Proving Lines are Parallel

So I am thinking about Open Middle problems, transformations and parallel lines.  As an 8th grader, is there more than 3 ways to “prove” two line segments are parallel?


Method 1: Slope

Parallel Lines1

Slope of line a = 2/5, slope of line b = 2/5.  Since the slopes are equal, they are parallel.


Method 2: Line of Reflection

Parallel Lines2

Find a line l so that when you fold on that line, line a and line b match up perfectly.


Method 3: Translation

Parallel Lines3

Find a Translation where every point from line a will map to its corresponding point on line b-> (X+4, Y-2).


(Method 2 and 3 may not be as formally worded here, just trying to anticipate possible student answers)

Reflection Forms, I want them!


I know there are not a lot of people following me or reading this blog yet, but I would like to ask those that are to respond and reach out to your contacts to help me out. 

I am looking for different types of reflection forms.  I want to know what students are thinking and learning in class.  I need valuable input so I can adapt to my student’s learning on a fairly regular basis.  I have a few different ones of my own already, but I also would like to hear what is working well in your classrooms.



What is a linear function?

So today we are reviewing Linear Functions; and when asked what those are, I get a textbook-like explanation.

“It is where each x only corresponds to one y and graphs a straight line.”  Another student asks, “What does that really mean?  How does it even relate to what I would do when I’m done with school?”

I will post later on how my conversation went, but I’d like to hear your ideas before I give away any secrets.  (For reference, I teach 8th grade students in a public school on the reservation with high poverty rates.)