today’s lesson:
DESCRIPTION
Today’s Lesson:. 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 _____!!! - PowerPoint PPT PresentationTRANSCRIPT
Today’s Lesson:
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 ?
slide
x y
SUBTRACT
y
Answer: (1, 9)
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 ____________________.
What about rotations ??
right
left
Let’s explore some rotations . . . Rotation Applet
turn
turn
turn
full turn
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
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: _____
Original Coordinates:
A (2, 1) B (2, 7) C (6, 1)
90º Quadrant ________
A ( , )
B ( , )
C ( , )
180º Quadrant ________
A ( , )
B ( , )
C ( , )
270º Quadrant ________
A ( , )
B ( , )
C ( , )
360º Quadrant ________
A ( , )
B ( , )
C ( , )
Rotating a triangle (together in class) . . .
A
B
CAIBI
CI
AI
BI
CI
AI BI
CI
II
III
IV
I
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.
Math-7 NOTES DATE: ______/_______/_______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 AI ?
A AI
Rotation Applet
What about rotations ??
Original Coordinates: A (2, 1) B (2, 5) C (6, 1)
90º Quadrant ________
A ( , ) B ( , ) C ( , )
180º Quadrant ________
A ( , ) B ( , ) C ( , )
270º Quadrant ________
A ( , ) B ( , ) C ( , )
360º Quadrant ________
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) . . .
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
Math-7 Practice/ HOMEWORK“rotations”
NAME: ________________________________________________________________________________DATE:_____/_____/__________
1) 2)
3) 4)