ 10

b. 0.65 65

_ 100

c. 1 15

_ 15

d. 0.90 90

___ 100 61 181

6. Shade more than 2

_

100 but less than

1

_

10 of the grid.

5 27

Sample answer:

cm

cm

cm

cm

cm3

4

4

1

2

1. Measure the sides of the figure to

the nearest centimeter. Then find its

perimeter.

Perimeter = 14

cm

�

5. Write each number in exponential

notation.

a. 100 = 102

b. 10,000 = 104

c. 1,000,000 = 106

d. 1,000 = 103

219-247_EMCS_S_MJ2_G4_U08_576426.indd 226 3/6/11 7:48 AM

Math Journal 2, p. 226

Student Page

� Study Link 8�2 INDEPENDENTACTIVITY

(Math Masters, p. 250)

Home Connection Students solve problems involving scale. They need a ruler to complete the page.

3 Differentiation Options

READINESS PARTNER ACTIVITY

� Measuring to the Nearest Foot 15–30 Min

(Math Masters, p. 251 and p. 388 or 389)

To explore measuring to the nearest foot, have students cut out the “foot-long foot” on Math Masters, page 251 and use it to measure objects or distances. Have students record their work in a Math Log or on an Exit Slip.

Discuss why it is important to avoid overlaps or gaps while measuring and how having the 1 _ 2 -foot marking helps to determine the nearest foot.

ENRICHMENT INDEPENDENTACTIVITY

� Making a Scale Drawing 30+ Min

of Your Bedroom(Math Masters, pp. 252 and 253)

To apply students’ understanding of scale drawings, have them make scale drawings of their bedrooms on Math Masters, page 252. Students then make a scale drawing

of the bird’s-eye view of each piece of bedroom furniture on Math Masters, page 253. Then they cut out the drawings of the furniture and tape them in place on the scale drawings of their bedrooms.

Ongoing Assessment:Recognizing Student Achievement

Use Math Boxes, Problem 1 to assess students’ ability to find the

perimeter of a figure. Students are making adequate progress if they are

able to find the lengths of the sides and add the measurements to find

the perimeter. Some students may be able to write a number model that

includes parentheses. (2 ∗ 4) + 3 + 2 + 1 = 14 cm

[Measurement and Reference Frames Goal 2]

Math Boxes

Problem 1 �

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251

Name Date

LESSON

8�2 Foot-Long Foot

0 fe

et

1 fo

ot

6 inc

hes o

r fo

ot1 2

Copyright

© W

right

Gro

up/M

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-Hill

247-277_EMCS_B_MM_G4_U08_576965.indd 251 2/1/11 2:16 PMMath Masters, p. 251

Teaching Master

Name Date Time

LESSON

8�2 My Bedroom Floor Plan

Make a scale drawing of your bedroom floor. Round your measurements

to the nearest 1

_ 4 foot (3 inches).

Scale: 1

_ 2 inch represents 1 foot.

145

247-277_EMCS_B_MM_G4_U08_576965.indd 252 2/1/11 2:16 PM

Math Masters, p. 252

Teaching Master

Lesson 8�2 669

Encourage students to think about ways to improve the layouts of their bedrooms.

● Would taking out or adding a piece of furniture make the room more comfortable?

● Would rearranging the furniture help?

● Are there ways to make better use of outside light? Of indoor light?

Students can experiment with various furniture arrangements on their scale drawings.

EXTRA PRACTICE SMALL-GROUP ACTIVITY

� Taking a 50-Facts Test 5–15 Min

(Math Masters, pp. 413, 414, and 416)

See Lesson 3-4 for details regarding the administration of the 50-facts test and the recording and graphing of individual and optional class results.

ELL SUPPORT SMALL-GROUP ACTIVITY

� Building Background for 5–15 Min

Mathematics WordsTo provide language support for scale, have students list possible ways of using the word scale. Then have them highlight and discuss the mathematical meanings. For example:

� The map scale shows that 1 inch represents 50 miles.

� Julie’s dollhouse is a scale model of her actual house.

� My thermometer has two scales (Fahrenheit and Celsius).

� My ruler also has two scales (U.S. customary and metric).

� Every morning, my dad weighs himself on the bathroom scale. Today he weighs 182 pounds.

� The adventurers decided to scale the mountain. They think it will take about 4 days to get to the top.

� The body of a fish is covered with scales. The body of a human is covered with skin.

� Chris scaled the fish and then placed it on the grill to cook it.

� The trumpet players warmed up for the concert by playing scales.

� The class did very poorly on the test, so the teacher decided to scale it.

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