## 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).

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.

## All aboard! Destination Function Junction!

(This post is part of my attempt to get all of my resources online for y’all. See more files and FAQs here.)  Are you ready to get this Precal train rolling???

I used to start Precal with the “Chapter P” in my book: basically, hey, remember this from Algebra II? No, ok, let’s teach it again. Because there’s no better way to start off a course than with absolute value inequalities, amirite?

Right….so I changed it up this year because (1) I had only PreAP Precal and I do expect them to be a little more prepared that regular and (2) the first full week of school we had a week of grade level meetings and picture days, which meant I saw some periods all five days and some three and some kids in and out throughout. So we did a review of equations instead. I just gave them the sheet and said “have at it! See what you remember and what your group can figure out, then we’ll follow up on the rest!”

A former coteacher made this, which is why it’s written with the new equation editor (HATE) and also why it says “Pre-Cal” instead of “Precal”.

File here (4 to a page!).  I think I remember it taking about 3-4 days for them to finish.

Then we started with the “Chapter 1” business: lots of definitions and descriptions and probably stuff they should know from Algebra II but don’t, e.g. functions.

File here. I really need to start using NAGS (Numerically, Algebraically, Graphically, Sentence) more throughout the year.

The homework for the chapter:

File here. (I print it 2 to a page)

Then everything you could possible want to know from a graph:

Oh, wait, actually that wasn’t everything you could want to know about a graph!  How about relative extrema and even/oddness?

File here.  I use a powerpoint to introduce even and odd graphs:

File here.  The animation on this is actually pretty neat. Once you download it, be sure to watch the actual slideshow (not just scroll through the slides) so you can see it.

Then we spend some time playing “Math Pictionary,” where we break out the whiteboards and make graphs that meet different conditions:

File here. If time allows, I also show a funky graph and have groups come up with as many descriptors as possible.  Then we go around and each group shares one, no repeats. The last group to have one to share wins!

By this time, everyone should have had a chance to get a graphing calculator, so we start using it:

File here.  Next time I may put some graphs on there that require changing the window to see everything.

I know I said I wasn’t going to reteach Algebra II (or, ahem, Algebra I) topics, but being able to write the equation of a line is just too important a topic not to spend a day on. Also, using this new way of graphing-by-translating and writing point-slope form is a nice (re)intro to (h, k).

Now I’m going to stop here because I think you may have just breezed by this without trying it, thinking “oh, just another graphing/writing equations worksheet” but it’s not! I promise!  Try this first problem:

1) Graph y = 2x. (it’s ok if you do it in your mind, but feel free to get paper. I’ll wait.)

2) Translate to the right 4 units by moving each point 4 to the right.

3) What is your new y-intercept?  Write your equation in slope-intercept form.

4) Now factor out the GCF.

WHAT?!?!?!?!?!?!?!?  Yeah, that just happened.  The mystery of why h is negative in y = a(x – h) + k is solved with a simple four-step line problem. (Ok, maybe not “solved” because that will come a little bit later, but for now it’s pretty cool, eh?)

Ok, enough amazement, back to work with piecewise functions (we haven’t started doing them in Algebra II yet, so this is the first time they’ve seen them):

File here. Regular Precal file (more graph practice, no writing equations) here.

Yeah, check out those first graphs…the gray graphs are already on there for them so we can focus on the restricting the domain of each one before we pull it all together and graph from scratch (which I do by graphing all the functions with dotted lines, then filling in the parts that I need, so it’s very similar to the first examples).

Then it’s time for Average Rate of Change, which didn’t go so well this year (I was also out for a meeting on the second day so that didn’t help).  And it started so well when I let them loose on this:

I print 2 to a page so this was all on the front.  And they were rocking and rolling. Then we flipped to the back:

(file here) I HAVE NO IDEA HOW TO DO ANY OF THIS BECAUSE IT’S USING DIFFERENT WORDS THAN THE FRONT!!!!!  WHAT IS THIS MADNESS?????? And now you want us to do these practice problems?

(file here)  We spent 3 days on this (again one of them I was out), and I can’t help but thinking if we started with this like I usually do:

(file here) and then spent two days applying it, they’d have a better feel for what AROC is than they did. Or maybe some hybrid of the front of the first worksheet, this, then the back?

