Math 10C

Chapter 6 Linear Relations and Functions

Lesson 65 Slope

Focus

The FOCUS section introduces the main concept that will be covered in the lesson.

TEXT Page 315

Read/Work through the  Focus  section at the top of page 315 in  your textbook.

Investigate A

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

TEXT Pages 315 - 317

Read/Work through the  Investigate  section on Pages 315 - 317 in your textbook.

A list of materials  you need for the Investigation is given in the side bar.

Your work will be a lot more efficient if you PLAN for and GATHER these items BEFORE you start the Investigation!

You may not have other students to work with.  
No worries!  
If you are working on your own,  answer the questions, AS BEST YOU CAN, before you view the Tutorial that follows.
Once you have done that,  view the video for help with this section.

NOTE,  this is quite a detailed investigation and since it involves measuring with physical objects, it will be hard to document using video.

I encourage you to DO the investigation, but I won't be creating a video for this section.

These ideas will all be covered in the LINK park of the lesson.

Alternatively,  do the INTERACTIVE investigation that follows.

Investigate B   computer based  INTERACTIVE

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

Work through the following sections,  one step at a time,  to help you connect with the ideas that will be presented in this lesson.

Getting started

What follows are several mini applications  or demonstrations  to illustrate the idea of slope.

We'll build the idea up, using several small steps.

Stage 1

Experiment with the points and the limited controls in this application.

What do you see and what do open and integer do?

Comments

In the demonstration you have two points that you can move around on the screen.

open  means you can move the points anywhere on the grid,  integer  means the points are limited to "lattice point"  locations

Stage 2

Just the addition of two controls here.

What do you see now?

Comments

Checking line  draws a line between the two points.

The reverse checkbox changes the direction of the line.

Imagine one point is a starting point, and one point is an ending point, and the arrow is telling you where you start and where you end.

Stage 3

Almost there...

The addition of another two controls here.

What do you see now?

Comments

Checking rise  draws two blue arrows.
These arrows show the vertical distance between the two points.
The arrows again indicate direction, which point you are going from and to,  and how much you are going up  or down  to get there. 
The word rise indicates the vertical distance between two points.

Checking run   draws two green arrows.
These arrows show the horizontal distance between the two points.
The arrows again indicate direction, which point you are going from and to,  and how much you are going right  or left  to get there. 
The word run indicates the vertical distance between two points.

THE DEMONSTRATION

Now that you know what is happening, here, finally, is the actual demonstration.

One more checkbox here, that allows you to see the calculation of the slope between the two points.

Watch

Here is a short movie talking just a bit about the demonstration, how it works, and one slope calculation

Movie Link 1

Link the Ideas

Link the Ideas summarizes the math in the lesson.
A presentation of ideas connected to the lesson focus.

TEXT Pages 317 - 318

Read/Work through the  Link the Ideas  section on Pages 317 - 318 in your textbook.

Examples

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

Example 1  Classify the Slope of a Line

TEXT Page 319

Work through Example 1 on Page 319 in your textbook.

Watch

Video Tutorial

Your Turn

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

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  Determine the Value of a Slope

TEXT Page 320

Work through Example 2 on Page 320  in your textbook.

Watch

Video Tutorial

Your Turn

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

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  Determine the Slope of a Line Segment

TEXT Pages 320 - 322

Work through Example 3 on Pages 320 - 322 in your textbook.

Watch

Video Tutorial

Your Turn

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

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  Use Slope to Graph a Line

TEXT Page 322

Work through Example 4 on Page 322 in your textbook.

Watch

Video Tutorial

Your Turn

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

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 5  Slope as a Rate of Change

TEXT Page 323

Work through Example 5 on Page 323 in your textbook.

Watch

Video Tutorial

Your Turn

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

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

Key Ideas

Key Ideas 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!

Check Your Understanding    (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

Practice questions require basic understanding of the ideas of the  lesson.

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

Extend questions offer enrichment and extension.

Create Connections questions connect the math to everyday contexts.

Mini Lab (optional)  your teacher may or may not have you do these.

Notes

Question 19,    I didn’t do a video for this one
This is a GREAT question, but in the interests of time (it would take a long time to do welll....)  and not knowing if any students will actually DO this, I decided to not make a video.

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 16", "Question 17", "Question 18",  , }})