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

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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 A I ? slide x y SUBTRACT y Answer: (1, 9)

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A AIAI 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 ____________________. What about rotations ?? right left Let’s explore some rotations... Rotation Applet full turn

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Exploring Rotations (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°clockwise rotation:(, ) Quadrant: _____ Coordinate after 180°clockwise rotation:(, ) Quadrant: _____ Coordinate after 270°clockwise rotation:(, ) Quadrant: _____ Coordinate after 360°clockwise rotation:(, ) Quadrant: _____ Rotation #2: Clockwise Rotation of Trapezoid: Original coordinate of given point: (, ) Quadrant: _____ Coordinate after 90°clockwise rotation:(, ) Quadrant: _____ Coordinate after 180°clockwise rotation:(, ) Quadrant: _____ Coordinate after 270°clockwise rotation:(, ) Quadrant: _____ Coordinate after 360°clockwise rotation:(, ) 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-clockwise rotation:(, ) Quadrant: _____ Coordinate after 180°counter-clockwise rotation:(, ) Quadrant: _____ Coordinate after 270°counter-clockwise rotation:(, ) Quadrant: _____ Coordinate after 360°counter-clockwise rotation:(, ) Quadrant: _____ Did the patterns/ observations you made about the clockwise rotations change when we performed the counter-clockwise rotation? Name:________________________________________________________________Date:_____/_____/__________ Rotation Applet

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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-clockwise rotation:(, ) Quadrant: _____ Coordinate after 180°counter-clockwise rotation:(, ) Quadrant: _____ Coordinate after 270°counter-clockwise rotation:(, ) Quadrant: _____ Coordinate after 360°counter-clockwise rotation:(, ) Quadrant: _____

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Original Coordinates:A (2, 1)B (2, 7)C (6, 1) 90ºQuadrant ________ A (, )B (, )C (, ) 180ºQuadrant ________ A (, )B (, )C (, ) 270ºQuadrant ________ A (, )B (, )C (, ) 360ºQuadrant ________ A (, )B (, )C (, ) Rotating a triangle (together in class)... A B C AIAI BIBI CICI AIAI BIBI CICI AIAI BIBI CICI II III IV I

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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.

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Math-7 NOTES DATE: ______/_______/_______ What: transformations (ROtations)... Why: To perform rotations of figures on the coordinate plane. What: transformations (ROtations)... Why: To perform rotations of figures on the coordinate plane. NAME: 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 ____________________. 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 A I ? A AIAI Rotation Applet What about rotations ??

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Original Coordinates:A (2, 1)B (2, 5)C (6, 1) 90ºQuadrant ________A (, )B (, )C (, ) 180ºQuadrant ________A (, )B (, )C (, ) 270ºQuadrant ________A (, )B (, )C (, ) 360ºQuadrant ________A (, )B (, )C (, ) Directions: Plot the original points as indicated. Connect the points to make a right triangle. Then, rotate the ORIGINAL triangle counter-clockwise as indicated: Rotating a triangle (together in class)...

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1.Where will Point A end up after a 90° clockwise rotation? _______ 2.Where will Point A end up after a 180° clockwise rotation? _______ 4.Where will Point A end up after a 270° clockwise rotation? _______ 3.Where will Point A end up after a 90° counter-clockwise rotation? ______ 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 A A A A NAME: ________________________________________________________________________________DATE:_____/_____/__________

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