Camera 1... Camera 2...

Sometimes I think planning a big unit like this is a lot like Wayne looking at Cassandra in Wayne's World... I'm constantly looking at the same ideas from different perspectives and it gets confusing.

image via

image via

When I was little, I used to do this a lot.  I was baffled as to how the perspectives changed.  Now, the only thing I notice is the vision in my left eye is getting worse than the vision in my right eye.

I've been planning the next little section of the unit, which was connecting the creative vs. descriptive aspect of linear equations.  Particularly through visual patterns.  I keep finding myself looking at a calendar and asking myself, "Will they KNOW that yet?  Wait... should I review that MORE?  What if THIS happens?  What if THAT happens?"  Here's what I mean.


Can they simplify?

One thing I want to make sure they grasp, is that no matter how they see the visual pattern, we can simplify their expressions and show that they're the same as someone who may see it differently.  Which made me panic a little bit... the last thing I want is to expect that they CAN do it perfectly, only to find out they'll need review (which they will).  So how do I add that review in to the daily schedule?

Below is the basic framework for our daily routines.  Number talks on Monday and Tuesday.  Visual Patterns on Wednesday and Thursday (block days) and Friday.  I have a "Quick Review" topic every week as well.  Where I put up ONE calculation problem and we focus on precision.    I figured during the first week of this unit I would review simplifying expressions, so that by the time we're actually doing it in our visual patterns work, it won't be so scary.  I also have to review integer and fraction operations in there somewhere...

As I looked at the planning from a broader perspective I started remembering all of the Desmos activities I meant throw in there too... like Battle Boats and Marble Slide.  Where the hell am I gonna find the time to do THOSE?  (Battle Boats will have to come BEFORE we actually start drawing and Marble Slide will come at the END of the 3D letters but before I make the connection to visual patterns)  This part of the planning stresses me out a little bit.  So I need to find a better way to handle it.


Here's the notes and drawings I've made with some visual patterns.  I'm asking myself this question as I work.

  1. What's the best way to explain the y-intercept at this point?

I think connecting slope will be fairly easy to show.  I'll show a slope of 2 one day and a slope of 3 the next.  I don't think that will be too hard for them to see.  When it comes to the y-intercept (and I could be overthinking this) is it better to illustrate it like the drawing on the left or the right?  Like most things, I need to be flexible here and ready to illustrate it a number of ways.  More importantly, I need to be ready for what they're gonna throw at me!  



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:


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.



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.


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.


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

Where Do I Begin?

- 1 hour of work -

I figured I would start by writing every topic I thought I would need to cover on a sticky note.  Then I could rearrange them, put them in order, add to them, make subcategories, or whatever it is people do when they plan these things.  It took me an hour.

I'm lying a little bit.  I was just trying to do what cool people do on their blogs.  This is what it really looked like.

Can you sense the never-ending stream of rabbit holes this sent me down?  It's just one thought after another and another.  The details are getting in my way and stressing me out.  I find myself thinking about this unit in terms of MONTHS and a second later in terms of MINUTES.  

To alleviate this stress, I think I'm gong to plan out the first couple days of this project (fairly detailed) to see if anything brilliant comes.

Developing a Project-Based (desmos) Linear Unit

I avoid projects like the plague.  

Coming up with deadlines, checking out a computer lab, grading the damn thing, dealing with absences, realizing my students don't know nearly as much as I thought they would... all things I loathe.  Do you know what it's like to have an 8th grader ask you how to graph a line in May?  It's something close to, but not entirely like, teaching a kid to dig a hole for 8 weeks and when given the task to dig they ask, "Do I dig up or down"?

I am ahead of the game this year, so I decided to try a desmos/linear art project.  Find a logo/picture you like, create a picture of it in desmos using linear equations, etc.  If it goes horribly wrong... no big deal.  

Here's what I noticed after Day 1

1.  This kid did more learning in one hour than the past 6 months.


That was enough for me to stop and take notice.  Next year will be different.

Teach an entire linear unit through this project.

Typing that out made me start shaking a little bit.  Where in the hell do I even begin?  What kind of questions will new 8th graders wonder about?  Where will they get stuck first?  Do I check out the computer lab for a week?  2 weeks?  Can they do it on their phone?  Should I cover vertical and horizontal lines first?  Do they even know what desmos is?

All I know is, I cannot, and will not, do another project at the end of a unit.  They forget what they knew (or what I thought they knew) and in the end... that tells me more about me, than my students.  Let's change it up.  I'm gonna start the unit with the project.  I'm gonna teach the unit through the project.  

I'm having a panic attack justing thinking about it.  This blog will document said project and panic.


I don't know what I'm doing...

I have this reoccurring nightmare that some mystical math person from the district main office walks into my room, watches me teach for awhile, then figures me out.  


After 12 years of teaching middle school math... I'm slowly starting to believe that maybe I know a little bit about this emotional profession.  

Today marks the beginning of a new chapter for me, professionally, as I try to blog.  

I'm not a writer and I still don't know what I'm doing.