Reflection: Connection to Prior Knowledge Construct Parallel Lines Through a Point Not on the Line - Section 4: Construction: Construct Parallel Lines

 

Throughout this unit, I have had to continuously remind myself that I cannot simply offer steps for how students should perform each construction.  Rather, I have to stay true to my belief that giving them time and space to tinker around with their ideas and conduct small experiments will result in a sound constructions method that they can defend with their own reasoning.  This is, for example, how we were able to discover two methods for constructing a perpendicular through a point (“the isosceles triangle method,” where we start the construction by making one arc that intersects the line in two places using the given point as the center, and the “kite method” also known as “Tony’s method” where we place two points on the line and use each of these points as the center of two different sized arcs that will intersect the given point to start the construction.”) 

 

I decided to give students a few minutes in their group to try to think about what tools they had for thinking about parallel lines.  I circulated the room, listening for students’ ideas about the types of angle pairs that had to be congruent for lines to be parallel and shared these ideas with other groups as needed.  Ultimately, students were able to use corresponding, alternate interior, and alternate exterior angles to construct a line parallel to a given line through a point.  Students haven’t yet shared (or discovered?) the idea that if two lines are perpendicular to the same line, they must be parallel, but I’m eager for them to see and construct this idea soon.

  Giving Time and Space to Make Connections to Prior Learning
  Connection to Prior Knowledge: Giving Time and Space to Make Connections to Prior Learning
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Construct Parallel Lines Through a Point Not on the Line

Unit 5: Constructions
Lesson 5 of 11

Objective: SWBAT to construct a parallel line through a point not on the line using at least three different methods.

Big Idea: By making connections to the last unit--angle relationships--students will make sense of how they can perform this construction.

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Subject(s):
Math, Geometry, modeling, Constructions, compass and straightedge
  110 minutes
construct parallel
 
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