Student Activity Sheets -...

Contents

Contents v

Section D Scale and RatioScale Drawings 30Scale Models 35Maps 36Summary 38Check Your Work 39

Additional Practice

Answers to Check Your Work

Student Activity Sheets

30 Ratios and Rates

Tim wants to rearrange the furniture in his room. He decides to makea scale drawing of his room, called a floor plan. He can use the floorplan to try out different room arrangements. This will save him thework of moving the actual furniture. He can move the paper furnitureon his scale drawing.

Tim’s actual room dimensions are 2.6 m wide and 3 m long.

Tim decides to use graph paper. His first idea is to draw a floor planwith dimensions 26 cm by 30 cm.

1. a. Explain why you think Tim decided on these floor plandimensions.

b. What are some advantages and disadvantages of making aplan with dimensions 26 cm by 30 cm?

DScale and Ratio

Scale Drawings

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DScale and Ratio

Tim decides to use dimensions of 13 cm by 15 cm for his floor plan.

Section D: Scale and Ratio 31

2. a. Why do you think Tim decided to use these dimensions?

b. Use Student Activity Sheet 1 to draw the same floor plan Timwill draw of his room. Indicate the location for the door to hisroom on the floor plan.

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A double number line is a useful tool to show the relationship betweenthe dimensions in a drawing and the actual room dimensions. Here isa double number line that belongs to the scale drawing of Tim’s room.

3. Copy this double number line under your own scale drawing onStudent Activity Sheet 1 and fill in the missing numbers on thebottom of the line.

Here is the furniture for Tim’s room.

On a separate piece of graph paper, draw each piece of furniture tothe same scale as the floor plan. Eachminiature piece of furnitureshould represent the space the actual furniture takes up on the floorof Tim’s room. Cut out these pieces andmove them around on yourfloor plan until you have an arrangement you like.

4. Draw your favorite arrangement for Tim’s room on your floorplan on Student Activity Sheet 1.

32 Ratios and Rates

Scale and RatioD

0 1 5 10 cm in drawing 15

300 cm in the room

0

dresserw � 80 cmd � 30 cmh � 170 cm

chairw � 50 cmd � 50 cmh � 100 cm

bedw � 100 cmd � 170 cmh � 100 cm

deskw � 110 cmd � 60 cmh � 72 cm

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DScale and Ratio

Scale 1:75

Length in Drawing (in cm) 1

Actual Length (in cm) 75

The double number line used for Tim’s floor plan indicates a scale

ratio of 1:20.

5. Reflect Look back at the double number line for Tim’s floor plan.Describe how you would explain to someone what it means that Tim’s floor plan has a scale ratio of 1:20.

Tim’s older sister, Jenna, wants to rent an apartment. Below is a floorplan of an apartment she likes a lot. She wants to use the floor plan tofind the dimensions of the living room.

6. a. Use this ratio table to help Jenna find the length of the livingroom.

b. What is the actual width of the living room? Show your calculations.

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7. a. Do you agree or disagree with Tim’s statement? Explain.

b. What are the actual dimensions of the court? Of the total volleyball space (including the part around the actual court)?

A scale drawing represents objects that are too large or too small todraw at actual size.

A scale ratio shows the relationship between the dimensions in thedrawing and the actual dimensions of the object. A scale ratio of 1:100 on a floor plan can mean:

1 centimeter represents 100 centimeters or

1 meter represents 100 meters or

1 millimeter represents 100 millimeters or

1 inch represents 100 inches

An architect makes a scale drawing. She uses 2 cm to represent 100 m.

8. a. What is the scale ratio for her drawing? Show your work.

b. What do you think she is drawing?

34 Ratios and Rates

Scale and RatioD

Tim and his friends want to build a sand volleyball court. They use thescale drawing below to begin to figure out the actual dimensions. Timsays, “One centimeter in the drawing is actually 3 meters.”

Scale 1:300

Volleyball court

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DScale and Ratio

Scale ModelsInstead of a scale drawing on a piece ofpaper, you can make a three-dimensionalscale model.

The photo on the left shows a plane witha scale model of the plane on its wing.

