"Knowing" and "Understanding" (2)

Students who sufficiently "understand" how to find the area of a trapezoid can also respond to the question "Why does that formula work?"
In order to explain the answer, they try to recall the concept of "parallel" and "height," how to find the area of triangles and squares, and general strategies of decomposing complex figures into simple figures. Then they combine them to construct a consistent explanation as a whole. Of course, they can correctly find the area regardless of the orientation and size of the trapezoids presented.
"Understanding" something means that you can give an explanation for it by associating individual facts and concepts you know with each other.

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