Today’s Lesson:

1. Today’s Lesson: What: transformations (rotations). . . Why: To perform rotations of figures on the coordinate plane. .

2. Translation Review: Remember, a translation is a ______________ . MEMORIZE: “RIGHT or LEFT changes _____!! UP or DOWN changes _____!!! This means that if a figure moves RIGHT or LEFT, we ADD or __________________ from the original x coordinate. If a figure moves UP or DOWN, we ADD or SUBTRACT from the original ______ coordinate. Point A, (3, 5) is translated two to the left and four up. Where is AI ? slide x y SUBTRACT y Answer: (1, 9)

3. What about rotations ?? Stations of Rotation: 90º: 180º: 270º: 360º: CLOCKWISE: from “12 o’clock” (top of coordinate graph), figure will rotate to the ____________________. COUNTER-CLOCKWISE: from “12 o’clock” (top of coordinate graph), figure will rotate to the ____________________. turn turn turn full turn A AI right left Let’s explore some rotations . . . Rotation Applet

4. Name:________________________________________________________________Date:_____/_____/__________Name:________________________________________________________________Date:_____/_____/__________ (To be used in conjunction with NLVM) A ROTATION refers to when a geometric figure is ________________________ around a center of rotation. For this activity, we will explore rotations on the coordinate plane. Our center of rotation will be the ____________________________ . Directions: As Ms. Dyson rotates the following figure (on the screen), let’s track the movement of one point: Rotation #1: Clockwise Rotation of Trapezoid: Original coordinate of given point: ( , ) Quadrant: _____ Coordinate after 90°clockwiserotation: ( , ) Quadrant: _____ Coordinate after 180°clockwiserotation: ( , ) Quadrant: _____ Coordinate after 270°clockwiserotation: ( , ) Quadrant: _____ Coordinate after 360°clockwiserotation: ( , ) Quadrant: _____ Rotation #2: Clockwise Rotation of Trapezoid: Original coordinate of given point: ( , ) Quadrant: _____ Coordinate after 90°clockwiserotation: ( , ) Quadrant: _____ Coordinate after 180°clockwiserotation: ( , ) Quadrant: _____ Coordinate after 270°clockwiserotation: ( , ) Quadrant: _____ Coordinate after 360°clockwiserotation: ( , ) Quadrant: _____ Do you notice any patterns among the coordinates above? Rotation #3: Counter-Clockwise Rotation of Trapezoid: Original coordinate of given point: ( , ) Quadrant: _____ Coordinate after 90°counter-clockwiserotation: ( , ) Quadrant: _____ Coordinate after 180°counter-clockwiserotation: ( , ) Quadrant: _____ Coordinate after 270°counter-clockwiserotation: ( , ) Quadrant: _____ Coordinate after 360°counter-clockwiserotation: ( , ) Quadrant: _____ Did the patterns/ observations you made about the clockwise rotations change when we performed the counter-clockwise rotation? Exploring Rotations Rotation Applet

5. Using the observations and/or patterns we just discussed, what would be a rule that we could use to know what each new point will be without seeing the rotation on the screen? Rule: Now, use the above rule to record the new coordinates for the below rotation (without seeing it on the screen). Rotation #4: Counter-Clockwise Rotation of Trapezoid: Original coordinate of given point: ( , ) Quadrant: _____ Coordinate after 90°counter-clockwiserotation: ( , ) Quadrant: _____ Coordinate after 180°counter-clockwiserotation: ( , ) Quadrant: _____ Coordinate after 270°counter-clockwiserotation: ( , ) Quadrant: _____ Coordinate after 360°counter-clockwiserotation: ( , ) Quadrant: _____

6. Rotating a triangle (together in class) . . . BI BI BI B CI AI AI CI C A AI CI II III IV I

7. END OF LESSON The next slides are student copies of the notes for this lesson. These notes were handed out in class and filled-in as the lesson progressed. NOTE: The last slide(s) in any lesson slideshow (entitled “Practice Work”) represent the homework assigned for that day.

8. NAME: DATE: ______/_______/_______ Math-7 NOTES What: transformations (ROtations). . . Why: To perform rotations of figures on the coordinate plane. Translation Review: Remember, a translation is a __________________ . MEMORIZE: “RIGHT or LEFT changes _____!! UP or DOWN changes _____!!! This means that if a figure moves right or left, we ADD or __________________ from the original x coordinate. If a figure moves up or down, we ADD or SUBTRACT from the original ______ coordinate. Point A, (3, 5) is translated two to the left and four up. Where is AI ? What about rotations ?? A AI Stations of Rotation: 90º: 180º: 270º: 360º: CLOCKWISE: from “12 o’clock” (top of coordinate graph), figure will rotate to the ____________________. COUNTER-CLOCKWISE: from “12 o’clock” (top of coordinate graph), figure will rotate to the ____________________. Rotation Applet

9. Rotating a triangle (together in class) . . . Directions: Plot the original points as indicated. Connect the points to make a right triangle. Then, rotate the ORIGINAL triangle counter-clockwise as indicated:

10. NAME: ________________________________________________________________________________DATE:_____/_____/__________ Math-7 Practice/ HOMEWORK “rotations” Where will Point A end up after a 90° clockwise rotation? _______ 2. Where will Point A end up after a 180° clockwise rotation? _______ A A 3. Where will Point A end up after a 90° counter-clockwise rotation? ______ 4. Where will Point A end up after a 270° clockwise rotation? _______ A A 6. Where will Point A end up after a 180° counter-clockwise rotation? _______ 5. Where will Point A end up after a 270° counter-clockwise rotation? _______ A A

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