Ride the Line...A Game for Parallel & Perpendicular

Last week we were investigating linear equations....in particular what parallel and perpendicular lines look like as equations, not just graphs.  When you do all the graphing by hand or even on a handheld graphing calculator, this is pretty slow.  Also the Common Core calls upon us to provide more discussion oriented kinds of learning designs....we're incorporate a bunch of the mathematical practices here---reason abstractly, construct viable arguments and accept feedback, model and use tools to investigate math ideas.  I'd say that this is a CCSS home run.

I tried a different learning technique, so in honor of #msSunFun this is my game contribution.  I give all credit to the Moving Straight Ahead ACE questions for Investigation 4.  I took one of their questions and expanded it into an investigative game.

So we jumped over to one of the free online graphing calculators.  Here's how we started the game.... Step 1:  I entered an set of equations into the calculator and show the resulting graphs of all those lines.  Students were able to immediately see the connection between the equations and the graphs.

I had them look for patterns in what the equations must look like in order to create a pattern of lines that looked like this.

They were quick to see that the coefficient on all the equations was the same and had the same sign.  And I encouraged them to come to the SmartBoard and check their conjecture (which is our new favorite word since we're trying to be very Common Coreish!)

Step 2:  We repeated this for learning perpendicular lines where I entered a set of equations and showed the resulting graphs for that set. 

This gave them more trouble.  The biggest hurdle we had was that kept calling the reciprocal the opposite.

So they tested out their ideas again.  The first thing they uncovered was that to make the line perpendicular didn't involve the reciprocal....it involved the negative reciprocal.

Step 3 :  Pause the game for just a second and do a mini-lesson on negative reciprocal and multiplying to get -1.

Step 4:  Resume the game.  This time I pulled name sticks and students would come up to author the first equation.  We encouraged people to be as wild and crazy as they could imagine.  So we had some real whopper equations.  Another stick was pulled and the next person got to specify whether the new equation was going to be parallel or perpendicular.  The next person got to specify where it hit on the y-axis.  And the last stick determined who had to write the next equation with all these conditions.

I literally sat at my desk and watched it all happen right before my very eyes.  Students would be yelling and screaming as people typed in their ideas....but we didn't allow anyone to reveal that there was a mistake until they had a chance to test their equation.  If they didn't know why it didn't work, they could get an "assist" from an audience member.   Everyone practically killed themselves to be the expert assist.

The best part here was not only the engagement, but the fact that we "tested" everyone's idea...rather than me telling them if they were correct or not.

Step 5:  Continue until everyone is exhausted or they yell "uncle"!  Honestly after a half hour practice, they were parallel and perpendicular equation/graphing pros.

I also had a lot of fun asking them to make something both parallel and perpendicular....and they realized if we had graphed more than 2 equations that other lines would be both.  That really sent them over the moon.

I know this isn't exactly a game.  But it is fun and creates a game like atmostphere.  It is very effective in teaching these properties, students practice what they know about learning the y-intercept and it also gives enough practice in these ideas that students really anchor the concepts into their thinking.

 

Comments

[Debi]

What is the grade level and CCSS mathematics domain and standard/s for this lesson? Thank you for posting it!

[Marsha]

I use this with my 8th graders.

CCSS.Math.Content.HSG-GPE.B.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

It's a starting step towards being able to do this.