## Alg II Files: Functions & Graphs

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TMC has got me all mathy-feeling, so here’s another unit! Or at least, the first part of it!

I didn’t really change much to this chapter as from previous years, but I’ll go ahead and post everything so it’s all in one place. As usual, find more files and FAQs on my Algebra II Files page.

Let’s begin with what is and is not a function:

(file here) I took the NAGS from Sarah at mathequalslove and I think the rabbits came from Shireen at MathTeacherMambo. (Definitely 2 of my top five math blogs).

Here’s part II, but according to my calendar, I did part 1 and 2 the same day.

(file) I’m just going to warn you if it’s the first time teaching Algebra II, the struggle is real when trying to find function values from a table or graph. Just be prepared.

Also the magic parentheses for evaluating a function = amazing. We took the parenthetical promise (h/t mathequalslove again) in Unit 1 that said every time we substitute in a value, we put it in parentheses. And we’re going to be substituting for x, so let’s go ahead and put the parentheses first like:  3(       ) + 2 then INPUT the INPUT INTO the parentheses!

Here’s some homework:

(file) Then it’s the ever-popular graph stories!

(file) Then…it’s time for….domain and range!!!!  Y’all, I just totally had a genius idea: have them figure out what the scale/domain/range should be for the graph story graphs first! One of you try it out and let me know how it goes. But since I didn’t think of that until just now, here’s what I used:

(file) Since we’re doing this before we did inequalities, it’s domain and range PLUS learning interval notation. Note the color with a purpose! I have them “box in” the graph before they think about writing the interval. I also use Sam’s domain and range meter, sometimes breaking out the spaghetti to use if I feel like picking a million tiny pieces of spaghetti off the floor.

Here’s some slightly lagging homework for the chapter:

(file) Then it’s a graphing line “review.”

(file) As you can see, I always go back and forth on graphing standard by converting or by x and y intercepts. Here’s the boring homework file.

Now here’s some exciting stuff! This is a pretty magical activity that is a really good introduction to the (h, k) form. Just read question 1 and let that awesomeness just sink into your brain.

(file) And some practice:

(file) Then it’s time for a study guide:

(file) And of course a study guide video!

Off to make another post!

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!”

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

File 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:

And some homework:

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.

File here.  (Legal, but it’s sized to shrink to 2/letter sized).

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

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:

File 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!

File 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)

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:

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

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

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!

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!)

Then 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.

File 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!

I 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:

File 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:

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!

File 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.