Unit 1, Lesson 13
Incorporating Rotations
Integrated Math 1
13.1
Warm-up
Instructional Routines
NoneMaterials
Activity Narrative
In this activity, students describe rotations. During discussion, students work together to determine that a complete description of a rotation includes a center, a direction, and an angle. Students also practice measuring angles with protractors to prepare for a subsequent lesson in which they will need to use protractors to draw rotations with a given angle measure.
Launch
Display this image, and explain that people use flags to signal messages with the semaphore alphabet. It was widely used to communicate ship-to-ship or ship-to-shore during the 19th century and is still used in some circumstances today.
Provide access to protractors.
Activity
NoneFlag semaphore is a way to use flags to signal messages. The diagrams show how to signal the letters Z and J in the semaphore alphabet. For each, precisely describe a rotation that would take the left-hand flag (L) to the right-hand flag (R).
Z
J
Student Response
Activity Synthesis
The purpose of this discussion is to identify the characteristics of a rotation and to practice using protractors. Invite students to share their descriptions. Record their responses for all to see by annotating the images and collecting important terms such as “around,” “clockwise,” and “degrees.”
Display the image with construction marks.
Demonstrate how to use a protractor to measure the angles. Invite the students to practice using their protractors. Students may get angle measures that vary slightly. Discuss the limitations of measuring with a protractor. When the diagram is labeled, we can know the exact measurement; otherwise, we have to estimate by using whatever tools are available.
Lesson Synthesis
Invite students to draw or act out (using their arms and paper as flags) a few transformations. To act out the letters, tell students the starting position of their left-hand flag.
- Rotate 135 degrees clockwise around the point of intersection of the arms. (Semaphore letter S)
- Reflect over a vertical line. (Semaphore letter N)
- Translate to the left, then rotate 45 degrees clockwise around the point of intersection of the arms. (Semaphore letter O)
S
N
O
Student Lesson Summary
The three rigid motions are reflect, translate, and rotate. Each of these rigid motions can be applied to any figure to create an image that is congruent. To do a rotation, we need to know three things: the center, the direction, and the angle.
Rotate 90 degrees clockwise around point .
Rotate 120 degrees counterclockwise around point .