Tuesday, April 3, 2012

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. 


  1. Brilliant. I actually like the first part better, because my daughter is not as intimately familiar with the map (and we live in a fairly big city). I have to try it out with a grid paper.

  2. Is there another area your daughter knows really well? A park/playground or even your neighborhood? Maybe you could scale up a portion of a map with a copy machine and grid it out from there? I noticed that on our bike map there was the 'close up' view of city center streets, and the zoomed out view on the other side. :-)


Thanks for reading. I would love to hear your thoughts and comments!


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