Thursday, April 18, 2013

Dinnertime Division

Scene: Dinnertime

7yo: I'm going to leave that [her dinner] for a while.

Me: Hey, wait a minute.  Let me see how much you have left in your haven't had much to eat today, you need to eat at least half of what's left.

7yo:  [Sitting back down, pause in conversation] I have 34 noodles left....

Me:  How do you know that?

7yo: I counted them.  I'm going to eat 17, okay?

Me:  Hey!  How'd you do that so fast?

7yo:  Well, I took half of 30 and half of four and added them together...

Me: You are super awesome! 

7yo:  Well, I knew that half of 30 was 15 and half of 4 was 2 so it was easy...


A question, full disclosure, and some context:

At what point did mental division of 2-digit numbers get "easy" for her?  I'm afraid I don't have an answer for that but I'm always curious and thrilled when she makes a leap past "hard" to "easy".

We haven't done much what I call "sit-down math" for weeks and weeks now. There. I said it.  We'd been going strong with daily math lessons for most of the school year yet somehow it has gone by the wayside the last month or so.  But, in its wake...

...I've been very aware of watching math happen throughout the day: her daily tally of savings for an American Girl doll (both how much she has and how much more she needs); her daily interest in telling analog time (and becoming stronger at base 60 as a result, hence the division of 30 tonight); continued interest in investigating and analyzing the weather report in the daily newspaper; her easy and quite enthusiastic use of the tape measure to compare heights and lengths and just about anything that enters her mind.  She's also taken to maps and geography and is now paying attention to the scale to get a sense of distance.

We're steady math learners, no bells and whistles and, obviously, not a lot a drill. She's a good math student but not brilliant.  And yet, I find the development of these mental math skills fascinating, bordering on magic  especially considering how number-phobic I've been all my life.  Apparently I was able to swallow my fear and do a pretty good job with her numeracy development (so far), and mine own as well.

What I've done in the last one and a half years or so really feels like some kind of super power, truth be told.  I can tell she probably feels the same about being able to compose and decompose numbers.  But I know it isn't really magic.  There are incredible resources out there for anyone to do what I did.  In terms of 1st and 2nd grade numeracy, here are what my resources and basic blocks of activity have looked like:

- Hundreds of Shut the Box games
-Just as many games of UNO (by adding up the loser's points)
- Lots and lots of hands on interactions with money (earning, saving, counting the change jar)
- Connecting geometry to number (and lots of Sidewalk Math -- walks outside to find structure and pattern all around us including triangles and other polygons, arrays, spirals, etc.)
- Having lots of hands-on maniupulatives around (tangrams, pattern blocks, pentominoes, Cuisenaire rods) to just play around with and occasionally use in lessons
- Reading Constance Kamii and making the conscious decision to focus on mental math and not worry about procedures (regrouping, borrowing, carrying the one, whatever)
- Playing games from Let's Play Math and Peggy Kaye's Games for Math
- Reading Living Math Books
- Investigating wholeness, halfness, doubles, even-ness, even and odd numbers
- The first two chapters of Beast Academy 3A (polygons and skip counting)
- Investigating the Sierpinski triangle to get a sense of three-ness and multiples of three
- Keeping the big picture of math in the picture, so to speak, with books like Penrose the Mathematical Cat and G is for Googol.

There's more, I'm sure.

I'm not sure why I'm wrapping up her second grade year in April, but it really feels like my often hands-off approach has created a great base.  Best of all, it is very apparent to me is that my daughter is really digging into the math she's learned this year and is now making it her very own.  She's using it to answer her own questions, express her own ideas, and find her own way.  Joy!


  1. I had never seen that site for living math books. My favorite proponent of living math, Julie Brennan, also has a list, here.

  2. Sue, I think that's her list, actually, just in a more searchable form. I think she put it up about a year ago. :-)


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