As a side note, using The Biggest Loser as an example of AROC is great. It always hurt my head if the graph went up and down, but the AROC was zero. “It can’t be ‘no change’!  We were totally changing the whole time!!” But if you think of it as a contestant gaining weight and then losing the same amount of weight in a week, at the weigh-in she’ll have 0 change.  (This is also a good time to do a PSA to your students about not being obsessed with your weight every day.)

Finally (finally!) it’s review:

and the study guide:

Whew! I think I’m going to get off the train at Function Junction and take a break, but stay tuned for the next installment of “Wow, Meg Wasn’t Lying When She Said She Killed a Lot of Trees.”

## All The Cool Kids Are Guessing and Checking

Last night I landed in the middle of this discussion with Julie:

Until we get Glenn to share his ideas (C’MON GLENN I DON’T WANT TO HEAR YOUR PhD EXCUSES),UPDATE: Glenn has shared part one of his ONE MATHS blog posts here! these are my big three goals for Algebra II this year:

1. Simplify stuff. Also, I want to check our simplifying.  Let’s plug 7 into (x + 8)(x + 3) and see if we get the same thing when we plug 7 into x^2 + 11x + 24.  Let’s graph it on desmos and see if we get the same graph! Oh, look, we’ll get the same output for any x!  (I think this would also help with the “plug in any number” method for the ACT, which totally blew my mind when I first read about it. “No, wait, it can’t work for any number I pick, can it? How does it know which number I’m going to choose?”)
2. Solve stuff.  We will do this by legally undoing things. And also check by plugging in the answer and by graphing.
3. Graph stuff.  90% of which we can graph by using the (h, k) method.

Our department is also planning on using Jonathan Claydon’s layout for Algebra II that hopefully will foster more connections as well!

Back to last night: as things often do in the #MTBoS, the discussion turned to factoring:

So if factoring by grouping or box or slide and divide or airplane or bottoms up is not working for you or your students (i.e. do they all remember the “slide” but forget the “divide” part?), join the cool kids and go back to Guess and Check.

“But wait, Meg, how can you be all hip and cool and use ‘guess and check’?  I mean, that doesn’t sound very mathy at all. I bet you don’t even wear pink on Wednesdays.”

Hey, Mean Girl, it’s not just guess and check….it’s educated guess and check! It’s like finding factors of 111…you could try every number from 1 to 111, but if you’re smart about it, you know not to try 2, 4, 5,… so you can focus on the ones that at least stand a chance!

True story: One year I taught Algebra II both guess and check and slide/divide. Those that had the least math skills chose slide/divide, but then they would get a really big number for ac that had a bajillion factor pairs, and since they weren’t great at arithmetic to start with, they couldn’t choose good number pairs (“hmm, I wonder if 2 and whatever 168 divided by 2 is will add to equal 13? Better break out the calculator and punch. every. button. so. slowly. so. very. very. slowly. Huh, wow, didn’t work. Ok, what about 3 and…”) so it took them way longer to guess and check ac than educated guess and check process. AND THEN THEY STILL FORGOT TO DIVIDE!  Also, in Precal, I have kids that are in love with slide/divide and then slowly but surely, they’ll come in for some extra help….”so could you show me your method again?”

Ok, so here it is:

And, no, it’s not like our first guess is right every time…but it usually doesn’t take too long!

Here are the above charts in a handy word doc in case you want to discuss with your department. I actually don’t do a NoteTakerMaker for these, because another big secret is to USE WHITEBOARDS or some other dry erase surface. Unless you want to hear them complain about the guess part of it all day long.

Also, I think next year I’m going to teach a equal and not equal to 1 the same day. If it’s equal to one, awesome, I can lock that in!  Maybe that way they won’t freak out as much when a doesn’t equal 1?  Because full disclosure: yes, mine still complain when a doesn’t equal one.

Let’s round out this post with some more Quadratics (part of my summer goal to get all of my resources online, see more on this page!)

Factoring homework (hint: I sometimes use the first problems as examples in class, then tell them they get to start on #____ or assign just the odds, with evens for optional practice).

And my first day of factoring review:

File here. Next year: save grouping for polynomial chapter.

Now let’s solve these puppies!

File here. (I can’t seem to find my solving by square roots, but I do teach it! Promise!)

And now let’s solve some with complex answers (I usually wait and do complex number operations later–it’s a good “oh, here’s three days before break” section that can really go anywhere in the year)

My favorite annual quote: “So, what’s this backwards j?”

