Kitty Census Redux

Perhaps you'll remember the kitty census that happened at our house last fall.  I just re-read the post and nearly fell out of my chair.  Not only is it touching and hilarious (at least to me) it was a completely different activity last year than what happened this morning.

Last year the kid was a newish six.  This year she's a newish seven.

Last year it was my idea; that morning, the kid just wanted to take her cats to the vet.  When I suggested we could do both she agreed, but only so she could take care of her kitties.  She had no interest in data whatsoever.

This year it was all her idea.  I ventured a suggestion about how to sort and classify all the cats, but it was clearly her gig and so I backed off.  I would have preferred to sort by material (stuffed, ceramic, plastic, flesh and blood, etc.) and then sort into sub categories from there, but the kid had other plans, as you'll see:



It may look straight forward, but the sorting process was actually quite involved.  I mean, really, what's the difference between a multi-colored cat and a spotted one? How come the otherwise solid grey kitties with the white paws didn't get put in the multi-colored pile?  The point is, she had to figure out what the parameters were to make those groupings; any one of us could come up with multiple variations on the same theme and we'd all be right as long as we were being consistent with the rules.  I'd say that's real math right there.

One more difference: Last year she was always performing, but unselfconsciously.  For this year's census she was intent on presenting her process and results in a formal way, specifically on video.  She's the one who decided what to say.  As always, I am just the faithful assistant who just happens to ask a few clarifying questions from time to time.



Yep, you heard right.  Our cat Lucy and my daughter have been added to the final kitty census tally.  72 cats!  Good thing only two of them need to be fed. 

p.s. I've got a new Facebook page where I'm sharing links to cool math activities I find and some other things I'm doing with math, making, dance and rhythm.  Hope to see you there!

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!

Totally Territorial: Cats, Maps, Area & Multiplication

I know it doesn't look like much, but there was a battle going on.  We rolled the dice (one six sided, the other twelve sided) and staked out our territory.  We're warrior cats, you know.  You didn't?  Have you read those cat clan books?  My kid hasn't -- too many kitties getting hurt makes her crazy -- but her best friend has.  They 'play' those stories every time they meet.  You should see them in their 'warrior training'.  It's crazy.

The minute we started rolling the dice I knew I needed to give this activity a special spin.  We had just finished a 'make fifteen' game where the last person to fill in a combination of fifteen wins.  There was no real strategy involved, hence her lack of buy-in.  In fact, she had been thoroughly unimpressed with it and didn't appear too eager to try something else. 

This new activity was basically built on the same model.  The goal was to see, after lots of dice rolling, who would come out with the most area colored in after the whole page was covered.  (For the life of me I cannot remember where I got this idea, but I know it was from a recent blog post.  If it's you I apologize for my lack of recall -- and please let me know so I can credit you!) 

Since success in this game was mostly left to chance, I knew I had to think quickly. "Let's stake out our clan territories and see who gets control of the most area!" I exclaimed.  Needless to say that's all the motivation she needed.  She decided almost immediately that each new piece of territory had some kind of real-life correspondence -- campus (the scene of our recent Tana Hoban adventure), our favorite hangouts, she wanted them all.  I pointed out that she could be strategic with where she filled in her boxes and, if you look at the first photo again, you'll see that she's surrounded parts of my blue territory so that I have to cross her land to get to other parts of mine.  Nice.

Then I realized that since she was thinking of real places we could probably do the same game on a real map!  Here's what we did later in the day...

We got a free map of our fair city at the bike shop.

With her watching, I took the yard stick and marked off a 1/2" grid over the entire city.  The grid was not to scale but was consistent across the entire map.  The area unit was 'one square'.

We looked at the map and found our landmarks -- hangouts, parks, campus, lakes, our neighborhood -- and at the map's key to find the roads, schools, bike and walking trails, etc.  Then we started strategizing about which areas we'd most like to 'have control over'.

