## Geometry Files: Triangle Congruence

(see more files and FAQs here).  So, I’m really concerned that I’m losing my mind, or at least at lot of my Geometry files. So what I do have today requires a bit of imagination on your part.

Imagine there’s a notetakermaker that goes with this powerpoint:

(powerpoint file here). The bottom three are from the end of the lesson where we practice identifying corresponding congruent angles before we even worry about proofs yet.

I bet the worksheet you imagined looked something this one, which was the next day’s practice:

(file here).  YES, those triangles are pre-marked and labeled. YOU’RE WELCOME.

Now imagine that I did some sort of awesome introductory activity before jumping into congruence:

More congruence:

Now let’s do this FOR REAL

(file here)  What’s that you say about those gorgeous Geogebra graphics? I’m blushing!

And some more!

(file here). Why yes, I am a sneaky devil putting the same picture for the last four, just with different givens!

Now this is the world’s most superfluous handout:

(file here) Yeah, good thing I made a handout so they didn’t have to draw FIVE triangles!  Whew!

You’re going to have to imagine another worksheet for this powerpoint, or you could just use it for whiteboard review:

(file here)  I know, I can’t believe it took me this many posts to figure out snipping the slide sorter view was better than a single slide.

Now imagine a study guide with everything typed in:

(file here)  If you’re having trouble imagining it, maybe this powerpoint will help:

(file here).  Also, let’s take a moment to discuss how I’m not imagining things when I’ve been saying that my home powerpoint acts weird.  See how you can see the previous screen behind the slides?  Does anyone else have this issue?

Now imagine that this blog has a counter for “____ hours saved by using Meg’s files and not making my own Geometry diagrams,” what do you think the total number would be?  😉

Category: Geometry | Tags: , ,

## Precal files: Conics

Posted on 0 comment

First of all, thanks for all the great comments/tweets/retweets about yesterday’s post. I want to be clear that I love the #MTBoS and I know everyone in it genuinely cares about improving math education everywhere, just we sometimes have a tendency to get a little bit evangelical about our beliefs.

Ok, now back to some boring ol’ Precal files! (See more files and FAQs here) How about some conics, eh?  This chapter really shows that I’m a visual learner/teacher at heart!

First, circles:

(File here) With some homework:

(file here) Then graphing parabolas using the focus and latus rectum (obvious proof that whoever thought up these labels did not think they would be taught in high school).  We started the day by making patty paper parabolas.

(file here) Instead of trying to memorize 1,000 different formulas in order to write an equation, we just draw a picture and find the important stuff from there:

(file here) Let them loose on #8 and see how many will tell you that the focus is at the origin.  (Spoiler alert: all of them).  At some point during this chapter, we also derive the formula for a parabola.  Hint: derive it with the vertex at (0, 0) and then just talk about how we can move it around with (h, k).

Then ellipses:

(File here) I need to update this answer key because instead of memorizing the focal length formula, we now draw the right triangle and label.  Then it’s time for writing equations:

(same file as above)  Homework:

(file here) And last, but not least, hyperbolas!

(file here)  Oooh, and this one is updated to show the right triangles.

The next day is a fun one.  We start off with this desmos file, which is totally mesmerizing (I had to use “p” instead of “e” because turns out desmos thinks e is a number!  Silly desmos, how could a letter be a number?)  We also talk about degenerate conics for about 2 minutes.  Then we talk about decision tree flowcharts and I usually show this one:

And then I tell them that secretly this one from buzzfeed is my favorite and should be dropped from the skies:

Then I tell them that they need to make their own flow chart to determine conic sections given an equation.  Then we go through this powerpoint and check that the flow chart works, making modifications as needed.

(file here) Ok, most of them are more straight-forward than this one, but I gotta challenge them sometimes, right?

Homework:

I also love to spend some time with conic cards during this chapter–if you haven’t tried them, you need to!  I’m planning on using them almost exclusively to teach the chapter next year in Algebra II.  But for now, let’s wrap it up with a study guide!

And a review powerpoint:

Now if you want to get super extra teacher bonus points, may I direct you to Julie’s Rice Krispie Treat conics?

## A Gentle Reminder That We Are All Trying Our Best

I’ve been seeing a few things around Twitter recently, and especially since TMC is less than a month away (!!), that made me feel like we may need this gentle reminder:

We as teachers are all trying, to the best of our ability, to have students reach the best of their ability.

