1. Page 407 #1-6 & Page 410-411 #1-4 ANSWERS!
Course 1
8-5
Indirect Measurement
6th Grade Math HOMEWORK
Page 407 #1-6 & Page #1-4 ANSWERS!

2. Page 414 #1-6 & Spiral Review (#21-27)
Course 1
8-6
Scale Drawings and Maps
6th Grade Math HOMEWORK
Page 414 #1-6 & Spiral Review (#21-27)

3. Our Learning Goal for Chapter 8
Students 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.

4. 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)

5. Scale Drawings and Maps
8-6
Scale Drawings and Maps
Course 1
Warm Up
Problem of the Day
Lesson Presentation

6. Scale Drawings and Maps
Course 1
8-6
Scale Drawings and Maps
Warm Up
Find 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

7. Scale Drawings and Maps
Course 1
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

8. Today’s Learning Goal Assignment
Course 1
8-6
Scale Drawings and Maps
Today’s Learning Goal Assignment
Learn to read and use map scales and scale drawings.

9. Insert Lesson Title Here
Course 1
8-6
Scale Drawings and Maps
Insert Lesson Title Here
Vocabulary
scale drawing
scale

10. Scale Drawings and Maps
Course 1
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.

11. Scale Drawings and Maps
Course 1
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?
Write a proportion using the scale. Let x be the actual number of miles between the two towns.
4 in.
1 mi
____
20 in.
x mi
_____ =
1 • 20 = 4 • x
The cross products are equal.
20 = 4x
x is multiplied by 4. 20 4
___ 4x 4
___
Divide both sides by 4 to undo multiplication. =
5 = x
The actual distance between the two towns is 5 miles.

12. Scale Drawings and Maps
Course 1
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

13. Scale Drawings and Maps
Course 1
8-6
Scale Drawings and Maps
Try This: Example 1
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?
Write a proportion using the scale. Let x be the actual number of miles between the two cities.
3 in.
1 mi
____
18 in.
x mi
_____ =
1 • 18 = 3 • x
The cross products are equal.
18 = 3x
x is multiplied by 3. 18 3
___ 3x 3
___
Divide both sides by 3 to undo multiplication. =
6 = x
The actual distance between the two cities is 6 miles.

14. Scale Drawings and Maps
Course 1
8-6
Scale Drawings and Maps
Additional 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?
Write a proportion. Let x be the actual distance from Mars to Jupiter.
1 in.
30 million km
___________
18.3 in.
x million km
_________ =
The cross products are equal.
30 • 18.3 = 1 • x
549 = x
The actual distance from Mars to Jupiter is about 549 million km.

15. Scale Drawings and Maps
Course 1
8-6
Scale Drawings and Maps
Additional 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?
Write a proportion. Let x be the distance from Earth to Mars on the drawing.
1 in.
30 million km
___________
x in.
78 million km
__________ =
30 • x = 1 • 78
The cross products are equal.
30x = 78
x is multiplied by 30.
30x 30
___ 78 30
___
Divide both sides by 30 to undo multiplication. = 3 5 __
x = 2 3 5 __
Earth and Mars should be drawn 2 inches apart.

16. Scale Drawings and Maps
Course 1
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?
Write a proportion. Let x be the distance from Mars to Venus.
1 in.
15 million km
___________
8 in.
x million km
_________ =
The cross products are equal.
15 • 8 = 1 • x
120 = x
The actual distance from Mars to Venus is about 120 million km.

17. Scale Drawings and Maps
Course 1
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?
Write a proportion. Let x be the distance from Earth to the Sun on the drawing.
1 in.
15 mil km
________
x in.
150 mil km
________ =
15 • x = 1 • 150
The cross products are equal.
15x = 150
x is multiplied by 15.
15x 15
___
150 15
____
Divide both sides by 15 to undo multiplication. =
x = 10
Earth and the Sun should be drawn 10 inches apart.

18. Scale Drawings and Maps Insert Lesson Title Here
Course 1
8-6
Scale Drawings and Maps
Insert Lesson Title Here
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
270 km
450 km
225 km
742.5 km