Understanding place value

Last night I had an interesting realization about my son’s understanding of place value. It is clearly incomplete.

We were continuing our made-up story about Max, the 701 hundred year old 7 year old. He was cursed at the age of 7 to never age and to never die, and now he is 701 years old and working hard with his friends to try and break the curse.

At one point Max gives an explanation of curse to the sea elf king in order to ask the king for help and Max says how many years old he is. I left the actual number of years Max had been alive out of the story though and so my son filled it in.

“Max has been alive for six hundred and four years,” my son said.

“Oh, how did you get that?” I asked.

“Six hundred and three plus seven is seven hundred, so six hundred and four plus seven is seven hundred and one,” my son replied.

He spoke so confidently and assuredly that I did not correct him. Also, I wasn’t totally clear at that time exactly at that time what he was thinking, and it was late.

I think that he was regrouping the ten and confusing a regrouped ten as a one hundred. He did the same thing when he first tried counting on from 100 at age four. I remember quite clearly him counting 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 200. I also remember how stubbornly he continued with this understanding.

I know of some strategies that I can use to continue building his understanding of place value. I am not sharing this story to look for help or a diagnosis but just to point out that a child who the previous night confidently and accurately multiplied 400 by 21 in his head still has unresolved issues with place value.

I think my take-away is that I need to be cautious about what assumptions of knowledge I make about my son (and of course the same is true of my students).

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One thought on “Understanding place value

  1. Yeah. Love this.

    So the pulling apart of numbers by place value (the bit he did well the other day) is one insight that helps to characterize and understanding of place value. But continuing the 10:1 pattern from one place to the next in a consistent way is a different skill. And it is as yet unresolved whether the boy as easily busts up 20 as 2×10 as he did 400 as 4×100.

    Thanks for sharing your son’s developing thinking.

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