The model is built with a scale of 1:6.The actual length of the plane is 6.6 mand its wingspan is 8 m.

9. a. What is the length of the scalemodel airplane?

The photo on the left shows six different modeltrains. Each of them is built to a different scale.The five scales below are commonly used.

Z scale: trains built to a ratio of 1:220

N scale: trains built to a ratio of 1:160

HO scale: trains built to a ratio of 1:87

S scale: trains built to a ratio of 1:64

Scale O: trains built to a ratio of 1:48

10. What scale was used to build the smallest trainshown? How do you know for sure?

You may want to use a ratio table like the one below for yourcalculations. (Note: Instead of using centimeters, you mayprefer to use meters.)

b. How long is the wingspan of the scale model airplane?

Length of Actual Plane (in cm)

Length of Scale Model (in cm)

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36 Ratios and Rates

Scale and RatioD

Sarita walks from the Marina Green to Fort Point National HistoricSite. The black dotted line shows Sarita’s walking path.

11. Estimate the length of Sarita’s walking path.

If you want to find a distance on a map, you need to go from onemeasurement unit to another. The following conversions arecommon. Do you know them?

12. Check what you know by copying and filling in the following measuring relationships. Add others that you might know.

1 meter � ……. centimeters

1 kilometer � ……. meters

You can transform a scale line on the map into a double number line.

Here is a double number line adapted from the scale line on the San Francisco map.

Maps

0

0 1,000

1 2 3 4 centimeters (on map)

meters (actual)

You may remember doing other work with scale lines on a map. Scale lines are like a ruler. You can use scale lines to estimate or evenmeasure distances on a map. The map below shows the northern part of San Francisco.

GOLDEN

GATE NATIO N A L REC R E AT I O N A R E A

MARINA BLVD.

DOYLE DRIVE

Ft. Mason

Golden Gate BridgeFort Point NationalHistoric Site

U.S. CoastGuard Station

Yacht Harbor

Marina

MarinaGreen

Palace of Fine Arts(Exploratorium)

0 1 km1 4 3 41 2

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13. a. Describe the differences and similarities between the scale lineon the map and the double number line on the previous page.

b. Use the double number line to find the missing numbers in thetable below.

c. What is the scale ratio of the map?

14. Suppose you have a map made on a scale of 1:50,000. Youmeasure 10 cm on the map. How many kilometers does this distance represent?


DScale and Ratio

29° S

168° E

NORFOLKISLAND

Kingston

Cascade

MiddlegateBurnt Pine

P A C I F I C

O C E A N

1 : 500,000

AUSTRALIA

NEWZEALAND

Nepean I.

Philip I.

Mt. Bates318 m

27° 45' N

18° W

HIERROISLANDValverde

Sabinosa

Restinga

Taibique

Isora

A T L A N T I C

O C E A N

El Golfo

1:1,000,000

ATLANTICOCEAN

A F R I C A

SPAIN

EUROPE

29° 45' N

141° 20' E

IWO JIMA

MotoyamaNishi

Minami

P A C I F I C

O C E A N

1 : 250,000

RUSSIA

PACIFIC

OCEAN

CHINA

JAPAN

Kangoku Rock

Kama Rock

Hanare Rock

Mt. Suribachi170 m

Hill110 m

AirBase

Kitano Pt.

Tobiishi Pt.

Distance on Map (in cm)

Actual Distance (in m)

Actual Distance (in cm)

1

Here are three different maps of three different islands: Norfolk (Australia), Iwo Jima (Japan), and Hierro (Spain).Each map was made using a differentscale. The scale is indicated on eachmap.

If you compare the size of the islands visually, you might think thethree islands all look about the same size. In reality, this is not true!

15. Write the names of the islands in order from the largest to thesmallest island. Explain how you decided what the order was.

Source: Times Atlas of the World. plates 10, 20, and 96

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38 Ratios and Rates

Scale and Ratio

You use a scale drawing to represent things that are too large or toosmall to draw. A scale ratio indicates the relationship between thedimensions on the scale drawing and the actual dimensions. You use a scale ratio to create scale models.

