I had a fascinating exchange with my son last night. I was telling him a made up story, and at one point this character who is cursed and very old said that his age was “Four hundred times a score and one.” My son asked what a score was, and I told him twenty.
He then tried to figure out the person’s age. He started by asking what is four times twenty, and I told him he could figure that out. He counted up by fours to get eighty, and then said that four hundred times twenty is eight hundred. He thought for a moment and said that no, it must be eight thousand, which meant the final answer is eight thousand four hundred.
This makes me curious about how he understands the number twenty. He knows apparently that four hundred times something is one hundred times whatever four times the something is, although I am not clear he would explain it like that. However, he apparently did not use the fact that twenty times something is the same as ten times two times the something.
This reflects the difficulty with learning math in English, compared with other languages. “400” is clearly “4 hundreds” and thus is more accessible to children’s mental figuring—but “20” is not obviously “2 tens.” And the teen numbers are a mess.
I think your hypothesis is a reasonable one. I can test it. Christopher Danielson suggests that I ask him to multiply eight by twenty and see how he approaches it.