Counting grapes

I am pretty sure I have mentioned this before, but one of my proudest achievements has been watching a “Talking Math with Your Kids” hashtag (#tmwyk) blossom on Twitter in the past few months. Now, on a nearly daily basis I (and you, if you join us over there) get to see conversational gems such as Kindergarten kids talking about Spirals and cool math prompts such as Counting Grapes.

Michael Fenton—a father and math teacher—sent this photograph into the #tmwyk world recently. Naturally, I had to talk with Tabitha and Griffin about it.

Two bowls—one with five grapes, one with eight half-grapes

The conversation with Tabitha (7 years old), I captured on video.

Here’s the transcript:

Me: Which one of these bowls has more grapes?

Tabitha: (7 years old): [points to a bowl, probably the one on the right but hard to tell] Obviously!

Me: What do you mean, ‘obviously’?

T: I mean look at this! One, two, three, four, do you mean halfs?

There is a thoughtful pause.

T: Actually…

She points to the bowl on the left.

T: Cause these are halves

Me: But how do you know that there’s more here than here?

T: Cause look.

She uses her thumb and finger to indicate that halves of grapes are getting put into pairs to make whole grapes.

T: One, two, three, four

Now she shifts to the bowl on the left and counts the whole grapes individually.

T: One, two, three, four, five.

So what do we learn?

The key moment is right here: I mean look at this! One, two, three, four, do you mean halfs? (This occurs 8 seconds into the video.)

That is when she notices—on her own—that half grapes are not worth the same as whole grapes. It is where she shifts her attention from items (of which there are 5 on the left and 8 on the right) to whole grapes (5 on the left, but only 4 on the right).

The rest is tidying up details. The learning happens in that one brief moment of insight.

Starting the conversation

Ask your own child this question when you have a spare moment. Don’t correct or interrupt. Just listen. Object if their explanations are incomplete, but otherwise just listen.

Technical notes (and acknowledgements and thanks)

This was our first video using Google Glass.

There will be many more, I am sure. I’ll write more about this in the future, and I am happy to discuss with any interested parties. (You can hit me through the About/Contact link here on the blog.)

In the meantime, I want to thank Go Kart Labs for their sponsorship and financial support. They funded most of the cost of my Google Glass through a generous donation. These folks are smart, kind and interested in the overall goal of the Talking Math with Your Kids project, which is developing a world full of intelligent, creative and curious citizens. Upstanding people who do beautiful web-design work here in Minnesota.

4 thoughts on “Counting grapes

  1. Pingback: Building Number Sense and Fraction Sense While #TMWYK | The Recovering Traditionalist

  2. “The learning happens in that one brief moment of insight.” What a beautiful statement! As we shift math instruction from “filling empty vessels” to “uncovering standards,” we must think about when and how learning occurs. These moments of disequilibrium or productive struggle are so critical to student constructing an understanding of mathematical concepts. Thank you for sharing your experiences and encouraging us all to share #tmwyk.

  3. Pingback: Fractions | Math 101

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