Discovering Rotation Rules



Hi y'all! Today I am sharing a simple idea for discovering the algebraic rules when translating 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. 

Prior knowledge: 
  • Vocabulary (rigid motion, transformation, rotation, quadrants, clockwise, counterclockwise)
  • how to graph on a coordinate plane
Materials:
  • 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
Check out this video I made for Instagram (Managing and Motivating Math Minds on Instagram) of how to construct the manipulative.

(I usually have the students make their own manipulative in class, but if you are short on class time, you can prepare these ahead of time. Also, patty paper can be used in place of the transparency paper. These just seem to last and hold up better in their interactive notebooks.)




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.






I then follow up with a foldable from Lisa Davenport so students can synthesize their thoughts and apply their new rules in problems.