Math = Love

NOTE: This post has been sitting in my drafts since October 14th. So, when it says "last week," it actually means "quite a few weeks ago." :)

This last week of school was a weird one. Monday and Tuesday were normal. My Algebra 1 students started factoring quadratic trinomials with a leading coefficient of one. My Algebra 2 students started graphing basic exponential functions and their transformations. On Wednesday, my students had a substitute while I took my student council kids to our district meeting. The speaker at our meeting was Lance Lang, and I really enjoyed listening to his message of hope. I was inspired to do a better job in my classroom of being a dealer of hope.

On Thursday, my school took two buses full of students to the state softball tournament. Our girls did an awesome job, and they advanced to the next level of competition. On Friday, my school, again, took two buses full of students to the state tournament. Normally, we have around 160-180 students in the school building. For the past two days, we've only had around 60 students in the building. This means that there was no way that I can go on with my intended lesson plans. Approximately a third of the remaining students did not go to the softball game due to their ineligibility. So, these students have been able to spend the past two days getting missing assignments completed and turned in. I've worked hard to help these students get their missing work caught up! Making sure a dozen students are all on task when they are all doing something different is a monumental task!

Friday morning, we had our students for the first two periods of the day before they boarded the bus for the tournament. Second period, I used this as an opportunity to measure where my Algebra 2 students currently stand with exponent rules. We are currently in the midst of our third unit of the year: Exponential Functions and Exponent Rules. Based on their responses, I'm not going to have to do quite as much reteaching as I thought. We finished with the exponent exploration with about 20 minutes of class left to spare.

Since it was Friday and game day, my students really wanted to play another game. One student begged to play "Heads Up Seven Up." I told him that we couldn't play that because it wasn't a math game. Of course, he argued that it was a math game because it had a number in the title. Instead, I offered to let them have a Rock, Paper, Scissors Tournament. Immediately, their interest was piqued. Of course, I had to put a mathematical spin on it.

Several months ago, I ran across a short video clip on pinterest of a brain break that involved Rock, Paper, Scissors and multiplication. I thought it was a cute idea, and I filed it away in my brain.

I actually let my students choose any number of fingers from one to five, instead of the one to four mentioned in the video. So, the premise is simple. Students say "Rock, Paper, Scissors," and then they throw out the number of fingers of their choosing. They look at their number of fingers and their competitor's number of fingers, and the first one to correctly multiply the two numbers together and say the answer aloud wins.

I'm pretty sure that this activity is meant for younger students, but my Algebra 2 students loved it.

My plan was for students to pair up and play a round. The winners would remain standing. The non-winners (sounds better than losers) would take a seat. Then, we would continue until a winner was crowned. My students were not satisfied with this plan. After all, if this is a tournament, we might as well go all out.

So, a tournament bracket was made. I quickly googled a website that made brackets. I typed in all of my students' names. Consequently, I shocked all of my students with my ability to type without looking at my fingers. They were amazed. Apparently, it sounds like bullets are shooting when I am typing. I guess my students aren't used to hearing someone type over a hundred words a minute.

I took a screen shot of the tournament bracket and put it up on the Smart Board.

The competition was intense. Instead of playing multiple games at once, everybody watched as each pair competed. The rest of the class served as judges as to who answered first. If I was to do this over again, I would have everybody play a few practice rounds before beginning the tournament. That would have solved a lot of our problems.

Also - I would change the rules to say that only the first answer you say counts. I still have quite a few students who struggle with their basic multiplication facts, so this was a nice review for them. The engagement level during this activity was AMAZING. I would love to adapt this activity to feature review of an Algebra 1 or Algebra 2 topic. Ideas? My Algebra 2 kids are never this engaged, and I would love to harness this power!

Oh, and the winner received a much-coveted award. (They got to pick their certificate.) I'm pretty sure I could get my kiddos to do anything for one of these awards. The tournament champion was actually a student that I had last year for Algebra 1. She never won an award in Algebra 1, so she was very, very, very excited to finally win one this year.

