Reading Mathematical Tasks from @ChrisMcGrane84 and @EmathsUK this morning. Reading about pedagogy in Chapter 4 and this sort of calculation from Wertheimer got me thinking.

I have way too many students who can do this, but would take almost 5 minutes. They're decent with procedures, but they don't see the overall strucure.

This would take less time, but they would get to 16, not 8 + 8.

I think that without the structural understanding of the calculation, and practicing only applying the procedure, I can't see them doing well when they get here:

"What is he even asking me to do?"
"I can't add things that I don't know"

And they'd have no chance of understanding that the answer here is x, unless we've explored those structures from images 1 and 2.

Only after seeing images 1 and 2, would they be able to approach this efficiently, or even have a chance.

So, more time exploring structures of calculations and developing that all-important number sense it is!