Lack of Connection….and Monopoly

[Tracy Proffitt]

Often as I read this book I find myself stopping to see how one or both of my kids would deal with the tasks presented.  Just now as I read about Emily and how she struggled to solve naked problems that she was able to solve with context, I had to try it!

First….some background:  Less than a week ago I watched my 6 year old play Monopoly with his nana.  He cons her into playing almost every time he sees her.  She’s much more patient than I am.  🙂  Their game was so full of math…4 times your roll for the electric company was one of my favorites.  I also remember him owing her $27, handing her $30, and immediately asking for $3 change.  I was amazed.

So just now I called him upstairs and asked the naked number problem verbally first, “I’m wondering, what’s 30-27?”  Our interaction went something like this:

Tripp:  Hmmm….ok.  Is 27 minus 10  17?

Me:  Yes.

Tripp:  Ok.  (Thinks more….quiet figuring that I’m not following.)  It’s -3.

Me:  Ok.  Tell me how you got that.

He explains that 27 minus 10 is 17.  17 minus 10 is 7.  Then he takes away 7 and then three more…he’s at negative three.  I realize he’s solved 27-30, not 30-27.

Me:  Ok.  So tell me again what problem we were solving?

Tripp:  30 – 27.  Oh wait.  I did 27 – 30.

Me:  Yep!  You solved a much harder problem. Wow!  (Ugh…there’s that word “hard”.  Old habits.)  So what about 30 – 27 then?

It takes him a while, but without prompting he walks me through 27 minus 10, and another 10, then minus 7 to get 3.

Tripp:  Woah!  -3 and 3!  That’s funny.

Me:  I know, right?!  Ok, now one more question.  Pretend you were playing Monopoly with Nana and you owed her $27.  If you gave her $30, how much does she owe you back?

Tripp:  (Instantly…)  $3!  That’s easy!

When I asked him how he knew so quickly, he didn’t say he counted up like I would have expected.  He said because 10 – 7 is 3.

I probably went too far and said too much, but I said something like, “Did you realize you’re doing the same problem when you make change?  You’re doing 30-27.  You’re taking the 27 out of the 30 that you paid.”

His response was a bit crushing:  “Oh.  I forgot.  It’s been too long since I’ve been at school. ”

Cringe.  Whose kid are you??  I feel like we’re talking and playing math all summer long, but apparently he doesn’t see it that way.  : /

Anyway….all this to say two things….

*First, you are so right!  Context matters, and I’m realizing it’s what often anchors that “low floor” idea in rich tasks.  Context makes a problem accessible in a way that a naked number problem does not.

*Second, I’m now thinking about how I will help Tripp get to the point where he sees 30-27 as “I owed 27, I paid 30, how much change do I get?”   Also….because I’m realizing these are two different things….how do I get him to calculate change and think to himself, “Oh….I just did subtraction.”  Yes, I know there’s no rush.  But just in the same way that I pointed out he multiplied when he got the electric company card, I could point out he was subtracting when he made change.   I’m thinking this is one way I would connect his “human daily sense with the vocabulary and symbolic representations of mathematics”.

I love this line…”We want no gap between street math and school math.”

And in our case….We want no gap between Monopoly math and school math.

 

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