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.