Math 7

Unit 8 Geometry

Lesson 8.7   Graphing Rotations

Focus

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

Graph rotation images on a coordinate grid.

TEXT Page 325

Read/Work through the  Focus  section at the top of page 325 in  your textbook.

Watch

Video Tutorial

Explore  (Textbook)

Explore an idea or problem.
The exploration provides the background for the ideas presented in the lesson.

TEXT Page 325

Read/Work through the  Explore  section on Page 325 in your textbook.

You can do this activity on your own.
For a more directed exploration, check the next section.

Grid Paper
Several links were provided in the previous lesson.
HERE is a link to a 0.5 cm grid paper file you can download and print.

Explore  (Online)

Explore an idea or problem.
The exploration provides the background for the ideas presented in the lesson.

This exploration looks at the same ideas as the one in the textbook, but is more interactive.

Video Tutorial A  (Explore A)

Explore by moving the point of rotation INSIDE the original shape,  ON the original shape,  OUTSIDE the original shape,  and moving it to the ORIGIN.
In each case try a clockwise and counter-clockwise rotation.
Do this first to get a good visual sense of how a rotation works.

LINK to the online page

For this class,  we are going to be looking at rotations that are multiples of 90°.
Using the online page,  explore rotations of 90°, 180° and 270°,  both clockwise and counter-clockwise.
Look at the coordinates of the points on the original figure, and the coordinates of the points of the  image.
Can you find a pattern that would let you give the coordinates of the image without actually doing the rotation?

Video Tutorial B  (Explore B)

Spoiler Alert
In the video that follows,  I GIVE you the pattern.
I hope you will explore the ideas and look for the pattern yourself FIRST!

Video Tutorial C  (Explore C)

Connect

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

TEXT Page 326

Read/Work through the  Connect  section on Page 326 in your textbook.

Example

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

Example

TEXT Page 327

Work through the Example  on Page 327 in your textbook.

Watch

Video Tutorial

Rotation Summary

For all these rotations,  the CENTER OF ROTATION is at the origin,  (0,0)

Angle of Rotation				Original Point Location		Image Point Location

90° Clockwise					(a,b)					(b,-a) 
270° Counter-Clockwise

180° Clockwise				(a,b)					(-a,-b) 
180° Counter-Clockwise

270° Clockwise				(a,b)					(-b,a) 
90° Counter-Clockwise

Use these like a recipe.
For example,  the recipe   (a,b)   to   (b,-a)   means to switch the coordinates, then make a   the  opposite of what it was.
Eg,  if you rotate the point with coordinates   (-2,4)  90° clockwise about the origin,  the new coordinates of the point will be  (4,2)

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

Assessment Focus a question that gives a good example of the kind of question you would be expected to answer after completing the lesson

Take It Further questions offer enrichment and extension.

Notes

Question 7,    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 8", "Question 9", }})