Monday, December 14, 2015

Writing Linear Equations, Domain, Range, and Desmos

My students in Algebra 1B have learned and tested on writing linear equations.  They did rather well, but I'm not ready to give it up just yet.  Every year this is what happens:  the students can write linear equations given certain information (slope and point, two ordered pairs, etc.), we learn something new, and then the students can no longer write linear equations.  I see you nodding your head.  It happens to your students too, right?

So, I wanted to stay here a little longer, but change it somehow.  A few things happened at once.  I wanted more, the Algebra II teachers here were frustrated with their student inability to understand piecewise functions, and I saw this:

Click here for the link.

Image from "Reflections of a High School Math Teacher"

It's a maze!  How cool is this?!?!  It's exactly what I was looking for:  more practice for my students with equations (and domain and range for that matter) and it will help the Algebra II teachers when they go to teach piecewise functions.

Days 1 & 2: Desmos Activity

In order to prepare my students for this maze activity we've been writing equations of line segments.  I created a desmos activity for us to work through as a class.  Here is the link to the desmos activity.  

The desmos activity is infinitely better than paper and pencil practice because of the immediate feedback.  In the activity, I graphed two ordered pairs and the students are required to create the line segment that will connect the two points.  They first write the equation, then restrict either the domain or range to make the endpoints.  The students could instantly determine if they were correct just by looking at their graph.  THANK YOU DESMOS!!!

As predicted the students didn't remember how to write the equations.  "How do I even find the slope?"  "What is the second number in the equation for?"  The good news is that they remembered quickly with a short explanation.

Day 3: Card Sort

After working through the desmos activity (it actually took us two days) I felt that we needed a stepping stone between desmos with its immediate feedback and paper and pencil that doesn't have it.  So I created a card sort.  Here is the link to the card sort.
Some advice on creating card sorts:  Copy each set of cards on different color paper.  This makes life easier once class is over and you find a card on the floor but you don't know what set it belongs to.
This was a hit.  The students like the hands-on appeal of this and it seemed to be right on level with their knowledge so far.

Next we completed a worksheet on creating the equations to make given line segments.
I was not in school the day they completed the worksheet (I was at the IU) and that didn't go well.  I needed to really walk the students through the process when I came back.

Next I had the students work through this maze that I created on desmos.  Click here for the maze.
I was not impressed.  The students were so needy throughout the whole process.
"How are we suppose to find the equation if there is no line?"
"I don't understand what I'm supposed to do."
"Mrs. Oswald, basically sit next to me and tell me exactly what to do."

I really wanted to cry and/or pull my hair out.  Really?!?!?  None of you understand how to complete a maze?  Not a single one of you?  It was awful.  I understand why many teachers just want to stand up front and lecture.  It's easier, the students understand this, it's less work for everyone involved.  I seriously thought about doing that for the rest of the year.  These activities are really starting to wear on me.  Not the activities, but all of the whining.  But then a student raises his hand and states that he's finished.  What?  He did it?  He did it!  Then she did it!  Then another, and another.  And before I knew it at least half the class was able to complete the maze.  Whew!

There were still a few students who said the activity was dumb, that it made no sense at all, when are they every going to need this.  Ugh!  But I reached a few.  And those students felt like a million bucks.


  1. Well, if it is any consolation, I enjoyed making 3 line segments, then two pieces of parabolas, then one cubic to solve your maze.

    Anyway, sorry to hear about the frustration. Do you have hypotheses about what is going on? Some ideas:
    (a) kids aren't used to these types of activities and are pushing back
    (b) most kids are getting it, but vocal minority are vocal and that gives their negativity a disproportionate amount of weight
    (c) they really don't get it
    (d) something else?

  2. I'm collecting posts about the desmos activity builder, which I also love, and I've added yours, but I can't find your name or twitter handle (if you're on twitter, which I hope you are), so if you'd like to complete the info, here's the link:

  3. Sorry, nevermind, I just woke up and realized all that info was already on twitter. Facepalm.