Math = Love

Wednesday, January 21, 2015

Weird Analogies: The Halloween Candy Tax

If you spend much time in my classroom at all, you will quickly realize that I use lots of weird analogies.  Some analogies I use once and forget about.  Other times I start analogies without really thinking about them and end up regretting my decision.  And, sometimes, my analogies actually work and I end up being able to use them more than once.

I don't remember the first time I used this analogy, but I think it must have been during my first year of teaching.  My students were struggling with factoring the GCF out of an expression.  We were looking at problems like this:


It didn't take much convincing that we should factor an 8 out of both terms.  But, my students were insistent that we could only factor out one x and one y.  Once I convinced them that it was okay to factor out more than a single variable, many of them defaulted to wanting to factor out the number of variables from the first term.  So, in this example, they would want to factor out x to the eighth and y to the sixth.  Telling them that we wanted to factor out the greatest number of things they had in common didn't really seem to help.

So, analogy time it was.  Be forewarned.  I used this analogy with my students today, and it resulted in one class accusing me of being cruel and cold-hearted.  As long as something helps my students see math more clearly, I'm okay with them thinking crazy things about me.



So, today, the class is confused.  Frustrated.  Ready to give up.  Fixed mindset statements are being uttered at every turn.  And, I'm pretty sure most of my students would describe themselves as being in the panic zone.  I sit on top of an empty student desk, and I look around at my students.  Eventually they seem to sense that I have something to say:

Okay, everyone.  Listen up.  From walking around and listening to your conversations, I can tell that we're struggling.  I'm going to tell you a story.  Maybe it will help.  Maybe it won't.  Maybe you'll go home tonight and tell your parents what a crazy math teacher you have.  But, maybe, just maybe, it will help to shed some light on the problems we've been attempting to work.

Some day you will have children.  [This statement usually gets their attention!]  And, every year you and your children will participate in this crazy tradition.  October will roll around, and you will dress up your little ones in adorable or spooky costumes.  Then, you'll go from door to door with cute, colorful pumpkin pails.  The simple act of uttering three little words will result in candy being placed in your kids' pails.  After visiting a number of houses, pumpkin pails will be overflowing, and you and your children will return home, excited to sort through the candy that has been amassed.

At this point, you explain to your children that there are certain things in life that...well...may not seem fair.  But, life goes on, and things like taxes must be paid.  To help your children learn about the tax system, a Halloween Candy Tax (HCT) will be applied to the night's acquisitions.  But, your children needn't worry too much because you will be very fair in collecting the tax.

The HCT requires that the candy must first be sorted by type.  Tootsie Rolls are placed with Tootsie Rolls.  Butterfingers with Butterfingers.  Twizzlers with Twizzlers.  I think you get the idea.  The main idea behind the tax is that the same number of each kind of candy will be taken from each of your children.  If one child has 5 lollipops and and your other child has 7 lollipops, the most lollipops you can take will be 5 lollipops because that is the most that you can take from BOTH of your children.  And, because you are greedy and jealous that you are now definitely too old to go trick or treating yourself, you will always take the greatest possible number of candies from all of your children.  Sure, you could just take two lollipops from each child, but your greed will cause you to take 5 lollipops from both children.

[At this point in the story, my students are outraged.  The one poor child now has zero lollipops.  Insert lots of comments about the injustice of the situation and what a terrible person I am.  My hope is that if they're engaged in the story, they'll be engaged in how it relates to the problem we're trying to solve.]

Imagine you have two kids.  Billy and Sally.  



Billy and Sally dump out their pumpkin pails to find tootsie rolls, lollipops, jawbreakers, and a caramel apple.  How many tootsie rolls will you tax your children if you want to be fair but greedy?  What about lollipops?  Jawbreakers?  What about that lone caramel apple?  Who gets it?  

Eventually, you end up with this:


The class decides that Billy really didn't end up well in this deal.  Of course, they word it a bit more crudely than that.

Back to the problem:


We decide to let the x's represent starbursts and the y's represent smarties.  If one child has 8 starburts and the other child has 9 starbursts, a greedy but fair parent will take 8 starbursts from each child.  And, the maximum number of smarties that can be taken from both children would be 5.  All of a sudden, lightbulbs start to come on.  Why didn't you explain it this way in the first place?  

Does every student need this analogy?  I don't think so.  Students who already understand the concept of finding the GCF will likely find the story annoying and pointless.  Why would you need to think about Halloween candy?  But, I've found that this analogy makes factoring a bit more tangible for my students who have traditionally struggled with math.

And, for the record, I don't tax my own children's Halloween candy.  I'd kinda need children to be able to do that.  And, according to my students, this would be a totally unfair policy.  So, I guess when I do have kids of my own one day, I'll just have to buy my own Halloween candy...  

Tuesday, January 20, 2015

Things Teenagers Say Volume 25

I can't believe I've already made it to Volume 25!  Here are the latest crazy things overheard in my classroom.



Previous Volumes:
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 | Volume 17 | Volume 18 | Volume 19 | Volume 20
Volume 21 | Volume 22 | Volume 23 | Volume 24



Ms. Hagan, thanks for corrupting my mom.  She started reading your blog, and now she's going around and trying to use all the crazy phrases teenagers say.

--

My sister said I need to be cuter so I can keep a boy for more than a week.

--

Student: You're a dime plus ninety-nine.
Me: I'm a what?
Student: You know, a dime.  That's 10 plus 99.
Me: Okay...
Student: That means you're a 101.
Me: You might want to check your math there.

--

Another Teacher: So, I heard a new rumor about you from a student this morning.
Me: Oh great.  What is it this time?
Teacher: The student said that you have an obsession with eating mustard.  You eat it on everything, including salad.
Me: Okay.  That is the most random, untrue rumor I've ever heard.

--

Ms. Hagan, does your boyfriend have a pet giraffe?

#Australianboyfriendprobs

--

Male Student: In the blank for period at the top of the paper, I wrote "two weeks late."

--

Student: Are you wearing tights?
Me: Yes.
Student: But, those have feet in them.  Tights don't have feet in them.
Me: Tights do too have feet in them.
Student: No, pantyhose have feet in them.  Tights do not have feet.
Me: I promise you that you can buy tights that have feet in them.
Student: I'm going to have to look for some of these at the store!

--

So, I told my mom you had a boyfriend. And, she's never met you. So, she was really confused about why I was telling her this. Then, she had you confused with another teacher. So, she had no idea why it would be a big deal that you had a boyfriend. But, she said she's happy for you.

--

I asked my dad if I could put bread in the blender to see what happened, but he wouldn't let me.

--

Can I have a different calculator?  I want one that's not from Texas.

--

Student: Have you ever got pulled over by the cops?
Me: No.
Student: Well, if you ever did get pulled over, would you want to know how to get out of a ticket?
Me: Sure.  Tell me how to get out of a ticket.
Student: You start by taking all of your clothes off.  Then, you jump out of the car and run as fast as you can.
Me: This sounds more like a plan for getting arrested than getting out of a ticket.
Student:  Yeah.  But, you'll make sure that you end up on the news this way.  

--

Me: Can anyone give an example of a mnemonic device?
Student: A calculator.

--

Can I please go to the restroom?  I have to tinkle twinkle little star.  

--

Student 1: He wasn't a very good teacher, but he sure was something to look at!
Student 2: Yeah, I asked for a LOT of help in his class!

--

Is it okay to date your ex-boyfriend's brother?

--

I don't get why we should have to learn all this stuff.  I mean we're never going to have to use it in real life anyway.  For example, why should I have to learn history?!?  Just so I can help my kids with their homework by telling them that Abraham Lincoln was the second president?  

--  

Student: You had AIDS last year?!?
Me: No.  I said I didn't have any classroom aides last year.

--

Do you need that one trash sack commercial? [Don't get sad; get Glad.]

--

Me: Name a famous inventor.
Student: Harrison Ford.
Me: Harrison Ford was not an inventor.
Student: Yeah he was.  He invented the assembly line.

