[BitWielder1]

They're attempting to teach head counting *tricks* without teaching the *techniques* those tricks are based on.
Without knowing proper techniques, the tricks become a jumble of incomprehensible rules.
As for the question in the problem, Jack forgot to subtract the *1* in 316.
CC does not seem to have any easy way to double check results.

[HiTech RedNeck]

It’s like trying to teach algebra without teaching algebra.

Why not just give in and teach algebra. It could be kept really simple. This doesn’t need to be your high school algebra. Then, from the simple algebra go to the numeric applications.

[KarlInOhio]

On the other hand without an understanding that 427 - 316 is solved by first subracting 6 from 427, then 10 from that difference and finally 300 from that difference, the standard algorithm just becomes a confusing mess. I remember in my early grades (I forget whether it was first, second or third) sticking my finger on a number line and moving to the right or left to add or subtract.

If the students spend a week or two drawing jumps on a number line then I have no problem with it. If that ends up being their primary method or they spend months doing it then I do have a problem. One page in a workbook doesn't show which of those is true.

One thing I don't like is how this problem subtracts 300 first instead of 6, because the standard method goes from the least significant to most significant digits to handle borrowing properly.

[Monitor]

They're attempting to teach head counting *tricks*...

Which is a good skill to have.

...without teaching the *techniques* those tricks are based on.

And you know this as a fact because you've seen all of the previous pages of the workbook in question? Or are you just jumping to this conclusion without any evidence to back it up?