A Useful and Beautiful Division

Me: Oh no!!  Four sets of Cuisenaire rods are all jumbled up!  I've got to get them sorted out before the next Math in Your Feet Family Night!  Do you think you could help me? 

Kid: How should we start? 

Me: I've set out four bags, one for each set of rods.  We need to divide up the rods equally so there is one full set in each bag.

Kid: (Finding all the orange rods.)

Me: "How many orange rods are there all together?"

Kid: "Twenty one."

Me: "How many orange rods go in each pile?"

Kid: (Starting with four in each group, then adding one more to each, one remains.)

Me: So, five in each group, with a remainder of one?

Kid: Look, Mama.  Four times five is twenty.  I knew that.

Yeah, I know.  I know that addition, subtraction, multiplication and division are steadily working their way into her consciousness and her skill bank, and all of this primarily by delving deeply into doubles, halves and evens.  I'm not kidding when I say that doubles/halves/even-ness comes up practically every day, one way or another.  I think it's a great way for a six year old to explore and learn about numbers, geometry, and the meaning of math.  There's actually something quite comforting in our daily discoveries of balance and symmetry whether in number play, through observations of our physical environment, or in the things we create with our own hands (the attributes matching game, for example, or our recent exploration of circles). 

I also know this kind of sorting activity is pretty basic, but having lots and lots of experience with operations in as many different contexts as possible is always useful.  In this case it was extra useful 'cause I didn't have to do this chore myself and I was able to work in some math inquiry -- sorting, classifying, measurement, division and a chance to get reacquainted with the rods -- all at the same time!   

Poem in Your Pocket Day! {Math Edition}

Yes, today is Poem in Your Pocket Day! 

"Celebrate national Poem In Your Pocket Day on Thursday, April 26, 2012!  The idea is simple: select a poem you love during National Poetry Month then carry it with you to share with co-workers, family, and friends. You can also share your poem selection on Twitter by using the hashtag #pocketpoem.

"Poems from pockets will be unfolded throughout the day with events in parks, libraries, schools, workplaces, and bookstores..."

The kid and I are going to write our favorite poems on the sidewalk with chalk!  Maybe at the park, maybe in front of our house too. 

In honor of this fabulous day, I thought I'd share one of my favorite math poems, one that really goes with the Math in Your Feet theme: squares.

School Lunch

Each food plopped by tongs or spatula
Into its own little space --
Square pizza here, square brownie there;
Milk carton cube, rectangle tray.

My snack at home after school?
Anything without corners.

From the book Sijo (Poems) by Linda Sue Park
____________________

[Edit P.S. Here's a picture of a poem my kid wrote -- I wrote it out in chalk on the basketball court down at the park and she illustrated it.]

It's a bit hard to read, so here's a transcript:

In the Night
by Isobel

The trees are whispering
in the woods
in the night.
The animals are sleeping
in the woods
in the night.
At break of dawn the animals
wake up and catch their prey.
The crystal clear waters of the stream,
you dip your paw in for rarest fish.

Circularity

For some reason, I had circles in my head.  Last night I gathered up a bunch of different sizes of circles...

...and this morning I taught the kid how to use a compass.  It took a little practice, but she got the hang of it fairly quickly.

She played around with concentric circles, circles that 'go off the page' and even discovered that three circles together can 'make a triangle!'

While she played around, I took a paper plate and a CD.  With the CD centered inside the paper plate, I drew one circle tracing the small circle in the center of the disc.  Then I played around...until, WOW!  Look at that!  I made a hexagon!  I felt like I had just discovered a dinosaur bone or something.  I decided to color it in to highlight the structure.

At that point it was time to go do Sunday things, but it took forever to get out the door.  The kid kept finding circles everywhere. 

When we got home from Sunday things, we started in on it again.  This time, the kid started experimenting with tracing the circles. A straw can make a smaller circle than the compass can.

I made another hexagon out of circles, but colored it in differently, the kid's favorite it turns out.

The kid constructed two different versions of concentric circles (mostly using the compass).  "See Mama!  They're the reverse of each other.  This one has a lot of rings on the inside, but not on the outside.  The other circle is the opposite!"  

And, then, she wanted to make a hexagon like mine so I showed her how to use the CD center circle.  I really like her design sensibility.  It's so different from mine.

And then it was time for lunch, but we still have unanswered questions waiting to be resolved.  Like, what else can you make with the compass besides circles inside circles?  Great question, kid. 

I'm fairly certain we've only just begun...

Transformation

It's amazing.  You can start with a square...

Which can turn into a triangle....

Which can turn into a square again....

And then into another triangle...

And then, after just a little bit of cutting, you get this!

It's a little bit a magic, that!

(If you're interested, these perfect little paper squares [just over 3"x3"] were 500 sheets for $2.00 on special at...um....[staples]....in six bright colors and two softer shades.  I found them in the notepad section -- looks like sticky notes, but no sticky. Also, the particular fold I used comes from a little book on Kirigami I had lying around, and the cuts were improvisational after trying out some of patterns in the book.  I'm going to use these, and many others, to decorate my summer classrooms up in the city not to mention the walls of my own house!)

