Translations with Preimages

Introduction (10 minutes):

1. Warm-up (5 minutes): Play a quick game of "Simon Says" with body movements that represent transformations. Examples: "Simon says hop two steps to the right" (translation), "Simon says turn 90 degrees clockwise" (rotation), "Simon says touch your left hand to the mirror" (reflection).
2. Introduce Transformations (5 minutes): Briefly introduce the concept of transformations in geometry. Explain that transformations are movements that change the position or orientation of a shape without changing its size or shape. Discuss the three main types of transformations: translations, rotations, and reflections.

Activity: Exploring Transformations (20 minutes):

1. Single Transformations (10 minutes):

   • Divide students into pairs or small groups.
   • Provide each group with geometry manipulatives (or pre-cut shapes) and a worksheet with a simple shape (pre-image).
   • Instruct students to explore each type of transformation one at a time.
     • Translation: Ask students to move the shape a specific distance in a specific direction (e.g., 3 units to the right, 2 units up). Discuss how the position of the shape changes but its size and shape remain the same.
     • Rotation: Demonstrate rotating the shape around a fixed point (center) by a specific angle (e.g., 90 degrees clockwise). Discuss how the orientation of the shape changes but its size and shape remain the same.
     • Reflection: Have students fold a transparency sheet in half to create a reflection line. Place the pre-image shape on the transparency sheet and trace its reflection across the fold. Discuss how a reflection creates a mirror image of the original shape.
2. Describing Transformations (10 minutes):
   • As a class, discuss each transformation performed.
   • Have students practice describing the transformations using mathematical language (e.g., "The square was translated 2 units to the right", "The triangle was rotated 180 degrees", "The rectangle was reflected across a vertical line").

Activity: Mapping with Transformations (20 minutes):

1. Introduce Sequence of Transformations (5 minutes):
   • Explain that transformations can be combined to create a sequence of movements.
   • Discuss how applying a sequence of transformations can map a pre-image (original shape) onto its image (final position and orientation).
2. Mapping Practice (15 minutes):
   • Provide students with new worksheets that show a pre-image shape and instructions for a specific sequence of transformations (e.g., translate 1 unit right, rotate 90 degrees counter-clockwise, reflect across a horizontal line).
   • Students work individually or in pairs to follow the instructions and apply the sequence of transformations to the pre-image shape.
   • Encourage them to draw the image (resulting shape) after each transformation and label it accordingly.

Wrap-up (10 minutes):

1. Class Discussion (5 minutes):
   • Have students share their completed worksheets and discuss how the sequence of transformations mapped the pre-image onto its image.
   • Ask questions to reinforce understanding: "What happened to the shape after each transformation?", "How did the final image (position and orientation) differ from the pre-image?"

2. Exit Ticket (5 minutes):

   Provide students with a quick assessment (exit ticket) with a simple shape (pre-image) and a description of a single or combined transformation. Students draw the resulting image (after the transformation) and write a brief explanation of the transformation applied.

Differentiate: provide additional guided practice with single transformations before moving on to sequences.

Extend: challenge them to create their own sequences of transformations to map a pre-image to a specific image or explore more complex shapes.

Observe student participation during activities and discussions. Use the worksheet to check for accuracy.