Like students, teachers have different backgrounds, knowledge, experience, comfort levels, and specialties; as well as different student populations and school climates.  Almost every teacher I work with is giving all that they have to give into being a good teacher, but what they have to give may vary.  Some teachers are there early every morning to tutor, but that doesn’t mean those who don’t tutor in the morning are any less dedicated. I can stay at school later than others because I don’t have kids to pick up, but I’m also not at the school until 9 coaching sports.  I tried having my class in groups this year, some teachers also had groups, some teachers had groups sometimes, and some teachers didn’t have groups at all.

Just because something works for you doesn’t mean it works for someone else.  The reverse of this is something that I feel we lose sight of in the MTBoS:

Just because something won’t work for you doesn’t mean it doesn‘t work for someone else.

Imagine you’re a teacher who has been teaching for a few years, mostly by following the issued textbook. You spend quite a bit of time on perfecting your lectures and you mostly follow the same routine of “I do, We do, You do” that you were taught in education school. Your students perform reasonably well in your class, but you’re usually not their “favorite” teacher.  You have made some students like math more (and probably a few like it less).  You’re putting in your best effort, but looking for ways to improve, so you join Twitter.  Within the next couple of weeks, you see comments like these:

“I can’t believe they actually lectured for the entire day.”

“If you don’t have solid relationships with all your students, you can’t be an effective teacher.”

“This teacher isn’t sharing her stuff”

“This teacher is sharing her stuff, but it’s on Teachers Pay Teachers.”

“Look at this stupid textbook problem, can you believe anyone would assign it?”

“_______ is the wrong way to teach ______.”

“Your role is not to tell them, but have them discover.”

“Don’t give hints.”

“Don’t give homework.”

“Don’t give notes.”

“You can give notes, as long as they are on pretty paper.”

“Students shouldn’t trust their teacher to be the math expert.”

Would you want to come back to twitter? Would you want to join in this conversation?  Would you think you even had anything to contribute to the conversation?  Would you want to go back to school the next day, feeling that you’re doing everything wrong?

Confession: I was and am that teacher. Even when I was just reading blogs, I had to unsubscribe to a few of the “top” ones because they just made me feel like I was doing irreparable harm to my students. I’m so glad I took a chance on going to TMC14, because most of the people there inspired me to be better instead of shaming me about where I am.  I would also say about 95% of Twitter also inspires and I’m trying to do better at culling out those who don’t inspire me (which doesn’t mean they can’t inspire you).

Confession II: I almost didn’t want to share my files that I’ve been posting this summer because then the ugly rumor that I lecture a lot and “mama bird” my students would be proven true.  But then I thought, “You know what? A lot of students love my NoteTakerMakers and I’ve had success with them so maybe someone else will, too, or maybe they’ll take them and make something better.”  I’m trying my best. This is what has worked for me before and it is what I have to give.

Confession III: I’m not saying I’ve never made the sort of statements that I’ve listed above.  Or thought about another teacher, “She doesn’t even read blogs!” But if I had to list the top five teachers that I’ve worked with in person, less than half are or were active on the Internet.  And even though I’ve been trained like Pavlov’s dogs to cringe when I hear “Khan Academy,” I still recommend it to my students who are struggling. Because, yes, even Khan Academy is trying to help students in the best way they know how.

Basically this is 1,000 words to remind you:

• Assume every teacher has the best of intentions. Yes, just like with our students, there are some that perform better than others, but I doubt there are many teachers that wake up and think, “I would like to make my kids really hate math today.”  That is not to say we don’t all have room to improve, but…
• You can only do what you can do. If you see a good idea that may be out of your comfort zone, try it out. If it doesn’t work, see if you can change it to make it better or if it’s just not for you at this time. If you see someone say that what you are currently doing is “bad,” read it and reflect.  Maybe there is something you need to change, but maybe there isn’t.
Think of improving your classroom like getting in shape. Sure, you could do a crash diet of Three Acts and ban all sugary worksheets forever, but if that’s not comfortable to you, you’re setting yourself up for failure. Try little modifications until you’re strong enough to try the big stuff (but not everyone has to run a marathon to be in shape).  What we are doing is important, but let’s remind ourselves it’s not life or death. If you’ve been up all night with a sick kid and have your kids do a practice worksheet in class the next day, the world will still continue to spin.
• You are all inspiring teachers. Let’s build on that by putting positivity out there (“This is something awesome that worked for me”) instead of negativity (“Doing this instead of that is bad!”). (This is not to say you shouldn’t let us know when something doesn’t work for you.)  Think about how you can inspire teachers to move out of their comfort zone without putting them in the panic zone (or the defensive zone).
• Mold your Twitter and blog feed into something inspiring for you. If every time you read a tweet from ____, you roll your eyes, feel like a horrible teacher, or get defensive, stop following that person. If your eyes glaze over every time you see another post from ____ in your feed, unsubscribe.  (That’s not to say you should only follow people that teach exactly like you do.)

