Rigid Transformations

My 8th graders are learning about rigid transformations. I want to add a bit more complexity to what our book is asking the kids to do. For example, the book is having them reflect a shape mainly across the x-axis or y-axis, or on a rare occasion, reflect it across “the horizontal line that goes through y = 3.” Well, right before this chapter, we’ve been working with writing and graphing linear equations, so I want kids to reflect a shape across any line, including one that may cut through the shape itself.


The book surprisingly has very few examples and exercises with rotations. And from what I can find, all these rotations happen about the origin or about a point coinciding with one of the vertices of the shape. Again, I want kids to be able to rotate a shape about any point, including one that’s inside the shape. (I used a playing card — number 7 works well because it’s asymmetrical — poked my pencil through it as the center of rotation, and turned the card. I think this helps them see what I keep referring to as the pivot or anchor point.)


Then I give each student this task:

  • Draw a shape that has between 5 to 8 sides with no curved edges.
  • Transform your shape through at least 3 rigid transformations of rotation, translation, and reflection — in any order.
  • On grid paper, give your teacher your complete work on this, including the written directions for the transformations.


  • On grid paper, give your teacher only the original shape and the written instructions. Your teacher will give this paper to a random classmate to follow your written directions to arrive at the intended location of the final image.


For students who want more challenge, they may ask for a copy that has just the original shape and its final image without the written directions. The task will then be to figure the appropriate transformations that connect the two images.


I really believe that it’s good practice to always give kids more than what we believe they can handle. Let kids tell us when it’s too much for them — and we find out soon enough. An ounce of struggle on something hard is worth a pound of completion on something easy.

(And I’m hoping to update this post with pictures of kids’ work when they turn them in on Friday.)

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