Like Bees to Honey

I'm at my final program site up in the city for this summer.  Every day we work with Jump Patterns for a while, learn some clogging and then it's time to sit down for a while and explore other kinds of patterns.  Nature's patterns, to be exact!

A couple weeks ago, at a different site, the kids got so excited about finding a 'nature's number' (Fibonacci!) inside an apple that I had to go out and buy a bunch of lunchbox apples and cut them in half so everyone could have their own apple star the next day.  I've never seen kids so excited about numbers, or apples for that matter. 

I did my apple 'magic trick' again yesterday, but for today I decided to focus on shape and design in nature.  First I taped out a pretty respectable hexagon on the floor in the middle of our dance space.

When it was time, I asked the kids if they knew what shape it was.  The older kids knew, but not the youngers.  (At this site I have five to twelve year olds in the same class.) 

I asked how many sides a hexagon has, but before I'd allow an answer I started asking for volunteers to stand at each of the sides.  "One child, one side," I said, "Who wants to stand on the next side?  Okay, two children, two sides..." and counted up from there. 

I picked the little kids on purpose since they had been the most challenged with the dancing. 

"Okay," I said, "Everyone put your arm in."  I guess I wanted there to be some sense of division of the space.  Tomorrow I'll got back and put down more tape to show some of the internal structure of this hexagon.

"How many corners does a hexagon have?  One child per corner...Oh look!  Six sides, six corners!"

Then each kid got their own pattern block hexagon, or two trapezoids, to add to the tiling I started.

"What can you find in nature that looks like this?" I wondered aloud.  Only the last class (with more older kids in it) knew right off the bat.

Then they got their very own taste of local honey.  It was a bit too strong a taste for most kids, but still a good new thing to try.

And then, much to my delight, something wonderful happened.  My first class was waiting to go on to their next workshop and were hanging around in the space.  They naturally found their way to the hexagon on the floor, made a circle around it and started playing song and chant games.  This is exactly the kind of thing that always happens when I put down tape where its never been before.  It changes the space and kids notice.

Another example from earlier in the morning: I was creating a set of parallel tape lines as I measured out the sides for the hexagon.  A little boy came over and jumped over the width and then the length.  I wish everyone would put tape down on the floor and then start the camera rolling to record all the awesome things that happen when kids discover this restructuring of their world.

This much I know: kids are to tape as bees are to honey.  Or maybe that's bears to honey?  Anyhow, here's the video of the girls playing 'Little Sally Walker' around the hexagon waiting for their next class:

Sumptuous Saturday | Treasure Map Math

It was the perfect, perfect, perfect Saturday, for math and just about everything else.

After months and months of cruelly hot weather with muggy 80 degrees by 7am every day, one recent Saturday morning we woke up to 60 degrees, a clear blue sky, and even some mist.

The kid and I walked the two-plus miles downtown to the Farmers' Market via a paved trail that runs miles through our little city.  Lucky for us and our walkabout math habits, the lamp posts on the trail are numbered.  I was considering musing aloud what the half of each number would be when the kid spontaneously starts marching and, along with this steady rhythm, she starts to chant: "Eight plus eight is sixteen. Sixteen plus sixteen is thirty-twooooo.  Thirty two plus thirty two is six-ty-four!  Sixty-four and sixty four are...hold on...[pausing, eyes unfocused, obviously concentrating internally] ... one hundred twenty eight! [marching resumes] One hundred twenty eight plus one hundred twenty eight are..."

I don't remember how it went at that point.  We've not really done mental addition that high, but she made some mighty efforts nonetheless.  And, as we still had a ways to go, she started a couple more rounds of doubling, one starting at fourteen.  The other I can't recall.

We finally arrived at our destination and and found our friend L whose parents have a booth at the market.  Have you ever had lemon cucumbers?  Theirs are divine.  Directly after we found him, we also found a banjo!   Here's a quick video of the movement that ensued:



My kid has been wanting a waltz partner for like forever.  I'm not sure L. knew what hit him!  And, as for dance (and math) my kid seems comfortable in the phrasing and ratios of a number of time signatures, 3/4, 4/4 and cut time included. 

We then moved on to other regular market activities, like meeting the kitties from the shelter.  No math there, but I suppose someday we'll find it.