And if you ever need a little more inspiration in your day, Coach needs to tell you something:

(link here if embed doesn’t work)  Now go be the awesome teacher that you are.

Category: Uncategorized

## Alg II Files: Polynomials

(see more files and FAQs here) This is one of my favorite chapters in Algebra II because it’s the first time we discover that:

(file here) and I just did the bottom part of the first page in class on the board. And during the same class period, we jump into this:

(this is the second page of the previous file). Then it’s time for some graphing!

(file here) but for the sake of time, I’ve been doing the same thing with this desmos file. Then we put all of our conjectures together and practice:

(file here) after teaching this about a bazillion times, I now really like how it goes.  The only thing I may change next year (and maybe more so in precal) is talking about how x^3 has three roots at 0, with (x-2)(x-3)(x+1) we just translate those three roots to 2, 3, and -1 just like we translated (x +2)^2.  Is this even a thing or am I just seeing transformations everywhere? Also, yes, we do call cubic functions and triple roots “John Travoltas” (I stole it from someone on the #MTBoS) because:

Then we spend a day practicing:

(file here).  I usually go around and stamp each row when they have completed it successfully, and then can only turn it in once it has all four stamps.

At this point I throw in solving sum/difference of cubics and quartic trinomials:

(file here)  S.O.A.P is a handy mnemonic that I learned from my coteacher. It tells you the signs of the sum/difference formula: Same, Opposite, Always Positive.  It becomes a bit of a chant: “Cube root; cube root, square, multiply, square; same sign, opposite sign, always positive.”

Some homework:

(file here) Because of scheduling, it was a good time to throw in complex numbers for a day or two:

(file here) Ugh, now there’s something that can be taken out of Algebra II if you ask me (but no one ever asks).

At this point I usually take a break and quiz:

(file here).  Yup, there’s a review powerpoint as well:

(file here).

Then it’s time to really get our hands dirty with some division:

But I really want to try the box method next year as promoted by @TypeAMathland (especially since I can probably get a tutoring session since Anna is going to be my #TMC15 roomie!).  But with just a bit of modification I can still use the same homework:

So the Algebra II book that we use likes to spend a section on “I give you a factor, you find all the rest” but that seemed like a waste of a day, instead I go with “I give you a factor, find all the zeros” as a lead-in for when “I give you no factor”:

I learned a while back that it’s handy to have them figure out how many answers there should be and write out that many blanks. Otherwise many would forget that the original given factor also told you about a zero.

Here’s another day that I’m not a fan of:

(file here).  I finally took a stand and stopped teaching the “what are the possible number of real/imaginary roots this could have?” because WHY?  I almost want to take a stand on “hey, I’m only going to give you 2/3 of the answers and one of them happens to be imaginary so do you think you could figure out the third?” because WHY? but I’m pretty sure that is specifically in our course of study. At least it’s a nice breather after all the heavy lifting we’ve been doing.

Then finally the moment we’ve all been waiting for!  Let’s solve some polynomials!

After doing a couple without the calculator, we start using the graphing calculator to find the first zero (or the first two if it’s a quartic).

Then let’s wrap it up:

(file here).  And of course a review powerpoint:

(file here).

Are polynomials one of your favorite things?  Do your kids know who John Travolta is or do you have to do the dance for them? Wait, am I the only one doing the dance?

## Precal Files: What’s our Vector, Victor? (+ Parametrics)

Posted on 0 comment

(More files and FAQs here) Because it’s required to watch and/or quote when discussing Vectors:

Ok, so even though we did a lot of talk about vectors at TMC last year, I still haven’t gotten full control of them and taught them in a way that shows how gosh darn handy and “easy” they are. This is the NoteTakerMaker I used this year:

File here. With this homework:

File here. The year before this, I thought because it was such an “easy” topic, that it would be a good chance for my Honors students to practice reading and understanding math without my “mama birding” it for them, which I think is a skill they need for college. So I made a worksheet that condensed the section from the book into one page:

File here.  Then the next day I had them read the actual textbook section on the dot product.  How did it go?  Well, let’s just say I didn’t try it again this year.  Maybe I should incorporate more of it throughout the year rather than just springing it on them?  Anyway, here’s this year’s dot product NTM:

File here. Then we did some bearings problems:

Oh, see my neat trick about remembering when to use Law of Cosines? C = if you know two sides and included angle and O = all three sides S = otherwise use Sines!

