Today I’m participating in the Funville Web Tour! The authors write:
“While on the surface, Funville Adventures is just a fairy tale, the powers of the, Funvillians are a vehicle for introducing children to the concept of a function. Each power corresponds to a transformation such as doubling in size, rotating, copying, or changing color. There is even a Funvillian whose power is to change other Funvillians’ powers.”
One of my very favorite things about Funville Adventures is that Funvillians all have their own special math power. Although not a function, my daughter’s special math power since she was little has been conceiving different and playful kinds of infinities. When I was a kid, knowing that I had math power would have been totally awesome. Luckily I’ve discovered my own math power from exploring the intersection of math and art making. And, inspired by my daughter, my affinity for infinity has grown as I reimagine (usually paper) Moebius Strips through the lens of hyperbolic crochet.
Now, without further ado… I am SO pleased to present to you an exclusive Funville mini-adventure about infinity and Moebius Strips by the authors of Funville…something you won’t find in the book!
Also, don’t miss out! There are some fun activity suggestions for investigating paper Moebius Strips at the end of the post!
The Funville annual parade is always a glorious sight! The Funvillians gather together to make colorful, intricate models for floats, and then Doug uses his power to double things in size enough times to make them spring to life as towering displays. Liza then uses her power to make things light so that the floats can literally float through the air – wafting down Main Street while all the Funvillians cheer and watch the show.
This year Constance and Connie decided to work together on a float. They began decorating the base of it with a chain of construction-paper rings of assorted colors. While they were making the rings, Connie decided to show Constance a trick.
“Do you know what 8 divided by 2 is?” Connie asked.
“It’s 4,” said Constance, without looking up from the construction paper rings she was cutting and gluing together.
“Not always!” Connie said. “Sometimes it’s 0.”
“How can it be 0?” Constance protested.
“Watch,” Connie said, and Constance looked up from her work to watch as Connie held up a figure 8 that she had cut out of the construction paper. “If you take 8 and divide it in 2,” Connie said, folding the figure 8 precisely and the middle and making the upper loop collapse on top of the lower loop, “you get 0!” She held up the now super-imposed loops with a magician’s flourish.
“Very funny,” Constance said. She turned back to her work. “Huh,” she said next.
“What?” Connie asked.
“Look.” Constance pointed to the construction paper loop she had just glued onto the chain. It wasn’t just a simple circle, like all of the others. It had a twist in it.
“How’d you do that?” Connie asked.
Constance shrugged. “I don’t know. I was watching you, so I wasn’t looking.”
Connie got up from her own work and came to look at it more closely. “It’s cool!” she said. “Rosalinda!” she called. “Come and see this!”
Rosalinda paused her work on her own float and came over to join them.
“How’d you do that?” she asked, looking closely at the loop with a twist.
“Can you do that with your power?” Connie asked Rosalinda.
“I’m not sure,” Rosalinda admitted. “Let me try.”
Rosalinda cut out a strip of construction paper and glued it into a simple loop. She set it on the floor in front of them so they all could see. Then she used her power, rotating the loop on the floor. The result was … still just a simple loop.
“Maybe you have to do it before you glue it,” Connie suggested.
Rosalinda cut out another strip of construction paper and placed the unglued strip on the floor. She rotated the strip and then quickly glued it, and then stepped back to reveal … still just a simple loop.
“I don’t think I can do it,” Rosalinda said. “My power doesn’t seem to have any effect on loops or strips.”
“Let’s try that one more time,” Connie said, determined to figure it out.
Rosalinda dutifully cut out one more strip of construction paper and placed it on the floor. Constance had lost interest, as she did not expect a second try of the same experiment to yield a different result. As she moved to go back to her work of continuing the chain, she inadvertently stepped on one end of the strip as Rosalinda used her power to rotate it. The end of the strip under Constance’s shoe stayed fixed, while the other end twisted.
“Ah ha!” declared Rosalinda. “I think I understand it now!” She reached for the glue. As Constance lifted her shoe, Rosalinda grabbed the two ends of the strip and glued them together, sealing the twist into the loop. “Do you see it, Connie?” she asked. “It’s pretty cool! You don’t really need a power, anyone can make a loop with a twist!”
“Let me try,” Connie said, cutting off her own fresh strip of construction paper. She twisted one end and then glued it together. She held it up in the palm of her hand and examined the result. “Neat,” she said. “I’m going to do all of mine this way!”
And when they’d finished, the border of the float was adorned with twisty loops. Constance and Connie stepped back to survey the progress they’d made.
“Looks great!” said Connie.
Constance shrugged. “Needs more elephants,” she said.
INVESTIGATE MOEBUIS LOOPS!
Here are some investigations you can do with Moebius strips without giving away too much before you start. It’s kind of an awe-inspiring activity if you’ve not experienced it before.
And here’s another more mathematically detailed set of instructions.
FOLLOW THE FUNVILLE ADVENTURES WEB TOUR!
The FUN continues on this absolutely amazing web tour. You’ll be sure to meet folks with math powers you and your learners/children can make their own.
Malke Rosenfeld is a dance teaching artist, author, editor, math explorer, and presenter whose interests focus on the learning that happens at the intersection of math and the moving body. She delights in creating rich environments in which children and adults can explore, make, play, and talk math based on their own questions and inclinations.