We rolled the twelve sided die first to get our length (or width, whichever, depending on where it was best used strategically).  In those boxes we placed a dot using a permanent marker.  (We wouldn't be able to read the map if we colored everything over.)  Then we drew a line to show the border of that 'territory'.  Using the six-sided die we rolled the other side and figured out the total area of our newly acquired land.

I used the words area, length, and width as well as north, south, east and west during our conversations about what parts of the city she and I wanted to acquire and why.  Some of our reasons were strategic and others were more personal -- I got a lovely lake with the hiking trails, for example, and she got the big park with two awesome playgrounds.  I also modeled a lot of multiplicative thinking.  Even though we did use skip counting to compute the total area, I would point out groupings: "How many rows of seven do you need to fill in?  Second row, two sevens are fourteen.  Third row, three sevens are 21..." 

The strength of this game is that we know our city pretty well.  We've been to a lot of the parks, we move through town frequently on foot, on bikes, on buses, and in the car.  Our personal landmarks relate to where our friends live and work and go to school.  It really is our territory which is why the map was so real to her; it made sense to her despite being an abstract 2D visual representation.  Plus, the cat clan narrative is one she knows intimately, further increasing the emotional connection to the material.  Tomorrow we might play the game again and total up the red and blue areas to see who has the most.  But then again, given the engagement level today, it almost doesn't matter.  I think we've both already won. 

Take Your Kid to Work Day

In this case it was "take your kid to 'help' set up the space" day.  For me, every new space presents its own unique set of challenges and it's nice to be able to set it up ahead of time.  That way I don't have to drive 60 to 90 minutes, set up a new room, teach five classes of kids I've never met before, and drive home, all on the first day of a residency. 

Here's what part of this one will look like on the first day (I was way too busy problem solving to take lots of pictures and, anyway, it's really a boring space without the kids):

Here's my dance board plus the student spaces for demonstrating to the class.  Notice the carpet.  In this case we have enough space, but the kids won't be able to hear the sounds their feet make.  But that's okay, we'll still be doing awesome work.

 Here's my kid on 'take your kid to work' day.  She helped me put up the posters, move some chairs and then decided to play with tape.  Lucky kid.  I don't have pictures, but she made two really long lines of tape so she could do cartwheels down one and roll tape rolls down the other. 

When I was helping her put the tape down I casually mentioned that we need to make them parallel so that they'd be the same distance apart all the way up and down the line.  After that she took a closer look at the Turns poster (see first picture) and went over to the table to make a poster for her own dance and math class.

Translated into standard English, it reads:  "Cat Dance. Cat Math.  Phone Number.  GO.  Choreography.  Performing Cats."  Sounds fun!

You also might notice the effect the environment and conversation had on her illustrations.  I especially like the square with arrows radiating out of it in all directions (probably influenced by the Turns poster).  And, in the illustration of shapes, along with the circle, triangle and square are a set of parallel lines! 

[A side note: Her spelling is making noticeable gains in the past week.  I have to say that's a pretty good go at 'choreography' and 'performing' for a kid who, as recently as last week, skipped all the vowels when sounding out her words, lol!  Isn't brain development spooky?]

She figures that six participants will be enough for the class to run.  If you sign up she'll send you more information in the brochure she made on the car ride home.

Math Books for Cats

I don't know for sure, but I suspect that every kid holds in his or her heart a metaphor or identity that can open the door to learning.

With my kid, you don't have to dig too deeply.  If it's a narrative that includes cats, she's interested (except with the Clan series -- too many kitties getting hurt make her crazy).  She is a cat, you know.  She started out a kitten at the age of two and now she's a cheetah (to account for the size of her six year old self).  Maybe you know a kid or two like her?

