# Activities

• • • ##### Subject Area

• Math: Geometry: Transformational Geometry

• ##### Author 6-8

60 Minutes

• ##### Device
• TI-73 Explorer™
• ##### Other Materials
This is Activity 12 from the EXPLORATIONS Book:
Shaping Middle Grades Mathematics: Activities for Geoboard and the TI-73

## Traveling Shapes - Motion Geometry

#### Activity Overview

In this activity, students describe how to move a shape from one place to another in a plane. They learn about translations, rotations, and line reflections.

#### Before the Activity

• Start the Geoboard App and format it
• See the attached PDF file for detailed instructions for this activity
• Print pages 133 - 144 from the attached PDF file for your class
• #### During the Activity

Distribute the pages to the class.

• Construct a triangle ABC
• Perform a translation called slide and move the triangle first 6 units to the right and then 3 units upwards
• Observe that the translation notation is given as (6,3)
• Observe that the translation can also be represented with a directed slide arrow and the coordinates of its final position is given by the amount of horizontal and vertical change between the first and the final position (6,3)
• Construct other shapes and move the shape according to the directed slide arrow and draw its final position
• Examine the shapes, draw the slide arrow, and give the coordinates for each translation

• Observe that the triangle can also be transformed by rotating about point A through any angle
• Rotate the triangle about point A clockwise 90 degrees, 180 degrees, 270 degrees, and 360 degrees
• Rotate the triangle counterclockwise 90 degrees and notice that this is the same as rotating it clockwise 270 degrees
• Try to rotate about point B, 180 degrees, and observe this cannot be done
• Rotate each shape through the given angle about the given point and sketch the diagram of the rotated position

• Construct a square ABCD and flip it 2 units about a line IJ
• Observe that the square is 2 units from line IJ on the other side
• Flip each shape about the given line and then sketch a diagram of the final reflection image
• #### After the Activity

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary