Math 20-2

Chapter 1 Inductive and Deductive Reasoning

Lesson 1.1  Making Conjectures:  Inductive Reasoning

GOAL

The goal of this lesson is stated at the top of page 6 in your textbook, and is also written below.
Keep this in mind as you work through the lesson material.

Use reasoning to make predictions

Explore...

Try to answer the question in the sidebar on page 6.

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 Page 6

Read/Work through the Investigate section on Page 6 in your textbook.

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

Demonstration (optional)

The investigation is based on a triangle tiling similar to what is in your textbook.   
If you think about these diagrams in a slightly different way, you will get more triangles than what the textbook indicates.   
Check out the video for some ideas about that.

Video Tutorial  (Investigate 1)

Introduction

Video Tutorial  (Investigate 2)

?  How did Georgia arrive at this conjecture?

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

Video Tutorial  (Investigate 3)

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  Using inductive reasoning to make a conjecture about annual precipitation

TEXT Pages 7 - 8

Work through Example 1 on Pages 7 - 8 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 2  Using inductive reasoning to develop a conjecture about integers

TEXT Page 8

Work through Example 2 on Page 8  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  Using inductive reasoning to develop a conjecture about perfect squares

TEXT Page 9

Work through Example 3 on Page 9 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  Using deductive reasoning to develop a conjecture about quadrilaterals

TEXT Pages 10 - 11

Work through Example 4 on Pages 10 - 11 in your textbook.

Watch

A super long video, because this is quite a complicated example.

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!

I answered this question at the end of the video for Example 4

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

Many of these questions were either very subjective, or had a reasonably simple answer (provided in the text)
I didn’t create a video solution for these since it didn’t add anything to the answers provided.

Question 10,    I didn’t do a video for this one.
You can check the answer in the back of the book for some ideas here.

Question 15,    I didn’t do a video for this one.
You can check the answer in the back of the book for some ideas here.

Question 16,    I didn’t do a video for this one.
You can check the answer in the back of the book for some ideas here.

Question 17,    I didn’t do a video for this one.
You can check the answer in the back of the book for some ideas here.

Question 18,    I didn’t do a video for this one.
A good question, but not something I would expect everyone to get an answer for!
I sure wouldn’t have been able to get this unless I had seen it before.
If you are interested, check this LINK for a video showing how to do it.

Question 19,    I didn’t do a video for this one.
You can check the answer in the back of the book for some ideas here.

Question 20,    I didn’t do a video for this one.
You can check the answer in the back of the book for some ideas here.

Question 21,    I didn’t do a video for this one.
You can check the answer in the back of the book for some ideas here.

Question 22,    I didn’t do a video for this one.
You can check the answer in the back of the book for some ideas here.

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 11", "Question 12", "Question 13", "Question 14",  }})