--

Can I call you Ms. H?  Cause you're a gangster.

--

Your pencil sharpener works too well.

--

Me: What are you doing behind my desk?  That is my domain.  
Student: If that's your domain, than this [pointing at the rest of the classroom] is your range!

--

Student 1: Hey guys, do you want to feel something soft?  Come feel Student 2's hair.
Student 2: Gotta keep the mullet fresh.

--

Does that say demon.com?  What is with you and all these satanic practices?  First, you asked us to ask ourselves "What would Satan do seriously?"  Now you want us to go to a Satan worshiping website.

(I may have a slight obsession with desmos.com.  And, for the record, I asked my students to ask themselves, "What would Slope Dude say?")

--

Student: Do you have a napkin in here?  Because I'm not going to the bathroom! 
Me: Why won't you go to the bathroom?
Student: This school is haunted.  
Me: How are you going to handle going to school here all day for the next four years?
Student: I'll always make sure I go to the bathroom with a large group.  Then, the ghost can't get me.

--

Look Ms. Hagan!  My thumb is a 90 degree angle! 

--

We didn't play Witzzle yesterday.  That hurts my feelings!  

--

I'm going to tell my future children that they have to take your class.  No excuses!

--

Your desk was so clean yesterday.  What happened?

--

Ms. Hagan, are you drinking germ-x?

--

Facebook is for old people.  


Monday, January 19, 2015

2014: Year In Review

I'd say that it's hard to believe that it's already 2015, but I accidentally named my first Smart Notebook file of the semester 01062016.  I guess I'm already wishing that it was 2016...

Since I started blogging, I've recapped the previous year each January in a blog post.  You can check out 2013 and 2012 if you're interested.  If you remember past years' reviews (or if you just followed the links to read them), I usually write out at least a paragraph for each month.  This year, I'm taking a slightly different approach - one non-comprehensive list.  After all, lists make me happy.  And, this year has been so busy and eventful that I can't quite keep straight what happened when.  

So, in no particular order, here's my 2014 in list form:

*  Through the MTBoS, I met and started dating an amazing, inspiring guy.  He's a maths teacher blogger from Australia, and we have a ridiculous number of things in common with each other.  His summer holiday and my Christmas break overlap, so 2014 was able to end with the beginning of his first visit to the United States.  :)  

* Applied to and started grad school.  I'm currently 1/6 done with my master's program in curriculum and instruction with an emphasis in math studies.

* NPR interviewed me/shadowed me for a day the week after Thanksgiving.  The story hasn't aired yet, but I'll be sure to let everyone know when it does.

* Finished my second year of teaching and started my third year.

* Set out to read as many books as possible.  I ended up reading 71 books.  All but 5 of those books were read during the first 6 months of the year.  The decrease in books read can be attributed to the first and second items on this list.

* Attended my first edcamp.

* Taught trigonometry for the first time. SO much fun.

* Decided to switch to standards based grading in all of my classes.  I should probably write a blog post about that..

* Became extremely addicted to 2048.

* Directed my church's Vacation Bible School program for the 3rd summer in a row.

* Presented at Global Math Department for the first time.  I spoke about teaching math with motion.

* Became involved with my local friends of the library organization.

* Presented for the first time at the Oklahoma Council of Teachers of Mathematics Summer Conference.

* Applied for my passport.

* Visited Colorado and New Mexico for the first time.

* Taught class dressed as Pi Girl for Super Hero Spirit Day.

* Had my first Twitter Math Camp Experience.  I even worked up the courage to present!!!  I met so many amazing, inspiring tweeps in person for the first time.

* Bought a guitar.  I still don't know how to play it.  But, I figure that I can't learn if I don't own one.

* Attended my first theatre performance - Wicked.

* Fell in love with a certain pencil sharpener.

* Wrote 214 blog posts and surpassed 2 million pageviews on my blog.

* Celebrated my 25th birthday.  I'm more than a little excited about being a perfect square.