To create a scale drawing or model, you need to know the relationshipbetween the scaled dimensions and the actual dimensions. This relationship can be given with:

a scale line

a scale ratio

1:1000

A scale ratio always begins with the number 1. Both numbers representidentical units. The scale ratio 1:1,000 means that 1 cm on the drawingrepresents 1,000 cm in reality.

a statement

On the map, a distance of 1 cm is actually 1,000 cm, which is 10 m.

A ratio table and a double number line can help you to organize yourwork and make your calculations involving scale easy.

Ratio Table:

Double Number Line

D

0 10m

1

0 1000

1000 centimeters � 10 meters

cm on map

cm in reality

Distance on Map (in cm) 1

Actual Distance (in cm) 1000

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1. A room is 3 m wide and 4 m long.

Make a scale drawing of this room using a scale of 1:50

Here is a photo of a Swallowtail butterfly (Papilio machaon). The wingspan of the actual butterfly is 10 cm.

2. a. If you wanted to make a life-size drawing of the butterfly, would it fit on a page in this book?

b. What is the size of the wingspan in thephoto?

c. Use a double number line or a ratio table to find the scale ratio of the photo.

d. What is the actual length of the body of the butterfly? Show your calculations.

Here is a scale line from a map:

3. a. What is the actual distance of 1 cm on this map?

b. What is the scale ratio of the map?

5 kilometers0

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40 Ratios and Rates

Scale and Ratio

The map below shows a part of downtown Philadelphia.

D

Inde

pend

ence

Mal

l

Walnut St

Market St

Ranstead St

Chestnut St

Sansom St

Arch St

Filbert St

Ionic St

AppleTree St

S 8

th S

t

S 6

th S

t

S 7

th S

t

S 9

th S

t

S 1

0th

St

S 1

1th

St

S 1

2th

St

N 8

th S

t

N 6

th S

t

N 7

th S

t

N 9

th S

t

N 1

0th

St

N 1

1th

St

N 1

2th

St

Walnut StreetTheater

Thomas JeffersonUniv. Hospital

National Archives

Branch

BalchInstitute

for EthnicStudies

ReedingTerminal

Market

HistoryMuseum ofPhiladelphia

African-AmericanHistorical and Cultural Museum

Scale 1:5,000

4. a. Copy and complete the following ratio table for the map.

b. How far is a walk from Sansom Street to Arch Street? (Use meters or kilometers for your distance.)

Suppose a map has a scale ratio of 1:20,000.

5. a. Do you think this map was designed to be used by someonewho is walking or someone who is driving? Explain your answer.

b. Make a scale line for this map.

Write a paragraph describing the need for using scale lines and scale ratios in designing toy cars. Be exact in your descriptions.

Distance on Map (in cm) 1

Actual Distance (in cm) .............

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Additional Practice 53

Additional Practice

Section Scale and RatioD

Members of the Lewis and Clark expedition (1804–1806) searched foran overland route from the Mississippi River to the Pacific Ocean.

Re

d

Missouri

Yellowstone

N. Platte Platte

Misso

ur i

O hio

Wisco

nsin

Mississippi

Arkansas

Colorado

LakeMichigan

LakeSuperior

S. Saskatchewan

Alban

y

N. Saskatchewan

Sn

a k e

Co

lumbia

Lake Winnipeg

P A C I F I C

O C E A N

MOHAVEDESERT

PAINTED

DESERT

DE

ATH

VALLEY

GR

EA

TP

LA

IN

S

BIT

TE

RR

OO

TR

AN

GE

BEAR PAWMTS.

CA

SC

AD

ER

AN

GE

BIG SNOWMTS.

BLACKHILLS

OZARK PLATEAU

OLY

MP

ICM

TS.

CO

AS

TR

AN

GE

SIER

RA

NEV

AD

A

RO

CK

YM

OU

NT

AI N

S

Fort Clatsop

Fort Mandan

St. Louis

LEWIS AND CLARK ROUTES

Clark’s return route

Lewis’s return route

Lewis and Clark

N

S

W E

1:25,000,000

The scale of this map is 1:25,000,000.

