Source: Cyberchase: "A Perfect Fit"
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In this video segment from Cyberchase, Harry decides to wallpaper his living room walls. He takes some measurements and then goes to a store to buy wallpaper, but he finds out the cost is much too high. Since he still wants to cover his walls, he realizes he can use some leftover scraps of wallpaper he finds in the trash to create a tessellation on his wall.
Download and ShareHere are some Frame, Focus and Follow-up suggestions for using this video in a math lesson.
What is Frame, Focus and Follow-up?
Frame: If you were going to cover a floor with pieces of wood, why would it be important that the pieces tessellate and have no gaps or overlaps? What shapes would work well when covering a floor with wood? Is it possible to create irregular shapes and have them tessellate?
Focus: In this video segment, Harry doesn’t end up using square shapes. What shape does he use instead? How does he make this new shape tessellate?
Follow Up: How would you describe the shape that Harry tessellates on his wall? What other shapes might he have cut out of the wallpaper to create a tessellation on his wall?
HARRY: I think I’m in love. Her name is Darlene. She’s meeting me here today, and we’re going on a picnic, together. She’s so beautiful. Hi Darlene. Are you on your way? Oh, okay. You want to meet there instead. Sure, I understand. See you soon. Darlene said she’d rather not meet me at my place, because of my clown poster. She said it gives her the creeps. But that makes me feel bad, ‘cause I really like it. It was a present from my grandmother.
I’ve decided my apartment needs a makeover. I want Darlene to feel comfortable when she visits. Without the clown poster, the wall is empty. So I’m thinking of putting up some wallpaper. Gee. There are a lot of choices.
SALESPERSON: Hi, how can I help you today?
HARRY: I would like to wallpaper my living room. Here are the dimensions.
SALESPERSON: I estimate you would need about 20 rolls of paper. Can I see the paper you like? Your total is six hundred dollars.
HARRY: No way. I’m afraid I can’t afford that. Sorry for troubling you. Are you throwing those out?
SALESPERSON: Yes, that’s all trash.
HARRY: May I have them?
SALESPERSON: Sure.
HARRY: I’m gonna make my own wallpaper! My plan is to cover the wall with pieces of wallpaper arranged so none of the wall shows through. If I cut all the pieces into the same size square, then all the pieces should fit together without any gaps or overlaps, because all the sides of a square are the same length. But I’d rather use a more interesting shape. How about if I turn the square into one of my favorite things about New York City… the skyline. This could be a problem. I don’t want the wall to show. Hmmm. I need to move the part I just cut off to the bottom of the square. If I use this as a pattern and trace it, I can create new pieces that are exactly the same shape that fit together without any gaps or overlaps. Wow! That is a really cool tessellation! Don’t run away! Darlene! Come back! I asked Darlene to come over to see what I’ve done to the wall. She said it’s e hideous than the clown poster!
SALLY: Hi Harry. I’m really thirsty. Do you think It would be okay if I came in for a glass of water?
HARRY: Sure, sally.
SALLY: Thanks. Wow, Harry! I love what you’ve done to your wall.
HARRY: You do?
SALLY: Yeah! Great tessellation!
HARRY: Gee, thanks.
SALLY: But I also really liked that clown poster you had. I think I kind of miss it.
HARRY: I think I’m in love.
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