Math = Love: September 2014

Tuesday, September 30, 2014

Things Teenagers Say Volume 17

So, apparently, my blog posts about things teenagers say has become the new, cool thing for the students at my school to read.  They've started reading them and trying to guess who said what.  High school students reading a math teacher blog.  Who knows where this could lead?  I know that my decision to become a math teacher was influenced by the fact that I started reading math teacher blogs in high school.  Maybe one of my students will take a similar route some day???

Previous volumes of Things Teenagers Say
Volume 1 | Volume 2 | Volume 3 | Volume 4 | Volume 5
Volume 6 | Volume 7 | Volume 8 | Volume 9 | Volume 10
Volume 11 | Volume 12 | Volume 13 | Volume 14 | Volume 15
Volume 16

--

Ms. Hagan, is your house number 314?  Because that would be awesome.  Your next house should have that house number!

What if you painted your house number on your mail box so it was a math problem that the mail person had to solve?  Could we help you do that?

--

If I ever get in a fight with her, I'm going to put on mittens.

--

Slope Dude makes the world go round.

--

Student 1: Do you have a life outside of school?
Me: Duh!  Of course I have a life outside of school.
Student 2: And, what do you do outside of school?
Me: I spend my time coming up with fun math activities and creative ways for you guys to take notes.
Student 2: So, basically, you're saying that we are your life.
Student 1: No, she's saying that I am her life.
Me: Yes.  Student 1, you are my life.
Student 2: Wait, I thought I was your life.
Student 1: We'll fight over this after school.  We're going to fight over you.  Only one of us can be your life.

--

Student 1: Oh come on!  You can tell us!  We won't tell anybody.
Student 2: Guys, there's a 50/50 chance that Ms. Hagan has had her first kiss.

What does this say about me that at nearly age 25 they think there is a 50% chance that I have never had my first kiss???  And, to those of you reading this, the answer to this question is also none of your business. :)
--

Guys, can you imagine what it would look like if Ms. Hagan was fighting someone?  She would probably throw a calculator at them, hit them with a ruler, and stab them in the eye with a protractor.

--

Ms. Hagan is my homie.  Seriously, she's my favorite teacher because she helps me with my grades and she ain't even rude.

--

By the trivia questions you ask us, we can tell that you have no life.

--

Student 1: Did you ever use one of those computers with the box on the back?
Me: What do you mean a box on the back?
Student 1: I don't exactly know how to describe it.  But, it looked like there was a box on the back of the screen.
Me: Oh, you mean a non-flat screen monitor.  Yes, I've used one of those before.
Student 2: You've actually used one before?!?  Have you ever see one of those tvs with the box on the back?
Me: Ha ha.  Yes, I've used one of those tvs with the box on the back.  When I was a kid, that's all there was.  The tv we had when I was growing up was inside a wooden console.  It was a legitimate piece of furniture.  And, it had buttons for each of the channels next to the screen.  Every time you turned the television off, it would revert to channel 2.
Student 2: Wow!
Student 3: I saw this big tv once that they probably could have watched Jesus' birth on.

--

Student: I saw a floppy disk in a museum once.
Me: Do you know how much data a floppy disk can hold?
Student: 1 gig.
Me: Ha ha ha.  No.

--

Student: I have an unborn fondness for math.
Me: You have a what???
Student: Oh, I have an inborn fondness for math.

--

I love math.  Math is my destiny.

We'll ignore the sarcasm that was dripping from that sentence...

--

He's not in a relationship.  He's in an extended friendship.

--

My circle looks like a "squoval."

--

If the object of math was to not get the right answer, I would be the best!

--

Me: Class, NEVER divide by zero.  It will cause the world to explode.
Student 1: So we could be like Osama Math Laden and make things explode by painting "divided by zero" on them?
Student 2: What if somebody painted 2 divided by zero on your car?  Would it explode if you got into it?

--

I want to dissect a cow tongue.  That sounds amazing.

--

After sharpening their pencil with the world's most amazing pencil sharpener:
I could stab somebody with this!

--

Ms. Hagan, I was doing the dance from Gettin' Triggy Wit' It, and my cheerleading coach made me stop.  She said it was inappropriate.  So, I told her that you taught it to us in class.

--

After using the document camera to demonstrate something:

You look like you have soft hands. Are your hands soft?

#Notanawkwardquestionfromateenageboyatall

--

I love my notebook.  I'm going to keep this thing forever.

--

Me: Are you staring off into space or are you using the number line?
Student: I'm floating down the number line in my space ship.

--

To the student who decided to pull down his sweatpants during class, you certainly made life interesting.  I'm thankful that you were wearing shorts under your pants.  When I asked you why you insisted on walking around the classroom with your sweatpants around your ankles, I certainly wasn't expecting this response:

When your pants are down, you're prepared for anything.

--

Does anybody know where I can buy a cute boyfriend for fall?  I need one.

--

Can I show you a video my friends and I made this weekend?  We were pretending to make whale constipation noises.

--

Student: Ms. Hagan!  I need to take your picture before class is over.
Me: WHY???
Student: I need your picture so I can post it on Drumright Singles on Instagram for you.
Me: Uhhhhh....no.  There is no way you are posting my photograph on the Drumright Singles page.

--

Student 1: Have you ever been to Dillards?
Me: Yeah.
Student 2: Isn't that like a sex shop?
Me: No.  It's a department store.

--

You are pond water.
I am Fiji Water.

--

Can I rise 2 and jog 3 instead of rise 2 and run 3?  We've got a football game tonight, and I need to conserve my energy.

--

Me: It looks like a tornado came through my room.
Student: Actually, there are lots of tornadoes in here right now.
Me: Touche.

Our school mascot is the tornado...

--

Said with much sarcasm...

Me: I love technology.
Student: Technology does not love you.

--

On the THIRD day of the school year:

Student: You're a good teacher.
Me: You barely know me.
Student: I've heard good review of you from last year though.

Monday, September 29, 2014

Solving Quadratics by Factoring and the Zero-Product Property

Ugh...I'm still finding random interactive notebook pages from last year that I never blogged about.  This is part of the reason that I'm trying to force myself to blog my notebook pages this year as entire units.

Here is Solving Quadratic Equations by Factoring.  I typed up the Zero-Product Property for students to cut out and glue in their notebooks.  In the future, I'd probably type up the steps as well to save time.  I might make them fill in the blank or something similar...

Sunday, September 28, 2014

Well, since I posted my very own quadratic formula song yesterday, I guess it's only fitting that I post the rest of my quadratic formula stuff from last year on my blog.  This post has been setting in my drafts folder since Pi Day.  I obviously need to blog more often...

