Unit 1, Lesson 3
Making the Moves
Accelerated 7
Preparation
Lesson Narrative
In the previous lesson, students were introduced to the terms “translation,” “rotation,” and “reflection.” In this lesson, students understand that:
- A translation is determined by two points that specify the distance and direction of the translation.
- A rotation is determined by a point, angle of rotation, and a direction of rotation.
- A reflection is determined by a line.
These moves are called transformations for the first time, and students draw images of figures under these transformations. They study where shapes go under sequences of these transformations and identify the steps in a sequence of transformations that takes one figure to another. They also label the image of a point as . While not essential, this practice helps show the structural relationship (MP7) between a figure and its image.
Students also encounter the isometric grid (one made of equilateral triangles with 6 meeting at each vertex). They perform translations, rotations, and reflections both on a square grid and on an isometric grid.
Students using the print version may make use of tracing paper to experiment moving shapes. For classrooms using the digital version of the materials: This is the lesson where students learn to use the transformation tools in GeoGebra. Whenever students choose to make use of an appropriate tool, they are engaging in MP5.
- Draw and label the image of figures that result from translations, rotations, and reflections on a square or isometric grid.
- Explain (orally) the sequence of transformations that takes one figure to its image.
- Identify (orally and in writing) the features that determine a translation, rotation, or reflection.
Let’s draw and describe translations, rotations, and reflections.
Required Preparation
Make sure students have access to items in their geometry toolkits: tracing paper, graph paper, colored pencils, scissors, ruler, protractor, and an index card to use as a straightedge or to mark right angles.
For classrooms using the print version of the materials: Access to tracing paper is particularly important. Each student will need about 10 small sheets of tracing paper (commercially available "patty paper" is ideal). If using large sheets of tracing paper, such as 8.5 inches by 11 inches, cut each sheet into fourths.
For classrooms using the digital version of the materials: If there is access to extra help from a tech-savvy person, this would be a good day to request their presence in class.
For the digital version of the activity, acquire devices that can run the applet.
An image is the result of translations, rotations, and reflections on an object. Every part of the original object moves in the same way to match up with a part of the image.
Triangle has been translated up and to the right to make triangle . Triangle is the image of the original triangle .