Tag Archives: word problems

Alg II Files: Systems

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(See more Alg II files and FAQs here)

So this was an interesting chapter…one that I think I improved from last year, but could still have used more connections and also some more activities (e.g. double stuf oreos wafers and creme).

It started with a great discussion:

(hey guys, hold out for a couple more chapters when I got a new phone that does pictures a whole lot better! Sorry for the random quality until then.)

 

(file) So, guess what? I had been teaching the types of systems wrong for a long, long time! To recap from that post, the correct way is:

Category One: Is there at least one solution?
Yes: Consistent  No: Inconsistent
Category Two: Are they the same line? (Technically, “can one be formed from the other with algebraic manipulation?”)
Yes: Dependent No: Independent

So the correct categorization would be:
Independent and Consistent: One Solution
Dependent and Consistent: Infinite Solutions
Independent and Inconsistent: No Solutions

Then we did some substitution, some new stuff here: being really conscientious on boxing equal things and also looky there in #6, doing substitution with quadratics!

(file with these questions and more practice)

and I even went a little crazy and did this:

(This may also be why so many of my students remembered how to expand (x – #)^2–we did them a lot of them throughout the year!)

Elimination.

I was pretty proud of the practice I prepared for the pupils:

unit 5 2

(file) The last set was interesting when they didn’t choose the method I thought they would!

Did I hear someone say they’d like to see more textbook-like systems of equations word problems? Here you go!

(File with these & more practice problems) But I was able to add a pretty cool activity from Amy (@sqrt_1) where the students made their own word problems. The only thing I changed was condensing all the work onto one page for easier grading:

unit 5 4 unit 5 5

(instructions and worksheet) It was a nice day and a lot of the students had fun with it (how often do they get to break out the colored pencils and color? I also gave bonus points for the most creative one from each class and put my favorite one on the test!). I will say next time I will have them show their work that they tried it! (I said they had to do it on their notes, but not turn it in.)

Have I told you how much I like doing group speed dating?

unit 5 6

(file) Then it was study guide time!

unit 5 7

(file and video key part I and part II) As I said, a lot of room for extensions, activities, and connections in this chapter that I just didn’t have the time to incorporate. TBH, if it’s the night before the lesson, go ahead and use some of my stuff, but if you have time to plan, please go see all the more awesome things there are out there in MTBoSland!

 

 

Category: Alg II | Tags: ,

Lines in Algebra II: SRSLY, You Should Know This By Now.

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(The continuation of my posting all of my resources for Algebra II.  See more files and FAQs here.)

So the students have seen lines in middle school, Algebra I, and Geometry, so this should be a nice easy review, right?  “Hey guys, let’s graph a line! And then let’s start in point-slope form and write an equation of a line!”

Lines 0

Until they find a cure for Math Amnesia, I guess we’ll start from scratch!  Starting with functions:

Lines from megcraig.orgFile here. (sorry for the some wonkiness in the scans… I use a roller scanner. If my phone had any sort of storage/wifi/3Gsignal in school, I’d use CamScanner instead, but alas..) Next year I’ll be sure to use the vending machine analogy that Justin (@JustinAion) shared on twitter:

Lines from megcraig.orgComplete File here.

And some homework:

Lines from megcraig.orgFile here.

What is it about domain and range that students have such a hard time with it? As you can see, I try both the “flatten the graph to the x or y axis” method and the “box in your graph” method.

Lines from megcraig.orgFile here.  (Legal, but it’s sized to shrink to 2/letter sized).

Somewhere about this time, I like to do graphing stories:

Lines from megcraig.org File here (not my original idea, I just made it into a worksheet instead of card sort).  Also, yeah, #6 always gets me. I want to say it’s the curved line, but only by process of elimination. I’ll have to do some filming of a bathtub one day.

However, I think I’d like to replace it with this graph matching instead:

Lines from megcraig.orgLines from megcraig.orgFile here. Again, not mine and I haven’t tried it yet, but it seems a little bit higher level.

Ok, now it’s time to get started with those lines!

Lines from megcraig.orgFile here. I used HOYVUX this year, but not sure if it’s my favorite. I usually go with “x(or y) = #” means we cross the x(y)-axis at that number. Also, note the hearts around #5) y = x. I tell them it is my favorite graph of all time, the graph all others graphs originate from and aspire to.  And because it’s my favorite, it will be on every single test until every single student gets it right, which usually means it is on at least 4 tests.

This year, instead of my normal writing equation notes, I did this Translating Lines discovery instead (yes, it’s very similar to the Precal one I shared because it’s awesome)

Lines from megcraig.org

File here. Next year, I’m going to add some more practice like the first 11, but wait on parallel/perpendicular/two points until the next day to reinforce the “new” point-slope form (they all learned it as y – y1 = m(x – x1) instead of y = m(x – h) + k) and also work a little on getting it into slope-intercept and standard (since that is what a lot of standardized tests use).

However, even without that, most did well on the in-class practice:

Lines from megcraig.orgFile here.

Or maybe you’d like a scavenger hunt with graphing, functions, and equations in slope-intercept and standard form?

Lines from megcraig.org

This is just the first 2 pages; it goes all the way to X and takes most of a period to finish.

File here.

Or maybe you’d like to stop here and give a test?  Well, here’s a study guide

Lines from megcraig.orgFile here.

Now let’s actually use these lines!  Next year, I think I’d like to start with Mathalicious Domino Effect, or at least make that the first type of problem on the notes.  Actually, I need to change a lot of the problems on here. I teach in a suburb, so my students have no idea about the ride fare of a taxi. Also, don’t set yourself up to talk about “expanding rods” in high school.  And look how quaint #4 is–a toll phone call!

Lines from megcraig.orgFile  here.

If you look below, I did take someone’s (??) suggestion about the new way of finding slope with a table and labeling the slope.  Also note the mad-libs portion of the worksheet describing what the slope and y-intercept tell us, an idea I got from Mimi (@untilnextstop) (side note: I miss regular posts from Mimi! If you haven’t read her entire blog, you are missing out on some AWESOME activities and teaching ideas. I’d say I get at least 1/3 of my ideas from her. Also, she lives the most adventurous life!)

Lines from megcraig.orgThen we did some linear regressions on the calculator (of course you could also use desmos), again practicing some “Math-Libs”  on what part of the equation tells us.  Note: next year, I need to add a negative correlation example.

Lines from megcraig.org Lines from megcraig.orgFile here.  I must say I like the two part version of #5, where we find more data = more accurate (or at least a better picture).  Which always reminds me of this xkcd comic:

This year I did Mathalicious Reel Deal (members only), which talked about movie length over the years.  It didn’t go as well as I had hoped; there was a lot of handholding throughout and little “oh, I get it now!” moments.  Maybe because it was the first time I’d done a Mathalicious lesson?

Then it was time for some absolute value, a discovery lesson that actually went well!

Lines from megcraig.org Lines from megcraig.orgI typed up the first part of the first sheet, file here.  It looks like the rest came from the Louisiana Comprehensive  Curriculum, the pdf file is here. The homework file is here.

Alternatively, if you’d just like some notes:

Lines from megcraig.orgFile here. Also, check out that nice vertical stretch work on #4.  I’d almost like them to do the chart and change the y-values instead of thinking of it as slope, since that won’t work for any other function.  But the discovery activity was also really nice…hmmm….decisions, decisions.

Well, at least I know how I like to teach graphing inequalities:

Lines from megcraig.org

Hey, look, it’s my favorite graph again!

File here. (The shading on the last row usually prints nicely from the printer–I think it was a copy of a copy that I was using, so you couldn’t see it very well.) Also, no, we don’t have time for test points, we just go above and below.  Hint: make them put their pencil on the line and then move it above (or below).  That seems to help for when they secretly want to go left/right.

And finally it’s a study guide!

Lines from megcraig.org Lines from megcraig.orgFile here (print it out on legal, then copy two-sided and cut in half).

My thing

Ok, this is going to seem like a weird thing, but have y’all tried the Command adhesive shower products? They are seriously awesome. I hate the suction cup caddies that either (a) slowly slide down the wall or (b) quickly crash to floor (usually in the middle of night).  We’ve had these in our shower for almost two years now and they haven’t slipped a bit!  So treat your shower to a makeover this summer and install some of these. You can thank me later when you’re not woken up in terror at the sound of a burglar shower caddy falling.