My first goal was to get kids to memorize the quadratic formula.  I know from reading a lot of other math teacher blogs that many states provide students with the quadratic formula on a formula sheet on their state standardized tests.  Oklahoma is not one of those states  If they want students to specifically use the quadratic formula on a certain problem, they may provide it in a box next to the problem.  But, what if my students want to use the formula at other times?  If they don't have it memorized, then it can't be a tool in their tool box.

Inspired by Journal Wizard, I decided to make a tangram puzzle with the quadratic formula written on it.  I've uploaded a template for the tangram puzzle below, but if you want to use this, you will have to write the quadratic formula on it yourself and cut apart the pieces to scramble the puzzle.  This was one of those interactive notebook pages that was thrown together 7 minutes before first hour started.  I tend to have a lot of these...

Give the kids the scrambled tangram pieces.  Let them cut it out and assemble the puzzle.  Glue in your notebook.

We've already talked about solving by factoring and solving by square rooting.  But, both of these required our equation to be just right in order to use the method.  The great thing about the quadratic formula is that it ALWAYS works.

After gluing in the formula, we did an example to keep in our notebooks.

Honestly, though, most of the first day we spent on the quadratic formula was focused on memorizing it.  It didn't help that 50% of my Algebra 2 classes were gone on this day either...

Emily shared several versions of the quadratic formula song with me.  I already knew the Pop Goes the Weasel version from high school.  The other two versions gave me and my kids trouble.  You never know until you try, though.

I'd read about a teacher having their students sing/recite the quadratic formula to another teacher as an assignment before, and I decided I had to try it.

Here's the very official looking form I made up:

To make sure that students could recite the formula to anyone, I wrote out the formula both in "math" and in "English."  We only have 12 teachers in our high school, so I was afraid that they were going to get mad at me/frustrated with hearing the song from the 36 or so Algebra 2 students I had last year.  But, I'm not sure a single teacher ever actually mentioned the assignment to me.  Hmmm...

There are several possibilities here.
1.  My students never actually recited the formula or sang the song for their teachers.  Instead, they forged their signatures.

2.  The teachers thought it was a perfectly normal assignment and felt no need to comment on it.

3.  The teachers thought this was a crazy assignment, but they also think of me as a teacher with crazy ideas.  So, this came as no surprise to them.

Hmmm...

Pop Goes The Weasel ended up being the most popular way, by far, to memorize the formula.  My Algebra 2 classes quickly fell in love with the song.  And, they would break out into song quite often.  Anytime I would write the quadratic formula on the board, I would sing the lyrics as I wrote them.  My students started doing the same.

Last year, I did a great job of getting kids to memorize the formula.  I did a much worse of getting them to use it properly.  Positive and negatives ended up tripping them up way too much.  Plus, they all preferred to solve their quadratics by graphing when given the choice...  This is on my list of things to improve upon for this current school year.

Saturday, September 27, 2014

A Most Tardy Reflection on Twitter Math Camp, the MTBoS, and Online Dating

I've put off writing about my TMC experience because, honestly, it was overwhelming.  And, when I say overwhelming, I mean it in the best possible way.  If you want recaps of various TMC sessions, you should probably look elsewhere.  This post is going to be less informative and more on the reflective side.  And by reflective, I mean completely random!

I'm going to compare Twitter Math Camp and the MTBoS to online dating.  I actually made this comparison at least twice during the four days of TMC.  And, each time, I just got weird looks.  Apparently, the majority of TMCers don't have online dating experience.  After seeing the results of Michael Pershan's survey, this made a little more sense.

The majority of TMC participants are over 30.  With the mean and median ages in the mid to upper thirties, I guess it makes sense that most would have experienced dating without the influence of the Internet.

I know that at age 24 I'm young.  But, in the TMC world, I'm apparently a baby.

Honestly, I wish I didn't have online dating experience.  I fully intended on meeting a guy in college and marrying right after graduation.  That did not happen.  Instead, I graduated and moved to a town in the middle of nowhere.  I wasn't really thinking about the prospects of finding someone to date in a town without a Wal-Mart or even a stoplight when I accepted this job offer.  But, what's done is done.  And, I have to trust that this is all part of God's plan for my life.

After a year of living in a tiny town and zero dates during that year, I decided to venture into the online dating world.  [To my sister who may or may not be reading this because she tends to skim my blog posts because she finds them "boring", I apologize for never telling you that I tried online dating.  I think the crazy stories that resulted from this experience are still funny.  I'll have to share them with you sometime!]  Entering the online dating world is actually kinda similar to becoming part of the #MTBoS.

Ways Online Dating and the #MTBoS are the Same

1.  You have to spend hours/days/weeks coming up with the perfect, clever username.  This will be the first thing people judge you on.  In the case of the #MTBoS, the more math-y your username is the better.  In the case of online dating, the opposite is probably true.  Once you settle on a username, there's a 97.2% chance that you'll be told that this username is already taken.  And, you have to begin the process all over again.

Side note: what does it say about me that I recently started trying to think up a cool mathematical username to use if I ever decide to try online dating again?  I mean, we all know that I already have the best mathematical username in the world with mathequalslove.  But, I'd kinda prefer to tell a guy in person that I spend a ridiculous amount of my life blogging about teaching math instead of letting him discover it before he ever meets me.  He needs to see the normal side of me before he sees the "I love teaching math with all my being" side of me.  Oh wait.  That is the normal side of me.  I can discuss things other than teaching math, though.  :)  So, I'll need a new username.  Current contenders: lessthanthree, lovejesusandmath, ratioofcircumferencetodiameter, or myfavnumberispi.  Of course, now I can't use any of these because they'll all lead back to this blog post.  Bummer...

2.  You get to decide what people see/know about you.  With online dating, this means carefully selecting photos for your profile that only capture you at the perfect angle or on your best side.  When writing your profile description, you can conveniently leave out the fact that you live in your parents' basement and haven't seen sunlight in seven years.  Or, as we all know, you can claim to be a French model.

There was a lot of talk at TMC about feeling inadequate.  And, it was mentioned that if you start comparing yourself and your teaching to what you read about on the blogs of others, you will feel inadequate.  The activities and lessons that most people write about on their blogs are the rare perfect days or nearly perfect days in their classrooms.  Most people don't write about the lessons that bombed.  They don't write about the day they gave their students boring notes or a mind-numbing worksheet.  Blogs tend to be highlight reels.  And, if you start to compare the ups and downs that are a reality of being a classroom teacher with a highlight reel of only the best lessons of another teacher, you will fall short in comparison.

If you've read my blog for any length of time, you know that I tend to blog about everything under the sun.  The lessons that went well.  The lessons that didn't go so well.  If I only shared super-polished lessons, this blog wouldn't exist.  Some in the blogosphere have made comments about how they aren't sure how I became a "superstar blogger" in such a short amount of time.  First, I don't view myself as a superstar.  I'm just a normal, everyday teacher who has a tendency to over-share with the world.  And, for some crazy reason, people read it.  Case in point: you are currently reading a blog post about my online dating experiences.  Someday I might regret putting all this out there on the Internet for the entire world to read...  I strive for honesty in my blogging.  I want my blog to be an accurate reflection of my teaching career--the good and the bad.  Others strive to showcase lessons that went well.  And, still others downplay their achievements through their blogs.  They claim that they have nothing worthy of sharing when they clearly do.

