decomposing numbers

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Decomposing addition

I was playing an online game today with my son (who had just woken up) watching over my shoulder.

“What does ‘split 28’ mean, Daddy?” he asked me.

“Well, I just looted 28 coins and I’m sharing them with my friend,” I responded.

“Oh…hrmmm…….so you’ll get 18 each then!” he responded.

“How did you get that?” I asked back.*

“Well, I took 20 and split it into 10 and 10, and then I took the 8…oh…I forgot to split the 8 too. You and your friend will get 14 coins each.”

* I always ask that question, whether he is right or not.

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How long is an hour and forty minutes?

My son and I had this exchange earlier in the day when we were negotiating about whether or not we would watch an afternoon movie.

Me: “Okay, so the movie is 90 minutes long. That’s an hour and a half.”

My son: “How did you know that?”

Me: “An hour is 60 minutes, so I just took 60 minutes away from 90 to get 30 minutes left over, which is half of an hour.”

My son: “So what if the movie was 100 minutes long? No, don’t help me! Let me figure it out… Uh… an hour and forty minutes.”

Me: “What if the movie was 110 minutes long?”

My son: “That’s easy. It’s just 10 minutes different. So instead of 100 take-away 60, it would be 100 take-away 50. Uh… That’s 50 minutes! So the movie would be an hour and 50 minutes long.”

Easier question: What’s the biggest success here?
Harder question: How does this kind of number sense develop in children?

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What’s 9 plus 9?

My six year old son and I were working on cutting out snowflakes (more on this later, it’s a fun project in itself) and at one point we wanted to count the number of symmetries our snowflake was going to have, which we worked out would be 9 + 9. My son said aloud, “Okay. 8 + 8 is 16. 9 + 9 is… uh… 18! Because 8 + 9 is 17!”

How often do you see students use counting as a strategy for finding a sum of two numbers? Is this common? How do we encourage this type of reasoning?