A Picture's Worth a Few Ideas

- 2 hours-ish of work -

I like to hunt down my friend Matt at school everyday and bug him with math ideas which led us to this drawing yesterday.  There's lots of good stuff on that board... but let me tell you how I got there first.

Like I said in my previous post, I was going to start planning the first couple of days of this project to see where it took me.  This is what it looked like.

bad idea

I don't know if it was or not... but it was hard to keep track of where I was and where I was going.  See that little note to myself in the upper left-hand corner?  "Quit thinking about this as each lesson but more of a flow map."

baby steps

Once I switched to a flow map, it started flowing a little better.  Imagine that.

introduce the project (draw a picture in desmos - they will have choice, but only of pictures with no slanted lines) > battle boats with desmos for review (start thinking about x's and y's) > start project > have kids figure out how to draw horizontal and vertical lines (they will) > teach them how to restrict the domain and range > finish up their picture

the big thing

I have no idea what kind of pictures I will have them draw yet, but I was imagining something like that "E" over there.  Drawing it with block letters is all horizontal and vertical lines.  Adding some slanted lines will make it a "3D-E"...

13 year old mind = blown

The "big thing" is where I got stuck... which leads me back to the whiteboard with Matt.

How do we talk about slope at this point? 

Here are the ideas came to mind.  

  1. They should understand slope and y-intercept in slope-intercept form before moving on.
  2. They should understand slope in point-slope form before moving on.
  3. They should just play with x's and y's and see what they come up with.
  4. I should give them the slope-intercept form and tell them to play with the numbers in front of x and the number at the end to make the line work.

My gut tells me to go with #3... but I'm kind of afraid of a kid doing something like 2y=x.  We obviously can work with this, but would this make it more difficult for them later?  My other gut tells me to go with #4.  What's the harm?  Or maybe it's both?  At this point, I don't really care if they really understand what slope is.  I just want them to see how that number in front of x affects the line and how that number on the end makes the line move up and down.  I want a neurological connection between whatever parts of the brain do those kinds of things.  

I think this is good enough for now.  I will revisit this idea later.

that's interesting man...

I kind of like this part of the whiteboard picture because I was wondering, if y= makes horizontal lines and x= makes vertical lines... would it make a slanted line if you mixed them together somehow?  Matt looked at me like I was crazy.

NEXT!

This is how I'm going to tie what equations look like to what equations can describe.  More on this later...