Unit 1: Transformations Day 3: Rotations

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Presentation transcript:

Unit 1: Transformations Day 3: Rotations Geometry Unit 1: Transformations Day 3: Rotations

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

Label the pictures as either a translation, reflection, or rotation! Warm-Up In groups Label the pictures as either a translation, reflection, or rotation! Come up with a “definition” of a rotation.

"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:

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?

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.

Independent Practice Adjust based on time!

Exit Ticket 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)

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