How To Discover Rotation Rules
Using discovery in geometry leads to better understanding. Today I am sharing a simple idea for discovering the algebraic rotation rules when transforming a figure on a coordinate plane about the origin. This activity is intended to replace a lesson in which students are just given the rules. It doesn’t take long but helps students to understand the correlation between the quadrants, the positive/negative ordered pairs, and the direction and degree of the rotation. It also allows them to discover the rules, which leads to increased engagement and deeper understanding.
- vocabulary (rigid motion, transformation, rotation, quadrants, clockwise, counterclockwise)
- how to graph on a coordinate plane
- pre-printed graphs with a figure in quadrant I (Here are the ones I use.)
- old laminating sheets cut into squares (I am sure your school has some old ones sitting around. Look around before you buy- they aren’t super cheap to buy new.)
- push pins
- tiny brads (These are super cheap. I have found them at Hobby Lobby and Amazon.)
- Sharpies or felt tip pens
Using the Manipulative to Discover Rotation Rules
Once they have made their manipulative, they should work in groups or go through it together as a whole class discussion. I provide them with a table/graphic organizer to visualize the patterns, which leads them to a discovery of the rules. They can also create their own table in their notebooks to write the observations.
Synthesis and Application
I follow up with these interactive notebook notes so students can synthesize their thoughts into one location in their notebooks. This resource includes a second page that teaches students to rotate around a non-origin point, too.