It's amazing how much you can learn through cats.  Interested in pioneer life?  No problem, there's the short chapter book called Pioneer Cat.  For a cat-led adventure through gripping transitional moments in world history, try Time Cat by Lloyd Alexander.  Flying cats?  The Catwings series by Ursula K. Le Guin is just the ticket.  Cookie's Week is perfect when you're learning to read.  Cross-species communication is covered in Jean Craighead George's How to Talk to Your Cat.  And, the cat book lover's ultimate cat book, Dewey: There's a Cat in the Library by Vicki Myron.

So, it probably comes as no surprise that I love any chance to work math into the cat obsession lifestyle.  Here are three books that have a special place in my heart. 

My very favorite cat and math book is Five Creatures, by Emily Jenkins.  It's about the similarities and differences (attributes!) between the members of a lovely little family. 

"Five creatures live in our house," it begins, "Three humans and two cats.  Three short, and two tall....Three with orange hair, and two with gray."  We read this book when my daughter was in preschool and it was fun for both of us to look at the pictures to see who matched each description.  The categories of family attributes are not always straightforward, which makes this a wonderfully interactive read.  I am planning to bring it out again and see how it looks through my daughter's now six-year-old eyes.

The tag line for One Hungry Cat by Joann Rocklin is "A greedy cat learns division."  When we first found it we read it over and over and over, giggling every time.  I'm going to go back to the library and get it again since we're heavy into arithmetic these days; it's got an introduction by Marilyn Burns, and a bunch of activities created by her to go with the story.  We play (and love) another Marylin Burns-created math activity using Cuisenaire rods called "Build What I Have" so I have a feeling there are some rich resources there.

So Many Cats! is also a favorite.  It's a straightforward story of a growing family of cats, but the rhyming text is musical and fun to read.  If you're a cat lover or, indeed, a real cat, you will read this with great affection for every new cat that joins the story.

If you have suggestions for more cat and math books to add to our list, both the kid and I would be thrilled to hear them! 

Kitty Census: Vet Edition

We have a LOT of kitties in our house.  And they're all real, too.  Most are stuffed, some are ceramic or plastic.  Others include a rare bookmark breed and one in a frame.  We also have an amazing example of the exotic puzzle breed, one who is an imaginary friend, an actual breathing, chipmunk-catching cat and, finally, one who is a special kind of human cat with white fur and a brown spot on her head.

When faced with multitudes like this, a mama's mind turns to math: Just how many kitties do we have and can we remember all of their names?  How many different types of kitties are living here?  How old are they?  Who is related to whom?

This morning the girl wanted to play vet.  I wanted to revisit the Kitty Census we started back in the summer.  As with many things, we compromised. 

ALL the cats went to the vet. 

I was the intake coordinator.  Each cat was registered by name, age, type/description, and malady.  Some of the issues included: "a little sad", "lying around, droopy whiskers", "smelly", "bedraggled", "music slows down at end" (that was the music box cat), and "hurt paw".  In the end, twenty eight showed up for well visits and eleven had some serious issues.  After a triage that took about an hour, we attended to the sickest first. 


This is the bunch that were there for their well-checkups.



We will revisit this data later.  For today we were concerned with 'sick' and 'well'.

Aventurine, of the rare 'puzzle breed', was assessed at intake as "needs fresh air and run around time without breaking."

First, the sick kitties, pictured above, all had a thorough examination, including temperature taking and whisker inspection.  Of the group, the Webkins family all had strep, two were afflicted by a 'fever' of undetermined origin, and two needed immediate whisker surgery.  Two others, originally thought to be sick ('lying around'), were determined to simply be acting like cats.

In the end, I think we simply set the stage for more questions about our brood.  I had her chart out the number of sick kitties compared to the well.  She was curious about how many kitties there were all together, and initiated a count starting at 28 (well) and counting up the sick column to find the sum total.

We'll revisit the intake records and mine it for more data in the near future.  How many family groups do we have?  How many different breeds and how many in each category?  What else do we need to find out about our household of kitties?

Until then, one thing's for certain: We've got a whole lotta' kitty loving going on 'round here.

"Mama!  Lucy's purring!"