There's a lot of great spiral math in the fountain outside city hall.  No water in it this day, but kids regularly start in the center and splash spiraling outward, or float bark boats in the reverse direction.  The spiral actually opens way up on the left there, meandering in curves around until it meets the actual fountain.

And, although the water in the spiral fountain had been turned off for some reason, it didn't stop the kids from playing.  Apparently my girl and L. had been searching for big and interesting pieces of birch bark on the ground when she ran over to me all excited about finding a map of the fountain drawn in pen on the bark "with an X on it!"   Of course, that had to mean treasure was close by. 

And, of course, they started trying to follow the map (surprisingly, almost to scale) of the fountain area.  They got completely engrossed in figuring out how to read the map to find the location represented on the map by that curious X.

At some point they recruited another girl, maybe older?  It's hard to tell because my kid is pretty short for her age.  Even L. who is a year and half younger is half a head taller than her.  Anyhow, they pondered, and searched, and retraced their steps over and over.  After about fifteen minutes I realized that they were looking for an actual X on the ground.  At that point I stepped in and wondered aloud whether someone who had hidden treasure would want to mark the spot on the ground or not.  I mean, really.  If you've got treasure you really don't want anyone to know about it, right?

The three kids finally decided they knew the exact place where the treasure was buried and I had to agree.  They had done a perfect job at reading the map but couldn't find anything.  The finally decided the treasure was under the cement trough somewhere and inaccessible.  A little downcast, but ever perseverent, they moved away from the spot to talk some more about the whole situation.

At that point I figured that, if they had spent over twenty minutes working together to analyze the map and the territory and actually succeed in pinpointing the exact spot (not to mention collaboratively analyzing the potential motives why someone would leave a map behind) they should be rewarded in some way.  Being short on change I petitioned bystanders who had been watching the proceedings with interest.  Between us I got three dimes and three pennies.  I made sure the treasure hunters weren't looking and poked the change into the dirt.  Then I said:

"Hey, guys!  Weren't you just over here?  Come here, and take a look.  I think I might see something..."

My bystander friends were looking on at a distance and we all just beamed at how excited the kids were to find their treasure.  They figured out how to divide the money equally.  I'm not sure, but they may have wondered why it wasn't more than 33 cents but that didn't stop them from telling their story over and over to anyone who would listen.

You know, the story about The Day -- the day they followed a found map to buried treasure on city hall grounds.  Perfect.

Math By Design: Paper Patterns

Summer programming has given me some room to experiment with ideas that have been brewing over the last year.  Ultimately, I designed three new non-dance making activities that reinforced the Math in Your Feet ideas of creating a pattern unit using multiple categories of attributes.  My favorite by far, especially for its flexibility with a range of ages, is this paper patterns activity.

If you've scrolled down already you'll probably be thinking that it looks a lot like a paper quilt activity.  It is, sort of.  What distinguishes it from other paper quilt activities is that there is no pattern to follow, only some guidelines to direct the design process.  Because there's been a day or two at each site this summer where dancing was just not an option -- too hot, too crazy, too distracted by thoughts of swimming after class, whatever -- this quieter activity has been perfect at reflecting and reinforcing the dance work we've been doing on other days.

Just as with the dance work, the individually designed paper pattern unit is made up of four pieces (beats in the dance, squares in the paper design) with choices of various attributes.  The pattern unit is then repeated, or joined with a different design, to make a larger pattern, revealing complexity in combination.  Here's how I introduced the activity at my first summer site:

























The idea was to experiment with different four-square designs, using a combination of squares and triangles.  At that point the kids would pick their favorite pattern unit and then repeat that favorite four times in the sixteen square grid, as pictured above.

This turned out to be confusing for the kids at the first site.  They were on the younger side (ages seven, eight and nine), most of them emergent or beginning readers.  This, in itself, is a clue as to the importance of an activity like this. A pattern unit is comprised of various smaller parts that make a larger whole.  In math this is called 'chunking' and is a crucial skill for algebra down the line.  If a child has not yet learned to 'chunk' words, they will also most likely benefit mathematically and in their reading from the challenge this activity provides. 

Unfortunately, it was a crazy site, and I didn't have the time or the support to help individual children the way I would have liked.  Since this was the first time I had tried the activity, I didn't anticipate some of the issues that came up.  For example, the kids had too many color choices and ended up using all of them.  It was okay to have four, five or six colors in one, four-square design, but when it was time to repeat the pattern unit, it was much too hard for them to slide the design over or down to repeat it in the grid. 