3.  Other people will judge you for your participation.  Have you ever tried to describe the #MTBoS to someone who just didn't get it?  Yeah, I've seen others raise their eyebrows in response to my gushing about how excited I was for Twitter Math Camp.  I have to remind myself that this is okay.  Not everyone needs the #MTBoS like I do.  Not everyone teaches in a math department of 2 where they feel isolated and starved for collaboration.  Then, there are the looks you get when you admit to trying online dating.  As my students so nicely put it, online dating qualifies you as "desperate."  There are those who get it.  Those who have tried it out themselves or who know of someone else who has had a positive experience.  And, there are those who will never get it.  My parents might fall in that second category.  I'm pretty sure they have watched too many Dateline specials on television about the dangers that lurk online.

Though, one of my Algebra 2 classes last year was all for me doing online dating.  A few students got together one day after we did Dan Meyer's Graphing Stories and wrote out an online dating profile for me.  "I like taking long walks along the beach and graphing them.  I love reciting the quadratic formula.  And, I enjoy reading math books by a roaring fire."  If that won't catch me the perfect man, I'm not sure what will!  ;)

4.  Statistics matter and don't matter at the same time.  There's nothing more frustrating than seeing that 50 people have viewed your online dating profile but haven't sent you a message.  But, I speak from experience when I say quality > quantity.  The messages that you do receive can cause you to begin doubting the effectiveness of elementary school literacy instruction.  I tried to be very specific in my dating profile about what characteristics I was looking for in a potential relationship.  If a guy was to read my entire profile, he would not need to send a "how do you feel about friends with benefits?" message.

It was difficult, but I restrained myself from sending back messages like this:

Dear Random Guy,
I really appreciated the long, semi-creepy message you sent me saying that you felt that we were soul mates based on the remarkable number of similarities we share.  It is cool that we are both vegetarians.  I'm a math teacher.  You are going to school to be a history teacher.  I fail to see, however, how these two facts make us destined to spend the rest of our lives together.  Additionally, the fact that you spend 2-3 hours meditating each day is nice to know, but it does not negate the fact that we do not share the same faith.
Sarah

With blogging and tweeting, it's easy to get caught up in how many retweets you get or how many pageviews your blog receives.  Building a community inside the #MTBoS takes time.  I would much rather have a few readers who take the time to leave thoughtful comments instead of a bunch of readers who read but never comment.  I follow a bunch of people on twitter, but if you looked at my tweets you would see that I tend to communicate with the same small group.  These tweeps get me.  They're always there for me.  And, it was them that I was most excited about meeting at TMC.

5.  Things can get awkward when you meet in person, but awesome, life-changing things can still result.

Have you ever tried to have a conversation with someone in person who you've only ever communicated with through the written word before?  Yeah, that's awkward.  I attribute the awkwardness to the fact that you feel like you already know the person and know nothing about the person at the same time.  I tend to be a wordy person, so the amount of information that a guy could know about me by the time we finally meet in person is substantial.  Maybe this is why all the relationship articles suggest taking your relationship to the in-person level ASAP.

I feel like going out on a date with someone you've been talking to online is like trying to jump to the conversations you would normally occur on dates 4, 5, or 6 with all the added necessary awkwardness of dates 1, 2, and 3.

I think that the nature of the MTBoS compounds the potential for awkwardness at an event like TMC.  In the MTBoS, I'm not just communicating my ideas with a handful of teachers.  No, there are thousands upon thousands of people reading what I write.  But, I really have no way of knowing who reads what.  Sure, I know when people leave comments that they have read a certain post.  I read a lots of blog posts without leaving comments, and I know most people do the same.  When I meet somebody, will they know that I read their blog?  Will they assume that I read their blog?  Should they?

Honestly, I think my introverted personality made things most awkward for me at TMC.  As much as I wanted to meet all of my tweeps, I just couldn't make myself go up and introduce myself to these people.  I am not an anti-social person at all.  I love to talk to people.  I love to hang out.  I just struggle with being the person to initiate the conversation.  This is something I'm currently working on in my life, but it's definitely a process.  (And, God has certainly been giving me plenty of opportunities to initiate awkward conversations of late!)

So, I was the girl standing in the hotel lobby 3 feet away from Dan Meyer who couldn't bring herself to say, "Hey Dan, I'm Sarah.  I started reading your blog when I was a junior in high school.  And, you're one of the main reasons I blog and tweet today.  Thank you!"

Picture proof that I met Dan Meyer:  :)

Thankfully, Dan doesn't have the same issues with starting conversations with random people whose blogs he reads as I do.  And, we ended up having a nice conversation after he introduced himself to me.  "You're Sarah Hagan, right?" "That's me." "Hi, I'm Dan."  If there was anybody at #TMC14 who shouldn't have had to introduce himself, it was Dan.  #Danweallloveyouandknowwhoyouare  Now why would I think that was such a hard thing to do?  We ended up talking about what makes for a good blog post, the crazy things that can happen as a result of blogging, and the major influence that blogging has had on my life as a new teacher.  Then, the next day, Dan referenced our conversation during his keynote address.  Ummmmmmmmmmm there are 150-170 math teacher bloggers in the room and you decide to talk about me?!?  That's cool.  Well, actually it's more than cool.  However, I found that when I tried to explain how cool it was to others not in the #MTBoS, they just didn't understand.

And, this was just one awesome conversation of many that happened during the 4 days of TMC.  I got to meet so many people whose blogs I've been reading since high school and college.  Plus, I was able to connect with a lot of my interactive notebook friends and share awesome ideas.  And, I met new people and found new blogs to read, too.

So, am I thankful that I went to Twitter Math Camp 2014?  Yes, yes.  A million times yes!  It was the most exciting, exhilarating, useful professional development I've ever experienced.  I've got more to write/share/reflect on, but this is a start.  TMC was in July.  It's almost October . I'm just a few months behind... :)

Singing and Writing Math Songs

My Algebra 1 students are currently working on graphing linear equations.  There are a ton of great math songs/videos out there about this topic, and I've been showing to them to my students.  We've watched Graph Shop, Graph!, Rise Up Run Out, Slope Rida, and The Adventures of Slope Dude so far this year.  I also showed Gettin' Triggy Wit' It to my trig class.  My Algebra 2 students are soon going to feel left out because we haven't watched a video all year...

