Counting Fish

Last night my oldest son (Caleb, 5) asked if we could play Monopoly before he went to bed. I said, “Uh, no thanks.” (It was after 8 pm, and I still had aspirations to be in bed while it was still called Thursday.) He then asked if we could play the “fish game” instead.

counting-fish-1

“That, my friend, is a great idea.” And with that, it was on.

Round 1

We played our first round; I was thoroughly destroyed. (I’m not sure how. I should at least be able to put up a good fight. He’s only five. And I’m not that uncoordinated.) Then—while channeling my inner Christopher Danielson and Andrew Stadel—I asked Caleb how many fish he thought we had each caught.

He made a guess about mine (7), and then we counted. I decided to line them up:

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“Off by one. Not bad.”

Then we looked at Caleb’s catch. His guess? 16.

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He then counted his fish. Not surprisingly, he lined his up (just as I had). But he made an interesting move:

[vimeo 111898481]

Was that a coincidence? Or was that move inspired by what he’s learned and learning about our number system?

Round 2

I find these TMWYK conversations wonderfully interesting, and Caleb is happy to play along, provided that we don’t linger for too long. With that in mind, we moved on to another round. I decided to capture a video of our second battle, and the counting that would follow:

[vimeo 111898482]

Another interesting move! Arranging in fives. Coincidence? Or is he starting to wrestle with 5 (half of 10) as another friendly number at his disposal?

counting-fish-6

Postgame

I shared the video with my wife before heading off to bed last night. She was similarly intrigued by the way he arranged the fish while counting. And though my curiosity has yet to be quenched (it will take some followup conversations to figure out his level of intentionality in arranging the fish in that way), I noticed on this second viewing that Caleb arranged the fish by color. In the first case (10 + 3), he ran out of room, and decided to put the last color (red, with three fish) on the next row.

As for the second round, where Caleb arranged things into fives? There were five different colors of fish, three per color (except for that last one).

Next Time

One of the things I love about sharing these conversations is that in writing them down I almost always think of another question or two I might have asked along the way. The arrangements of fish (complete or otherwise) now look to me like fertile soil for rich mathematical conversations about addition, subtraction, multiplication, and factors. In making estimates and checking them by counting, we have a great opportunity to discuss about “more than” and “less than,” and could easily reflect on whether we tend to over- or underestimate in our guessing.

Granted, those are things I thought of only after the fact, while writing down the less-interesting version of things (reality). But for me, that’s the value. In the same way that reflecting on my teaching practice helps me grow as a teacher, reflecting on my conversations with my kids will help me grow in my ability to challenge and encourage and excite them through our father-son or father-daughter discourse.

Update

I showed the video to Caleb. (“Look, little man! You’re on the Internet!”)

Then, regarding the first round: “Why did you arrange the fish like that?”

Caleb: “Because I ran out of room.”

And for the second round: “Why did you line them up that way?”

Caleb: “Because I love rainbows, and I made them like a rainbow.”

Well, numerical motivation for (10 + 3) and (5 + 5 + 4) arrangements may be a few months off. But he does have a nice eye for design. 🙂

And if I can pull another classroom takeaway from this conversation, it would be this: The best way to know what they’re thinking? Ask! In a parent-child exchange, this happens naturally and easily in conversation. In the classroom, we’ll have our fair share of individual conversations like this, but also a great number of whole-class-all-at-once interactions. The manner in which we ask for their thinking changes (e.g., a written response instead of a spoken one), but the importance of inquiring remains.

Comments 2

  1. I know this is an old post but I figured I’d leave my comment anyway. Looks like his thinking could also lead into some discussions of bar graphs and visual displays of data. As a kid, I used to line up my Halloween candy this way (and also the contents of each bag of m&m’s/skittles #dork) and I’d eat the candy which I had the most of first. And after that there was an elaborate system to the order in which things were eaten… There was a touch of constructing viable arguments in my day after Halloween decision making. Just some random thoughts.

    Thanks for your blog. I really enjoy reading your posts and creative lesson ideas. I’m an instructional coach (former Alg 1 teacher) and I’ve passed many of your posts on to my colleagues throughout the district.

    Thanks again,
    Christine

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    Author

    @Christine, thanks for the comment, and for recommending the blog to your colleagues. I love the idea of lining things up to drift toward data displays. Next time on #tmwyk… 🙂

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