There was some interesting experimentation with the triangles and squares, though, which is always good in my book.

Do you see what I mean about too many colors (design on the left, specifically)?

Here are two kids who figured it out:

Well...sort of. 

By the time I got to my second site I had adjusted the activity.  I split the sixteen square grid into four smaller, separated parts, and when they had created a design they liked on that sheet I gave them the larger grid. This helped focus kids on the individual unit itself and then make the transition to the larger grid.

The kids at this site were also older (nine, ten, eleven, even twelve).  This time around I decided to limit it to a choice of two colors which I think helped focus the activity tremendously.

This design is a little out of the box, but it doesn't surprise me as this girl was the only one to use a combination of turns in the dance patterns she created.  Her brain was already 'there' if you know what I mean.,

This final picture sums up why I love this activity so much.  Small, simple pattern units get combined to make something surprising, beautiful and mathematically interesting.  The elements of personal choice and action on the design process creates unique results for each child.  Just like in Math in Your Feet.

And the math?  Flips, slides, turns.  An inventory of attributes.  A problem solving process.  Grids.  Patterns. Attending to precision. Just like in Math in Your Feet!

Most importantly, the idea of pattern unit and the concept of chunking is reinforced throughout the entire activity.  And, if they can do it, great!  If they can't, you first and foremost find the beauty in their efforts.  It is this personal work, full of thought and energy, that becomes a self-generated incentive for moving forward to the ultimate goal.  Not only does this activity allow you to celebrate the individual efforts of each child but also makes it easy to immediately assess where the learning points are -- because the evidence is right there in front of you! 

The Elephant in the Room

The last few days I've been five hours away from home (by car) working with teachers at the Lighthouse Academy's national conference.  While they were learning the Math in Your Feet program and, much to my delight, having a whole lot of fun making rhythm, patterns and math with their feet inside their very own blue tape squares, my seven year old was at home...making other kinds of math:

I found this geoboard on the table this morning.  She says her doll Amelia wanted to show her how she could tap dance inside a square.  And then a circle.  And then a hexagon.  "Which has the most area, do you think?" I asked, not even knowing if she'd know what I meant.  "Oh, the square," she answered blithely.  Certainly looks that way to me:

"Oh, and Mama," she says, "I also made a napkin.  A fancy one, for parties.  And look, I did some beading on it.  It's a frieze pattern, white, pink, white pink.  Oh, and I didn't use two pieces of thread.  I used the same thread, up and down, up and down.  See?"  I am often delighted by her explorations, but this one took the cake.  I had no idea she had been paying such close attention when I doodled frieze patterns for her, on the day she had a high fever.  I also had no idea she had such facility with beads.

It's amazing to watch the myriad ways she finds (all on her own) to represent her growing mathematical knowledge.  Pianos, geoboards, sewing, straws and beads, even while riding her bike.

This flurry of math in the making has me reflecting on how I used to think that math was some kind of  inaccessible, abstract magic trick, a sort of in-joke that excluded us common folk, but now I realize that math is completely not that at all.  The reality of math as most of us know it is like that story where three men are standing in a dark room touching different parts of an elephant.  None of them has the full picture because they're only perceiving individual elements of the whole animal.  

The reality, I'm discovering, is that math is just like that elephant: a large, expansive, three dimensional, intelligent, sensitive, expressive creature.  The problem is that most of us have been standing around in that dark room since about kindergarten, grasping its tail, thinking "this is what math is and, personally, I don't think it's for me".  We've been blind to the larger, incredibly beautiful picture that would emerge if only we would turn on the lights and open our eyes.  (Or, in reality, if we could find someone who would help us understand what we're looking at once those lights go on.)

I'm so glad that my daughter and I are starting to really get to know, understand and, amazingly, even have fond feelings for this math elephant.  The kid is just heading into second grade and I know we have so much more math to do and learn about, but what math we do understand seems to be connected to pretty much everything we see, or do, or observe.

Small Moments of Infinity

[Edit: This post was originally titled Vignettes. About two seconds after I posted it, I came up with a title I liked better.]

