Scaffolded Math and Science: Geometric transformations in the coordinate plane with a hole punch

In this post I share an easy, hands-on method for demonstrating reflections and rotations of geometric shapes and their coordinates in the coordinate plane. The video included in the post covers reflecting over the x-axis, over the y-axis and over the line y = x. This same method will work for reflecting over any line of symmetry in the coordinate plane, even linear equations. I then share an idea for showing geometric rotations with a hole punch.

Last week, I wrote a post about using a hole punch to find function inverses in algebra. A few people asked on Facebook if the process would also work for geometric reflections, and it absolutely does!

High school geometry ideas post

In this post I want to share a few templates for geometric transformations in the coordinate plane, along with a couple videos showing how the templates work.

1: Geometric Reflections

Above is a quick video showing how to use a hole punch and a template to reflect a geometric shape in the coordinate plane. I glued the colored paper behind the holes just so that they were easier to see on the video.

2: Geometric Rotations

If you don't have any patty paper, I made a different template for rotating figures in the coordinate plane.

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I cut cut into half of the y-axis to show the clockwise rotation from quadrant 4 into quadrant 3. I've been posting the videos on my Facebook page, Instagram, and on my YouTube channel.

The hole punch that I used in the videos is a 1/8th-inch with a 2-inch reach. It looks like the one in this picture. I had gotten mine from a craft store years ago. If you don't have this longer reaching hole punch, an alternative is to have students poke holes in the paper with their pencils.

A teacher on social media commented that she prints the templates smaller so that they can be glued into student notebooks. I thought that was a really great idea.

Here is the link to the PDF transformation templates in my Google Drive: TRANSFORMATION TEMPLATES (Please note that the first pages of the PDF are for inverse graphs in algebra 2)

UPDATE: Teacher Eric Funke was super generous in creating and sharing a printable set of lessons he made based on the videos and templates in this post. You can make a copy of his lessons here.