I teach a ten-session “Math Art” class for middle-school students. The classes are based on Vi Hart’s amazing videos. Three of the classes are on hexaflexagons. Here are my lesson plans for those classes. (If you need a slower explanation for making the hexaflexagons, here are the links to my videos on them.)

Hexaflexagons Day 1: Introduce the video by saying, “We’re going to be making these, and they’re really tricky, so watch closely. We’ll probably need to show it once more, but see if you can catch it the first time.” Then show this video: Vi Hart Hexaflexagon Day 1 Video

Ask the students if they think they got it just from that one quick run-through. If they do, hand out paper strips and glue sticks, and let them try to make one on their own. At some point, they’ll probably realize they need to watch the video again. Play the video again, pointing out how to fold and glue the hexaflexagon. Then hand out new paper strips as needed. Any of the kids who figure it out quickly should help the others who are having trouble.

Once everyone has a working one, show the video one more time, watching for the colors. Then hand out markers or crayons, and let them color them how they like. Leave some time for them to show each other what they made and how they work.

Hexaflexagons Day 2: Start by having everyone make a working hexaflexagon. Then say, “Before we color these, we need to see some more tricky things about how these work, which might give you some really cool ideas about what you can do with them.” Then show this video: Vi Hart Hexaflexagon Day 2 Video

Ask whether they saw how she made the lines that showed where curves matched. Ask whether they saw how to make the planet. If they want to see it one more time, show them.

Then let them color their hexaflexagons. For the planet, have them draw it as a circle in the middle, first, making sure that each of the three elements is drawn only on a fold, NOT on a separate edge– otherwise half of their house will be on a different panel when they flex it.

Homework is for them to make their own new hexaflexagon, decorate it, and bring it next week to show everyone.

Hexaflexagons Day 3: In advance, make working hexa-hexaflexagons for everyone, but don’t reveal that you have them. Prepare LONG strips of paper for them to use. Also, have an unglued, labeled hexa-hexaflexagon prepared– the kids who are more advanced will be able to use that model to quickly make their own.

When class starts, give each person a moment to demonstrate the hexaflexagon they made during the week.

Introduce the next video by saying, “This video is about a more powerful hexaflexagon, that has SIX faces. Watch carefully, because we’re going to be making these.” Show this video: Vi Hart Hexaflexagon Day 3 Video

Then have them try to make their own hexa-hexaflexagon. Tell them it starts just like a regular hexaflexagon, but they’ll have 19 triangles instead of ten. Once everyone has the strip with 19 triangles, have them watch while you take apart your model. Show them how you labeled it. Then have them watch while you slowly fold it back up, showing how the labels tell you what to do.

When there’s about 20 minutes left, if any haven’t managed to make their own, hand out your pre-made ones to everyone. Let them decorate them, reminding them that they have six faces.

Probably most kids will only find three faces. Ask them if they remember seeing the word “DIAGRAM” on the video, and how the diagram showed that some sides were hidden, and only appeared when they flexed it certain ways. Tell them they might have to pinch it differently when they fold and flex it in order to make the hidden side appear, and that the missing side appears when they start from a certain face. Then let them experiment to find the missing faces.