Every year in Geometry, I spend a class period “playing” with optical illusions. I usually spend one full 45-minute lesson on optical illusions (bellwork, homework questions, and everything as well). I know that there usually isn’t a lot of time for fun because there is so much pressure around testing.

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Why I Teach About Optical Illusions

I think that this lesson serves an important purpose in class and just in life in general. The main objective that I’m trying to drive home with this lesson is that you can’t always trust your eyes. I talk about how in math (and in life!), we can’t just take things at face value, they must be proven. Also, we can’t just make up our own rules, they must be agreed upon rules/laws/theorems so that everyone can come to the same conclusion. I use optical illusions as a fun way to drive this point home.

I teach this lesson at different points in the school year, depending on what I feel like doing that year. I do this lesson at one of three times in the year.

- The first day of school (as a fun intro to Geometry)
- Sometime in the first week or so of school (usually right before I introduce congruence)
- Right before we start proofs (and I emphasize the point about proving things with rules)

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How I Teach Optical Illusions

First, I tell my students that we are going to have a different kind of day that doesn’t require them to take notes. I let them sit on the floor, sit on their desks, or get comfortable (by this time, they are SUPER interested). Then, I tell them that as long as they are being respectful, raising their hands, and participating, there will be no homework. I usually don’t make kids raise their hands, but they tend to get a little excited by the end of the lesson and want to call out, so I make that a requirement for the day.

I have

a powerpoint with all types of optical illusions that I show the students (click the link to download). The first picture is below. I show them his picture and ask them not to comment. After a few beats of silence, I ask someone for their comment about the pictures. We talk about seeing the vases vs. the faces.

I continue through the powerpoint in this way. I always ask for silence first, then a few comments, then let them discuss amongst themselves for a second or two until everyone sees the picture.

The old vs. young woman is always a favorite.

As the slides progress, they get more geometric. At this slide, I make them prove to me that the lines are straight. I’m annoying enough about it that an exasperated student will finally get up and find a straightedge (book, ruler, binder, etc) to prove it to me.

This slide is where I talk about our eyes playing tricks on us. Some students pick this up right away, and some take forever to figure it out.

Once we finish going through the powerpoint together, I talk about the importance of proof and not making assumptions. Then, I give

this handout (click to download). A few types of optical illusions are explained and there are a couple of good websites linked at the bottom. Sometimes, I just project the handout and we discuss it that way.

At this point, there are a few things you could choose to do for classwork if you have extra time. I never do, but I usually have one of these activities ready to go, just in case. Students could...

- use their devices to search about M. C. Escher. Maybe they could write a few sentences about how he used optical illusions in his work.
- find another optical illusion and write about how it tricks the eyes.
- work review problems.
- work on an optical illusions worksheet.