1. Unit 1: Transformations Day 3: Rotations 1/25/2013
Geometry
Unit 1: Transformations
Day 3: Rotations
1/25/2013

2. Agenda Warm-Up Homework Check Intro to rotations Activity
Formalizing rotations
in the coordinate plane
Practice
Exit Ticket
Homework

3. Warm-Up 1/25/2013 Solve the following equations:

4. Include with Warm-Up for 1/25/2013

5. CARPENTRY You are assembling pieces of wood to complete a railing for your porch. The finished railing should resemble the one below.
How are pieces 1 and 2 related? pieces 3 and 4?
In order to assemble the rail as shown, explain why you need to know how the pieces are related.

6. Homework Check Part 1 D 2. F 3. R 4. Q 5. EF 6. <FED 7. ST 8.QR
9. A’(3,-3); B’(-3,-6); C’(-3,-3) 10. G’(8,-4); H’(6,-2)
11. W’(3,1); X’(2,2); Y’(2,3); Z’(3,4) M’(4,0); N’(6,-3); P’(2,-4)
14.a. I’(0,-2); J’(3,-1); K’(6,-2); L’(3,2)
14.b. I’(0,2); J’(-3,1); K’(-6, 2); L’(-3,-2)
15.a. W’(2,1); Y’(-1,3); Z’(1,-2) b. W’(-2,-1), Y’(1,-3); Z’(-1,2)
16.a. B’(-6,2); T’(-8,2); A’(-3,-4) b. A’(-3,8), B’(0,2); T(2,2)

7. Homework Check Part 2 1. 1= D, 1.2=C, 1.3= B, 1.4=A
2.1= B, 2.2=A, 2.3=C, 2.4=D
6. S’(-2,2), E’(3, 2), B’(6, -4), T’(-2,-4)
7. B’(-4, 9), T’(4,9), S’(4,3), E’(-1,3)
8. S’(0,4), E’(5, 4), B’(8,-2), T’(0,-2)
9. T’(-2,6), S’(4,6), E’(4, 1), B’(-2, -2)

8. "Rotation" means turning around a center:
Rotation: Turns a figure about a fixed point. (a spin) *** All rotations are counterclockwise about the origin unless otherwise stated*** Counterclockwise:

9. Visualizing a Rotation
Draw a figure on your paper and label the vertices
Place a point on your paper.
Put the tip of your pencil on the point to hold the paper in place.
Rotate the paper Counterclockwise to see the different rotations.
Is there ever a time when the rotated figure is back in the same place as the starting point?

10. Formalizing Rotations in the Coordinate Plane
Algebraic Rule for Rotations:
90°
180°
270°
360°
Give students graph paper (cut into 4ths) each student needs 5 pieces.
Have students draw a coordinate plan each pieces. And place an ordered pair in Quadrant 1. cannot have same x and y values!!!
Lay the second piece of paper on top of the first. The coordinates plane needs to line up EXACTLY! Place your pencil on the origin (0,0). Rotate the bottom piece 90° counterclockwise. The ordered pair should now be in Quadrant 2. Trace the ordered pair onto the top sheet of paper. Give the correct coordinates for the rotated point. Have students create the algebraic rule for this rotation.
Lay the third piece of paper on top of the first. The coordinates plane needs to line up EXACTLY! Place your pencil on the origin (0,0). Rotate the bottom piece 180° counterclockwise. The ordered pair should now be in Quadrant 3. Trace the ordered pair onto the top sheet of paper. Give the correct coordinates for the rotated point. Have students create the algebraic rule for this rotation.
Lay the fourth piece of paper on top of the first. The coordinates plane needs to line up EXACTLY! Place your pencil on the origin (0,0). Rotate the bottom piece 270° counterclockwise. The ordered pair should now be in Quadrant 4. Trace the ordered pair onto the top sheet of paper. Give the correct coordinates for the rotated point. Have students create the algebraic rule for this rotation.
Lay the fifth piece of paper on top of the first. The coordinates plane needs to line up EXACTLY! Place your pencil on the origin (0,0). Rotate the bottom piece 360° counterclockwise. The ordered pair should now be in Quadrant 1. Trace the ordered pair onto the top sheet of paper. Give the correct coordinates for the rotated point. Have students create the algebraic rule for this rotation.
**Have students label the rotated pieces of graph paper by 90, 180, 270, or 360 and label the original. Have students staple to notes.

11. What is Isometry?
Isometry: is a transformation in which the preimage and the image are congruent. Do the transformations we have discussed have isometry? Translations? Yes Reflections? Rotations?

12. Exit Ticket – Should be placed in notes
Draw and label a picture of each type of transformation that we have discussed thus far.
Do the above transformations hold the property of isometry?
**Challenge combine any 2 transformations – make sure to show each step and label which 2 transformations you have combined to create the final transformation. (extra credit if done correctly)

13. Independent Practice Page: 649-651 #: 2,3,4, 6-9, 36 Page 652:
Check point Quiz 1: 1-6, 10
Adjust based on time!

14. Homework Complete Rotation worksheet
Study for Quiz, need to be familiar with all three types of transformations we have discussed.