Wednesday, January 20, 2016

Intro to the Coordinate Plane

I always had a handful of students that continually reverse coordinates or plot points incorrectly because they forget that a negative sign indicates going down or left.  So I designed a lesson that I was hoping would help students understand the importance of conventions in the idea of an ordered pair.

I told students that they would be on a mini-treasure hunt.  We blindfolded a student and sent them out of the room.  The rest of the class was charged with giving the blindfolded student directions to the "treasure".  For my class, I used a dollar bill and put it in the ceiling which conveniently had square drop tiles.  The class had to give all of the directions to the blindfolded student BEFORE that student was allowed to move.  

They brainstormed and came up with a plan to tell the student to walk 5 steps forward and 3 steps right.  Immediately they began to see some issues with the directions.  The blindfolded student took much smaller steps than the student that had measured the 5 and 3 steps.  The student was way off.  We had a discussion to decide where things may have gone off track.  After some more brainstorming, students decided to use the tiles on the floor as a way to track distance.  This required me to change the blindfold for a "You're only allowed to look straight down" direction to the treasure seeker.  This process allowed students to understand the need for a consistent interval when plotting on the coordinate plane.

We repeated a few times with success (I kept the dollar bill though!).  After two successes, we did the same, but I went into the hall and had the student come in through another door.  The directions the class gave were assuming we were going to use the same door as the last few times.  The class was upset with me because I was being "unfair", but it opened the discussion that if we were to give directions ahead of time, we needed to know WHERE to start.  Again leading to the understanding of why we always plot points starting at the origin!

The last twist was that I put a challenge to the students to give directions in as few words as possible.  They quickly reduced directions to something like 2 left, 5 forward.  Then I said, no words, all numbers.  Having familiarity with a number line, students were able to arrive at a negative for one direction and a positive for the opposite, but it took some serious prodding for them to get to the point where they understood that they needed to come to a consensus about WHICH number would come first.  This was exactly what I was looking for in terms of their coming to grips with the coordinate plane.  

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