Reflection: Checks for Understanding Prove Slope Criteria for Parallel and Perpendicular lines - Section 4: Assessment


When I taught the section on proving the slope criteria for parallel lines, I thought I done a very thorough job of laying out the rationale for the proof, modeling the algebra required to complete the proof, and providing clear reasoning. I made sure students had good notes and I also explained things verbally. So I figured students would take their notes home and study and then be prepared to do well on this topic on the unit test.


I was disappointed to find that students generally performed poorly on this topic on the unit test. Many students had no idea how to derive the formula for the x coordinate of the point of intersection. They literally left the problem blank. Several others could give only a superficial explanation as to why x=(b1-b2)/(m2-m1) ==> the lines are parallel only when m1 = m2. They used very general language like when m1 = m2 it (what?) is undefined which means the lines are parallel. They left out the fact that x is the x coordinate of the intersection and if x is undefined, there is no intersection, which means the lines are parallel. This is what I would have wanted all students to explain.


Many other students wrote things like, "We know that parallel lines have the same slope because if they both rise and run the same amount every time they'll never touch."


What I realized when I was looking at these summative assessments was that I did not do an adequate job of conducting formative assessment and check for understanding. I had assumed that students had gotten it or, knowing that they would be responsible for understanding the proof, that they would take time outside of class to really understand it, but I was clearly wrong in that assumption.

I should have given a formative assessment such as the one that has now been included in this section. That way, I would have known how well students had understood and I would have still been able to intervene before the summative assessment. 

  Can't assume they've gotten it
  Checks for Understanding: Can't assume they've gotten it
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Prove Slope Criteria for Parallel and Perpendicular lines

Unit 9: Analytic Geometry
Lesson 1 of 7

Objective: SWBAT use analytic geometry to prove that non-vertical parallel lines have equal slopes and perpendicular lines have opposite reciprocal slopes.

Big Idea: X-Games?? In this lesson, students are gettin' extreme on the slopes...of parallel and perpendicular lines that is.

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perpendicular slopes
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