#1

On Monday I read The Cat in Numberland by Ivar Ekeland with my daughter at the library (thanks to a reminder about it from Sue VanHattum at Math Mama Writes).  We read it last summer when she was a new six and the kid was really excited to see it again.  She's at a better math comprehension level for it now and we consume it whole in a quiet, sunny corner of the children's section.  This time around we notice the title page with the cat looking at itself looking at the title page looking at itself looking at the title page...recursion!

Anyhow, the hotel owner is griping about Zero and how there's no room for Zero at the Hotel Infinity.  And, to top things off, the owner doesn't think it's a good idea for Zero to room with Number One at the Hotel Infinity because how will he tell them apart from Number 10? 

Luckily the numbers are personified in the illustrations.  Unfortunately the hotel owner doesn't seem to notice this.  My kid does, though.  She says [referring to the illustration of 1 and 0 next to each other, compared to the number 10]: "There are two heads [one for 1 and one for 0].  Ten only has one head." (The head on 10 was on the numeral one.)  Not that this has any direct math 'value' per se, but it was still interesting to me that she noticed this.

#2
I forget exactly which part of the book we were in at the time, but at some point the cat, who is always thinking and "trying to figure things out", wonders why, if the hotel is full now, there are always more rooms available. (Or something like that.)  The kid notices the infinity sign in the illustration (figure 8 on its side) and she starts tracing it in the air saying to herself: "It goes on, and on, and on, and on..."

(Here's an interesting review of the Cat in Numberland by James Propp which includes a fascinating discussion of math pedagogy in relation to this story.)

#3Still at the library, the kid is chatting up the librarians about the resident frog 'Henri'.  She asks how old the frog and it turns out she came to the library as a tadpole, in March a couple years ago.  The kids says, unprompted:

"Well, human months are actually frog years.  There are twelve months in every year, and twelve plus twelve is twenty-four, plus two more months, so that makes Henri twenty-six years old!"  [Never mind it's July, not May...the shocking thing for me is that we were so busy playing UNO and Shut the Box all last year that I completely neglected calendars.  Turns out she's figured it out by osmosis.]

#4
This morning, a summer virus with a fever (after a winter of no illness) has the kid on the sofa listening to the Charlotte's Web audio book.  At some point even that isn't enough to distract her from her discomfort so I head to the couch to entertain her.  She asks me to draw pictures for her (and graciously tells me I can use any of her sketch books that I want!).  I'm really not inspired to do draw but I remember something I saw recently on the Math Munch blog -- Vi Hart doodling musically/visual frieze patterns.  I've always been a doodler, so I decide to experiment with my own frieze patterns.  I'm not sure if they're exactly what they're supposed to be but they're fun to make.  I erase a few, especially the ones that look like they have eyes.  Too much for a kid with a fever!  The kid is absolutely thrilled with the ones we kept, especially the last two. 

I think the frieze patterns/designs have something to do with infinity, and so I end this post now where I began it, discussing recursion and infinity.  I love it when that happens!

Floor Tape, How Do I Love Thee? (Video Edition)

I'm in the middle of summer programming.  It's Math in Your Feet in a lot of ways but also not completely like the program I do in schools.  It's more like a whirlwind of percussive choreography, rhythm, and patterns of all kinds. There's also a lot of math in there as well, just not explicitly. 

My reasoning for this that kids need as much exposure as possible to patterns in multiple, diverse contexts.  These kids I've been working with, for example, are a perfect case in point.  When asked on the first day to find patterns in the room in which we were working, they were at a loss.  In all the groups, color patterns were found first.  Then somebody would notice a sequence of objects, but it didn't repeat.  A potential pattern unit, but not a pattern in itself.  Even the three examples of simple tilings in the room (floor, ceiling and walls) escaped notice, even when I pointed them out. 

Patterns are more than sequences of colors.  They are more than two dimensional shapes.  They are sounds, movements, expressions, order. They are long and short.  They repeat.  They change.  They're everywhere. So, when I say we're not talking about math explicitly I mean we don't need to talk about it because we're doing it.  Calling it 'math' interrupts the flow we've created -- sometimes just doing and experiencing is enough.  This doing time is a chance to get swept up in the creating, to be fully engaged and amazed and delighted in your own abilities.  I believe this because, simply put, that is what I find best about learning something new.

On top of the sheer fun of watching kids engage in new pursuits like percussive dance, one of the reasons I'm enjoying doing the summer version of Math in Your Feet is that I have leeway to experiment with how I deliver the program, engage my young dancers (right now ages eight to eleven) and how I set up the space.