I'm sure there are a ton of things that I haven't even thought to list.  It ended up being a pretty awesome year.  I've got this feeling, though, that 2015 is going to turn out to be even more amazing.  I can't wait to see what the rest of this new year has got in store.

Tuesday, December 16, 2014

Things Teenagers Say: Volume 24

So, I've decided that my motivation of late for blogging is pure procrastination.  At the moment, I'm procrastinating on cleaning my house by typing up this post.  The washer and dryer are both running at the moment, so this still counts as being totally productive, right? ;)

Also - where has this semester gone?!?  Just a few more days until Christmas Break!  I don't know how I'm going to cope with not hearing crazy things come out of the mouths of teenagers for a couple of weeks...


Previous Volumes:
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 | Volume 17 | Volume 18 | Volume 19 | Volume 20
Volume 21 | Volume 22 | Volume 23



While playing review Jeopardy...

Student: But, Ms. Hagan, you're not even playing.
Me: Hello! I'm Alex Trebek.
Student: Who is that?
Me: [No words...]

--

Ms. Hagan, I think you should be an Aztec warrior.

--

When you were little, did you lick the television when Veggie Tales came on?

#vegetarianteacherprobs

--

Student: I sound more like a parakeet than a goat.

--

Student: Do you know how many letters are in the word perfect? 7. Do you know what else has 7 letters? 
Me: Ms. Hagan.

--

Student: Ms. Hagan, are you Internet famous?  Did you know most internet famous people sit at home eating chips and petting their cats?  I bet you sit at home eating chips and petting your plants.

--

Student comment while I was typing:

You sound like a newspaper maker. 

--

Really? Math on Halloween?!? That is NOT fair.

--

Student 1: Do you just go home and sit in your room and do math?
Me: Yes. (Sarcastically)
Student 1: Really?
Me: No.  Guys, I really do have a life.
Student 1: Yeah.  You have cats.
Student 2: Actually, she has plants.  Get it right!

--

Melted cheese fills the crack in a broken heart.

--

If your boyfriend breaks up with you, are you going to start giving us lots of homework?

--

Student: Ms. Hagan, did you know that there are different Americas?
Me: What do you mean there are different Americas?
Student:  Guys, Ms. Hagan didn't know that there are three different Americas either.
Me: And, what are the three different Americas?
Student: Well, there's North America, South America, and America America.  Did you really not know that?!?
Me: I knew that.  Did you just learn that?
Student: Yes.  But, what I don't get is why isn't Africa also named America?

--

If I make a B on this quiz, I'm going to kiss you.

--

Student: Look at my arm!
Me: Oh no.  What did you do?
Student: Well, I was chasing a donkey down the road on my motorcycle...

--

Student: Ms. Hagan, is it against your religion to wear jeans every day?
Me: No.  You do know that teachers are only allowed to wear jeans on Fridays, right?
Student:  But, you could still wear pants or slacks.  Instead, you wear dresses and skirts every day.
Me:  I was wearing slacks yesterday.
Student:  The way you dress is old and boring looking.
Me: Okay then...

--

Student 1: How do you spell pedophile?
Student 2: Just google it.  I google how to spell pedophile all the time.

--

This isn't a cheat sheet.  A cheat sheet would give me the answers.  This is a think sheet.

--

Student: Ms. Hagan, I took a picture of your house this weekend.
Me: That's kinda creepy.
Student: Do you want to see?
Me: Sure.
Student: [Shows Picture on Phone]
Me: That's not my house.
Student: Oh, I knew that.  But, the house had five cats in the front yard so it made me think of you.

--

Instead of chocolate, your boyfriend could buy you a bouquet of celery.

--

It's not called stalking.  It's called following your dreams.

--

Do you know what's dumber than a box of rocks?  A box of sticks.

--

Student: Ms. Hagan, I think I need to get a life.
Me: Why?
Student: Because I've started going home and doing math.

--

He's not late; he's fashionably not present.

--

I'd rather eat a human than a cat or dog if I was starving.

