Rorschach Inkblot Test

While studying reflections and reflectional symmetry in 8th grade math, I showed the class images of the Rorschach Inkblot Test. I also showed the test to one of my geometry classes, and they had a blast with it! They were bursting to share their answers. A couple of times students saw the same image without talking about it first. Some of the images they saw:

 

two pigs

two pigs carrying a beetle

Patty Cake explosion

two Asian mean giving high-fives

two men pushing a fat woman down a well

Miley Cyrus looking in the mirror

Two people twerking

 a bat

a moth

 an iguana breathing fire

 two lion fish (in blue)

My First Favorite Proof

I have been struggling with finding good proofs for my geometry classes - ones that aren't obvious and that are within reach of my students' abilities. Then I found this problem on Don Steward's blog.



It fit well with the work we were doing in class about parallel lines and transversals, so I presented it to the students. The directions I gave were:

• Draw two parallel lines (maybe using both sides of your ruler).
• Draw a line that cuts the two parallel lines (called a transversal). Measure the two consecutive interior angles.
• Bisect the angles that the line makes with the two parallel lines. Measure one of each of the bisected angles.

Every student created the same construction, though their transversals all met the parallel lines at different angles.

Then I asked: What is the angle at their intersection? Why? 

I had them think about the problem silently for about 5 minutes. Then we talked. Not many students got it the first time around. I explained it, as well as had other students explain it. Then I gave them the assignment to write 5 sentences explaining why the two bisectors intersect at a right angle. 

The next day, very few people had completed the assignment, presumably because they didn't understand why it happens. Or they didn't know how to communicate it in written word. Or some other reason. So we spent about 15 minutes the second day talking over the problem. I had as many students as I could in that time give an explanation. That way, students could hear explanations from multiple perspectives and different wordings, and they could practice communicating verbally. I have found that just because students understand a problem doesn't mean they can explain it. I tested the waters by asking how many understand it, how many can explain it to someone else, and how many have no clue. There were students in all categories. So I had students keep explaining until they got tired of it or no one else was willing to explain. I also showed them an applet I made in GeoGebra of the problem to make it more dynamic.

This is the very first proof that I felt comfortable presenting my students. I wish I could find more!