And then the quadratic formula (I save completing the square for converting to vertex form; see it in this post.).  And now let me reveal Jim’s (@mrdardy) awesome quadratic formula manipulation:

It’s only 1,000 times easier to simplify AND you can still sing “Pop Goes the Weasel” because it is still “all over 2a” AND whoa look at that vertex just pop out!!

And here’s some practice (6 to a page!):

And the study guide.

Now go forth and spread the news of educated guess and check throughout the land!!!

## HERSHEY’S TORTE! (and Alg II Unit 1)

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Yes, I am going to make you scroll through all of my NoteTakerMakers to get to the most delicious cake recipe in the entire world.   And, boy, do I have a lot a lot to share for this unit: number sets, order of operations, equations, inequalities, and absolute value equations/inequalities.  (Want more? Visit my new Alg II files page!)

Let’s begin with this HORRIBLE HORRIBLE first day of Algebra II notes. Hey, did someone say lots o’ definitions and then stupid review problems?  I’m interested! The good news is I’ve scrapped it for better things (e.g. Desmos Function Carnival), but you never know when you need a good number sets graphic organizer.  I usually just casually mention the sets as needed, but I think maybe this year, I’ll give each student a number and have them group themselves however they want. Maybe they’ll do even/odd, positive/negative, fractions/whole numbers, but then we could divide into even more specific groups?  And then reverse it: start engulfing each other until we are all one big happy Real Numbers Family?   Anyway, here’s the NTM:

(Ok, less talk, more files, then cake!) Order of Operations:

File here.

I even tried doing a Talking Points for Order of Operations!

Then I don’t even want to talk about my actual solving equations notes. I’m going to totally change them up next time. But for now, how about some Find The Mistake?

I only used Comic Sans to make my fellow teacher happy. Plus it can be counted as one of the mistakes to find!

File here.

And did someone say word problems?

I do so enjoy the travel chart, however, next year I’ll have them figure out what to do for each case instead of telling them.

File here.

And here’s the homework for these two sections:

Now it’s time for some inequalities!  Algebra II is the first time the students see interval notation, so this year we played a match game:

Word file here.  PDF File here-print 2 per page to get it all on the front of one sheet.

Full disclosure: it was a bit of a struggle and not sure if it was worth the time. I may revert back to this instead, or do a mixture next year.

File here.

I made a powerpoint for #1-14 so we could quickly go through them the next day in class, but you may want to use it for whiteboarding or review (each problem is animated step-by-step)

These are the notes we did this year, jumping right into compound inequalities the same day:

Next up, absolute value. I almost feel bad sharing this because I cannot teach this well.

File here. Here’s how I fill in the top boxes:

Moving right along…

Some homework:

And some practice powerpoint for the whole chapter, heavy on absolute value:

And the study guide, which as promised in my #MTBoSDirtySecrets, is very similar to my test.

And now the moment you’ve all been waiting for!!!

My Thing

My thing today is Hershey Torte. This is the yummiest cake in the entire world. On Mother’s Day I tried to make a chocolate cake with peanut butter icing. The cake part went horribly, so I rescued it by making the cake portion of this with the peanut butter icing. Then, upon tasting the final result, questioned why I didn’t just make this to start with.  Warning: I cannot be left alone with this cake.

Hershey’s Torte

CAKE:

1 box German Chocolate cake mix
1 small package instant vanilla pudding
4 eggs
1 1/2 cup milk
1 cup vegetable oil

Mix well. Pour into 3 round (greased) pans and bake for 30 minutes at 325 degrees. Cool completely before frosting.

FROSTING:

Cream together:
8 oz cream cheese
1 cup confectioner’s sugar
1/2 cup granulated sugar

8 oz Cool Whip
1/2 cup pecans (optional if your husband is anti-nut)
6 Hershey’s plain chocolate bars, chopped fine

After you have mixed everything together, frost between layers and on top. Refrigerate.

One taste and then you’ll want to:

## Derivatives Part II: You Mean There Was Shortcut This Whole Time?

(See Part I for Intro to Derivatives.)

Ah, that fun day in Precal (or Cal) where you get to tell your kids all that work with the f(x+h) is about to be forgotten. Depending on time and interest, we talk some about patterns they’ve noticed so far, then we formalize it:

File here. And some homework.

If you notice, we also throw sine and cosine in there as an added bonus (plus it makes the chain rule more exciting in few days).  The next day I like to do this practice from MathTeacherMambo (but I can’t find the original post for it). before we jump in product/quotient rule so they can get really good at the problems like the ones at the bottom before they try to solve all of them with the quotient rule. Because of time, we couldn’t do that this year and just did some derivative applications instead (which I just pulled from the textbook and are too boring to share).