Awards

(I promise there are graphic organizers and downloads at the bottom of this post. But, I'm so behind on blogging that I have a rather long back story that I must tell you in order for these pictures to make any sense. Feel free to scroll to the bottom to get to the good stuff. But, you'll likely end up scrolling back to the top to understand what you're looking at.)

This year, I am taking a big risk with my Algebra 1 kiddos. I taught them to factor quadratic trinomials with a leading coefficient greater than one before we ever discussed solving equations. Last year, I crammed in factoring quadratics at the very end of the school year. I was feeling rushed, and I needed to cover factoring quadratics and simplifying radicals before the end-of-instruction exam. I didn't feel like I really did either topic justice because I was so rushed.

This year is different. Really different. My Algebra 1 students came in at a much lower level than my students last year. After spending weeks on integer operations and the order of operations and all that fun stuff that students should already know from middle school, I still had a lot of kids who were just not getting it. That was nothing new. Last year, my students struggled with these topics, too. And, last year, I moved on to solving equations and HOPED that the rules for dealing with integers and all that good stuff would "click" when they started seeing it in equations. That worked to a certain extent.

This year, I could tell I was more frustrated and my students were more frustrated than normal. The kids who understood integer operations were bored out of their minds. They wanted to move onto something new. The kids who didn't understand integer operations still didn't quite know that they didn't understand them. So, my constant review as futile. My students had solved equations in middle school, so that wouldn't be something new and exciting. After teaching them the distributive property, I had an epiphany.

Okay. I need to pause the story. Yes, I know you're wanting to know what my epiphany was. But, you're just going to have to wait. If you're protesting with me in your mind right now, I'll tell you what I tell my kids a lot. You'll live. Is that a little harsh? I probably say that more in my classroom than I should. Anyway... I made a commitment to myself last year that I would stop teaching students to FOIL. I learned to multiply binomials by FOILing. But, I'm learning that some of the tricks that I was taught in Algebra are just that. They are tricks that work, but students don't quite know why they work. If my students can see a problem as an extension of the distributive property, they can solve a myriad of problems in different forms. If students only know how to FOIL, they are going to be stuck and not know what to do when they are asked to multiply a trinomial and a binomial. Last year, instead of teaching students to FOIL, I taught students what I called "The Double Distributive Property." This could be extended to the triple distributive property as well. And, it worked out pretty well.

Back to my epiphany. What if didn't teaching the double distributive property as a separate property? What if just told my students that when they see two polynomials being multiplied together that it is a distributive property problem? So, I did just that. Day one of the distributive property featured monomials times binomials. Day two of the distributive property featured polynomials times polynomials. I made no distinction between the two. When my students see two polynomials being multiplied, they automatically think distributive property. And, that makes me insanely happy.

After teaching students to distribute, the natural thing to teach students is to undistribute, or factor. When my students were first reviewing integer operations, I gave them a sheet of diamond puzzles or X-puzzles to complete. I taught my students to factor quadratics with a leading coefficient of 1 using the X-puzzle.

Then, we moved onto factoring quadratics with a leading coefficient greater than 1. Again, I changed my teaching approach from last year. Last year, I taught my students to do the Airplane Method. This worked. But, I still had a few students who never caught on. This summer, at the Common Core conference I went to, I was introduced to the Slide and Divide method of factoring. Another teacher mentioned that she called it the Bottoms Up Method. I combined these two ideas to create the "Slide, Divide, Bottoms Up!" Method. My students LOVE it.

Yes, this is a trick. But, I haven't figured out a better way to teach it. When I took Algebra 1, I learned the guess and check method. And, I found that method to be torturous. But, I didn't know there was a better, faster, easier way. Now that I do know there is a better way, I would never go back.

So, without further ado, I think I've given you enough back story to help you understand the context behind these foldables and interactive notebook pages for Algebra 1.