One of my usually very quiet eighth graders raised her hand this past week and asked, "Why don't you make awesome math videos for us?"  Well................ummmmmmmmmmmmmmmm...........you see... it turns out I'm not the most creative person.  I tend to leave this job to the professionals.  And by "professionals," I clearly am referring to math teachers who are much cooler than me.  I know the fact that there are cooler math teachers than me in this world is hard to wrap your mind around, but please try.

My trig students have just started working with radians.  I wanted them to get a grasp of just what a radian is.  I know that when I took trigonometry in high school, I knew how to do a lot of trig, but I didn't quite know the "why" behind a lot of what we did.  I was the type of student who didn't ask questions.  If a teacher gave a rule or showed a procedure, I followed it.  Since I've started teaching, I've become a lot more curious about mathematics.  What is a radian?  Why does that shortcut work?  What is that little number perched by the radical sign called?  Why are they called conic sections?  I'm continually learning, and this is one of the reasons why I LOVE my job.

When I started researching just what a radian was, I found a great discovery activity that I'll blog about soon.  In one of the lessons I found, there was a song to help students remember the circumference of a circle.  The students at my school have a tough time memorizing formulas.  I'm not sure if that is a universal trait or if our students are just especially bad at it.  When I asked my students if they knew what the circumference of a circle was, they almost unanimously agreed that it was pi * r squared.  Eek...  I guess I should be happy that they at least know a circle formula...

So, class, would you like to learn a song that will keep you from forgetting the formula for circumference of a circle?  Yes.

They insisted on writing the lyrics in their interactive notebooks.  Out of all my classes, my trig class loves our interactive notebooks the most.  Twinkle Twinkle Little Star.  Circumference equals 2 pi r.

Of course, some of my students missed the lyrics the first time, so I had to perform an encore.  99% of the people reading this blog have never heard me sing.  That's probably a good thing.  None of my students have ever asked me to stop singing because it was a painful experience.  And, they're usually more than willing to be honest with me.  Ha ha ha.  That's the understatement of the century!  I still wouldn't classify myself as a good singer, though.

So, bless the child who referred to me as the "Song Bird of My Generation" after hearing my rendition of Twinkle Twinkle Little Star.

Maybe there is hope for me...

Of course, there was that one time I wrote my own math song.  It wasn't that great, so I never did get around to blogging about it.  But, if I want this blog to be a honest reflection of my teaching, I guess I should be transparent when it comes to my #songwritingskillz.

It was last spring.  Algebra 2.  Unit on Quadratics.  I was trying to find a way to get my kids to memorize the quadratic formula.  In high school, I learned the formula to the tune of Pop Goes The Weasel.  So, of course I had to sing this version with my students.  My teacher friend Emily pointed me towards this version set to Adele's "Rolling In The Deep."  I also showed this One Direction version of the Quadratic Formula.  So, I've now given my kiddos 3 different ways to memorize the quadratic formula.  And, are they happy?

No.  One student asks, "Why can't there be a Johnny Cash version of the quadratic formula?"

I'm pretty sure I just laughed and moved on.  But, I went home that night and started thinking.  Could I write my own math song?  After all, I ask my students to step out of their comfort zones every single day in my classroom.  It's only right that I do the same.  Seriously, what's the worst thing that could happen?

Step 1.  Find a famous Johnny Cash song to modify.  Ring of Fire?  Nope.  Folsom Prison Blues?  Hmmm...  I Walk the Line?  Uhhh...yes!  Because "I Walk the Line" could easily become "I Walk the Curve."  #seewhatididthere #itoldyouihavesongwritingskillz

Step 2.  Copy and paste the original lyrics to a word document.

Step 3.  Count the syllables in each line of the song.

Step 4.  Mathatize it.

If you've made it all the way to the bottom of this post expecting a video of my singing the song, you're going to be disappointed.  This song never really made it past the lyrics stage.  When you scroll down to my lyrics, you'll probably understand why. :)

In case you're not familiar with Cash's "I Walk The Line," here's the song so you can get an idea of how the tune goes.  (If you're reading via e-mail or an RSS reader, you may need to click here to watch the video.)

I WALK THE CURVE BY SARAH HAGAN

OH QUADRATIC FORMULA, YOU ARE MINE
YOU HELP ME SOLVE QUADRATICS ALL THE TIME
I JUST PLUG IN NUMBERS AND SIMPLIFY
TO FIND THE ROOTS, I WALK THE CURVE

GET ALL MY TERMS ON ONE SIDE OF THE EQUAL SIGN
FIND A B C AND MAKE SURE I WATCH MY SIGNS
FROM THE DISCRIMINANT I'LL LEARN A LOT
TO FIND THE ROOTS, I WALK THE CURVE

OH X EQUALS THE OPPOSITE OF B
PLUS OR MINUS THE SQUARE ROOT
OF B SQUARED MINUS FOUR TIMES A AND C
IT'S ALL OVER TWO-OOH A!

I PUT EVERYTHING IN MY FORMULA
NEXT I'LL SIMPLIFY AND REDUCE IT ALL
COMPLEX SOLUTIONS WON'T MAKE ME PANIC
TO FIND THE ROOTS, I WALK THE CURVE

OH QUADRATIC FORMULA, YOU ARE MINE
YOU HELP ME SOLVE QUADRATICS ALL THE TIME
I JUST PLUG IN NUMBERS AND SIMPLIFY
TO FIND THE ROOTS, I WALK THE CURVE

So, there you have it.  The beginning and ending of my mathematical song writing career.

Thursday, September 25, 2014

Completing the Square Interactive Notebook Page

So, I didn't do the best job of posting my interactive notebook pages for my Algebra 2 unit on quadratics last year.  The pictures for this post have been sitting in my draft folder for months, just waiting on words to go along with them.  I tend to be a perfectionist when I blog, and this isn't necessarily a good thing.  Honestly, with starting grad school, I just don't have the time to be a perfectionist anymore!

If I wait until I have an hour to craft the perfect blog post, this post will never happen.  And, it certainly can't help anybody if it's sitting in my drafts folder.  And, you can't tell me how to make this lesson better if it's sitting in my drafts folder.  So, this post is going to be quick.  If you have questions, leave them in the comments, and I'll try to answer them!

Completing the square.  AKA my least favorite way of solving a quadratic equation.  I would skip teaching it if I could.  If I'm dealing with a quadratic, I'm going to either factor it if it's factorable, solve it using a graphing calculator if one is handy, or turn to the quadratic formula.  The majority of my students prefer the graphing calculator route, as well.  But, there is a high likelihood that my students will see a question on their EOI at the end of the year that asks them what number must be added to both sides of the equation in order to complete the square.  So, I spend a day on completing the square.

This student obviously did not pay attention on that day.  I guess he did complete the square, but...

To illustrate completing the square, I got out a set of algebra tiles.  I only have one set of algebra tiles, so I used these under the document camera.  I began by putting out the blue x squared tile and two green x tiles.  Class, how many yellow tiles are needed to complete the square?  One.

