Math 20-2

Chapter 1 Inductive and Deductive Reasoning

Lesson 1.7 Analyzing Puzzles and Games

GOAL

The goal of this lesson is stated at the top of page 52 in your textbook, and is also written below.
Keep this in mind as you work through the lesson material.

Determine, explain and verify a reasoning strategy to solve a puzzle or win a game.

Explore...

Try to answer the question in the sidebar on page 52.

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 52

Read/Work through the Investigate section on Page 52 in your textbook.

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

Introduction

You can do this investigation yourself using some kind of counter (coins, colored paper, etc.)
If you like, you can do the exact investigation at THIS website

?  What is the minimum number of moves needed to switch the five counters of each color?

Video Tutorial

Reflecting

I covered these questions in the video from the previous section.
The formula is  n (n+2)  where n is the starting number of counters.

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 reasoning to determine the possible winning plays

TEXT Page 53

Work through Example 1 on Page 53 in your textbook.

Watch

Video Tutorial 

NOTE!  I will also answer the Your Turn question when I do the video.
It just makes more sense to talk about the whole question at the same time.
Make sure you think about the Your Turn question before you watch the video!

Example 2  Using deductive and inductive reasoning to determine a winning strategy

TEXT Page 54

Work through Example 2 on Page 54  in your textbook.

Watch

Video Tutorial

NOTE!  I will also answer the Your Turn question when I do the video.
It just makes more sense to talk about the whole question at the same time.
Make sure you think about the Your Turn question before you watch the video!

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 10,    I couldn’t find an answer for the first puzzle,  and went online and found one “solver” that couldn’t do it, and one that could.    SUDOKU is a great puzzle, but they can be really hard.   I didn’t want to “waste” too much time here,  so I did not complete the puzzle.
(P.S.  I went back and tried again, and when I got stuck,  I made a guess.  Two possible numbers that could have worked,  and so just guessed, and proceeded from there, and ... it worked...   I don’t view that as a really good way to solve a puzzle.  It worked, and sometimes you HAVE to guess, but I figured, for this course,  using logic more formally should have been the key...)

Question 13,    another (probably...) great question, but I tried for a while and wasn’t immediately able to get an answer,  so I stopped.   If you were able to solve this easily, I am sure your teacher (and me!) would love to hear about your logic.

Question 14,    I didn’t do a video for this one.
Check the answer in the back for a sample solution.

Question 15,    I didn’t do a video for this one.
Check the answer in the back for a sample solution.

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",  ,  ,  }})