Why 5+5+5 does not equal 15
The third-grade child was asked to answer the sum 5×3. Common Core says the sum must be 5×3 as “five groups of three” not “three groups of five.”
Because thinking of 5 x 3 as, literally, “five groups of three” will help them when they learn how to divide. (That’s what the Common Core standard here is getting at.)
When they see a problem that says 5 x ___ = 15, they’ll be thinking “I need five groups of SOME NUMBER to get to 15.” In other words, they’ll be able to pick up division a little more quickly because they’re learning the proper way to think now.
I don’t know if that’s exactly what the teacher was doing, but it’s plausible.
What about the array problem? This one’s even more straightforward.
It actually matters which way you draw the picture. But it’s not something kids will understand until they start using matrices in algebra class.