What if I have four or six green tiles?

We kept adding green tiles and determining how many more yellow tiles we would need to add.  Some students could visualize what we were doing.  Others acted like this was the hardest concept in the world.

As we experimented, I had several students collect data in class.  If we have 2 green tiles, we need 1 yellow tile.  If we have 4 green tiles, we need 4 yellow tiles.  As I started to run out of tiles, I asked the students to begin generalizing.  How many yellow tiles would I need if I had 26 green tiles?

In each class period, one student ended up discovering that you halve the number of green tiles and square the result to find out the number of yellow tiles needed.  After this discovery, we talked about how the number of green tiles represents the coefficient of the x term in our quadratic.

Only after discovering the formula for determining what to add to each side of the equation to complete the square did I pass out our notes to fill in.

Here's the notes and the facing page for reference.

I'm not completely happy with this lesson, but that's normal.  Every year I strive to teach things better.  I learn by posting my stuff on the Internet for others to modify, tweak, and critique.

Wednesday, September 24, 2014

Learning Love and Logic

Today, I’m going to tell you about the time I accidentally attended a parenting seminar.  If you’re wondering why this is a big deal, well…  I’m 24 with no husband, no kids, and no plans to have kids until I'm married.  AKA No reason whatsoever to go to a 2 hour parenting seminar.

So, why was I there?  It’s totally Shelli’s fault.  She tweeted me a few weeks ago to ask what I was doing on September 18th.  TU was hosting a free Love and Logic Parent-Teacher Institute with Dr. Charles Fay.  I’ve never read the Love and Logic book, but I could definitely use some help with my classroom management skills.  Shelli ended up not being able to go with me due to Back to School Night, so I ended up going by myself.

At this point, I’m starting to feel a tad bit awkward.  Everybody else has been raising their hands and looking around at each with understanding glances.  Not me.  I’m trying to avoid eye contact with those around me out of fear that they will ask me what I think I’m doing here.  I obviously don’t belong.  EVENTUALLY, the speaker gets around to asking if anyone is there because they are an educator.  A handful of hands go up, but you can tell that we’re definitely in the minority.

To be honest, 97.24% of the presentation was focused on parenting and not teaching.  But, it was definitely not a wasted evening.  I walked away with lots of things to think about and apply to my classroom.

Major Takeaways:

I let a select few students pull me into arguments.  This reduces my effectiveness.  I don’t have to explain myself and my actions to my students.  Also, I need to let my kids struggle more.  I need to let them experience the consequences of their lack of effort.  I deserve to feel respected in my classroom.  And, my students should be working harder than me.

Here’s my notes.  I bolded the statements that I feel I can definitely apply to my classroom.  Now, I’m intrigued and want to know more about what the Love and Logic Program actually looks like in the classroom.  Now, I just need to find some time to read again!  :)

When dealing with children, always ask yourself, “Who is the adult in the room?”

1. Stop fighting with your children.
2. Take the energy you have been spending fighting with your children and pour it into building their character.  Teach them patience.  Teach them respect.  Teach them how to wait.  Teach them to say “Please” and “Thank you.”

Ask yourself – what is at the heart of how our kids do in life?  The grades on their transcript or their character?

Q: What can I do to help my child in school?
A: Give them chores.  No reminders.  No pay.  Just chores.

“I will be more than happy to do XYZ as long as I feel respected and your chores are done.”

When we focus on character instead of grades, we have guaranteed success.

Allow yourself to love your kids just as they are right now.

Allow kids to experience consequences of their lack of effort.

Want to confuse a misbehaving kid? Smile at them!

If a kid can argue with you, will they ever come to respect you?
If a kid can argue with you, are you still the authority figure?

When talking to a misbehaving kid, be brain dead.  Don’t think about the words coming out of the kids’ mouth.

It’s good for kids to hear the word NO.

The more words I use with an angry, arguing kid, the less effective I become.

You do not have a solemn obligation to make sense to your kid.

ONE THING TO FOCUS ON: Don’t get pulled into arguments.

The most powerful consequences come like a bolt of lightning wrapped in empathy.

Resisting wind makes trees grow stronger roots.

We’ve got to love our kids enough to let them struggle.
Struggle produces growth.

It’s okay if your kids think you’re a wimp!  They’ll find out the truth later.

Chores
• As soon as your kids can walk, they should be doing chores alongside you.
• Do chores together with kids.  Do chores together with teenagers.
• Kids should see us doing things with great enthusiasm.
• Your motto with chores should be: “I help as long as you’re working harder than me.
• Chores are an opportunity for children to experience being helpful and being a part of something.
• If you nag and remind kids to do their chores, who is really doing the chore? You are!
• The more reminders we give our kids, the more reminders our kids will come to need.
Mistakes are the road to wisdom.

If you want an exceptional child/family, don’t have a television in your home.

Empathy THEN consequences.

When you don’t know what to do, it’s okay to delay the consequence.

Tuesday, September 23, 2014

Things Teenagers Say Volume 16

My students continue to spout off the most random statements in class.  For your benefit and enjoyment, I record them here on a regular basis.

Check Out Previous Volumes Here:
Volume 1 | Volume 2 | Volume 3 | Volume 4 | Volume 5
Volume 6 | Volume 7 | Volume 8 | Volume 9 | Volume 10

--

Me: Class, does anybody have a good thing to share today?
Student: I caught a fish this weekend that didn't have a dorsal fin.

#Random

--

Student 1: Ms. Hagan, what's your good thing?
Me: Well, I got a letter in the mail saying I got accepted to grad school.
Student 2: You're not leaving are you?
Me: No, I'm not planning on leaving anytime soon.
Student 2: The last teacher who said she wasn't leaving us got knocked up and moved.
Student 3: I'm pretty sure it's not called getting knocked up if you and your husband decide to have a baby.

--

You better bump up my grade or it's about to get real in here.

--

Me: On the top of your folder, write last name comma first name.
Student: Isn't it going to be confusing that everyone's folder says the same thing?

This student literally wrote "Last Name, First Name" on his manila folder...

--

Guys!  Look at Ms. Hagan.  She looks like a serial killer right now.  It's okay, though.

--

Student: I swallowed a fluffy thing and it got stuck in my throat and it got infected.  But, I went to the doctor, and they gave me an inhaler.  So, I'm going to be okay.
Me: You swallowed a what?
Student: A fluffy thing.
Me: What's a fluffy thing?
Student: Do you know what those little fluffy things are inside pillows?  I swallowed one of those.

--

My sister ran over a coyote with her car.  Did you know you can get \$50 if you kill a coyote?

--

A few months ago, my grandmother's aunt died.  And, they cremated her.  Well, this weekend we had a ceremony for her.  I thought that was weird because ceremonies are only supposed to be for weddings.  But, they put her ashes in a jar, and we buried the ashes.

