Math 20-2

Chapter 8 Proportional Reasoning

Lesson 8.6   Scale Factors and 3-D Objects

GOAL

The goal of this lesson is stated at the top of page 495 in your textbook, and is also written below.
Keep this in mind as you work through the lesson material.

Solve problems that involve scale factor, surface area, and volume.

Explore...

Try to answer the question in the sidebar on page 494.

Watch

Video Tutorial

Investigate the Math

Investigate an idea or problem, with a partner if possible.
The investigation provides the background for the ideas presented in the lesson.

TEXT Pages 494 - 495

Read/Work through the Investigate section on Pages 494-495 in your textbook.

Go through this material,  AS BEST YOU CAN,  before you view the video tutorials that follow.

What is the relationship between the scale factor and the surface areas of two similar objects? What is the relationship between the scale factor and the volumes of two similar objects?

Note!  You can do this investigation using linking cubes, pattern blocks, etc.   You can measure and do all the calculations.  That would be excellent!

But... it’s quite possible to do this investigation without doing any measurements at all, and you will get to the same idea.   This is the approach I will use in my video presentation of this concept.

Video Tutorial  Cubes

Video Tutorial  Triangular Prisms

Video Tutorial  Rectangular Prisms

Apply the Math  (Examples)

Examples will give you TOOLS for solving problems, and also show you that there may be different ways to approach a question.

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the examples as models.

Example 1  Reasoning about relationships among scale and volume

Proofs ARE important,  but I won’t create a video here.
You are welcome to work through these proofs but that is not at all necessary, you can use the ideas without proving them!

TEXT Pages 496 - 497

Work through Example 1  and the Your Turn question on Pages 496 - 497 in your textbook.

Example 2  Solving a surface area problem

TEXT Pages 497 - 498

Work through Example 2 on Pages 497 - 498 in your textbook.

Watch

Video Tutorial

Your Turn

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

Example 3  Solving a capacity problem

TEXT Page 499

Work through Example 3 on Page 499 in your textbook.

Watch

Video Tutorial

Your Turn

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

In Summary

Key Ideas and Need to Know 
Presents and summarizes  the main new concepts of the lesson

•	Carefully read through each of the bullet points in this section.

•	If you are unclear about any of these ideas,  ASK YOUR TEACHER FOR HELP!

Practice Problems

Doing Practice Problems

Practice problems reinforce the math presented in this lesson.

•	Work through the practice problems for this lesson.
	These problems are for practice, you don’t need to hand them in!
	(your teacher may assign specific questions for you to complete)

•	Use the answers in the back of the book to CHECK YOUR WORK!

•	If you make a mistake, TRY TO FIX IT!

•	If you need help or want more information, view the video solutions provided.

•	If you still need more help,  CONTACT YOUR TEACHER!

Types of Practice Problems

Check Your Understanding questions require basic understanding of the ideas of the  lesson.

Practising questions will require you to dig deeper for a solution.

Closing  A summary question that often asks YOU to explain ideas in your own words.

Extending questions offer enrichment and extension.

Notes

Question 16,    I didn’t do a video for this one.
A great question, but well beyond the scope of this class.
I’m sure your teacher would be delighted to do this “proof” for you if you are interested.

Video Solution Links

Check your work for every problem you do!
If you make a mistake,  try to fix it!
Use the video solutions for more information.
If a problem still doesn’t make sense, ASK YOUR TEACHER FOR HELP!

({{"Question 1", "Question 2", "Question 3", "Question 4", "Question 5"}, {"Question 6", "Question 7", "Question 8", "Question 9", "Question 10"}, {"Question 11", "Question 12", "Question 13", "Question 14", "Question 15"}, { , "Question 17", "Question 18", "Question 19", "Question 20"}})