A short waffles conversation

Those Eggo mini-waffles are paying off.

We had this conversation the other day…

Me: There you are, Tabitha. Two sets of waffles.

waffle.array

Tabitha (six years old): That’s 7. No…8!

Me: [washing dishes with my back turned to her] Right. Two sets of four is eight.

T: That’s not how I know.

Me: You counted?

T: No.

Me: Oh. How did you know, then?

T: Three plus three is six. And there’s 2 more.

Me: [Big smile and thumbs up for encouragement]

So What Do We Learn?

I recently pushed Tabitha past the limits of her patience by asking about lobsters and half-lobsters. But in doing so, I was continuing to lay the groundwork—how she thinks about things is interesting to me. I want to know, I value and reward her thinking. So she talks about it.

When you consistently talk math with your kids, you will make progress. It may seem slow at times, but you’ll make progress.

Mathematically, there is something really wonderful going on here. She is trying to figure out 4+4, but it’s not a fact she has handy. So she thinks of 4 as 3+1.

Now it’s 3+1+3+1, which she rearranges as 3+3+1+1, which is the same as 6+2.

She uses a fact she knows (3+3) to find one she does not (4+4). This is an example of using derived facts, which Griffin did also in a recent conversation about the number of fives in an hour.

Starting the conversation

Listen for the times that children announce how many things there are. Ask them how they know.

Another example: Griffin had his ninth birthday party recently at a local swimming pool. The cake was provided; the high schooler who brought over the cake asked me his age and proceeded to count candles from the pack. It was hot; the candles must have slightly melted into the container because she was struggling and took a good minute or two to dislodge the candles, leaving them on the table before disappearing.

She had left eight candles behind.

For a nine-year old’s cake.

Needless to say, this was a topic of great conversation among the children present. Somehow Griffin didn’t notice. But his friend from up the block, W, did. She asked me, “Hey wait! Why are there only 8 candles?” I don’t know, I replied, but how did you know there were 8? She gave me a funny look. Did you count them one by one? “No,” she said, “by twos…2, 4…”

It is that easy.

You just have to put up with a few strange looks from children sometimes.

Waffles [Product review]

From time to time, we will be reviewing products here at Talking Math with Your Kids. Sometimes they will be products that are intended to foster mathematics learning, but not always.

Today, we consider one that is not.

We recently bought Kellogg’s Eggo Homestyle Minis waffles.

Tabitha is obsessed with waffles. We typically get the store brand, which as far as I can tell are mathematically uninteresting. But every so often Eggos go on sale, and then it’s game on!

Consider the Minis.

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The minis come in sets of 4.

Here is the kind of fun we can have (and, I assure you, that we have had) with this:

  • Say, “I’m making frozen waffles this morning. How many do you want?” Leave the unit deliberately unspoken. Child says “one” and is served one mini waffle. Discuss.
  • Do the same thing again the next morning.
  • Hold up a set of four waffles and ask a young child (say, 2 to 4 years old) how many you have (answer is likely “four”). Then point out to the child that it says there are “10” in the box. Dump them all out and discuss. Key question: What are there ten of?
  • Ask a somewhat older child (say 7 to 9) “If there are 10 sets of 4 waffles in the box, how many waffles are there?” Follow up with “How do you know that’s right?”

Finally, this: In addition to (1) waffles, and (2) sets of waffles, there is a third unit to count in that box: servings.

It turns out that 1 serving is 3 sets of 4 waffles. How awesome is this?

You can ask an older child to predict what the number of “Servings per Container” will be on the Nutrition Facts label. I would have gotten it wrong. I would have applied too much mathematics to the problem and said 3\frac{1}{3}. You can see the “correct” answer below.

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You didn’t think I had something to say about the waffles as food, did you? I’m sure they are everything one would expect of Eggo waffles. You probably already know whether you consider that a good thing. Tabitha likes them.

P.S. My own father turns 70 today. He certainly supported my own mathematical development growing up. Thanks, Dad! And Happy Birthday.