--

I have two cats.  One cat is an obese cat.  The other cat is a skinny cat.  And, the obese cat is scared of the skinny cat.

--

I can't do my homework at home.  My cat is obsessed with me.

--

Ms. Hagan, are you EVER going to be absent?

--

Ms. Hagan, I know how you could meet a guy.  You could go to Stillwater to OSU where the grad students are.  Then, you should stand outside the building looking really lost.  When somebody asks what you are looking for, you can say "I'm looking for you."

--

Me: What did Thomas Edison invent?
<Blank Stares>
Me: Come on, guys.  What did Thomas Edison invent?
Student 1: Oh, isn't he the guy that who discovered electricity?
Student 2: No, that was Ben Franklin.
Student 3: I thought Albert Einstein invented electricity.
Student 4: Just because Albert Einstein looks like he got electrocuted, it doesn't mean he invented electricity.
Student 2: Albert Einstein is the one who invented math.

In another class the same day:
Student 1: Albert Einstein is the guy who invented math.
Student 2: I bet he has a lot of haters, then.
Me: Albert Einstein didn't invent math.
Student 1: Then, what did he do?
Student 3: Albert Einstein worked on the atomic bomb.
Student 1: Oh.  We've never had a nuclear bomb before, though.  Isn't it true that if there was a nuclear bomb, it would start World War III?
Student 3: Have you ever heard of Hiroshima and Nagasaki?
Student 1: Yes.  But, those were just regular bombs.  If they were nuclear bombs, I would know it.
Student 3: They were called atomic bombs for a reason.
Student 1: Yeah, ATOMIC bombs.  Not nuclear bombs.  We've never had a nuclear bomb before.

Monday, September 22, 2014

I've told a few people about this decision, but I guess it's time to make this "blog official."  (That just doesn't have the same ring to it as "facebook official..."  :)

As I posted before, one of my goals for the #Next5 years of my life is to earn a master's degree.  This is something I've been thinking about since my days of undergrad, but I'd always thought of it in a "someday..." kind of way.  I guess the reason for this is that I didn't know what I wanted a master's degree for.  I think I wanted one just to have one.

But, if you don't really have a reason for pursuing one other than to have one, it's kinda hard to decide what type of degree to pursue.  One master's program will let you be a school counselor.  Another, a principal.  Yet another, an instructional specialist.  There were degrees in educational technology, math education, educational psychology, education theory, special education, etc.  The list keeps going on and on.  There is no one degree that lets one do it all.  And, I haven't even added the option of pursuing a master's in pure or applied mathematics to the list.  Then, there's always the option of going for a master's in an unrelated field.

In high school, I thought I would one day take the school counselor route.  After becoming friends with our school counselor, I see that the job isn't exactly what I envisioned.  I think I love the act of teaching too much to give it up.  I still think it would be rewarding to help students with the college application and scholarship process, but I know there is much more to being a school counselor than that.  It's true that I do love math.  But, I'm not sure if I love the idea of graduate level math.  I'm kinda glad to be away from proofs and all that fun stuff.  I look on those years of studying challenging math fondly, but I'm not eager to relive them.

I keep coming back to the fact that I love teaching.  I love being in the classroom.  School administration would take me out of the classroom, and I think I would miss it dearly.  This summer, I started thinking seriously about grad school for the first time.  I think this renewed interest was probably a result of the 5(!) different math teacher conferences I attended this summer.  When you surround yourself with people who love math and people who have graduate degrees, it inspires you to think about your own future.

I was able to have some conversations with people this summer about my thoughts/concerns regarding grad school.  Thanks to all those who listened to my ramblings/attempts to process my life goals and trajectory.  I remember one late night conversation well.  "Sarah, what are you waiting for?  Start the process now."  Well, I finally got around to doing that.

When I started researching grad programs, I came to the conclusion that I had a few options.  Pack up my life and move closer to a metropolitan area in Oklahoma so I can attend classes at night without having to drive an hour to and from class.  Commute back and forth to class and go insane in the process.  Put off grad school for a few more years until I can decide what to do.  Or, do an online degree program.

Ideally, I would prefer to take actual physical classes, but I live in the middle of nowhere.  I think I may have alluded to it in the past, but I'm going to just come right out and say it.  I truly believe that God led me to accept this job in this town.  Had I chosen a path to take after college, moving to a town without a stoplight where I didn't know a single soul would not have been how I wrote my story.  But, God is infinitely more wise than I can ever comprehend.  My experiences these past few years have reassured me that He has a plan.  I'm still not sure what that plan entails.  And, I have no clue how long He means me to stay here.  I have to trust that He will make it abundantly clear when it is time to move on.

Until that time, I've decided that I need to stop living my life on "pause" and start going after my goals.  This is the rationale behind my decision to do my master's degree online.  This allows me to pursue my goal of furthering my education while staying where I believe God is using me to make a difference for His kingdom.

The program I chose is a M.Ed. in Curriculum and Instruction with a Math Education Emphasis through the University of Texas at Arlington.  One class every five weeks.  One week break in between classes.  Eighteen months from now, I will have a master's degree.  I'm slightly nervous about taking classes online because I've never taken an online class in my life before.  I have enrolled in some MOOCs, but I've never finished one.  This is NOT a good sign.  I think this will be different since the classes will be part of a degree program, and there's always the fact to consider that I'm paying for them.

Thanks to the federal government and a TEACH Grant, I will only have to cover 20% of the tuition costs in exchange for agreeing to teach 4 years after finishing my master's in a low-income school district.  I'm not planning on leaving the classroom anytime soon, so this should work perfectly for me.  I will end up paying less than \$2,000 for my master's degree.  Seeing as I will get a \$1,200/year raise as a result of the additional degree, I think it will be worth it.  Plus, I'm excited to hit the books again.  I miss the challenge of college.  Now that I've been in the classroom, I think the reading and assignments will be more meaningful to me than if I had gone straight into a master's program after graduation.

So, if I'm not posting as much as normal, I have a new excuse.  It's called grad school.  And, it starts TODAY.  :)

Sunday, September 21, 2014

Trig Interactive Notebook Pages for Unit 1: Algebra and Geometry Review

This year, I'm teaching Algebra 1 and Algebra 2 for the third time and Trigonometry for the first time.  Every year, my school offers a different advanced math elective above Algebra 2.  We've cycled through college algebra and statistics.  They were both just okay.  But, this year, I am LOVING trig.

