Graphing and Describing “Rotations” Be sure to read notes section on each slide for additional instructions and answers. Transformations Day 5

we spent a day focusing on “Translations” A translation is a slide that moves a figure to a different position (left, right, up or down) without changing its size or shape and without flipping or turning it.

We spent a day on “Reflections” A reflection (flip) creates a mirror image of a figure.

Today… We will focus on “Rotations” A rotation (turn) moves a figure around a point. This point can be on the figure or it can be some other point. This point is called the point of rotation. P

Congruency 1) Translations 2) Reflections 3) Rotations 4) Dilations The first 3 transformations preserve the size and shape of the figure. That means… If your pre-image (the before) is a polygon, your image (the after) is a congruent polygon. If your pre-image contains parallel lines, your image contains congruent parallel lines If your pre-image is an angle, your image is an angle with the same measure. Could this represent a translation? Point out in the top image that you can determine congruency by counting the number of units that make up each corresponding line segment. Then click mouse and see if students can determine if the right triangles could represent a translation. Answer: No because translations preserve the size and shape. Figure A is bigger than Figure B.

Let’s Get Started Section 1: Describing Rotations Section 2: Graphing Rotations 180º

Describing a Rotation When you rotate a figure, you can describe the rotation by… Giving the direction: clockwise or counter-clockwise Giving the degrees that the figure is rotated around the point of rotation: 90º, 180º, 270º

NOTE: 180º rotations turn the figure upside down! Describing a Rotation pre-image What are 2 ways to describe the rotation from A to B ? What are 2 ways to describe the rotation from A to D ? What are 2 ways to describe the rotation from A to C ? 90º rotations move the figure over 1 quadrant (CW or CCW) 180º rotations move the figure over 2 quadrants 270º rotations move the figure over 3 quadrants Explain the different rotations: 90, 180 and 270 (both clockwise and counter-clockwise) Make sure students understand that a 90 degree CW turn is same as 270 degree CCW. Make sure students understand that a 90 degree CCW turn is the same as a 270 degree CW. Click mouse and go through questions. Answer B is a 90 degree clockwise or 270 degree CCW C is a 180 degree turn clockwise or CCW D is a 90 degree CCW or 270 degree clockwise NOTE: 180º rotations turn the figure upside down!

Turn and Talk Which can be described as a 180º rotation around the origin? Be prepared to share your reasoning with the class. A B A B Figure #2 is the 180 degree rotation. You can tell because the figure has been turned upside down. Figure #1 Figure #2

Turn and Talk Which describes the rotation of the cell phone? Select ALL that apply. 90° clockwise 180º clockwise 270° clockwise 90° counter clockwise 180º counter clockwise 270° counter clockwise HANDS ON… As students Turn and Talk, give them the opportunity to pull out their own smart phones and do a similar rotation. Answer: A, F If you look at the word “Samsung” you can tell that the phone has been turned 90 degrees clockwise (or 270 CCW).

You Try #1 Describe the given rotation. Give both the CW and CCW description. Figure Q is the pre-image. It was rotated 90 degrees clockwise or 270 degrees counter-clockwise.

You Try #2 Analyze the given transformation. Which of the following could map the Blue square onto the Green? Reflection across the x-axis. 180º rotation around the origin. A translation 6 left and 6 down. Both B and C. Answer: C You can tell that this is not a 180 degree rotation by looking at the letters. The Green box has not been turned upside down. Show students how the translation 6 left and 6 down maps the Blue box on top of the Green box.

You Try #3 Describe the rotation from Figure A to Figure B. Give both CW and CCW description. 90 degrees counter-clockwise or 270 degrees clockwise

You Try #4 Which describes the rotation of the cell phone? Select ALL that apply. 90° clockwise 180º clockwise 270° clockwise 90° counter-clockwise 180º counter-clockwise 270° counter-clockwise Answer: C, D

Moving on… Section 1: Describing Rotations Section 2: Graphing Rotations 180º

Rotate the figure below 180° clockwise about the origin. Graphing rotations Rotate the figure below 180° clockwise about the origin. Graphing a rotation can be very challenging. Most of us have difficulties envisioning what a figure will look like after a 90º, 180º or 270º turn. Don’t actually perform this rotation. Just read the screen. This rotation will be done on slide 18.

Another Way Another method for graphing rotations is to apply some RULES.

