Connections to Visual Patterns

I decided to stop drinking coffee a couple of days ago.  You'll never believe this... but I feel a little less productive these days.  Yesterday I thought I was going to cry around 9AM, but I held it together like a big boy.

In my last post I was left wondering what I was going to do about kids messing around with slope while they draw.  For instance, if they write 2y=x as opposed to y=1/2x, how am I going to handle that?  I want to steer them away from 2y=x because I'm afraid it may cause confusion later (not that they couldn't grasp it... but I'll address it when we're solving equations).  Thanks to a comment from Mike in my last post, I was reminded about orchestrating a discussion.  As they're working on their drawings and playing around with drawing slanted lines... I will watch for kids writing them in different forms and use them in a class discussion.  I'll stress the idea that if we all write our equations in the same format, it will be easier for us to communicate with each other.  Put a note on your refrigerator to check the blawg out around August 10, 2017 and you might find a post about said discussion.  Thanks for the help Mike!

Here's where I'm at today.  Once they've drawn their picture or logo... I hope they'll have a pretty good idea about the following:

2017-05-09_1137.png

1.  the number in front of x controls the steepness of the line

2.  the number they add or subtract at the end moves the line up or down

My next question.

What's the best way to connect using linear equations for drawing with using linear equations to describe situations?

My answer.  Visual Patterns.

My next next question.

What's the best way to use visual patterns to teach this?

This shouldn't be too difficult, right?  I have always used number tricks to start my linear units... which is awesome for solving equations, but it might not be the best idea for starting linear units, hence the reason for this blog.  I'm going to do some linear visual patterns and see what brilliant ideas I come up with.

 

CRAP

I'm afraid I might be going down a rabbit hole, now that I think about it.  One of the problems with planning alone.  What if going to visual patterns is NOT the best way to go next?  What if they want to know WHY the number in front of the x controls the steepness?  I have awesome lessons for this.  Should I go there?  Or let that come out through the visual patterns?  This is hard.