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Are students expected to identify triangles specifically as equilateral, isosceles and scalene? If so, what standard/grade level does that appear?
There is no specific expectation, but the standard
4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
represents a starting point for this sort of activity. And by the time students get to Grade 7,
7.G.2. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
they would probably be familiar with these terms. Here, as in many places, the standards avoid a list of terms and describe the mathematics directly. And indeed, not all the terms you ask about equal: “scalene” strikes me as much less important than the other two, for example.
Just to add a little more to the discussion: this topic was chewed over quite a bit on this page: http://commoncoretools.me/2012/06/27/le-nouveau-elementary-geometry-progression-est-arrivee/
Brian Cohen highlighted how page 14 of the Progressions lists side length and angle measure as two ways that triangles can be classified and even cross-classified (e.g. right isosceles triangle). Brian finished with a question to Bill, “To be clear, classifying triangles by side lengths would be a “natural extension,” but not required by the standard (with exception to “equiangular,” for the reason you state)?”
I too have this question.
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