In the videos, below, you can see what I'm trying out right now.  This big grid isn't the normal setup for Math in Your Feet but I was really excited to tape out the space this way.  Normally, when kids start making up their own dance patterns they usually get their own personal square dance spaces taped out in individual groups of two, each pair slightly separated from the other groups. I'll be very interested in how the new set up works out (or doesn't). 

This new set up came about because the floor really lent itself to a large grid format. The girls in the room were hanging out with me before class while I set up and helped me tape out the floor.  Any time I have a chance to let kids help me tape, from preschool to upper elementary, my helpers invariably end up spontaneously exploring their newly taped environment without any prompting.  This is actually my favorite time with kids -- manipulating the floor space with tape and then seeing what they do when they first discover it.  Here's a peek at the space and the only part of their exploration I could capture on video:



Their movement is a natural kid reaction to squares -- Hop Scotch!  But in this second little clip you can see how they started exploring rows as well as columns.



Later, during our class time, when we were talking again about other kinds of patterns they could find, other than the ones we were making with our hands and feet, they noticed that each square of the large blue grid was made up of four smaller tile squares.  Given that on the first day they never even noticed how the floor was designed when I asked them about patterns in the room (before I put down this grid), this was a huge step forward at identifying and describing the structure of their environment.

Speaking of patterns, I've also been sneaking in some Fibonacci numbers as well.   But that's for a future post...  In the mean time, here's my original love note about floor tape and its myriad uses.  And, one of my favorite posts in this blog about how the tape on the floor serves as the 'third teacher' in my Math in Your Feet residencies.

Videos: Piano Math!

I'm excited to share one of my daughter's math discoveries via video, for the first time ever!  I just caught up to this technology last week and am thrilled that I can put my new phone to immediate use.

Yesterday she called me over to the keyboard to share something she had discovered. We have always left all kinds of musical instruments around the house for her explore as she will.  She has not yet had any formal music lessons (except for three or four penny whistle lessons from her dad) but her current piano style can be loosely categorized as jazz improv and/or piano bar; she really listens to the rhythms and melodies she creates and, even without 'technique', she is making real music to my ears.

Anyhow, on this particular occasion, she had been noodling around and suddenly yelled to me from the piano, "Mama!  I discovered how I can use the piano to count up by threes!"  As you watch you might notice how her hand movement shows her understanding of groupings.  I've been especially tuned into children's gestures since I read this study on how children show what they know mathematically through their gestures.  Here's what she did:



After she showed me what she had discovered about threes, she realized she could do the same thing with fives.  In this video I love her excitement about finding other, unexpected patterns in the black keys:



None of this is really earth shattering, but any time a child moves her understanding of a math concept into a new mode or realm, it is cause for celebration.  I think it shows that real learning is happening.

Math is Everywhere: Storybook Edition

As the mother of a narrative-driven first grader, I have become a huge fan of the math storybooks out there.  I wish there had been more of them when I was a kid.  My daughter and I love books written by or supported by Marilyn Burns, like One Hungry Cat by Joanne Rocklin (it's about division).  I also like Loreen Leedy's books, on all sorts of math topics, and the Math Start series as well.  Our favorites are probably all the books in the Sir Circumference Series. 

On the other hand, we've really enjoyed learning math by finding it wherever we are and in whatever we're doing.  Since about February we've been paying attention to our physical world and finding as many different examples of geometry in our lives as we can.  It's quite stunning how beautiful and full of math even a city sidewalk can be if you have your math glasses on. 

Back in May I wanted to start looking for spirals but only found two examples.  One in a garden and one in our local playground.  Long story short, at some point my daughter picked up on the spiral thing and started pointing them out, only to have me say, "No, those are actually concentric circles," which then lead to a few days of clarification about what a spiral is and isn't. 

Now she sees them everywhere!  We're a team, her and I.  It's really fun that things we have taken for granted all our lives suddenly have a new dimension. Which is why, I think, that a recent return to reading familiar picture books from our home library made me notice math in otherwise non-mathy books.  Here are some examples.  Maybe you have more?