--

Student 1: You can't boil stuff in the bath tub.
Student 2: Yes you can.  Just our gasoline in and set it on fire.

--

One student to another: He called you "sweetheart."  That means he is too old for you.  You just got friend-zoned.

--

Student 1: Who's Noah?
Student 2: Noah and the Ark.
Student 1: I've never seen that movie.
Student 2: It's in the Bible.

--

I love kangaroos.  They have that pouch.  I just want to climb inside that pouch.

--

My gum told me to not listen to you for the next ten minutes.

--

One student to another: If you get that close to my face again, I'm going to assume you want me to kiss you.  So, I'm going to lick your face.

--

When you trip and fall and the spaghetti falls out of your pocket...

--

Do you know what I found out?  There's a day called Daughter's Day.  My parents have been hiding this fact from me.  My mom gets Mother's Day, and my dad gets Father's Day.  They each get their own special day.  I should get my own special day.  I mean, I'm so special.  I'm like the 2nd Baby Jesus.  I'm the Virgin Mary of 2014.

--

What would you have to do to be in a math play?
You'd have to "addition." 

Saturday, December 6, 2014

Things Teenagers Say: Volume 23

I'm thinking that maybe I should rename "Things Teenagers Say" to "Chronicles of the Crazy Cat Lady Who Doesn't Actually Own a Cat" or something like that...  

You know things are bad when a reporter spends a day in your classroom, and your students tell said reporter about the fact that you are a crazy cat lady.  The reporter then asks the students just how many cats you own.  Zero.  Confusion follows.  Confusion and laughter.  



Previous Volumes:
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 | Volume 17 | Volume 18 | Volume 19 | Volume 20
Volume 21 | Volume 22

Our FACS program includes a class on Marriage and Family.  One of the major projects students complete is planning and carrying out an entire wedding and wedding reception.  The class votes on two students to get married.  Other students in the class serve as bridesmaids and groomsmen.  Committees are formed to decorate for the wedding and the reception.  It's actually a big undertaking.  On the morning of the wedding, my class asked if we could postpone our lesson for fifteen or so minutes to attend the nuptials.  

Student:  Can we go to the fake wedding?
Me: I was really planning on us doing a math lesson today.
Student: But, I hear there's going to be cats in the goodie bags.

--

Written on the cover of a student's algebra notebook:

Satan's Class... Welcome to Hell!

#soloved  

--

You're right. I'm wrong. Let's eat pie.

--

If you DM every girl in the state of Oklahoma, no one is going to date you.

--

You're the only mean teacher in this school.

And, this is what I get for insisting we do math instead of watching a movie on the last two days before Thanksgiving Break...

--

Your definition of fun and our definition of fun are not the same.

--

Ms. Hagan, you won't live past the age of 25 if you give us homework on your birthday.

--

Student 1: Tuck your shirt in. You look like a hillbilly.
Student 2: No he doesn't. He looks snazzy.

--

Ms. Hagan, you're a mathaholic. You need rehab.

--

I always knew Pi Girl was a villain.

--

Student 1: Ms. Hagan, I saw something at the store, and it made me think of you.  So, I took a picture of it.  Do you want to see it?  
Me: Sure.  I'd love to know what made you think of your math teacher in the store.  
Student 1: It's a baby onesie.  If you had a baby, I would totally buy this onesie for them.  It has a cat on it, and it says, "Meow's it going?"  
Student 2: Wouldn't it be better to get Ms. Hagan's baby a mathematical onesie?  A onesie with a fraction on it would be adorable!  I wonder if they make those...

--

You should do the right thing and date her best friend.

--

Student 1: Ms. Hagan, did you know that I am addicted to shoes?  I have over 400 pairs.  
Me: No.  
Student 2:  Guys, I bet Ms. Hagan is the same way with plants as [Student 1] is with shoes.
Me: Guys, I seriously don't have that many plants.
Student 2:  I bet you have so many plants your house looks like a rainforest inside.  
Student 1:  Ooooh, you could paint all of your cats to look like tigers. Then, it would look like you had tigers wandering around in your rainforest.  
Me:  Y'all are never going to believe me when I say that I don't own any cats are you?

