1. Math CC7/8 – May 17 Math Notebook: Things Needed Today (TNT):
Pencil/Math Notebook/Transformation Brochure/ 3 different color pencils, markers or pen
Transformation #4
Math Notebook:
Topic: Rotations of 90, 180 and 270 degrees
HW: Rotation Worksheet & Rotation page in brochure

2. What’s Happening Today?
Transformation #4
Rotation
Finish part of the brochure

3. Vocabulary the point about which a figure is rotated.
transformation: a transformation where a figure is rotated, or turned around a center of rotation (a given point)
the point about which a figure is rotated.
Rotation
Center of Rotation

4.
Geometer's Sketchpad
Investigation

5. Rule Pre-Image Image
Table for Rotations

6. Describing a rotation To describe a rotation we need to know 3 things:
The angle of rotation.
For example,
¼ turn = 90°
½ turn = 180°
¾ turn = 270°
The direction of rotation.
For example, clockwise or counter-clockwise.
The center of rotation.
This is the fixed point about which an object moves.

7. Rotating shapes
If we rotate triangle ABC 90° clockwise about point O the following image is produced: B
object
90° A A’
image B’ C C’
Explain that if the centre of rotation is not in contact with the shape, we can extend a line from the shape to the point. A line extended from the corresponding point on the image will meet the centre of rotation at an angle equivalent to the angle of rotation. O
A is mapped onto A’, B is mapped onto B’ and C is mapped onto C’.
The image triangle A’B’C’ is congruent to triangle ABC.

8. Rule for Rotations Rotation 90°: (x , y ) (-y, x)
Example: (-2, -4) (4, -2)
Rotate 180°: (x , y ) (-x, -y)
Example: (-9, 3) (9, -3)
Rotate 270°: (x , y ) ( y, -x )
Example: (-7, -4) (-4, 7)

9. Essential Understandings
Do you understand and know the critical vocabulary words for Rotation Transformation?
Can you describe a Rotation(always remembering to indicating the direction and about which point the figure is being rotated?
Can you identify a Rotation?
Can you create the table and add it to your brochure for Rotation?
IMPORTANT Note
Use the method of “spinning” the graph to determine mapping points.

10. Rotations on a coordinate grid
The vertices of a triangle lie on the points A(2, 6), B(7, 3) and C(4, –1). 7
A(2, 6) 6 5
B(7, 3) 4 3
Rotate the triangle 180° clockwise about the origin and label each point on the image.
C’(–4, 1) 2 1 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 –1 –2
C(4, –1) –3
Pupils should notice that when a shape is rotated through 180º about the origin, the x-coordinate of each image point is the same as the x-coordinate of the the original point × –1 and the y-coordinate of the image point is the same as the y-coordinate of the original point × –1. In other words the coordinates are the same, but the signs are different. –4
What do you notice about each point and its image?
B’(–7, –3) –5 –6
A’(–2, –6) –7

11. Rotations on a coordinate grid
The vertices of a triangle lie on the points A(–6, 7), B(2, 4) and C(–4, 4). 7
B(2, 4) 6 5
C(–4, 4) 4 3
Rotate the triangle 90° counter-clockwise about the origin and label each point in the image.
B’(–4, 2) 2 1 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 –1 –2 –3
Pupils should notice that when a shape is rotated through 90º anticlockwise about the origin, the x-coordinate of each image point is the same as the y-coordinate of the the original point × –1. The y-coordinate of the image point is the same as the x-coordinate of the original point. –4
What do you notice about each point and its image?
C’(–4, –4) –5 –6
A’(–7, –6) –7

12. Learning Target - Rate yourself:
Exit Task #4
Learning Target - Rate yourself:
4 - I get this so well I could teach the class with my eyes closed.
3 - I get this pretty well
2 - I'm starting to get it
1 - I'm lost, send out search dogs