As a middle-school math teacher, I have seen many students who do understand abstract concepts, and even enjoy learning about things like Pi and the Pythagorean Theorem, but who appear to be unable to do so due to a weak grasp of math fundamentals.
Subtract 1- or 2-digit number from a 2-digit number with/without renaming
For many middle-school children, math is a real challenge. It is at this age that the concepts begin to get more abstract, and work goes beyond "concrete" ideas like adding and subtracting. It's no surprise that at this age, math can become something the student avoids, or begins to dislike.
For example, since I want to make sure my students get accustomed to reviewing the various math concepts and standards we've learned all year, I have them practice regularly. I want them to get to a point where they are so familiar with grade level math content, that solving these types of problems becomes automatic.
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