File here. We were told to teach it both ways (geometrically and component-wise). WARNING WARNING WARNING! Some of these have some ambiguous Law of Sines issues!  That I was completely unaware of when I pulled the questions because the key was also wrong!  It lead to a great discussion the following day when the geometric and component-wise answers didn’t match, but it would have been nice to have some warning, so I’m giving it to you now.

ANYWAY, then it was onto parametric equations.  I used this modified introductory activity:

File here. It was quick and went pretty well,  although I secretly like this introduction that I actually made way back when I was a student teacher, which introduces vector equations and ties it into parametric:

File here. and coordinating worksheet:

File here.  This is the NTM I used this year:

File here. Followed by day two:

File here.  Then some applications:

File here. For the first part, we watched three different dog jumping videos and tried to guess which velocity/angle matched with each one.  See them here, here, and here (!!!! OMG SERIOUSLY YOU HAVE TO WATCH THE LAST ONE, it’s the famous corgi flop:

Then it’s time for our study guide:

File here. Video key here and here.

Or maybe you’d like to use this one if you focused on vector equations as well as parametric:

My Thing
Hey, I haven’t done a “my thing” in a while!  With everyone packing for various conferences and vacations (and soon TMC!), I thought it might a good time to mention  ebags packing cubes:

These are the bestest!  You can fit so much in one bag, then stuff the bags into your suitcase. Everything is neat and organized when you get to your hotel, you can just put the bags directly into the closet or dresser drawers, then you don’t feel like you’re living out of a suitcase all week. I have the red, but I’m really digging this tropical blue, too!

Category: Precal | Tags: , ,

## Precal Files: Polar Coordinates and Complex Numbers

Posted on 0 comment

A quick aside before I start sharing: in one of our tours in Iceland, the tour guide mentioned that 3 Miss Worlds have come from Iceland.  Since there’s about 320,000 citizens, and about half of those are female, it means that you have a 1 in 50,000 chance of meeting a Miss World in one of the bars (there was also a side note about the Vikings choosing all the pretty women from Ireland and Scotland to take and leaving them with….). Then the punchline: “Iceland: where everyone is statistically exceptional.” How could I not like this country? Plus over half the population does not discount the fact that there could be elves. Oh, and they eat ice cream all the time.

One thing they do not have in Iceland is polar bears. But if they did, wouldn’t that be an awesome segue into polar coordinates?

Alas, I guess we’ll just have to start with some Polar Coordinate Battleship then these notes:

And some equations, and a hint of graphing by hand:

The first year I did polar equations, we just did them all by hand and did some noticing. If you’d also like to, here’s a worksheet:

This year, I did a desmos exploration (read more about it here):

Sadly, the title is cut off of the next worksheet, it’s labeled as “The Greatest Polar Graph NoteTakerMaker Ever.”

Does the fact that a negative rotates a lemniscate 90 degrees make you freak out because HOLY CRAP THAT’S WHAT IMAGINARY NUMBERS DO ON A NUMBER LINE WHAT THE HELL, MATH??? or is that just me?

File here.

We did some practice with matching (from Mastermathmentor) and some practice sketching worksheets (from another teacher).  Also a wee bit of “where do two polar graphs intersect?” I’d also point you to Michael’s Reason and Wonder polar posts for some more ideas on introducing and graphing.

Then some complex numbers:

File here.  I did a lot of stuff in class (this actually took us two days) from the Better Explained website: here, here, and here.

Finally a study guide:

File here. And study guide videos: #1-16, #17-26, and #27-37 (even though it says 17 as the first problem-doh!)

Find more precal files and FAQs here. Hope you’re finding these helpful! 🙂

## Algebra II Files: Matrices

(See more Algebra II files and FAQs here)I’m sure this is post you’ve been waiting for!  This is totally how I feel after I typing up a matrices worksheet:

But have no fear, my little math darlings, I’m here to save the day….with handwritten notes:

Ok, but at least I typed up the homework for ya!  With graphs!