I think there are several reasons for this.  First, it's my first year to do interactive notebooks with my advanced math class.  I guess for my first two years of teaching, I didn't think my advanced students really needed notebooks.  I was wrong.  They need notebooks.  And, maybe even more than that, I need notebooks.  As Megan can attest, I kinda like interactive notebooks.  :)  Then, there's also the fact that I have 15 kids in my trig class to get excited about!  In the past, we've only had 5-7 kids enrolled in advanced math.  (Have you ever tried to collect data to analyze in a class of 5 kids?  So many of the ideas I wanted to try needed more kids to make them work.)  I've taught all but 3 of these kids before, so they already get me and my teaching style.  They are working super hard for me, and the notebooks have been a big hit!

Our first unit for trig was a review of algebra and geometry.  This is especially important for this group of kids because some of them have taken a year long break between math classes.  You can forget a lot of math during a year of no math.  These students were in my Algebra 2 class my first year at Drumright.  And, you can forget a lot of geometry concepts during a year of Algebra 2!  It's refreshing to teach a class that does not require a state-mandated end-of-instruction exam.  We have no curriculum that we *have* to cover.  We're moving at our own pace, and I have no clue how far we are going to end up getting.  I'm hoping to wrap up our study of trig by January/February so we can fit in a few months of other pre-calculus topics this year.

Though, I'm not sure if that will happen.  Many of my students have expressed an interest in our school offering an ACT prep class.  Last year, I stayed after school one day a week for a month or two to help a group of students prepare for the ACT.  I would love to teach an ACT prep class, but our school is too small to offer electives beyond agriculture, FACS, Spanish, FACS, or computers.  And, this is the first time we're offering Spanish in the 3 years I've been here.  I've decided to dedicate Fridays as ACT prep days.  We're working through practice math problems under the testing condition of one minute per question.  I'm hoping it proves to be useful to my students in raising their ACT scores!

Oh, and another thing that makes this advanced math class different than previous years is that I'm using standards based grading.  I've played with SBG a little in my Algebra 2 class before, but this year I decided to go all out.  I do not regret this decision!

For my learning goals, I slightly tweaked Elissa's Unit 1 Learning Goals for her trig class.

Here's my modified version:

Each student was given this score tracking sheet to keep at the front of their Unit 1 notebook section.  Each unit in our notebook begins with a score tracking sheet, a table of contents, and a tab.

My SBG grading scale has 3 levels.
A = Perfect Work (100% in Grade Book)
B = Demonstrates understanding but work may have a few minor errors (85% in Grade Book)
NOT YET = Student has not demonstrated mastery.  (0.5% in Grade Book)

Students are required to reassess all on NOT YET quizzes until they earn an A or a B.  Once students have earned an A or a B, they can place a sticker in the mastery box on their score tracking sheet.  I have a tub of stickers that students can pick from.  I guess you could call it a self-service sticker station.  :)

The consequences of this new grading process have been...interesting.  Some students love it.  Others hate it and have left my room in tears.  The negative feedback has been greater than I anticipated, but I'm sticking with it.  I have the support of my administration, and I believe I'm acting in the best interest of my students.  This should probably be an entire blog post in itself.

Ready to see in side my trig notebook?  I'm so excited to share it with you!

Title Page:

Here's the score tracking sheet next to the TOC.

A student's copy with some mastery stickers.

At Twitter Math Camp, I had a terrible time figuring out which morning session I wanted to attend.  You see, I teach Algebra 1, Algebra 2, and Trig/Pre-Calculus.  So, I could have easily gone to any of those three sessions.  I ended up being a part of Elizabeth's Group Work Working Group, and I don't regret it at all.  But, I still wish I could have gone to all of them!

In one session I attended, we were given the task of creating a lesson or task in a small group.  One of the people in my group had been a part of the Algebra 2 morning session.  And, she mentioned Glenn's 3 Essential Rules of Math.  We were instantly intrigued and made her tell us more.  We never actually ended up designing our task, but we did all walk away with some exciting ideas to use in our classrooms, and I think that's what TMC was all about anyway.

Here's a link to where Glenn discusses the 3 rules.  He does a way better job of explaining it than I ever could.  I can make a pretty notebook page about it though. :)

By the time students get to trig, they should be able to solve equations.  But, I wanted to start the year off with a quick refresher.  I included the properties to remember box at the bottom for students to record various properties in as we come across them in problems.

I planned 3 example problems to work out in our notebooks.

My kids hated having to write out the justification for doing each step.

But, that's nothing compared to the riot that almost broken out after trying to solve a problem that involved factoring a trinomial.  It was totally my fault.  You see, I have this problem with teaching factoring.  In my first two years of teaching, I taught factoring 4 different ways.  My Algebra 1 teacher taught us to guess and check in the 8th grade.  I never knew there was another way.  After realizing how tedious that method was once I began teaching, I went looking for a better way.  That same year, I tried the airplane method of factoring.  It went better than guess and check, but kids could never remember the steps.  Year 2 comes along.  I learned the Slide, Divide, Bottoms Up Method at a workshop.  I decide to try it.  Again, it works, but the kids can't memorize the steps.  And, why should they?  The steps make ZERO sense whatsoever.  They work, but they're a trick.  And, we're supposed to be nixing the tricks.

Finally, Shelli showed me how to split the middle term of the trinomial in two and factor by grouping.  I LOVE this method.  But, my kids who had already seen one of the trick methods saw it as a lot of work and thinking.  So, they were not excited to use it.  Okay.  Back to the almost-riot.  I start working through an example that involves factoring.  As soon as I start splitting the middle term, a student raises their hand and asks why we can't do the method from last year.  They don't remember what it was, but they know it wasn't this.  Another student who I had in Algebra 2 two years ago wants to use the airplane method.  Then, I have students in my classroom who took Algebra 2 at another school or our local technology center.  They learned yet another way to factor.  OH MY GOODNESS.  It was terrible.  More like on the verge of tears terrible.  Honestly, I finished the problem, handed out the homework assignment and asked them to cross out all of the problems involving factoring.  I needed to make up my mind about how to approach factoring from here on out.

Here we are, over a month into the school year, and I'm still avoiding factoring with my trig students.  Eventually, we will have to overcome this hurdle.  Until then, I'm still working on my game plan.  Note to self: find one way to teach factoring and teach it that same exact way for the next thirty years of your career.

If these notes look familiar, it's because they are.  I took my unit on radicals from Algebra 2 last year and condensed it into a quick review.  After all, there's no sense in reinventing the wheel.  (I've posted extensively on how I taught radicals before here and here.)

I still love the birthday cake method for finding prime factorization.  Since I had almost all of my trig students in Algebra 2, I neglected to mention to the class that the 1 on top of the birthday cake was the candle.  One student who wasn't in my Algebra 2 class was SUPER confused by what this new math symbol was on top.  Oops.  (You can read more about the birthday cake method for prime factorization here.)

