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

2. 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.

3. 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)

4. 8-5 Indirect Measurement Warm Up Problem of the Day
Course 1
Warm Up
Problem of the Day
Lesson Presentation

5. 8-5 Indirect Measurement Warm Up
Course 1
8-5
Indirect Measurement
Warm Up
Find the missing value in each proportion. = = = = 6 t __ 18 45 __
t = 15 k 19 __ 20 76 __
k = 5 6 8 __ 42 n __
n = 56 21 11 __ x 44 __
x = 84

6. 8-5 Indirect Measurement Problem of the Day
Course 1
8-5
Indirect Measurement
Problem of the Day
Bryce, Kate, and Annie have drawn rectangles. Each side of Bryce’s rectangle is twice the size of one side of Kate’s. The same side of Kate’s rectangle is congruent to one side of Annie’s. One side of Annie’s rectangle is congruent to one side of Bryce’s. Which two rectangles could be congruent?
Kate’s and Annie’s

7. Today’s Learning Goal Assignment
Course 1
8-5
Indirect Measurement
Today’s Learning Goal Assignment
Learn to use proportions and similar figures to find unknown measures.

8. Insert Lesson Title Here
Course 1
8-5
Indirect Measurement
Insert Lesson Title Here
Vocabulary
indirect measurement

9. 8-5 Indirect Measurement
Course 1
8-5
Indirect Measurement
One way to find a height that you cannot measure directly is to use similar figures and proportions. This method is called indirect measurement.

10. Additional Example 1: Using Indirect Measurement
Course 1
8-5
Indirect Measurement
Additional Example 1: Using Indirect Measurement
Use the similar triangles to find the height of the tree. 6 h __ 2 7 __
Write a proportion using corresponding sides. =
h • 2 = 6 • 7
The cross products are equal.
2h = 42
h is multiplied by 2. 2h 2
___ 42 2
___
Divide both sides by 2 to undo multiplication. =
h = 21
The tree is 21 feet tall.

11. 8-5 Indirect Measurement Try This: Example 1
Course 1
8-5
Indirect Measurement
Try This: Example 1
Use the similar triangles to find the height of the tree. 6 h __ 3 9 __
Write a proportion using corresponding sides. =
h • 3 = 6 • 9
The cross products are equal.
3h = 54
h is multiplied by 3.
6 ft h 3h 3
___ 54 3
___
Divide both sides by 3 to undo multiplication. =
3 ft ft.
h = 18
The tree is 18 feet tall.

12. Additional Example 2: Measurement Application
Course 1
8-5
Indirect Measurement
Additional Example 2: Measurement Application
A rocket casts a shadow that is 91.5 feet long. A 4-foot model rocket casts a shadow that is 3 feet long. How tall is the rocket?
Write a proportion using corresponding sides. h 4 __
91.5 3
____ =
4 • 91.5 = h • 3
The cross products are equal.
366 = 3h
h is multiplied by 3.
366 3
___ 3h 3
___
Divide both sides by 3 to undo multiplication. =
122 = h
The rocket is 122 feet tall.

13. 8-5 Indirect Measurement Try This: Example 2
Course 1
8-5
Indirect Measurement
Try This: Example 2
A building casts a shadow that is 72.5 feet long when a 4-foot model building casts a shadow that is 2 feet long. How tall is the building? h 4 __
72.5 2
____
Write a proportion using corresponding sides. =
4 • 72.5 = h • 2
The cross products are equal.
290 = 2h
h is multiplied by 2.
Divide both sides by 2 to undo multiplication.
290 2
___ 2h 2
___ h =
4 ft
145 = h
72.5 ft 2 ft
The building is 145 feet tall.

14. Insert Lesson Title Here
Course 1
8-5
Indirect Measurement
Insert Lesson Title Here
Lesson Quiz
1. On a sunny day, a telephone pole casts a shadow 21 ft long. A 5-foot-tall mailbox next to the pole casts a shadow 3 ft long. How tall is the pole?
2. On a sunny afternoon, a goalpost casts a 75 ft shadow. A 6.5 ft football player next to the goal post has a shadow 19.5 ft long. How tall is the goalpost?
35 feet
25 feet

15. Page 407 (Ch. 8-4) #1-6 & Page 410-411 (Ch. 8-5) #1-4
Course 1
8-5
Indirect Measurement
START YOUR HOMEWORK
Page 407 (Ch. 8-4) #1-6 & Page (Ch. 8-5) #1-4