--

If you could have an affair with any married celebrity,who would it be?

--

Me: Class, I have sad news.  
Student: Did your cat die?  

So, I said this first hour.  This was not the response I was hoping for.  So, I tried it again to see if my next class would give me the same response.  Second hour, a student asked the same question.  Third hour, the same question. Fourth hour, I forgot to ask.  Fifth hour, another student asked me if my cat had died.  Sixth hour, the same thing happened all over again.

--

Ms. Hagan is a totally different person now that she has a boyfriend. I can't even look at her the same way now. It's like we know we're not first in her life anymore...

--

I'd rather cheat off you than cheat on you. 

--

I just had a realization. All old people are is fermented babies.

--

Let me see what you're doing in Algebra 2 so I can decide if I want to drop out or not.

--

If your boyfriend breaks up with you, there are plenty of other coordinates on the plane.

--

You being sarcastic is you saying you're good at math.

And, yes, this was directed at me.  #OUCH  

--

You made this?!? I didn't think you ever did anything except eat lettuce.

--


Dude, I've been baeless forever. You've been baeless for 3 days.

--

I have handwriting like a dinosaur, man!

--

You should get a pet bunny.  Then, you guys could share your food.  

Friday, December 5, 2014

Trigonometry Unit 2 Interactive Notebook Pages

Hi guys.  I am so behind in posting stuff from this school year.  So, so, soooooooo behind.

Here's what Unit 2 ended up looking like in my trig class.  I posted Unit 1 back in September.  Unit 1 was mainly a review of algebra and geometry.  Unit 2 was the start of actual trigonometry!  Yay!    


Our geometry standards include basic right triangle trig, but I've found that my students' experience with this topic is greatly lacking.  They remember learning SOHCAHTOA, but they never really did know what they were doing.  It's been so fun to teach them trig from the beginning and see the light bulbs start to go off.  "Oh, this is what we were supposed to do in geometry!  Why didn't they ever tell us it was this simple?!?"



Before I introduced my students to the basic trig ratios, I wanted to make sure we were all on the same page when it came to naming the parts of a right triangle.  My students had a hard time wrapping their minds around the difference between the adjacent side and the opposite side for some reason.  


We made a simple three-door foldable with the formulas for sine, cosine, and tangent.


Inside the flaps:


My students referenced this foldable A LOT!  In fact, they're still referencing during our unit on the unit circle.

Thanks to Meg, I learned about the song Gettin' Triggy Wit It by WSHS on YouTube.

If you haven't seen this video, stop everything and watch it now.  I'll even be nice and embed it for you. :)


My students enjoyed the video the first time we watched it, but they had a hard time understanding a few of the lyrics.  So, I printed the lyrics off for them the next day to glue in their interactive notebooks.  In the future, I would print these off and have students draw example problems on the paper as they watched it.


The page unfolds to show the rest of the lyrics.


One of my students apparently got in trouble by the cheerleading coach for dancing like the students in the video.  She was told that the dance moves were inappropriate...  Of course she threw me under the bus and said "Well my math teacher taught it to me."

Now that we knew how to find the basic trig ratios, it was time to start thinking about radians.

I don't ever remember really learning what a radian was when I took trig in high school.  I'm sure my teacher told me, but I guess it didn't really stick.  We're going to be dealing with radians a lot, and I decided I didn't want my students to flip out every time radians were mentioned.

Naturally, I turned to google.  Let's just say I am a frequent google user.  Some people in town refer to me as "Google Girl" because I use google so much.  :)

SEARCH: "What is a radian?"

I quickly found a great discovery activity that involved circles and pipe cleaners and tracing and cutting and folding paper and basically everything I love and adore in life.

I would link you to the actual activity I used, but I actually ended up combining what I liked from five or six different resources.



Step 1: Raid your kitchen cabinets for every circular lid you can find.


Step 2: Instruct each student to pick a lid when they enter the classroom.