Also, my trig students thought that our review of simplifying radicals and performing operations on radicals was the easiest thing in the world.  These are the same kids who HATED radicals last year in Algebra 2.  For days, all I heard was, "Why is this so easy this year?  I did not get radicals last year.  But, now I'm like "How could someone not understand this?""  They finally decided that their brains matured over the summer or something like that.  All I know is that seeing them work with radicals so confidently made me a very proud.

Here's our simplifying radicals notes together.

Next up: Rationalizing the Denominator

Again, they were shocked that rationalizing the denominator was not as complicated as they had made it in Algebra 2.  Adding and subtracting radicals also went very smoothly.

The one problem with my unit on radicals is that if somebody entered my classroom and listened in on our conversation, they would probably think we were crazy.  My kids don't talk about "simplifying radicals."  They say, "Oh, I need to birthday cake it."  By birthday cake, they mean find the prime factorization and use that to simplify the radical.  I know exactly what they mean, but I should probably work on fixing this vocab issue in the future.

Multiplying and dividing radicals did not go nearly as well as adding and subtracting.  I still need to work on this.

The distributing problems proved especially difficult for them.

And, I need to come up with a way to make dividing radicals seem less scary.  After we wrote out the six steps, they were in panic mode.  The actual process wasn't that bad, but I made it sound terrifying.

At this point, my kids were begging, "Can we just do radicals for the rest of the year?"  Ha ha.  No.

Now it was time to begin a little geometry review.  I've never taught geometry before, so this was a fun experience for me!

We started off by taking some notes about useful angle facts.

I borrowed the amazing Kathryn's Angles Formed by Parallel Lines Cut by a Transversal Foldable.

Here's the inside:

Kathryn took many more detailed pictures of the inside flaps and posted them on her blog.  You should definitely check it out!

Fair warning.  My kids hated the next notebook page.  You may think hate is a strong word.  But, I'm serious.  You see, I thought I would be creative.  And, I guess I didn't think my creativity all of the way through.

Class, use a marker, highlighter, or colored pencil to draw a giant C on your notebook page.

Inside the C, we were going to take notes on the meaning of "complementary angles."

Then, we were going to turn the C into an S and add notes about supplementary angles.

If they could remember that complementary meant 90 degrees, the S was made up of two Cs, so that would mean 90 degrees times 2 or 180 degrees.

Great idea, right?

Well, I didn't tell my kids what the end product was going to be.  So, they drew some Cs that could not be made into attractive Ss.  Oops.  Their notebook pages were not pretty and perfect now, and it was all my fault.  One of the students in class decided that I had earned myself a "NOT YET" for the day.  Remember my grading scale?  Now, my students are using it to get back at me...  On a side note, they also decided to give the pencil sharpener a NOT YET one day because it made their pencil point too sharp...

Ironically, when I went to put the C/S drawing in my notebook, mine turned out looking not that great either.  I guess that was payback.  I sketched it out several times on scrap paper, but putting marker to notebook paper proved to have less than stellar results.

Here's some of my students' pages.

This student insisted on gluing colored paper over his botched attempt and crafting a perfect C/S combination.

Our next geometry topic to review as the pythagorean theorem.

The Pythagorean Theorem booklet was stole from the blog of Jessie Hester.  She has a ton of resources for teaching the Pythagorean Theorem!  If I was teaching geometry, I would have gone way more in depth and used a lot more of her amazing activities!

As soon as I passed out the booklets, my trig students wanted to know if I would give them time to color the covers.  Yes, we did take some time to just sit and color.  It's fun to watch my trig students get so invested in creating their notebooks!  I'm actually kinda glad that my school does not own any trig or pre-calculus books because I probably wouldn't be doing notebooks with this specific class if they did.

Inside the Pythagorean Theorem Booklet:

I liked the table set-up for these pythagorean theorem problems a lot!  I would have never thought of setting them up this way.

This next page was also stolen from Jessie Hester.

This was a new foldable type for me.  I love trying out new foldable designs!  The flap folds down to reveal two more flaps underneath.  :)

I'm going to be honest.  I'm a math teacher, and I have to really, really, really think about the distance formula.  It's just not something I have memorized off the top of my head.  I know how to derive it, and I can come up with it if you give me a minute.  But, it's not my weapon of choice for calculating the distance between two points.  I prefer to use the Pythagorean Theorem for finding the distance between two points, but I wanted to show my students both options and let them choose for themselves.

They agreed with me that the pythagorean theorem made the work of the problem seem a lot more efficient.  And, since I have students who really struggle with integers, they liked the fact that there were a lot less positives and negatives to watch out for.

I printed off this practice sheet from Jessie's blog for students to glue in their notebooks.

Here's our notes for finding distance between two points together.

Our last geometry topic to review before delving into actual trigonometry was special right triangles.  I don't know exactly what it is about special right triangles, but I LOVE them.  Okay.  I guess I say that about a whole lot of math topics.  I guess this means I'm in the right profession. :)

Me: Class, today we are going to be learning about two special types of right triangles.  These two triangles are going to become your BFFs.
Student: You said there are two of these triangles?
Me: Yes.
Student: Oh goody.  That means I will have at least two friends now.

My students make me laugh so much.  They are the best.

My entire goal for interactive notebooks is to create a resource for my students that they actually use.  I decided that we would put each of the special right triangles on an index card.  Then, we made a cute little pocket to hold the cards in our notebooks.  The kids got SO excited over these little pockets.

Here's what we wrote on our reference cards:

The idea behind these cards is that students could keep them out while working on their assignments.  When I teach trig again, I will tweak these cards a bit.  I would have students label the 45-45-90 card as a; a; a radical two right underneath the 45-45-90 heading.  And, I'd do the same for the 30-60-90 card.  I do like that students had to check which side length was opposite the angle they were interested in.  This really made them stop and think about what opposite means on a triangle.

One of my students thought that making the cards was a silly little exercise.  But, a day or two later, she told the class that these were the most helpful things in the world.  It was awesome to watch my students use these cards and encourage their classmates to use them as well.  Hearing them tell somebody to get out their cards and use them = PRICELESS!

I would love to find a way to include more index cards in my notebooks in the future.  Hmmm....

A go-to foldable for me to make is a poof booklet.  I have a file on my computer where I can quickly change out the practice problems, and I instantly have a new foldable to use.  My students never cease to be amazed by these poof booklets!

I think the smiling right triangle adds the perfect finishing touch to the page!  :)

Inside the booklet:

I made students circle whether the triangle represented a 30-60-90 right triangle or a 45-45-90 right triangle.  In the future, I would probably have students fill in the blanks for both the angles and the side length ratios so they sat exactly on top of each other.  Hindsight is 20/20.

Because I LOVE my students, I also included two word problems.

For more info on how to assemble a poof booklet, check out this tutorial I wrote for a poof booklet for another topic.

And, that was the end of Unit 1.  Unit 2 is all about trig ratios and trig basics.  I'll be posting those pages as soon as the unit is finished.