But in Perfect World School (or at least a couple years ago), we went on to product rule and quotient rule.  I showed them how we derive (pun intended) the rules and I remember last year, one student came in late and another told him, “You just missed the most mindblowing thing EVER!”

Also, check out that Color With A Purpose. I found the boxes really helped to see if you needed the product/quotient rule at all–each box must have a variable!  For non-example, in #3, there are no boxes on 2 sin t because 2 doesn’t have a t, so no product rule on that part.

More boxes, and also more reinforcement of STOP DOING THE QUOTIENT RULE EVERY SINGLE TIME YOU SEE A FRACTION.  SRSLY.

Files here and here.

We also did some quotient practice from (guess who?) MathTeacherMambo. (Holy cow, how did I have all this time last year and NONE this year??)

Then the chain rule:

More boxing/Color With A Purpose. This time to see if we actually have a function inside a function.

Warning: Take your time with the table derivative problems-they require A LOT of mental workout!

File here.

Also, because it got cut off in my scan:

Then let’s throw it all together:

The first 6 we did together in class, the rest were homework.

and practice it:

The “answer sheet” was a grid with 15 boxes on it. Nowadays, I would have them use group whiteboards/vertical non-permanent surfaces.

Files here and here.

And because I like you, here’s the study guide for Part II of Derivatives (with bonus flashback to determining things from a derivative graph).

Next time, I’d like to spend more time on *good* application problems…like optimizing volume or maybe talk about when to enter the water to fetch a ball…WAIT WHY IS THIS A MAYBE?? OBVIOUSLY I NEED TO BRING ADDISON TO SCHOOL:

My Thing:

Just in time for wasting summer days, my thing this week is the game 1010!  (I’ve already seen students play it, so maybe I’m behind the curve?) Were you a fan of Tetris? This is very similar, except they give you 3 pieces at a time and they don’t fall.  It’s the perfect airport game if you’ve already completed Game About Squares.

What’s your favorite time wasting game? And what’s your favorite, “hey guys, wait til you see what math came up with to save you guys HOURS of time?!?” moment?

## Graphing Trig: On the Verge of Something Better

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I think this is maybe the tenth time I’ve taught trig graphs, and I think I FINALLY like it. Almost. Except for tangent.  But who likes him anyway, amirite?

Here’s what I used to do, and it worked ok. Some years we started with this ferris wheel group work:

File link. Except I’m not sure if I ever made the connection well enough between the Ferris wheel and the sine graph the next day, and some years we were short on time, so I would usually just jump into this:File link. Basic plan: know the pattern of sin (0, 1, 0, -1, 0) and cos (1, 0, -1, 0, 1), find the period, divide by four to find the “exciting spots” divide your x-axis as needed, graph the pattern, connect. Repeat.

The nice thing is that the divide period by four, graph exciting spots worked for tangent, too:

File link. And my kids usually did pretty well.  But I had tried a little bit of windowpane graphing in Precal earlier this year and wanted to give it a shot, so I came up with this:

File link. Basically: know the general shape of one cycle, then repeat it.

Things I would like to do differently:

• Have them watch a desmos or gif animation of extending the sine wave past 2 pi.
• Have them extend the cosine graph past 2 pi.  A lot of their cosine graphs looked like UUUUU instead of “gentle rolling hills” no matter how many times we talked about how sine and cosine look the same! Just moved over!
• Spend one day (1/2 day? homework? assignment after quiz?) before this on (non-trig) periodic functions and “picking out the smallest cycle that will give you the whole graph” and “stretch this to be twice as long/three times taller/moved to the left”  Also maybe patty paper?

BUT!  The thing that was definitely on the verge of something great was, don’t give them the equations to start with.

“Hey kids, I know you’ve never seen a periodic function before or had to deal with a b value stretching or shrinking horizontally, and we’re going to measure in radians because that’s normal and you love fractions, and now find all this crap from a weird looking equation…why are you all looking at me in terror?”

And ok, some of them still looked at me in terror. I think this is where the patty paper would help tracing one pattern. And I ended up switching the order and graphing 7-12 first, which helped a lot.

Then the next day was a breeeeeeeeze with equations!

File link. The next day was *slightly* less of a breeze.  Patty paper would also help-many students have trouble with moving the period with the origin.  As in, if you move back to -pi/2, they would still have the period end at 2pi, not 3pi/2.