Linking to Saturday's Artist at Ordinary Life Magic. :-)

Story Math: Introducing Square Numbers, Sets & Subsets

I feel comfortable doing a lot of things, but storytelling isn't one of them, especially when my kid insists I make one up on the spot. Today was no different, but luckily I got inspired.  There have been a few math-y things I've been wanting to introduce, but she's been having none of it.  Fortunately, a narrative (even a thin one) is often the way to get her hooked so I decided to go for it.  Here, then, are three of today's stories.  The first two illustrate different aspects of square numbers.  The third was actually mostly for me to start figuring out how to explain sets -- I'm not quite sure I've got subsets yet. 

As you read my modest stories, please imagine me simultaneously illustrating while I narrate.  The illustrations build as the story develops...one red cat, three orange kitties, five blue raindrop cats, etc.

Story #1: Rosie's Wish

Once upon a time there was a little red cat named Rosie [one red box colored in] who was very lonely.  She wished on a star for the company of a few new friends.  [You tell good stories mama!  Just as good as papa...!]  The star said, "I think I can do that!" and sent down three orange cats to play with.

The little red kitty loved playing with her new friends, but soon wished for even more friends.  She looked up into the sky and this time made a wish to the cloud she saw floating by.  The cloud obliged and sent her five blue raindrop kitties.  They played and frolicked, but soon wanted to share the fun with even more cats!  The little kitty made this wish to the trees around her, and the trees sent her seven little green leaf cats and, later, nine pink cherry blossom kitties. 

The whole group, all 25 of them, played and frolicked the night away.  When the sun came out in the morning, they were all tired out.  And what do kitties like to do in the sun?  Why, they curl up and take a nap!

The pink kitties lay down first, and made a soft bed of flower petals.  The green leaf cats added to the bed, then the raindrop kitties, and then the orange cats.  Rosie lay on top of the whole pile of friends, purring happily.

You probably noticed that this story ended up illustrating the growth progression of square numbers, first in a square and then in a line.  I didn't mention anything about squares or numbers in this story.  My thought was that I wanted to present the image and show the growth, which I think is cool to look at; laying the same number of squares out in lines was an in-the-moment inspiration and shows the pattern of growth more clearly. The kid loved the story and, interestingly, didn't bat an eye at the fact that the characters were represented as little colored squares!

Story #2: Lucy's Square Meals

Lucy, our cat, likes to eat.  She begs and begs us for food.  Today she said, "Give me something to eat, I'm starving.  You haven't fed me in weeks!"  So, we gave her four orange mice. 

Lucy said, "That was a great square meal but I'm still hungry -- give me more to eat!  I'd love if it could be another square meal but even bigger this time, meow!"  So we gave her nine blue chipmunks. 

Of course, that was only a tiny snack for Lucy...[I want things to fall from the sky! the kid interjects]...and she wanted another square meal, bigger than the one before.  So, we got some of the green birds that were flying around up in the sky.  As before, the meal had to be bigger than the last one, so let's count out four birds in a column, but look!  That's not a square, that's a rectangle!  If we add four more, that's still a rectangle...oh look!  Four columns of four green birds in each column make a square that is bigger than the square of blue chipmunks.  How many birds did she eat all together? 

I can't imagine Lucy is still hungry....she IS?!?  What does she want to eat this time?  Okay, a square meal out of cubes of pink cheese.  How many cubes of cheese will she get....?  I think that's enough food for Lucy, don't you?

There was actually quite a bit of buy-in from the kid on this story, especially when I was 'trying' to figure out how to make the green square bigger than the blue one.  She actually leaped in to help her apparently inept mother, ha!

Story #3: {The Family in the Fancy House}

Once there was a family who lived in a fancy house [Meaning the brackets { } used to denote a set].  The family included Lucy (a living cat, red square), Isobel (a living cat, blue square), Mama (green square) and Papa (orange square).  Sometimes they are in different rooms of the house, but no matter where they go in the fancy house they are all still part of the same family. Lucy and Isobel (red and blue squares) are included in the family who lives in the fancy house.

In addition to Lucy and Isobel, there are other kinds of cats in the fancy house as well.  There are soft cats, and china cats, and plastic cats too.  The two living cats in the house (Lucy and Isobel) were also included in a set of 33 soft (living and stuffed) cats...

...and I left it there for the day.  To you, Lucy our cat and Isobel the daughter/cat might not be in the same set, but they are to Iz.  In fact, things got a little rocky when I defined the other soft/stuffed cats as 'not living'.   The set/subsets concept is new to me and, honestly, a little challenging.  The kid and I have lots of conversations about same/similar/different, in a Venn Diagram style, but this seems different somehow.  I actually think it will make more sense when we figure out sets using numbers.  Or maybe it's time to ease in the Cuisenaire rods?

I'm not yet sure what she made of all this math-y storytelling today.  But, the beading/pattern experiment from last week is really bearing fruit this week (lots of spontaneous observation of and creation of patterns) so I'm fairly sure square numbers and sets will show themselves in her play or drawings in one form or another some time soon!