Parallel and Perpendicular Lines

Bleh. I don’t know of a clever way to teach parallel and perpendicular lines. I’ll try asking kids questions and maybe their answers will guide me and make me look smart until 2:50 p.m.

Me: Using your arms, show me parallel lines.

They do. One boy clasps his hands together like he’s praying.

M: What do you know about parallel lines?

Students: They don’t touch. They don’t intersect. They don’t meet.

M: Okay. Please draw this line in your journal. We’re all drawing the same line, so make sure yours also passes through the points (0,-2) and (4,0)… Now, draw another line that runs parallel to the first.

I walk around the room and see that most of them have drawn pretty good “parallel” lines, not perfect.

M: How are you going to convince me that you drew parallel lines?

No one is talking. One kid has his hand up, but he’s repeating algebra this year, so I ignore him. Poor kid is used to me ignoring him. His mother is adorable — and a friend of mine — and she ignores him sometimes too. Finally…

S: Check the lines?

M: What do you mean? How?

S: Extend the lines to see if they’ll meet.

M: Extend until…? China? Where are we going?

S: The lines never meet!

M: So how do I check that? I need a way to check for parallelity. You say they never meet. Never, like infinitely-never-kind-of-never? I don’t know how to check these infinitely long lines.

I’m stalling here. Say something smart, kids, so your clueless teacher can learn. I put my arms out, moving them together across my head like I’m doing a rain dance.

S: Measure the angle. Find the slope. Use a ruler.

M: Okay, let’s find the slope because we know how to do this! So, find the slope of both lines. Don’t talk to me again until you’re done.

Jonathan: You can’t die, Mrs. Nguyen. The Ducks would have one less fan.

M: I said don’t talk to me. What are you talking about? Who’s gonna die?

J: Remember you said that at the beginning of the year that if the Ducks lost a game, you’d die?

M: I do love you, Jonathan. Now, be quiet. Find slopes.

Jonathan draws the Duck mascot for me often, on his homework, corner of his test, on the big whiteboard. He also interjects random comments regularly.

The kids start talking, their heads nodding one by one, and they make this bold claim that parallel lines have the same slope. They say, “Let’s do it again!” So we do it again. And again. After drawing three sets of parallel lines and finding their slopes, they tell me that parallel lines have the same slope. Hmmm.

1

They seem happy and gullible at this point. Best time to take advantage of them.

M: Show me your arms again. Wave them. Twist your hands like this. Do this… then this…

These kids kill me. So damn funny. They are like monkeys, doing everything I’m asking.

M: Okay, using your arms, show me perpendicular lines.

Yikes!!!!! Maybe, just maybe a fourth them show me arms crossed at right angles. The rest of them have no arm muscles.

M: What are perpendicular lines?

S: They cross. They intersect. They cross at right angles. Like an X.

So I put my arms up, crossing them like an X, but intentionally nowhere near ninety degrees.

M: Like this?

S: More straight. Like this. Yeah, that’s it!

M: I heard right angles. Is that true?

S: Yes.

M: Draw me another line, please. This one going through (-2,0) and (2,1). Then, I need you to draw, as best as you can, a line running perpendicular to it.

Holy cow. Even the kids who say the words “right angles” and “ninety degrees” draw nothing near that. But one student, after I look at five others’, does have a good sketch, so I show it to the class.

M: C’mon now. Please try again. Then what should you do after that?

S: Find their slopes!

Here’s one student’s attempt at drawing perpendicular lines. But you can see her second attempt is better.

2

(The first line has a slope of 1/4.) Unfortunately the kids who do have a decent looking “perpendicular” line find the slope to be 4 when it should be -4. Again, we do a total of three sets of these. They describe the two slopes: opposites, inverses, flip around, reciprocal, upside down. I don’t really care what they call the relationship right now because when I give them a line having a slope of 3/7, they know the slope of a line perpendicular to it is -7/3. They know when one is -8, the other is 1/8.

Everyone draws the same original line together. But instead of trying to draw the perpendicular line to this (like we did on that first round) — a difficult task to perfect via eyeballing — and then find the slopes of both, I ask them to find the slope of the original line first, then find the perpendicular slope, then use this fact to draw in the second line. They think it’s cool that they can start the second line using any point on the coordinate plane.

I’m saved by the bell. And I think know this is still better than my just telling them.

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