Math Stories – Moebius Ants
httpv://www.youtube.com/watch?v=4mdEsouIXGM
This is a story inspired by Vi Hart’s “Wind and Mr Ug” video. I so wanted to tell it to my son myself, but my drawing skills fall way short. So instead we talked about ants. 
Once upon a time two ants lived on a strip of paper. A strip of paper has… how many sides? how many edges? [I drew two ants on a strip of paper] Each ant lived on his own side of the strip. They never saw each other, but since ants have an excellent sense of smell, they smelled each other. And they really, really wanted to have a playdate or maybe a tea party one of these days. They tried visiting one another, but each time they reached an edge of their little flat worlds and would get scared. Then one day something happened. There was much shaking and twisting and the ants got scared and closed their eyes and covered their heads and tucked their antennas. When the twisting and shaking stopped, they opened their eyes and saw something strange. Their flat world was no longer flat. Instead, it became cylindrical [At this point I glued the edges of the strip together to create a cylinder] 
Hooray! said the ants. Maybe now we can visit each other! One of the ants, who was a bit braver and more adventurous than the other, immediately set out on a round-the-world trip in hopes of meeting his friend. He crawled and crawled along, leaving tiny prints behind him [I’m drawing ant’s path with a marker]. Will he ever see his friend? Soon the ant came to a set of tiny footprints. At first he got excited. Was that the marks left by his never-before-seen friend? Is he getting closer? But soon the ant realized that those were his own prints and he’s been crawling round and round his little world. But what about the other ant? He too sat out on a journey, crawling along. Will he have better luck? [I’m drawing second ant’s path with a different colored marker]. Nope, he too finds no one, just his own footprints. Their world had… how many sides? how many edges? Poor tired ants needed a rest. But just as they were going to take a nap, their cylindrical world shook and twisted again. Again they got scared and closed their eyes and covered their heads and tucked in their antennas. [Here I cut the cylinder to turn it back into a strip; then I twist the strip and glue to form a Moebius strip]. When the twisting and the shaking stopped, they opened their eyes and looked at their strange new world. Maybe now that it changed they will be able to meet each other. The first ant, the braver one, set out on his round-the-world trip once again. He walked up the hill and down the hill and across the valley [I’m tracing the ant’s path with a marker] until… he saw the other ant! Hooray, the two cried and hugged each other. And then they walked back to the first ant’s home [a child is tracing the ants’ path with a different color marker]. Their world was no longer flat. Was it a cylinder? Nope, it became something called a Moebius strip. How many edges does it have? How many sides? 
And that was the story. But then we experimented some more. We made another cylinder and another Moebius strip, each with its own pair of ants. This time my son traced ants’ paths all by himself. Then I brought out the scissors and both worlds underwent another cataclysm, this time it was a continental drift (thanks, Ice Age 3, for the idea) as I cut the cylinder and the strip in half. Want to know what happened to the ants? Try it for yourself. It’s really very fun!
Posted in Grow
Newsletter August 15, 2012
Welcome to adventurous math for the playground crowd! I am Moby Snoodles, and I love to hear from you at moby@moebiusnoodles.com
Moby’s mail
I adored the responses to our last newsletter. It feels good when your work is supported and appreciated. Take a look at these examples…
I love the 3D function machine drawing. It makes me think of a train going up and/or down a large mountain, and every time the train passes through a tunnel the number of cars increases (or decreases). Thanks for sharing. – Ryan M. Combs, M.S., HRD, Instructional Design, eLearning Development, First-Rate Human Being
- How interesting, Ryan! We actually have a picture of a train doing just that later in the chapter. What an interesting coincidence – or maybe the chapter’s front picture evoked the same image both in you and in Ever, our illustrator? Wow… – Moby S.
These newsletters are so beautiful, and so full of goodness, I’m delighted each time I read one. I see, though, that Moby must be struggling a bit with English grammar. (Is Moby’s first language whalish?) I’d be happy to be your final copyeditor/proofreader, to catch those just before it goes out. Warmly, Sue VanHattum, Math Mama Writes
- Thanks, Sue! I would love this! The newsletters go out twice a month. I can send you the text a few days before the letter goes out. – Moby S.
“Welcome to adventurous math for the playground crowd!” Love that. Is it alright if I use “adventurous math” and “playground crowd” in the future? I won’t make it a tagline, but those are brilliant turns of phrase. – Paul Salomon, Math Munch
- Thank you for your kind words! Yelena, the lead writer of “Moebius Noodles”, came up with this one. One of my favorite aspects of Yelena’s intrepid style is the bold, clear, but also metaphoric way she names entities such as math concepts, games, and in this case the main idea of the project. The whole project is Creative Commons, so you can share the motto too. I think it would be good if the idea of advanced math for the young kids – the playground crowd – spread as a meme! – Moby S.
Book news
One of the big challenges in making the “Moebius Noodles” book is the balance between three key types of the content.
- Mathematics. We need to introduce topic-specific math actions. Our topics are way beyond “counting and shapes.” Many of the readers, even adults, have never seen this math or never thought that its deep roots can be made accessible for young kids.
- Pedagogy. There are very few people in the world who work on making advanced math accessible to young kids. The lore on how to do it is far from being common knowledge. Last year at a conference in London, I met one of my pedagogy heroes, Richard Noss, who said it well: “Are you on the quest, too?”
- Well-being. We are inviting people, who often suffer from math anxieties, into adventures in uncharted territories. To help overcome fear and ease the anxiety, we provide some techniques for supporting cheerful disposition, mindful state of consciousness, and relaxed stance of the body.
Last week, we worked on games with grids. The mathematics of grids has to do with covariation between two aspects, organized along rows and columns of the grid. But young kids don’t see it this way. Pedagogical observation: young kids see each cell in the grid as a separate entity!
