Here is one from the archives.
Nearly a year ago, Griffin was seven years old and I was doing some thinking about the number course I teach for future elementary teachers. I decided to see how Griffin was thinking about place value.
Me: How many tens are in 32?
Griffin (seven years old at the time): Three, and then two leftover.
Me: How do you know that?
G: Thirty—that’s three tens, and then the zero means no ones.
Me: How many tens in 268?
G: [long thoughtful pause] Twenty-six, and then there would be 8 left over.
Me: What would you say to someone who thought there were six tens in 268?
G: I’d say there are 20 more than that.
That’s my boy.
Overthinking my teaching 
Chris – Does he still think this way or has the educational world manipulated him into looking only at the place values?
Peter A. Kalenik OPMS – Math Teacher
You are going to have to put those kids on a stage soon. A child panel, so to speak.
Pkalenik, I saw your question over breakfast and asked him as he picked apart his bacon.
Then I showed him the post and had him read it. When he got to my question How many tens in 268?, he muttered, Easy! Twenty-six point eight.
SUPER-LIKE! 😉
My son is using this kind of decomposition to do his own addition. For example, he was wondering what three times twelve was, and so he tried to add up 12 + 12 + 12. He knew that 12 and 12 was 24, and then he told me that 12 and 24 was 36. So I asked him about his reasoning.
He said, “I know 10 and 10 is 20 and 2 and 2 is 4, so 12 and 12 is 24, and I know that 24 is 10 and 10 so 24 + 12 is 10 + 10 + 10 and 4 + 2, which is 36.”
One thing which I think has been fantastic for his number sense is learning how to count numbers in other languages. For example, he learned in Aikido how to count to 10 in Japanese. I told him that in Japanese, if you want to say 20, you say literally “two tens” (but in Japanese obviously), so then he worked out how to count to 99. At 100, he said “Ju-ju” which literally means “Ten tens.” I found a student at my school which is learning Japanese, and she gave me a chart for the different place-values, and apparently “Ju-ju” is actually “Hyaku.”
I JUST realized that you are not just the road to calculus guy…you’re Griffin and Tabatha’s dad. I really love these posts and am an avid reader. Your kids and my kids should have breakfast together sometime!
Thanks very much LOL