Step 3: Trace your lid onto colored paper.


Step 4: Cut out the circle. Fold it in fourths to find the center.


Step 5: Mark the center of the circle.


Step 6: Cut a pipe cleaner the same length as the radius of the circle.

Apparently, pipe cleaners are now called "fuzzy sticks."  What is up with that?!?


Step 7: Draw in the radius on the circle.  Line up the pipe cleaner with the edge of the radius.


Step 8: Start wrapping the pipe cleaner around the circumference and marking where it stops.


Step 9: Divide the circle into sections based on your markings.


If students have attended to precision, They should end up with 6 equal sized sections plus a tiny left over section.


Glue the circle in your notebook.


Define a radian as the angle that has an arc length equal to the radius of the circle.


I wasn't planning on this, but my students decided we needed to glue our pipe cleaners to the radius.  They turned out looking pretty cool!


We wrote in the definition of a radian.


Then, we set about figuring out just how many degrees are in a radian.  If there were just the six equal sized sections, how many degrees would a radian be?  360 degrees divided by 6 is 60 degrees.  But, there are six sections AND a little section, so each section must be less than 60 degrees.

We decided to set up a proportion to determine just how many degrees are in a radian.  Okay.  Let's be honest.  It was my idea to do this, not my students' idea.  But, they did go along with it, so I guess it still counts.  At least, that's what I'm telling myself.  ;)

Before we could set up a proportion involving radians, we needed to review the formula for circumference of a circle.  When I asked my trig students for the formula for circumference, they gave me the formula for area of a circle.  They told me that "pi r squared" was the only circle formula that they knew... #sigh

When looking for information online regarding teaching radians, I ran across a song to sing that features the formula for circumference of a circle.  There's just something about song that helps me remember things.  And, I assume that some of my students are like that, too.  They decided we should write the lyrics for the circumference song in our notebooks.  It's a simple song set to the tune of Twinkle, Twinkle Little Star: "Twinkle, Twinkle Little Star.  Circumference equals 2 pi r."  Isn't that the most brilliant thing you've ever heard in your life?!?


They remembered from geometry and our geometry review earlier in the year that a circle is equivalent to 360 degrees.  And, the circumference of a circle is 2*pi*r.  We eventually found that a radian is approximately 57.296 degrees.  




I'm hoping that this activity helps my students to never fear when the word radian appears.


After learning what a radian was, it was time to learn how to convert between radians and degrees.  We made a much-referenced foldable over this.

Outside of Radians to Degrees and Degrees to Radians Foldable:


Inside of Foldable:


Close up of radians to degrees notes/examples:


Close up of degrees to radians notes/examples:


The next page is one of my favorites.  If I'm I may have created this page in order to have an excuse to use a brad in our notebooks.  Does that sound like a crazy thing to do?  It probably is.  It's definitely a long story...


I had students cut out the initial side and terminal side for their angle out of card stock.  The initial side was glued down on the x-axis.  The terminal side of the angle was attached to the paper with a brad.  Apparently, these are called "paper fasteners" in other countries.

Once students had constructed their handy, dandy, spinny angle page, I asked each student to move their terminal side to form a 45 degree angle.  Then, I instructed them to take a look at the angle formed by their neighbor.  They soon realized that some students had made their 45 degree angle in the first quadrant, and others had made their angles in the fourth quadrant.  This led to an awesome discussion.

We added notes to our page regarding how to graph positive/negative angles.


I had the bright idea to make a card sort for my students over coterminal angles.  They were going to write the definition of coterminal angles.  Then, I was going to give them a page with all kinds of angle measures.  They would sort them into groups that were coterminal with one another.  Then, they would take a blank square and write an additional angle that was coterminal with the other angles in the group.

This. Did. Not. Go. Well.

And, I'm not really sure why.  


Next up, some pretty boring notes about reference angles.  Sorry, nothing exciting on this page.


 I stole the bowtie idea off of pinterest.


The last standard for students in this unit was to be able to find the trig ratio of angles formed by various ordered pairs.


