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8-5 Indirect Measurement

6th Grade Math HOMEWORKPage 407

#1-6

& Page 410-411

#1-4

ANSWERS!

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8-6 Scale Drawings and Maps

6th Grade Math HOMEWORK

Page 414

#1-6 &Spiral Review (#21-27)

Our Learning Goal for Chapter 8Students will understand ratios, proportions, and percents by being able to write ratios, find unit rates, solve proportions, identify similar figures, find unknown measures, make scale drawings, understand relationships, and solve problems including those involving discounts, tips, sales tax, and simple interest.

Our Learning Goal Assignments• Learn to write ratios and rates and to find unit rates (8-1)• Learn to write and solve proportions (8-2)• Learn to use proportions to make conversions within the

customary system (8-3)• Learn to use ratios to identify similar figures (8-4)• Learn to use proportions and similar figures to find unknown

measures (8-5)• Learn to read and use map scale and scale drawings (8-6)• Learn to write percents as decimals and as fractions (8-7)• Learn to write decimals and fractions as percents (8-8)• Learn to find the missing value in a percent problem (8-9)• Learn to solve percent problems that involve discounts, tips,

and sales tax (8-10)

8-6 Scale Drawings and Maps

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Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Warm UpFind the unknown heights.

1. A tower casts a 56 ft shadow. A 5 ft girl next to it casts a 3.5 ft shadow. How tall is the tower?

2. On a sunny day, a 50 ft silo casts a 10 ft shadow. The barn next to the silo casts a shadow that is 4 ft long. How tall is the barn?

80 ft

20 ft

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8-6 Scale Drawings and Maps

Problem of the Day

Hal runs 4 miles in 32 minutes. Julie runs 5 miles more than Hal runs. If Julie runs at the same rate as Hal, for how many minutes will Julie run?

72 minutes

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8-6 Scale Drawings and Maps

Today’s Learning Goal Assignment

Learn to read and use map scales and scale drawings.

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8-6 Scale Drawings and Maps

Vocabulary

scale drawingscale

Insert Lesson Title Here

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8-6 Scale Drawings and Maps

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8-6 Scale Drawings and Maps

The map shown is a scale drawing. A scale drawing is a drawing of a real object that is proportionally smaller or larger than the real object. In other words, measurements on a scale drawing are in proportion to the measurements of the real object.

A scale is a ratio between two sets of measurements. In the map above, the scale is 1 in:100 mi. This ratio means that 1 inch on the map represents 100 miles.

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8-6 Scale Drawings and Maps

Additional Example 1: Finding Actual Distances The scale on a map is 4 in: 1 mi. On the map, the distance between two towns is 20 in. What is the actual distance?

20 in. x mi

_____ 4 in. 1 mi

____ =

1 • 20 = 4 • x

20 = 4x

20 4

___ 4x 4

___ =

5 = x

Write a proportion using the scale. Let x be the actual number of miles between the two towns.

The cross products are equal.

x is multiplied by 4.

Divide both sides by 4 to undo multiplication.

The actual distance between the two towns is 5 miles.

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8-6 Scale Drawings and Maps

In Additional Example 1, think “4 inches is 1 mile, so 20 inches is how many miles?” This approach will help you set up proportions in similar problems.

Helpful Hint

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8-6 Scale Drawings and Maps

Try This: Example 1

18 in. x mi

_____ 3 in. 1 mi

____ =

1 • 18 = 3 • x

18 = 3x

18 3

___ 3x 3

___ =

6 = x

Write a proportion using the scale. Let x be the actual number of miles between the two cities.

The cross products are equal.

x is multiplied by 3.

Divide both sides by 3 to undo multiplication.

The actual distance between the two cities is 6 miles.

The scale on a map is 3 in: 1 mi. On the map, the distance between two cities is 18 in. What is the actual distance?

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8-6 Scale Drawings and MapsAdditional Example 2A: Astronomy Application A. If a drawing of the planets were made using the scale 1 in:30 million km, the distance from Mars to Jupiter on the drawing would be about 18.3 in. What is the actual distance between Mars to Jupiter?

18.3 in. x million km

_________ 1 in. 30 million km

___________ =

30 • 18.3 = 1 • x

549 = x

Write a proportion. Let x be the actual distance from Mars to Jupiter.

The cross products are equal.

The actual distance from Mars to Jupiter is about 549 million km.

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8-6 Scale Drawings and MapsAdditional Example 2B: Astronomy Application B. The actual distance from Earth to Mars is about 78 million kilometers. How far apart should Earth and Mars be drawn?

x in.78 million km

__________ 1 in. 30 million km

___________ =

30 • x = 1 • 78

x = 2

Write a proportion. Let x be the distance from Earth to Mars on the drawing.The cross products are equal.

Earth and Mars should be drawn 2 inches apart.

30x = 78

30x 30

___ 78 30

___ =

x is multiplied by 30.

Divide both sides by 30 to undo multiplication.

35__

35__

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8-6 Scale Drawings and Maps

Try This: Additional Example 2A A. If a drawing of the planets were made using the scale 1 in:15 million km, the distance from Mars to Venus on the drawing would be about 8 in. What is the actual distance from Mars to Venus?

8 in.x million km

_________ 1 in. 15 million km

___________ =

15 • 8 = 1 • x

120 = x

Write a proportion. Let x be the distance from Mars to Venus.

The cross products are equal.

The actual distance from Mars to Venus is about 120 million km.

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8-6 Scale Drawings and Maps

Try This: Example 2B B. The distance from Earth to the Sun is about 150 million kilometers. How far apart should Earth and the Sun be drawn?

x in. 150 mil km

________ 1 in. 15 mil km

________ =

15 • x = 1 • 150

x = 10

Write a proportion. Let x be the distance from Earth to the Sun on the drawing.The cross products are equal.

Earth and the Sun should be drawn 10 inches apart.

15x = 15015x 15

___ 150 15

____ =

x is multiplied by 15.

Divide both sides by 15 to undo multiplication.

Lesson Quiz

On a map of the Great Lakes, 2 cm = 45 km. Find the actual distance of the following, given their distances on the map.

1. Detroit to Cleveland = 12 cm

2. Duluth to Nipigon = 20 cm

3. Buffalo to Syracuse = 10 cm

4. Sault Ste. Marie to Toronto = 33 cm

450 km

270 km

Insert Lesson Title Here

225 km

742.5 km

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8-6 Scale Drawings and Maps