In Ezra Jack Keats' The Snowy Day, cut paper illustrations show math from the very first pages.  In addition to great spatial vocabulary (up and down the hills, tracks in the snow, on top of, snowballs flying over the boy's head) patterns abound. Check out this wallpaper -- I love how the pattern units are so different from each other, and yet the overall pattern is so regular:

Parallel lines made by sticks and feet and gates:

 The foot prints alternate:

I love this grid pattern in the mother's dress, and it's not just a color pattern.  If you look closely there's another attribute of shading (solid and striped):

This background is a great example of 'scattered' like in a scatter plot.  Which section has more dots, and which has less?  How do you know:

In nature, every snowflake has the same structure yet each one is different from every other snowflake.  That's not exactly the case here.  How many different kinds of snowflakes can you find?  How are they different and how are they the same?

Caps for Sale by Esphyr Slobodkina is another classic picture book and also full of pattern and sequencing.  In my summer work recently, and also from years of work in my residencies, it's clear to me that children don't have enough experience identifying patterns and sequences in different contexts. 

"First he had on his own checked cap, then a bunch of gray caps, then a bunch of brown caps..."  

I imagine that none of this is new news, but with my new math eyes if I ever have the opportunity to read this book to a three or four year old again I will probably pause the story after the monkeys throw down all the caps and see if the child can tell me the order the caps should be in when the peddler puts them back on.  And then have fun dressing up with our own hats!

One final book, for now, is our beloved Llama Llama Red Pajama book by Anna Dewdney.  I still remember leaving early one morning for work when my kid was 22 months old and having her look up at me reprovingly and quote the line:  "Llama llama red pajama, waiting waiting for her mama..."  Sniff. 

Anyhow, when you first open up the cover you see an incredible variety of painted squares that show up again on little llama's quilt.  Look at all those colors!  And the patterns?  Some are circles some are lines, but there are differences.  Can you tell me what they are? 

My eye was also drawn to the shapes in the doors, windows and railings within the illustrations.  This story is so engaging that you may not want to interrupt the rhythmic, rhyming flow to discuss this stuff, but...if you're going to make comments about the wonderful illustrations anyhow, a few math themed comments like "Oh, look here!  I just noticed..." would fit in seamlessly.

I think that any time a teacher or parent can share a discovery in the moment with a child or a group of children that there's potential for learning and understanding that might not be available otherwise.  I'm not saying that this approach is better than other approaches to teaching and learning out there, not at all.  But, I think that being in 'discovery mode' is a crucial piece of the learning puzzle.   My own program Math in Your Feet is one example of structured 'discovery' that includes a variety of approaches to learning (discussion, teacher led, student led, observation, writing, directing, group work, individual work, etc.) 

So, now I'm curious what other books are out there that have this kind of 'hidden' math?  I just thought of one more book: My daughter listened to the novel Half Magic on CD back in the fall.  The kids find a charm that gives them half their wish, and they quickly learn to wish for twice as much as they want.  It's fabulous.

What other kinds of books have this kind of hidden math?  I'd love to hear your ideas!

p.s.  If it's not already clear, I am not financially involved in any of the books I've mentioned or trying to make money with the use of these images.  This blog is about sharing ideas and thoughts only.

Extra Fancy Math

Here are two brand new varieties of the Platonic solids, the extra-fancy beaded cube and tetrahedron, from the mind of my seven year old:

We had a nice mini-conversation about how many straws/edges she needed to build up from the triangular base to build the tetrahedron.

And, later in the day, the beaded tower with pyramid topper (and flag, which I couldn't get into the photo) was finally complete:

Proving, yet again, that children are like cats.  When you're engaged in an activity (like cutting straws for next week) and not paying them any attention, both a child and a cat will become intensely interested in doing what you're doing, or at least something related.  At least my daughter doesn't lie on top of my laptop's keyboard.

Scissor Stories: Tales of Transformation

This whole activity was inspired by Yelena's blog post about the symmetry and cut paper stories she told and made for her son.  It was perhaps also inspired in the moment by a memory of reading the book The Greedy Triangle.  In the wonderful spirit of good ideas converging and diverging, I respectfully present to you the following:

Title: Scissor & Paper Stories in Three Acts

The Scene:  Very small karate studio in a Boys & Girls Club

The Context:  Summer version of Math in Your Feet programming

The Characters: 30 excited, wiggly seven and eight year olds who like to dance but who needed a story to help calm down and focus before we could start.