Rotating 180º clockwise or counter-clockwise RULE: Keep the same coordinates; Change both signs to the opposite. (x, y) → (-x, -y) EXAMPLE: Preimage Image X(1, 2) X’(-1, -2) Y(3, 5) Y’(-3, -5) Z(-3,4) Z’(3, -4) Notice how image is upside down with a 180º rotation! These means “take the opposite”, not “make it negative” ! Explain the RULE for rotating 180 degrees clockwise (same as 180 degrees CCW). Make sure students understand that we are not turning everything to negatives. The negatives is this case mean that we are changing the signs to be the opposite of what they are. If the sign is positive, change it to negative. If the sign is negative, change it to a positive. Review example with students. If able… Play YouTube video for students. Watch as teacher performs 2 different 180 degree rotations. You will probably need to click on the “Activate Adobe Flash” and then “Allow and Remember” for it to run. You will also need speakers. I would also make sure that there is a link on your website to this video. https://www.youtube.com/watch?v=8ZeeDYIlNFk

Guided Practice Rotate ∆ABC 180º clockwise about the origin Preimage Image A(7, -2) A’(-7, 2) B(11, -5) B’(-11, 5) C(3, -5) C’(-3, 5) Point out that the figure moved over 2 quadrants to the right. Rotate ∆ABC 180º clockwise about the origin

You Try Rotate Figure ABCD 180º clockwise about the origin Preimage Image A(-4, 1) A’(4, -1) B(1, 3) B’(-1, -3) C(-2, 5) C’(2, -5) D(-5, 3) D’(5, -3) Notice, part of the image ends up in Quadrant III and Part ends up in Quadrant IV. However, if you look at each point, they each moved over 2 quadrants to the right. Rotate Figure ABCD 180º clockwise about the origin

Guided Practice #1 Rotate ∆EFG 180º clockwise about the origin. RULE: Keep the same coordinates; Change both signs to the opposite. (x, y) → (-x, -y) Pre-image Image E(-3, 7) E’(3, -7) F(-7, 3) F’(7, -3) G(-9, 6) G’(9, -6)

You Try #1 Rotate ∆QRS 180º clockwise about the origin RULE: Keep the same coordinates; Change both signs to the opposite. (x, y) → (-x, -y) Pre-image Image Q(2, -2) Q’(-2, 2) R(9, -2) R’(-9, 2) S(9, -6) S’(-9, 6)

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More on… Graphing and Describing “Rotations” Be sure to read notes section on each slide for additional instructions and answers. Transformations Day 6

Prior… Yesterday, we began looking at “Rotations”. We focused on 180°. Today, we will learn how to graph 90° and 270° rotations.

Definition A rotation (turn) moves a figure around a point. This point can be on the figure or it can be some other point. This point is called the point of rotation. P

Moving on… Section 1: Graphing Rotations 90º Section 2: Graphing Rotations 270º

Another Way You can use RULES to graph 90° rotations that go about the origin.

Rotating 90º clockwise https://www.youtube.com/watch?v=LwGmA9F3hbw RULE: Swap the x and y values; Change the sign of the 2nd coordinate to the opposite. (x, y) → (y, -x) EXAMPLE: Preimage Image A(3, 5) A’(5, -3) B(4, 1) B’(1, -4) C(2, 1) C’(1, -2) These means “take the opposite”, not “make it negative” ! Explain the RULE for rotating 90 degrees clockwise. Make sure students understand that when changing the sign on the second coordinate, you are taking the OPPOSITE sign of what it was originally. If positive, it will become negative. If negative it will become positive. You can point out that the RULE always comes up with the correct signs for the quadrant that the each point falls in. In this example, the image fall in Q4 where x will always be positive and y will always be negative. If able… Play the YouTube video (Time 13:33). The lady does a really good job explaining a 90 degree clockwise rotation. I would also make sure this video is a link on your website. Help on remembering which sign to change: A 90º clockwise rotation is a rotation going right. You change the sign on the right. https://www.youtube.com/watch?v=LwGmA9F3hbw

Rotating 90º Counter-Clockwise RULE: Swap the x and y values; Change the sign of the 1st coordinate to its opposite. (x, y) → (-y, x) EXAMPLE: Preimage Image A(1, 2) A’(-2, 1) B(2, 3) B’(-3, 2) C(3, 1) C’(-1, 3) These means “take the opposite”, not “make it negative” ! Explain the RULE for rotating 90 CCW. If able… Play YouTube video for students to watch. Help on remembering which sign to change: A 90º counter-clockwise rotation is a rotation going left. You change the sign on the left. https://www.youtube.com/watch?v=4Q70ZHVFKPc

Guided Practice #1 Rotate ∆EFG 90º clockwise. Answer can be found on answer key to the student notes in lesson plan.

You Try #1 Rotate ∆𝑸𝑹𝑺 90º clockwise. Answer can be found on answer key to the student notes in lesson plan.

Guided Practice #3 Rotate ∆EFG 90º counter-clockwise. Answer can be found on answer key to the student notes in lesson plan.

You Try #3 Rotate ∆𝑸𝑹𝑺 90º counter-clockwise. Answer can be found on answer key to the student notes in lesson plan.

Moving on… Section 1: Graphing Rotations 90º Section 2: Graphing Rotations 270º

270º Rotations If asked to rotate 270º clockwise… Follow the rule for 90º CCW. If asked to rotate 270º counter-clockwise… Follow the rule for 90º clockwise. Use the image to remind students that these mean the same. Figure A to Figure B is 90 degrees clockwise or 270 degrees CCW Figure A to Figure D is 90 degrees counter-clockwise or 270 degrees clockwise.

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