1. Estimate the distance Lewis and Clark covered when they traveled from St. Louis to Fort Clatsop.

Here is an excerpt from a journal.

May 14, 1804 Expedition begins in St. Louis.

October 24, 1804 Expedition discovers earth lodge villages

of the Mandan and Hidatsas Indians. The

captains decide to build Fort Mandan across

the river from the main village.

2. a. Use the information in the journal to estimate the average distance the expedition covered per month during this period.Note that Fort Mandan is about halfway between St. Louis and Fort Clatsop.

b. Also find the average distance per day.

54 Ratios and Rates

Additional Practice

Eiffel Tower Puzzle

The wrought-iron original hasattracted millions of visitors andis the symbol of Paris. Now youcan construct your own EiffelTower to a scale of 1:500.

The height of the actual tower is312 meters.

3. What is the height of themodel?

58 Ratios and Rates

Section Scale and Ratio D

Door

Bed

Desk

Chair Dresser

Win

do

w

8 cm

6 cm

1. Here is one sample drawing. Your room dimensions should be 8 cm by 6 cm.

The scale ratio of 1:50, means 1 cm on the map is 50 cm in reality.Working up to 300 cm (3 m) and 400 cm (4 m), you can get thedrawing dimensions needed. 1 50, 2 cm 100 cm, 8 cm 400 cm and 6 cm 300 cm.

2. a. Yes, a life-size drawing of the butterfly would fit on a page inthis book because it is 10 cm. Here is how 10 cm looks.

b. About 2.5 cm.

c. The scale ratio is 1:4.

Sample strategy using a double number line:

Sample strategy using a ratio table:

10 cm

In Drawing (in cm) 2.5 25 1

Actual (in cm) 10 100 4

0

0 10 24 0 Actual (in cm)

2.5 51 In Drawing (in cm)

d. The actual length of the body of the butterfly is 3.6 cm.

Here is one strategy.

The body length in the reduction is about 0.9 cm. Since thisrepresents 1

4of the length, the body length is about 3.6 cm.

(0.9 4 3.6).

3. a. 1 cm represents 1 kilometer, which is 1,000 meters.

b. The scale ratio is 1:100,000

On the map, 1 cm represents 1,000 m. In reality, 1,000 m is 100,000 cm. So 1 cm on the map represents100,000 cm in reality. The scale ratio is 1:100,000.

4. a.

b. About 385 m or 0.385 km.

The distance on the map is about 7.7 cm. Since 1 cm represents5,000 cm, you can calculate 7.7 5,000 38,500 cm or 385 m. If you measured a distance between 7.3 cm and 7.8 cm on themap, your answer must be between 365 m and 390 m.

5. a. The map is designed to be used by someone who is walking.

Here is one way of reasoning.

1 cm on the map represents 20,000 cm in reality. This is about200 m. If 1 cm represents 200 m then 10 cm represents 2,000 m,which is 2 km. I chose 10 cm, because that fits nicely on a page.The map is not for driving because you would be off the mapbefore you knew it. 2 km is a short distance.

60 Ratios and Rates


On Map (in cm) 1

In Reality (in cm) 1,000 1,000

In Reality (in cm) 100,000

Distance on a Map (in cm) 1

Actual Distance (in cm) 5,000

b. Here is one possible scale line.

Your scale line might look different. You might have other distances indicated like 400 m (at 2 cm); 600 m (at 3 cm); etc.Instead of meters, it may show kilometers, and every 5 cm is 1 km. Note that for a scale line to be correct, 1 cm must represent 200 m.

Answers to Check Your Work 61


1,000 meters0 200

Student Activity Sheet 1 Ratios and Rates 73

Student Activity Sheet 1Use with Section D, pages 31 and 32.

Tim decides to use dimensions of 13 cm by15 cm for his floor plan.

2. Draw the same floor plan Tim will drawof his room. Indicate the location forthe door to his room on the floor plan.

Double Number Line:

A double number line is a useful tool to showthe relationship between the dimensions in adrawing and the actual room dimensions. Anexample for Tim’s room is in your student book.

3. Copy the double number line underyour scale drawing and fill in the missingnumbers.

Name ________________________________________

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