Math 20-2

Chapter 8 Proportional Reasoning

Lesson 8.5   Similar Objects: Scale Models and Scale Diagrams

GOAL

The goal of this lesson is stated at the top of page 483 in your textbook, and is also written below.
Keep this in mind as you work through the lesson material.

Understand and use scale models and scale diagrams that involve 3-D objects.

Explore...

Try to answer the question in the sidebar on page 483.

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 483 - 484

Read/Work through the Investigate section on Pages 483-484 in your textbook.

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

How can you create a new box that is similar to the original box?

Note!   If you want your work to match mine,  use a scale factor of 1.5  for Part B of the Investigation.

Be sure to work through the investigation as best as you can, before you watch the video!!

Introduction

Video Tutorial A  (background)

Video Tutorial B  (similar figures)

Video Tutorial C  (creating a net)

Video Tutorial D  (scaling the net)

?  Answers to the reflecting questions

Part G    you would use the Pythagorean Theorem to find lengths of diagonals, and YES,  they will be proportional.  For example,  below are two faces,  and note that 1.5 × 7.21 = 10.82
The diagonal in the larger face is 1.5 times the diagonal in the smaller face.

Part H   ALL boxes will be similar, no matter what scale factor is used.
(assuming the new dimensions are calculated correctly!)

Part I,  yes, true,  if any two objects have proportional measurements, they are similar.

Part J,  yes, true,  no matter what shape you are dealing with, if the corresponding dimensions are proportional, the objects are similar.

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  Determining if two objects are similar

TEXT Page 484

Work through Example 1 on Page 484 in your textbook.

We have to trust that the given measurements that Sandeep takes are correct.   
Based on that,  the fact that we get the same proportion each time indicated that yes, the pans are similar.

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 2  Determining actual dimensions from a scale model

TEXT Page 485

Work through Example 2 on Page 485  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  Enlarging from a scale diagram to determine actual dimensions

TEXT Page 486

Work through Example 3 on Page 486 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 4  Drawing a scale diagram of a 3-D object

TEXT Pages 487 - 488

Work through Example 4 on Pages 487 - 488 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 11, somehow I missed this one,  after uploading all  my video...
Here is a quick sketch to support the answer  (2 planes will fit)

Question 12,    I didn’t do a video for this one.

Question 13,    I didn’t do a video for this one.
A great question, but it would require a lot of time to do it well.
There is a good diagram provided in the back of the book if you do this one and want to check.

Question 14,    I didn’t do a video for this one.
Note that this is an enlargement, multiply all the given dimensions by 4.
There is a good diagram provided in the back of the book if you do this one and want to check.

Question 16,    I didn’t do a video for this one.

Question 18,    I didn’t do a video for this one.

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 15"}, { , "Question 17",  , "Question 19", "Question 20"}})