re: (Not Common Core)-- Why are they teaching math this way?

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I don't think it is memorized.

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You are completely wrong. They are taught to memorize it and then use it as a technique. Notice it was given as a technique in the first question. Not number line, or grouping, or sticks or tallies.....

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I wouldn't know, I'm not being taught it.

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That explains your commentary.

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And even if it isn't, it gives a base to figure out more complex operations.

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So you are fine memorizing doubles, 5's, 10's, doubles -1... what else is good memorization and that is bad memorization to you?

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Of course 5+3 isn't complex to an adult. But adults aren't being taught this, now are they?

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No, and amazingly we all know it is 8 without having to pull out a number line.

And you are missing a few questions - remind me again how these help with your question of 354x286? Since the ability to do these more complex calcs seems to be your basis, which of these techniques we discussed are building the skillset to answer 354*286?