Also writing equations is still hard.

We then spent the rest of the day and the next practicing. I was down with some pretty big allergies, so instead of walking around, I had them come to me, which was a bit fairer than usual (didn’t get stuck at one table), but also a few kids never came up to get checked, so I still need a system where everyone can get checked equally.

Then I did something foolish.  It’s AP testing season and state tournament season and hey-why-don’t-you-just-take-a-day-off season, so I should have ended there and done another practice day with one of my favorite worksheets:

This will take some students 10 minutes, most of them 30, and some will need to finish for homework.

File link.   Or maybe done a day with biorhythms or some such, but instead I decided to be completionist and talk about tangent.  Where the window pane graphing doesn’t really work as well.  And all the wheels fell off…

File link.  Just no.  Especially no need to phase shift tangent, goodness, what was I thinking?  And yes, DEFINITELY need patty paper on this.  Not sure how to make it better/easier to understand.  The students were having trouble placing asymptotes at the end of the period instead of the middle or vice versa (making the period end where the asymptote should be).

But anyway, except for tangent, most of the grades were pretty good on the test.  They even did pretty well writing equations, which is always tricky.  And maybe they’ll remember it a little bit better next year in Precal?  At the very least, they can tell me the shape of each, which is what the AP teacher says they need to know.

My Thing

My thing this week is British Dramas That Are Not Downton Abbey. Have you tried Call the Midwife? Gracepoint? Broadchurch? Orphan Black? If not, you’re missing out on some fine, fine television. All of them are shows that never get backed up on our DVR because both my husband and I want to watch them RIGHT NOW PLEASE.  Midwife and Gracepoint are both great period pieces, in about the same time frame (vaguely after World War II). Broadchurch was a great police procedural the first season and a great courtroom drama the second season. And Orphan Black is totally modern with 5 clones played by the same actress (#TeamAllison). Who cloned them? Why did they clone them? Why is somebody after them? So many questions!  Go check any of these shows out if you’re looking for some summer binge watching!  Or let me know that you like them so we can bond!

Category: Uncategorized

## Vegetables and Classroom Catchphrases

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Two things I’ve been meaning to share:

1) I am required to mention how good Wonder by R.J. Palacio is at least once a month (this requirement has now been modified to include A Man Called Ove by Fredrik Backman).  Because I loved it so much and I’ve put a quote on the whiteboard every day, I of course bought 365 Days of Wonder, a collection of quotes/precepts. It had this gem of a story about a three-year-old son who was in his chicken nugget phase and the parents had given up trying to make him eat his vegetables.  The pediatrician replies:

Well, you can’t really force him to eat the vegetables, guys, but your job is to make sure they’re on his plate.  He can’t eat them if they’re not even on his plate.

I’ll wait while you let that sink in.

Here are some of my vegetables I’ve been serving:

• So, yes, not every kid got the “plug-in-any-number” method for the ACT.  But did some say it helped them? Yes. Would they have known about it if I hadn’t taken 10 minutes to talk about it as bellringers?  No.
• “Hmmm…..I’m not sure if they’ll get this discovery worksheet on concavity, but we can always abandon it for chicken nuggets if there’s a meltdown.”
• “You are each The Most Magnificent Thing [by Ashley Spires], even if you lean a little to the right. Or maybe you’re still in the process of becoming The Most Magnificent Thing and everything feels all wrong, but know that at least part of you is perfect right now and will go towards making you The Most Magnificent Thing. [Yes, even you who decided it was too silly to listen to a book being read to you and played on your phone instead].”

I also keep this in mind when I’m teaching something that I would LOVE to go more in depth on, but I know it would be too much after just introducing a topic. As in, let’s start with some corn and peas before we jump into [insert sophisticated-taste vegetable here].

What are some of the vegetables in your classroom?

(As a side note, Ron Swanson and I have same opinion about vegetables.)

2) Do you have “classroom catchphrases”?  Like when your students see a tangent graph for the first time, do they yell, “Oh, it’s like a John Travolta?” (Our name for the cubic graph (stolen from the #MTBoS).)  Or do they write on their year-end survey, “I only killed four kittens”?  Or maybe they watched a video and in their write up said, “at one point she talked about 24 times something equals dolphins, but I was used to that because my math teacher talks about ’24 times something equals corgis’.” Or do they talk about radians in terms of quesadillas? I always want to sit in on their next math class when they start bringing these terms out and see what the other teacher does.  🙂

What are some of your classroom catchphrases?