I think I could have done a better job of writing out these steps.  Maybe next time I teach trig I will make these steps clearer...


We took a piece of graph paper and folded it into a poof book.  This let us fit three practice problems onto our page.  I let students pick ordered pairs for the class to work with.  I would choose the quadrant, and students could pick any ordered pair in that quadrant.  This prevented all of our examples from being in the first quadrant.

First Quadrant Example:


Second Quadrant Example:


Third Quadrant Example:




Want to download the files from this unit?  Click here.

Thursday, November 27, 2014

Things Teenagers Say Volume 22

Happy Thanksgiving!  I know I have so much to be thankful for this year.  One thing I'm thankful for is that not a day goes by where my students don't make me laugh.  So, I think it's only fitting to share some things teenagers say today.  :)



Previous Volumes:
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 | Volume 17 | Volume 18 | Volume 19 | Volume 20
Volume 21


In high school, my trig teacher taught me to use the sentence "All students take calculus" to remember which trig ratios were positive in each quadrant of the coordinate plane.  I told my students that they were free to create their own sentence.  I was kinda hoping that creating their own sentence would help it stick in their brains a little better.  Here's what they came up with:

Satan always tempts children.  [Then, we had to discuss how the letters needed to reflect the numbering of the quadrants...]
Adults sometimes tickle children.
All selfies; too cute.
All sisters talk crap.
Aliens sometimes take cows.

--

Note to self.  Don't wear all black to school.  Your students will ask all sorts of crazy questions?  

Student 1: Why are you wearing all black today?  Did your cat die?
Me: [Sigh] I don't own a cat.
Student 1: Well, you don't own a cat now.  It died.
Student 2: Guys, maybe her plant died.  Maybe that's why she's wearing all black.

In another class:

Why are you wearing all black  Did you run over a cat on your way to school?  I bet you left your house dressed all colorfully like you normally are.  Then, you ran over a cat and went back to your house to put on black clothes in mourning.  

Student 1: I know why you're wearing all black.  You're actually a werewolf.  
Student 2: Wait - Ms. Hagan can't be a werewolf.  She doesn't eat meat.
Student 1: She must be a vegewolf, then. 

--

Student: Can you PEMDAS this for me?
Me: What?!?
Student: Oh, I meant can you DESMOS this for me?
Me: Of course! :)

--

Sure. My number is 918-BACK-OFF.

--

Student 1: If I buy you a cat can I have an A?
Student 2: What if I buy you three cats, could I have an A?
Student 3: What if I buy you a boyfriend?
Student 4: What if I buy you a plant?

--

Student: Did you meet your boyfriend at church?
Me: No.
Student: Well, that means you can't marry him then.

--

Pi Girl is mean.

--

Would you still love me if I had ebola?

--

Stop "Not Yetting" and start writing "Almost There."

--

I just got strangled by a ghost in Ms. Hagan's class.

--

Do you know what my dad calls people who don't eat meat?  Un-American

--

A misdemeanor isn't THAT bad.

--

I sent a girl a direct message on twitter.  I told her that I had looked through her insta photos, and it looked like she was suffering from a lack of Vitamin "ME." 

--

Your patience is really short right now.  I think you should lengthen it. 

--

If you were an angle, you'd be an acute one.  

--

She ain't Chef Boyardee or Paula Deen. 

--

I hope the desk breaks and he breaks his pelvis bone. 

--

I've got chemistry on my hand.

--

If you're wondering why I wrote "elims" on my homework, it's "smile" spelled backwards.

--

Wow Ms. Hagan.  You have a good mind.  Sometimes.

--

Wow, in five years, you're going to be 30!  

--

Student 1: Look at Ms. Hagan, all bundled up.
Student 2: Yeah, she's like a little vegan burrito over there. 

--

Do you know what?  I've never seen an ugly twin in my life.  I wonder if they even exist. 

-- 

I hate twins.  [Said by a twin.]

--

I saw that homework you're going to give us today.  And, I want to punch you in the forehead because of it.