File here. Is that not the prettiest worksheet ever?  Now let’s try some multiplying:

File here. And some practice:

File here. What’s that you say? You’re totally awed and inspired by my ability to put a fraction inside a matrix?  Aw, it was nothing.  If you’d like to learn how to do it yourself, may I recommend my equation editor post?

Then, yup, it’s back to handwritten again:

I’m taking a stand on not teaching finding 3×3 determinants by hand.  I almost want to take a stand on not solving matrix equations by hand, too, I mean it’s pretty much just witchcraft at this point and it’s not like we don’t have calculators, which we’ll learn to use the next day to solve some systems:

File here. Then some more applications practice (after the first four, we did the rest in groups on the whiteboards) and the study guide:

In the same file here.  Added bonus: Study Guide Key videos!  #1-12 here and #13-25 here.

Does your school teach matrices in Algebra II? (We moved it to Precal for a year which was great, but then they decided to move it back)  Do you do them all by hand or all technology or a mix?  Anything to make them more exciting?

Category: Alg II, Precal | Tags: ,

## Geometry: Transversals & Linear Equations

Posted on 0 comment

tl;dr: Another chapter’s worth of files for Geometry: transversal angles, graphing lines, and writing equations of lines (more files and FAQs here).

To repeat my previous warning: it’s been 3 years since I used these to teach Geometry, so they’re not the bestest, but sometimes you need a quick file or something to build off, right?  With that said, let’s get started: File here. Yeah, looks like I ran out of time and/or motivation on labeling everything on the document, but why I just didn’t copy and paste from the following powerpoint I made, I can’t explain. Also, these are legal which works out perfectly to print 2 to a letter page (which reminds me I need to do a post about “how to get a lot of crap on one sheet of paper”).

As for how to label each diagram, look no further than the following powerpoint, which also goes through each problem with highlighting lines and angles. I find this is a great way to both introduce topics and go over student work, especially if you have a remote clicker.

Next up, let’s talk about parallel lines and transversals:

File here, again needs hand-labeling.

Then some practice (hey, look, I actually labeled everything in the document!):

file here. And a powerpoint to go with it (alternatively, you could just use the powerpoint as a quick review or with whiteboards)

File here.

Now for some lines…why does it feel like I’m teaching these from scratch every year?  No matter if it’s Geometry, Algebra II, or Precal?

Slope:

File here (“ugly 17 refers to our workbooks because we had two different ones that year. One that was nice and had a pretty cover and one that was “ugly”).

Graphing (yes, this worksheet probably looks familiar if you’ve been paying attention):

File here. The elevator is because you ride up/down to your floor first, then go to your hotel room.  You don’t go to where your hotel room would be on the first floor, then have your own personal elevator take you up.

Then we wrote some equations of lines, then the next day brought in parallel/perpendicular. Notice I’m still using the old-school point-slope form, I like y = m(x-h) + k form now.

File here. We mark out the original equation after we steal the slope from it so we’re not tempted to use anything else from it in our new equation.

And some practice (I sometimes make worksheets with more problems than I assign, maybe doing evens in class with a partner and odds for homework):

File here. Then it’s time for a study guide.

file here. and a powerpoint key

And that’s all I got!

Category: Geometry | Tags: , ,

## We Interrupt Math to Bring You a Vacation

Posted on 0 comment

My husband and I love to travel, and I love having something to look forward to during the school year.  To tell you how rough this past school year was, we started planning this trip last October. 🙂  My husband got to choose the destination because of his milestone birthday and he chose…Iceland?  We ended up spending a week in Paris and a 3 days in Iceland.  A week was just perfect in Paris, but three days is definitely too short in Iceland!  If you are traveling to Europe, I would I highly recommend taking advantage of Icelandair’s cheaper fares and their free Iceland stopover offer!  And since you twisted my arm, here are some pics:

Notre Dame and one of the “locks of love” bridges that hadn’t been dismantled yet:

Obligatory Eiffel shot:

This was one of my favorite things we did! If you’re ever in Paris, make sure you take a ride with Romain in Clementine:

The view from our apartment:

Dancing in the ballroom at the Musee D’Orsay:

We also happened to have dinner one night right where they were setting up for the annual White Party, and did some twitter tracking to find them at the Louvre. The story is it started with 10 people, you’re only on the invite list if you’ve been before, and they don’t tell you where it is until 2 hours before it starts. You’re also supposed to bring a table, chairs, wine, food, and a guest.

We went on a bicycle tour of Versailles,

including Marie Antoinette’s fake village that she had built:

(Does that not look like Belle’s house??!?!?)

