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!):

I like this idea of an introductory activity as well:

But 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:

Ok, 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:

File here. And in case you need some word problems:

File here. And some linear inequalities systems:

File here. This is a fun worksheet to assign for homework:

Let’s stop here and have a quiz, eh?

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!

So 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.

File 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:

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

File 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.

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.  🙂

Precal Files: Dude, I Could Trig All Day.

tl;dr: Files for unit circle, graphing trig, and inverse trig functions.

So I’m going to post my precal files in the order that I taught them (see more of my precal files and FAQs here).  I met with a PreAP curriculum committee at the beginning of last school year, and they suggested that we do all the trig stuff in the fall, then go all the way from functions -> quads -> polys -> exponentials -> rational -> limits -> derivatives in the spring. It did work really well in the spring, but I need to do better at spiraling back to trig–I have a fear they won’t know what sin of pi is next August!

Ok, are you ready?  Here we go!

Starting with trig values at a point:

Then angles review, but I think I like the worksheet from Algebra II better.

Then the unit circle review:

File here. We also talk about the hand trick.  The hotmath at the bottom is for one of the better trig value flashcards website I’ve found.

The next day we expand past 0 and 360:

I use a worksheet from an Algebra II/Precal joke book for homework (which I just learned is frowned upon? I must say that these are usually well done and have some good questions that catch conceptual errors).

Then it’s time for one of my favorite group work worksheets, (that I already wrote about here):

At this point we stopped, reviewed, and took a small quiz.

Then it’s onto graphing. This is about the time I first learned about the windowpane method, so I taught some classes one way, some the other, and some both. This shows the window pane.

File here. This should have gone faster, but took over a day. The graphing from scratch at the top was like pulling teeth.

This is their practice/hw, which shows the old way of marking the graph into “exciting points”

Then we did a real life sine problem from Math Teacher Mambo.

Here’s her post on it. Be prepared: it looks like a cosine graph so they all wrote cosine equations because who reads directions?  Then I had to tell them to actually read #7.  Next year, I may have them choose whichever function they want, then make the last question be “convert from sin to cos or cos to sin.”

Next, cosecant and secant:

File here. I teach cosecant and secant graphs using a suggestion from a student: we sing “The Grand Old Duke of York,” since when you’re up, you’re up, when you’re down, you’re down, and when you’re only halfway up, you’re neither up nor down (asymptote!).

Ugh, tangent graphs.

File here. This is another example of the “exciting point/pattern” method of graphing, which looking back, I think I like better. Or maybe I need to come up with some hybrid.

Then, because it ties in so well with graphing, we did inverse trig functions in this unit.

File here. Even if you’re not a homework gal or guy, you may still want to use those last 3 problems as a lead-in for the next section

File here. Although next year I want to spend more time on the even/odd/unit circle-ness of sin/cos to discuss, “ok, well, we can’t use 4p/3 in the allowable region for cosine, but what angle in the allowed region should have the same cosine value?”

File here. *Note! The answer to #17 should be pi/3, not 2pi/3! It should be fixed in the file. Thanks to Chikae for spotting that!

Study guide time!

File here.  And, yes, it comes complete with review powerpoints (that could also be used for whiteboard practice).  And they come in both exciting points and windowpane varieties–choose one or both!

But wait there’s more!  If you act in the next 20 minutes (just like the real commercials, the 20 minutes starts whenever you read this 🙂  ), you can get a video of me working out some of the study guide problems!

I post these the night before the test and the students who watch them are very appreciative.

So, be honest: am I the only one who could Trig all day?  (Except for tangent graphs, obvs!)

Giving Geometry Some Love: Definitions & Logic/Proofs

It’s been about 3 years since I taught Geometry and there are people doing a lot more creative and deep-thinking stuff than myself  (see: Jim, Julie, Lisa, Mimi, Shireen, and many others), but ugh, having to draw a geometry diagram in Word?

(Hint: draw it in Geogebra, then use the snipping tool to grab it and insert, but even then it’s a pain).  So just to save you some time and hassle, I’ll also be trying to share my Geometry files this summer; stay tuned to this page!  Since it has been three years, much of it will be presented without comment. 🙂

Ah, the dreaded first chapter full of definitions. I guess I hated it so much I didn’t keep many files, but here’s what I do have:

Oh, here’s one thing I’ve done that’s pretty creative: I made my own Angle Awesomeness Rap  (I used to have a bit of a commute and planned it out on my drive one day).  It even has a snazzy powerpoint:

(file here) And NoteTakerMaker:

File here. Yeah, I know, I’m the next Beyonce.

Then I guess I did some sort of other work, and then a review

Now for Chapter 2: Logic and Proofs.  First up, logic! With symbols! And lots of corgi references!

Now…dun dun dunnnnnnn….. PROOFS!  First, some properties:

File here. And hey, let’s figure out what we know from givens:

And then remind ourselves that We Can Figure Things Out (without a formal proof yet):

Then, we do the same problems with some proof handholding:

File here (and yes, the file has proofs for all 5 problems).

Then finally (finally!) we can start on some real from-scratch proofs:

File here. Also, look below at me being clever with using “G.I.F.T.” for proofs!  And also Color With A Purpose.  I also tell them that you should use every line in a proof, which is what the arrows are for.  It seems to help if they’re stuck, “Well, is there anything you haven’t used yet?”

And also step-by-step powerpoints for the study guide!

But I’m guessing we didn’t do so well on the test, as there is a “repractice” worksheet

And powerpoint:

So maybe now instead of making that 417th drawing in word, you can copy and paste from these and then:

Right?

Category: Geometry | Tags: , , , ,