We also talked about two, to, and too the other day and I mentioned that “too” has “too” many letters. One girl was so excited about finally remembering the difference.

Another teacher said to remember the difference between it’s and its, think of a towel rack: HIS HER ITS  (also THEIR and YOUR). No apostrophe!

Also, if a fish is missing a fin, then he’ll sink-y. Capital of Finland? Helsinki.  Feel free to whip that one out at your next faculty luncheon.

Bonus 3) Ok, one more thing and it’s My Thing. I’ve been listening to StoryWonk’s Light Bulb podcast, and at the end of each episode each host talks about their “thing” for the week, i.e. whatever they’d like to recommend.  So I think I’m going to start ending my blog posts with My Thing.

And My Thing this week is….

Do yourself and favor and marathon it this weekend. Or savor it and watch it once a week. I don’t know why it’s has never turned into a cult favorite. Here are two gems to finish this post, and if they don’t get you to watch, well, don’t say I never served you any vegetables.

Category: Uncategorized

## Introduction to Derivatives

Ok, let’s do this.  Not saying any of these things are life-changing, but I’m just helping my fellow precal teachers out with some resources. 🙂

Day 1:

Can you guess what type of graphs these are in this desmos file?

YOU ARE ALL WRONG.  WRONG WRONG WRONG. BIG FAT DUMMIES.

This was the best introduction to tangent lines I’ve done. So much so I’m going to take out the bit about what are and are not tangent lines in the NTM below because they were all “duh, of course those aren’t tangent lines–because it’s not the line the graph would look like if we super-zoomed in!”

(they filled in b-g to watch the AROC get closer and closer to 2.)

File here.

Next year, I think I want to make the graph bigger at the bottom, so then we could look at, say, the derivative value when x = 3, then go to desmos and zoom in on the original and see if it looks like a slope of 6.  “Well, wouldn’t that be a handy thing to know just from the derivative graph!”

Day 2:  Modified MathTeacherMambo worksheet.  1) I added a t-chart with specific x-values to use (the first time I did this they couldn’t make smart choices about what points to pick) 2) only did the function to derivative portion and 3) Added this summary at the bottom.

Next year, I’ll do this table instead:
I drew this on the board one day a few days into the chapter and BOOM everything made sense.

• The value of f(x) tells us nothing about the derivative value
• We don’t care (yet) about the slope of the derivative graph
• If I know f'(x) is positive, then I know f(x) is increasing
• If I know f(x) is positive, then….uh….I know f(x) is positive.
• WHO CARES WHERE THE DERIVATIVE HAS A MAX OR MIN? Not me.

Day 3: Derivative Match Game

Dude, you have to do this activity, even if you do nothing else in derivative land.  Such a great review of everything and good thinking about derivatives!!  Because I like to sketch on my graph, I made the kiddos a worksheet where they could sketch and record (also helpful if it continues to next day and easier to check).

This is how I like to sketch information about derivatives, as seen in #1 below: Mark your max/mins as boundaries/x-intercepts (blue), determine if graph is increasing/decreasing in each section, determine where derivative should be (yellow), play connect-the-highlighting-and-x-intercepts (red).  Obviously there are some times that you need more thinking than that, but you can get a good starting idea. (This method may be “DUH!” to y’all, but it was a revelation when I walked some kid through it a couple years ago.)

File here. (I also changed the cards to be categories instead of D1, etc because “France Pink Otter” is more fun to say)

Day 4: I introduced the derivative function at one point formula which I’m going to skip and let Calculus pick up next year.

Day 5: Let’s derivatize some things!  And see what happens!  And what it could tell us!

After they solve #10, have them do the same with ax^2+bx+c and wait for the gasps when you get -b/(2a)!

File here.

I think also next year, I’d like to go back and do the second part of Math Teacher Mambo’s worksheet, except give them f(x) and have them find f'(x) using the formula. Use f'(x) to fill in t-chart from the first worksheet, then use that t-chart to sketch graph of f(x).  Check in calculator.

Day 6:  The derivative workout!   SO MUCH SWEAT!!  (I need to take out question (b)–it just confuses everything, and put question (a) later.)File here.

A day to review and digest everything, then a test that involved using the derivative formula, matching derivative and function graphs, and telling information about f(x) from f'(x). Stay tuned for “Derivatives Part II: You’re Telling Me There was a Shortcut THIS WHOLE TIME?”  (Update: Now posted here!)

Category: Precal