Now off to Iceland!!!  It reminded me a lot of Ireland, which is one of my favorite places in the entire world, so that is a really big complement!  Even though they were about a month behind in spring coming, there was still a bit of green around.

And a lot of waterfalls.  🙂

And of course geysers!

But some of the landscape was a bit more moon-like:

or just misty:

One of my two favorite things in Iceland was a midnight horseback ride on Icelandic horses.  (We used Viking Horses and LOVED them)

and my other favorite was going INTO a glacier!

This used to be a German torpedo truck and we rode it in up the glacier (added bonus: Fitbit thought I was walking and I got 82 flights of stairs!)

Pictures do not really do it justice– it is eerie and awe-inspiring and beautiful all at once.

And one more picture because MATH!

Yes, their history museum is called “871 +/- 2” because they thought it was settled in 871, but now there may be evidence to the contrary.  Is that not the most adorable thing you’ve ever seen?

Category: Uncategorized

## Precal Files: Dude, I told you I love Trig.

tl;dr: Notetakermakers, homework, and study guides for trig sum/difference/double/half angles, trig identities, and solving trig equations.  Part of my ongoing series of posting all of my files; see more and FAQs on this page.  Plus I tell you about an awesome book at the end!

Yes, I love trig. I love that I there’s always new ways to think about and teach it. I love that it’s so elegant. And I love that it’s one of those topics that looks scary and is scary and new but eventually most kids get it and feel so smart about it.

Now, check out the middle box of the “three fraction hints” above. If it’s the first time you’ve seen this multiply-by-the-common-denominator-of-the-small-denominators, then be sure to read this post about it.  It’s totally awesome and is so handy in Precal and Calculus!

Now, don’t worry, we don’t do all of those in identities in one day!  We do the first six together:

This is also the first time I talk about Q.E.D and I tell them they could use any symbol to show “YES! I DID IT!” such as a check, smiley face, corgi, or unicorn.

Then I have them work on the rest of the first column for homework with the rule: if you’ve been on a problem for more than 5 minutes without getting anywhere, stop and move on. Since I teach honors, I know some of them would get trapped in a problem for 20 minutes and then just get frustrated with the whole thing. Then we work on the others in class on group whiteboards for a day, and finish them up whenever we have a few minutes throughout the week.

Another reason I like trig is because there’s ACTING! involved. Sure, you could just show the powerpoint of Sinbad and Cosette when you teach the sum and difference formulas. But why tell it, when you can get four chairs at the front of the room, make some nametags (write the names really big, put them in page protectors, then tie some string through the holes of the page protector), and then act out the whole thing with 3 volunteers?  I even bring in a tie and a scarf for when I’m playing each driver. And yes, as Cosette, I wear sunglasses so I can do this move:

and say, “we do not have the same sign.”  Although, confession: I have no idea how the story is supposed to help memorize the tangent sum/difference formula–please let me in on the secret if you know it!  Another confession: Crazy Stupid Love is one of my favorite movies of all time.

FOCUS!  Back to sum and difference:

File here. We also decided this year not to do the problems like 7 and 8 so I will allow you to skip those as well.  You’re welcome.

File here.  If you do skip 7 and 8, also skip 12, 13, 18-20 on the homework.

Some double/half angles:

File here. Fun tip: have them derive the double angle formula of sin and cos from the sum formulas and then everybody gets to feel smart.

File here.  Now’s a good time to consolidate all our knowledge:

File here.  (omit #19 if you’ve been omitting stuff) And then begin solving trig equations!

Check out that awesomeness about sin 2x having twice as many answers, but 1/2x could have the same number of answers or even no answers between 0 and 2pi.

Yeah, I was really clip-art happy when I was making all these.

File here.

And then some quadratic and mixed equations!

Cute and cuddly, boys, cute and cuddly….

File here.

It’s only one section, but worthy of its own study guide and test.

File here.  There’s even a couple showme videos for the study guide: #1-9 and #10-16

My Thing

My thing this week is Simon vs. The Homo Sapiens Agenda. I read about 50 pages of it the night before last, then spent all afternoon yesterday finishing it because I HAD TO KNOW WHAT WAS GOING TO HAPPEN TELL ME TELL ME TELL ME.  And it’s obvious that the author works with teenagers because the dialogue is spot-on.  And they’re normal teenagers doing normal teenager-y things which is a rarity in YA. And it’s just a nice pleasant story where no one dies, not even the dog. 🙂