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I’m thinking most of the formulas expected to be memorized can be related to a variation of bh: (1/2)bh, (1/3)bh, average 2 bases for a trapezoid (or calculate two triangles), and b is the surface area of the base when calculating volume…with the main exception being circles…?
Awhile back, we had a hierarchy of curriculum topics: review/mastery/introductory. I’m thinking that once we get the progressions firmly nailed down, a hierarchial list might help clarify questions like these in such a way that “eventually” is set up to happen.
I’m thinking that the complexity question would depend on the students we teach. I like the idea that “A student who avoids them entirely by always converting them to a/b form is doing just fine.” That tells me I would need to make sure every student mastered that much, but I would also want to raise the bar for those who are capable, including higher complexity in our discussions and assigning challenge problems.
