High School: Geometry
5. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
Rotations, reflections, and translations might sound like moves in a Cirque du Soleil show. Rotating about the trapeze, reflected in a shiny disco ball, and translated from French to English. But really, rotations, reflections, and translations are all about staying rigid rather than flexible. Sorry, contortionists.
Students should already be well aware of rigid transformations, only now, they'll actually be using them instead of theorizing about them. Students should come up with sets of transformations (meaning more than one) that map figures onto themselves and other figures.
So, while not death-defying like some circus acts, what's exciting about this standard for students is that they are taking definitions and rules they've learned and actually bringing them into practice on paper.
Following this lesson, students should be able to use visuals to improve their sense and knowledge of how a transformation maps one shape onto another. They should also understand why moving and manipulating figures is a useful tool in real-world situations.
Make sure to keep your students motivated. This standard is the last of those dealing with working on transformations in the plane. Since they've already learned so much about congruence and transformations (or they should have, anyway), it's not as if they have to jump through hoops to master this concept.
All they have to do is put pencil to paper and start drawing. Well, transforming drawings, actually.
- Translating Shapes on the Coordinate Plane - Math Shack
- Rotations on the Coordinate Plane - Math Shack
- Reflections on the Coordinate Plane - Math Shack
- Developing Definitions of Translations - Math Shack
- Reflecting Figures on the Coordinate Plane - Math Shack
- Translations on the Coordinate Plane - Math Shack
- Developing Definitions of Rotations - Math Shack
- Reflections - Math Shack
- Experimenting with Transformations - Math Shack
- Coordinate Rotation - Math Shack