## 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.

## Sunday Summary

It’s time for the weekly (ok, technically bi-weekly since I was at the beach last week for a very rejuvenating weekend with the parentals) #mtboschallenge 3-2-1 Sunday Summary!

3 Things I’ve Done Recently That Were Not Half-Bad.

1. Question Brainstorming

I usually try not to reward promoted links on twitter, but this article about students asking questions was too tempting not to click.  I read it Thursday night and then tried it out Friday morning in PreAP Precal where we were preparing for a test on Monday.  I handed each student a piece of scrap paper and let them have 3 minutes to jot down any question they had–it could be general (“how do you write an equation for a tangent graph?”) or specific (“how do you do #11 on the study guide?”).  Then I gave them 6-8 minutes to try to answer the questions in their groups–I saw A LOT of good peer helping at this stage!  Then I collect any remaining unanswered questions and answered them

…Except for “why is -1 used for inverse notation?” (unless you count “because it is” as an answer).  I did a little googling this weekend and all I was able to come up with was if you want to perform f on x, you write it f(x).  If you want to perform it twice, you could write it as f(f(x)), or f²(x).  Following that same notation, undoing f once could then be written as  f‾¹(x).  Anyone have anything better?

2. Using Graphing Calculators to Graph Absolute Value

I found great discovery activity worksheet online and actually used the entire thing with limited modifications (I took out graphing the piecewise lines because we hadn’t discussed piecewise yet and one battle at a time, amirite?)  It went over great!  The kids were enthralled at using their calculator to do this.  (Actually, they were more amazed that it could graph y = |x + 2| than the fact it could give you a line of best fit when given 15 different ordered pairs.)   Hint: Have them turn their grid on (under “format”-the top middle button on TIs) for better transferring of graphs to paper.

3. Linear Modeling in Algebra II

Totally stealing from Mimi’s (@untilnextstop) fabulous worksheet, I made some math libs of my own.

(doc file here)We did these by hand (well, as in putting equation in point-slope form and then converting to slope-intercept).  Things I need to change: kids have no idea about having to pay a fare just for getting in a taxi nor do they understand #4 at all.  I should throw something in there about having to pay for both AOL and internet service just to complete date myself.  Also it’s best not to have a question about a rod expanding or growing if you’re teaching high school boys.

Then I made another worksheet to use the linear regression on the calculator.

(doc file here) As I said, I did steal the first two questions directly from Mimi.  One thing that I didn’t notice until a kid pointed it out is that the answers to 4D don’t correspond very well to the chart, which led to a great discussion of what the line of best fit can and can’t do for us.

You can’t see it in the picture, but the next problem has the y-scale in billions which was something good to discuss as well.

We then did Mathalicious’s Reel Deal lesson, which was using a scatterplot and line of best fit to determine the movie lengths.  Maybe it was because I was pressed for time, but it did not go over as well as I thought it would.  I think next time I will just add it as another example to discuss in class.

Two Things That Are Not So Great

1. Even after all the work we did with the linear equation mad libs (and we did more work in bellringers and study guides) some students still had trouble telling me what the slope or intercept meant on the quiz.  (As in being able to fill in the blanks: for every _____, the something will increase _____.  At the beginning, there was _____.)  Maybe I should have done Mathalicious’s Domino’s activity instead of Reel Deal.  I also waver back and forth between “they should know this already!” and “they need to know this and they don’t so I need to spend a lot of time on it!”

2. Time is still a huge stress, since we are also nearing the end of the nine weeks and I am struggling to get in 6 major test grades.  Do I just have one test on a single topic to get the required six?  Or cram a lot of material in to have the test cover more than one topic?  Ugh.

One Thing I’m Looking Forward to This Week

Trig Identities!!!!!!!!!!!!!!!!!!!!!  I could do those all day.

Ok, so maybe I just like them for the puns.  🙂