Multiplication Numbers & Operations in Base 10

Multiplication Shortcut Fail

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  1. What exactly is the shortcut?
  2. Why does this shortcut seem reasonable?
  3. We’d all agree, I think, that 2 x 6 = 26 is not a result of this kid not understanding what multiplication is. I’ve made that mistake before, and I bet that you have too. So, why is it a  common mistake? What does this say about how a mind works while working on math?

[Any advice on how to tag this, CCSS-wise?]

2 replies on “Multiplication Shortcut Fail”

I wonder if there was a small multiplication error compounding the common mistake of multiplying some parts of the decomposed numbers but not others (for example, multiplying the ones by the ones and the tens by the tens). One way to read this might be that the product 2 x 6 is mistakenly written as 24:

5 x 4 = 20 (the ones)
2 x 6 = 24 (tens) – plus the 20 above = 26 tens, or 260

It’s hard to uncover the thinking without talking to the student or seeing their work.
For example, if 5×4=20 then why is 2×6=26? mpershan commented that’s a common mistake. I don’t see it a lot, so does it mean the student put the two digits together to make 26? If so, why didn’t s/he put 5 and 4 together to make 54?
Ana’s wonderings are a good possibility. When kids jumble the parts together, they’re using a short cut that’s not based on place value. Seems like this student needs more time to compose numbers.

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