Tag Archives: linear programming

Algebra II Files: Systems

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tl;dr: notes, homework, and study guides for solving systems, graphing systems, and linear programming

Ok, I’m in the mood to knock some more of these posts out.  See more Algebra II files and FAQs here.

As teachers, we divvied up some chapters a couple years ago to try and fancy them up, so some of this was found by my co-teacher and not made by me.  We were really pressed for time this year, so I had to cut out this intro activity that I had success with in the past (and, yes, it’s for Algebra I…don’t tell!):

System of Equations files from megcraig.orgDownload it here. I really liked this part:

System of Equations files from megcraig.org I like this idea of an introductory activity as well:

System of Equations files from megcraig.orgBut I can’t find the source so I don’t have the worksheet with points (although I guess I could make my own.)  Anyone recognize it?!?!? Please??!!?

We then do some formal solve with graphing:

System of Equations files from megcraig.orgOk, this is awkward…this file is so old, I don’t have a blank version on my computer!  But you get the idea. 🙂

No notetakermaker for solving systems by substitution or elimination (we take them on our own paper or else it gets a wee bit scrunched).  But here’s a tip: talk about substituting is just like substituting a player on a team because (1) some players are more beneficial are certain times in the game (ooh, I just thought of this…do the players have to also be “equivalent”?  As in, I assume you substitute a defensive player for another defensive player?) and (2) you can’t have both players on the field. That seemed to help so struggling students not substitute y = 7x + 2  into 3y + 9x = 8 as “3y(7x + 2) + 9x = 8.”  Also, it makes me seem like I know about sports. (Obviously false.)

Some homework:

System of Equations files from megcraig.orgFile here. And in case you need some word problems:

System of Equations files from megcraig.org

File here. And some linear inequalities systems:

System of Equations files from megcraig.orgFile here. This is a fun worksheet to assign for homework:

System of Equations files from megcraig.orgDownload here.  You have to shade the correct portions to make a path!

Let’s stop here and have a quiz, eh?

System of Equations files from megcraig.org

File here. Then Linear Programming, which, to be honest, there are 1,000 things out there that are better than what I have.  For example, Fawn’s Funky Furniture .  It seems Steve had a similar idea and made a worksheet. Let’s all say hi to Steve!

System of Equations files from megcraig.orgSo here’s an idea that sprung from someone scheduling an IEP meeting during one of my Alg II classes one year. I certainly couldn’t waste a day (since I would be seeing all the rest of the classes) and I certainly couldn’t leave them to “discover” linear programming with a sub. So I made these notes instead and gave that period filled-in copies.

System of Equations files from megcraig.orgFile here. I’ve kept doing this as a day’s worth of notes because it makes the next day of introducing linear programming much less stressful!  We’re not trying to graph more than two inequalities (new), finding possible max/min values (new), and plugging them in to find max/min (not new, but not common) AND read these really long word problems (scary), come up with constraints (new) and objective functions (new) all on the same day!

Here’s the next day:

System of Equations files from megcraig.orgSystem of Equations files from megcraig.orgPg 1 file here Pg 2 here.

And some more practice. I usually have them do this in pairs.

System of Equations files from megcraig.orgFile here. Warning: #4 is a doozy!  Sometimes I count this as a quiz (but I assist and they work together and I don’t tell them until the end), other times we solve some  three-variable equations and have a bigger quiz.

System of Equations files from megcraig.orgFile here.

I’d really like to find some linear programming problems where the answer isn’t just where the two slanted lines intersect.  And by “I’d really like to find” I mean “does anyone want to provide me with.”

I feel this chapter is kind of meh. The first half they’ve already seen before and about half are great once we refresh their memories and half consistently struggle. Maybe this year it will improve because we’re going to do it at the end of all the different types of equations and focus on the graphing aspect a bit more.  Basically I want to do what Jonathan did.  Any other suggestions would be more than welcome.  🙂

Sunday Summary

3 things to share

1. Man, don’t you hate it when you figure out a better way to teach something the day after you teach it?  Although trig equations went pretty well this year (well, we’ll see tomorrow on their quiz), I think next year I will structure it differently. Here’s where we started:

CaptureCapture2Next year, I’m going to start at the end with the calculator/desmos, with a -4π to 4π window to discuss the general form.  Then do some examples with θ between 0 and 2π, then non-calculator examples.  Then on day 2, graph 2θ (or θ/2) on the same graph to discuss getting more/less answers.  If you’d like to modify this for me (doesn’t hurt to ask, right?), or if you want to use it as is, here is the .doc file (with bonus homework at the bottom!)

2. Now, day 2’s note-taker-maker, I’m kind of in love with. (ok, technically this was day 3 because I ended up teaching day 1 slowly)

Capture3The only thing I might change is super-reinforcing the ZERO product property rule is not the “ZERO or sometimes 2 or 3 or -7 product property rule” because some of my students are still having issues with that. (btw, Snoops is dancing because it’s already factored.  Also, it is super fun to have a kid ask later, “How can we solve this?” and you reply, “Cute and cuddly, boys!”  File link.

3. I finally figured out about 3 years ago how to make linear programming less painful…get the mechanics of it out the way first!

Capture4Let them spend a day finding the feasible region, vertices, and max/mins.  Then the next day you can focus on the finding the equations from those long scary problems and the rest is the same as these notes.  Much less stress than trying to introduce all of it the same day.  File here.

2 good books I’ve been reading

We took a quick weekend trip to Chattanooga last week where I started David Benioff’s City of Thieves and could not put it down!  It’s like a buddy cop movie set in the absurdity of World War II.  It reminded me of Anthony Marra’s Constellation of Vital Phenomona, one of my favorite books of the last few years.



Hector Tobar’s Deep Down Dark is the reason I haven’t gotten anything done today!  How did he make this so compelling when I already know the outcome?  I’m about to go draw a bath and try to finish it tonight; it’s such a page turner!  And don’t worry, he does a really good job making sure the reader doesn’t get lost with all the people in the story (I’m horrible at remembering names in both book and real life.)


1 thing I’m meh about

I have to write a unit plan about complex, polar, and parametrics using some premade lessons (and adding others as I see fit). The premade lessons are really expecting a lot from our students and I’m not sure if I will get the outcomes desired by using them (unless the desired outcomes are tears and frustration).  But I’m having trouble finding a lot of great stuff that I can easily replace them with (I have a few things thanks to @mrdardy and @crstn85).  So if you have some cool stuff to share, please do so!  The state of Alabama will thank you!