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I’m wondering about the importance of identifying and drawing points, lines, and line segments in Grade 4. Rays I can see as being useful for developing the concept of angle, though not crucial apart from the fact that the term is used in the Standards. The Progressions for Grade 4 don’t seem to shed much light on points, lines, and line segments either. In Grade 4 there seems to be little point to it all (pardon the pun). What is the purpose of these tasks?
Duane, does “these tasks” refer to 4.G.1? Would it help if we put references to this standard after:
“For instance, what series of commands would produce a square?” (p. 14)
“Given a segment on a rectangular grid that is not parallel to a grid line, draw a parallel segment of the same length with a given endpoint.” (p. 15)
Or does your question refer to the point of the tasks such as the two above?
The tasks of identifying and drawing points, lines, and line segments is what I am querying. Even rays, really. The tasks you mentioned from the Progressions would benefit from being referenced to the Standards. More importantly though, drawing can be completed using the everyday, non-mathematical understanding of “point” as a particular spot on the page (or screen) and “line” as a shorthand for “line segment”. In other words, differentiating between lines, line segments, and rays doesn’t seem necessary for turtle geometry or for drawing parallel lines. Knowing the difference may help at some later stage, but I can’t see it strengthening ability or deepening understanding in Grade 4. Is it all leading to something greater and in the immediate future for these students?
Also, when the students draw lines, line segments, and rays I assume it has to be something like this: http://youtu.be/JcqCf762y9w?t=2m2s
Is that correct?
Re figures: Maybe we need to include a few more figures in the geometry progression. There’s a figure of an angle on p. 22 of the geometric measurement progression and a figure of two lines on p. 23.
It will be up to assessment consortia about how to assess understandings about line vs line segment and angle vs two line segments with a common endpoint. The geometric measurement progression touches on the latter issue on p. 23 and may perhaps help to suggest why it’s helpful for students to understand angles as two rays with a common endpoint rather than two line segments with a common endpoint. And if two intersecting lines create angles, then students will need to understand lines as different from line segments.
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