You can conduct an experiment to see this. Several parents told me this experiment is an eye-opener because it shows how different, and bizarre, the young mind really is. Offer a young child a printed or drawn grid and ask them to draw a copy. More often than not, children will draw each cell separately, often forgetting about row/column structure altogether.
Several of the “Moebius Noodles” games help kids see a row or a column as a whole, rather than as a collection of separate disjointed cells. This more advanced reasoning is a cornerstone of many concepts, such as multiplication. In grid games, it has to do with how you draw. Explaining a totally new concept of drawing, in words, to a very young kid, is a sure road to much frustration!
Our favorite well-being technique here is a mixture of kinesthetic guidance, caressing touch, and a tango where the child leads almost all the time. It looks like a parent drawing with the child’s hand. What you actually do is support the child’s own movements most of the time, but convey mild changes by slight hand pressure, so the child can follow your guiding hand as needed.
In the illustration, we tried to show all three aspects of the grid activity: the math, the pedagogy and the well-being technique. Here is a sketch, where you can see the typical kiddie “nongrids” in the background.
Our blogs
From the “math stories” department comes a story of cutting and folding.
The story I told my son was about three friends. He immediately made it about him and his two best buddies and how they were ninjas. Each friend was represented by a square of origami paper. We then folded each square, trying to predict what would happen to them after each fold…
We have been nominated for a top site award at the Circle of Moms. We entered the voting late (just a day before closing), though. If you know of a good lists of resources we should be trying to join, please let us know!
Talk to you again on August 30th!
Moby Snoodles, aka Dr. Maria Droujkova
Posted in Newsletter
Knot Theory for Young Kids
A couple of weeks ago I discovered a wonderful math blog called Math Munch. Now, with a name like this, you know this is going to be good! And it is even for someone who is not a professional mathematician and who was pretty scared of math as a child (I’m pointing my finger at myself now, tsk-tsk-tsk). Basically, Math Munch is a weekly digest of the beautiful, surprising, strange, engaging, and fun math out there on the Internet.
As I was browsing the site, I came across a post about knots. I love knots because they are a) beautiful and b) because I have such a hard time following the instructions and learning how to tie them (something so simple, even a hagfish can do it). Well, I was in for a surprise – turns out, mathematically speaking, the knots we (hagfish and I) usually tie are not really knots at all since the knots we tie are not closed loops.
Intrigued, I followed up with Anna Weltman, who teaches math, folds paper, ties knots and co-authors Math Munch. I wanted to know what kind of activities can I do together with my 5-year old to further explore mathematical knots. Anna’s suggestions were so awesome, that I felt they needed to be shared with you. Note: I added names to each game just because bullet lists are boring. Feel free to rename the activities.
So here is Anna’s response to my question:
A big mathematical question that knot theory is really good for exploring is, “Can I turn this into that without breaking something about it that I think is important?” Another question that knot theory is good for is, “How can I make an object that will do this particular thing I want it to?” I’m not an expert on 5-year-olds, but here are some ideas I had for approaching those two questions through knots:
The Game of Moebius Strip
A fun way to make knots and links is to make moebius strips with different numbers of twists and cut them in half. You can make two different knots – a trefoil knot and a knot with 5 crossings – but cutting a 3-twist strip and a 5-twist strip in half, respectively. You can play with cutting differently twisted strips in half and describing the similarities and differences between the results.
The Game of Twisted Cords
Get some pretty slippery string – maybe lanyard/gimp, or headphones (though with only 1 phone would be best). Tangle it up – either haphazardly or methodically, your choice. Then, tape the ends together. Can you untangle it? Untangle it as much as you can and describe what you have in the end. You can do this a bunch of times and keep track of the untangled results. You can then try to make a tangle that you can untangle – ask, what should we do or not do with the ends of the string so that we are sure to be able to untangle it in the end?
The Game of Steer Roping
Get some string and a bunch of differently shaped objects – make sure some have at least 1 hole in them. Challenge your child to tie the string around the objects so that you can’t just slip it off. See if the child can describe what kinds of objects are tie-up-able and what kinds aren’t, and what kinds of tying are best for mastering the challenge. This is less knot theory than it is study of surfaces, but it involves knots!
The Game of Un-Twister
This game is really fun, but you need several people to play it. Stand in a circle. Everybody take hands, but not with the person standing next to you and not both hands with the same person. Then twist and climb and duck under each other’s arms – but don’t let go of each other’s hands! – until you’re standing in a circle again, completely untangled! If you have enough people, it sometimes happens that you end up in two circles. If you want to really analyze the game, you can make a sketch of how everybody took hands and map out the untangling process.
The Game of “I Am Knot Myself Today”
Another fun thing to do along those lines is to try to make a knot out of your arms, torso, and a stick that you can’t untangle without dropping the stick.
httpv://www.youtube.com/watch?v=4mdEsouIXGM
Oh, and Anna pointed me to this great Vi Hart video which seems like a perfect conversation starter.
Awesome applesauce! We’ve already tried the first game Anna suggested and it was a huge hit. I can’t wait to try the rest. Thank you so much, Anna!
If you haven’t done this yet, do check out Math Munch blog. Every single post is chock-full of links to beautiful and engaging math sites many of which could be explored with young children.
Posted in Make
Thank You for Voting
Turns out, we’ve been nominated on the Circle of Moms Top 25 Teacher Moms Sites! And we are in a great company too, including Kim and Amanda from The Educators’ Spin On It. You remember their fun grid art activity they shared on our blog, right?
We are a late entry (the voting ends on August 9), but better late than never. So please take a second and vote for us on the Circle of Moms site today and tomorrow (you can vote once daily through August 9). Thank you for your support of the Moebius Noodles blog!
Posted in Grow
