This morning we had mini-pancakes for breakfast. I gave my youngest son (who is two) three mini-pancakes. When he was still hungry, I gave him two more.
Half-way through his final pancake, he said:
There is interesting research that suggests, through an ingenious experiment, that we are literally born with some knowledge of numbers. Not symbols, like the word “five” my son is using above, but numbers. It seems to me that while my son is developing his language, it is an excellent time to develop his innate understanding of number and connect it to the language he is learning.
So I pay attention to what my son says and even at two years old, when he is first developing language, we count together, we group objects when we play, and I help him give language to the thoughts he is already having.
Screen-shot from one of the puzzles included in the block game.
I wrote this puzzle/game last year with the hope it could be used to help generate some thinking about area, multiplication, and addition.
Here are some questions you could use with the game.
Try solving the problems, if possible, in a variety of different ways. Which ways give you the most points? How much is each piece worth? What is a general strategy you can use to get as many points as possible? How do you know your general strategy is effective?
Note: This game does not currently work in Internet Explorer.
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.
Here are a couple of addition problems. Can you figure out what the student is thinking here? Thanks to Chris Hunter for the submission.
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?
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?