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.

Photo of supplies needed to discover the rotation rules

Prior Knowledge

  • 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

The Process

Check out this video I made for Instagram (@the.efficient.classroom) on 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.)

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.

Photo of manipulative in use
Rotation Rules in a Table

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. 

After students have had a chance to engage with and understand how rotations work, this set of task cards is the perfect practice activity. Get them by clicking here or read more about how to use task cards in your classroom here.



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