G-CO.1

[scottlape]

I am trying to write multiple-choice questions to test this standard. But I don’t know how to use “the undefined notions of point, line, distance along a line, and distance around a circular arc” to develop “precise definitions of angle, circle, perpendicular line(s), parallel line(s), and line segment.” I can make some reasonable guesses, like a circle is the set of points a certain distance from a given point, a line segment is a portion of a line between two given points on the line, two lines are perpendicular if they subtend a quarter of a circle… but I’m just shooting in the dark.

I would love to see the precise definitions that this standard refers to. Do they exist anywhere on paper? Any suggestions or thoughts would be greatly appreciated!

[Bill McCallum]

Here’s the standard in question

G-CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

These definitions will eventually be in the geometry progression, when it comes out. For perpendicular line, I would say that two lines are perpendicular if the adjacent angles formed when they meet are congruent. (Or, perhaps you have already defined right angle this way, and then you say they are perpendicular if they meet at right angles.) Your definitions of circle and line segment sound fine to me. There a couple of different approaches to defining what an angle is, depending on the stage of development. One possibility is to define it to be the region between two rays emanating from a point. This is pretty nice conceptually, but people might find it weird for an angle to be a region. You can also define it to be the two rays, but then you have to specify which angle you mean, then one that is less than or equal to 180º or the other one.

[countteach]

Scottlape,

H. Wu from Berkeley is a hero of mine when it comes to understanding the mathematician’s approach to teaching mathematics.  Search for his article, “Teaching Geometry According to the Common Core Standards.”  He answers your question.

[scottlape]

Thanks to both of you for taking the time to reply to my question. I’ll look forward to reading H. Wu’s article.

[Author]

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