The Barest Bones of an Idea:  Scissors meet origami paper plus impromptu dialogue. (Meaning, I wung the narrative.  Yelena's stories are much more beautiful.)
.......................................

CHAPTER ONE
Me: Here, let me show you this square.  He's a little discontented.  He likes being a square...sort of.  But, truly?  He's bored of being the same shape day in and day out.  No matter how you turn him, [turning it so the corners are like a compass rose] he's still a square.  He's got a front [showing the colored side of the origami paper] and a back [flipping it over to show the white side] and he's very thin [showing the edge].  He's thinking he'd like to be a bit thicker so he decides to fold himself in half.  Oh my gosh, now he's a...

The Masses: ...rectangle! [Yes, it's easy to identify the shape, but I got the sense when I made the fold that it was a real surprise to them...]

Me: Well, that's okay with him but now he's having second thoughts.  Maybe he'd like to turn back into a square?  So he decides to fold himself in half again!  Now he's four layers thick and he is really enjoying the fact that he's not going to blow away in the next gust of wind.  [Pulling out the scissors.] 

Wow, it's really hot outside today.  You know where it's really cool?  At the top of a mountain. [Cutting a triangle out of the paper.]  But when you climb a mountain you have to work really, really hard, step by step.  [Speaking dramatically, while cutting steps up the side of the triangle.] And when you get to the top of a mountain, you're so excited to be there that you shout HOORAY and the sound echoes all over the place. 

Me: Now the square finally feels happy.  I think he likes his changes.  Let's open him up and see what he looks like...

Masses: Woah...

Me:  Would you look at that!  He's got a rhombus inside him.  Who knew?

Me:  Let's see what the square looks like when we open him all the way up...

Masses:  Ooooooooooo....!  A mask!  A monster!

Me: And look...if I turn it upside down and it looks the same!
..................................

CHAPTER TWO
Me:  Here's another square.  He's a bit discontented too.  He saw how the other square changed himself into something amazing so he thinks he wants to try.  Except, this time, when he folds himself in half, instead of folding edge to edge, he's going to fold corner to corner.  Oh my gosh, now he's a... [holding up the paper while I fold]

Masses: ...triangle!

Me: No doubt.  And, look!  He's now two layers thick.  Oh no, now he's saying that he'd like to be a little bit thicker.  What if he folds himself in half again?  Now he's an even smaller triangle and he's also now four layers thick.  What's that?  Oh, now he says he'd like to be a bit smaller.  Okay, so he folds in half again and now he's now eight layers thick. [Holding it up.]

Me (holding scissors and cutting while I talk):  Well.  Look at that.  The square really likes being a triangle but he's finding it hard to walk down the hall.  Two of his corners are manageable, but that extra one sticking out is causing him some trouble -- he keeps poking his friends.  He's thinking he might like to smooth out those corners. [Cutting away at the point where all the folds meet.]  I think he'd like a few more curves as well.  [Cutting, cutting.]  But he'd still like some triangles on the inside.  [Holding the cut triangle up.]  What does he look like now?

Masses: A dog!

Me: Yeah, he does, sort of, doesn't he?  Maybe a terrier.  Now the square has really changed!  Let's open him up and see what he looks like...

Masses:  OOOOOOHHHH!  Two dogs!  Or a moose with antlers!

Me: And let's open up the square again...

Masses: [Bouncing up and down on their knees, squeeling.]  A....   A...

Me: And now all the way open...

Masses: Ahhhh...
.................................

CHAPTER THREE
Me: And here is one more discontented square.  He wants to be a triangle just like the other square.  I can't blame him. [Folding.]  [The whole folding procedure was covered in my earlier Transformation post.]

But what's this?  Being a triangle feels weird to him.  You know, one less corner and all.  So, he's deciding to turn himself back into a square...

Masses: Oooooohhhh.... [This particular fold was really a revelation to them.]

Never mind, he likes the thought of being a small triangle. [Last fold.] Let's see what happens when he gives himself some curves and cuts...

Masses: [Applause and shouts of 'Can I have that?!?']
..................................................

Suspense.  Drama.  Intrigue.  These stories had it all and I was thrilled to provide a moment of awe and wonder with these simple tools.  Funny thing was, the next day it was old news. But, in the moment? The kids' reactions while I was folding and cutting and scraping up a story to tell with it?  That was a pure magic math moment.