Last year, I had a conversation with a student that changed my outlook on vocabulary. This was not my own student but the child of a coworker. Before tutoring him one day, he was sitting in his mom's office, discussing why he was having so much trouble in algebra. He said, "My teacher just keeps going on and on and on. And, he keeps saying this word that nobody knows what it means. And, the whole class is lost." Naturally, I wanted to know what the word was. "I don't know. I think it starts with a b." Since they were working on polynomials and factoring, I took an educated guess: "binomial." Yes, that was the word. Once I described to this student what a binomial was, he began to realize that maybe this wasn't as hard as he had made it out to be.

This year, I am emphasizing vocabulary more. I don't want students to think that I use words without ever telling them what they mean. At the very least, they should know that the vocabulary word should be in their interactive notebook somewhere.

Polynomial Frayer Model

Rules for Naming Polynomials

We spent an entire 50-minute period on the definition of a polynomial and how to name polynomials. Is this on the EOI? No. But should I still teach it? Yes! When my students see one of these words, I want them to feel confident, not confused or frustrated. These are words they will encounter for the rest of their mathematical careers. I'm hoping that by putting emphasis on them now, I will save my students a lot of grief later on.

I told my students that when polynomial parents have children, they don't get to choose their names like human parents do. Instead, polynomial parents must follow strict naming rules. I lamented about how sad this was. I mean, what if the parents wanted to be creative? What if the parents wanted their child to have the same last name as them? The first name of any polynomial child is determined by its degree. The last name of any polynomial child is determined by its number of terms.

One of my students asked me if I was going to use these rules to name my own children. Apparently, I seem like the type of person who would name my child "Cubic Trinomial." I guess I should take that as a compliment...

Introduction to Polynomials Interactive Notebook Pages

Factoring Quadratic Trinomials with a Leading Coefficient of 1

Examples of Factoring Quadratic Trinomials with a Leading Coefficient of 1

Basic Factoring Interactive Notebook Pages

Factoring Quadratic Trinomials with a Leading Coefficient Greater than One
(More Affectionately Known as: Slide, Divide, Bottoms Up!)

Examples of Factoring Quadratic Trinomials with a Leading Coefficient Greater than One

Slide, Divide, Bottoms Up Factoring INB Pages

Factoring Difference of Squares

Factoring Difference of Squares Examples

Factoring Difference of Squares INB Pages

Downloadable Templates:

If you have trouble viewing these files, please send me an e-mail. I would be more than happy to attach the files and send them to you.

Naming Polynomials Graphic Organizer

Blank Frayer Models

Factoring Quadratic Trinomials with a Leading Coefficient of 1 Graphic Organizer

Factoring Quadratic Trinomials with a Leading Coefficient Greater Than 1 Graphic Organizer

Factoring Difference of Squares Graphic Organizer

After factoring polynomials, my Algebra 1 students finally moved onto solving equations. Again, I approached this unit in an entirely different way this year than last year. I will post more specifics about the Do/Undo Method that I taught my students later, but I did want to get pictures of these pages posted now. If you have any questions at all, send me a message or leave a comment. And, I will do my best to write up a blog post with more details.

Algebra 1 - Unit 3 Writing and Solving Equations Table of Contents

Equation Frayer Model

Inverse Operations Graphic Organizer

The notes at the bottom were my attempt at helping my students who were having trouble determining if a number was being added, subtracted, or multiplied in an equation. I don't know if it helped or not.

Do / Undo Method for Solving Equations Foldable

Inside of Do/Undo Method for Solving Equations Foldable

The next two pages (on solving equations with variables on both sides of the equal sign) were stolen from Sarah at Everybody is a Genius. I did exactly as she said to. I passed out these 6 balanced scale problems to my students. It was shortly after Halloween, so I still had leftover trick or treat candy. I promised candy to the first student who could figure out all six problems. Instant engagement. That instant engagement was, of course, followed by instant frustration.

Finally, I agreed to go over the answers with my students. We discussed 1, 2, and then 4. Oh, my students were SO mad at me. I was loving every moment of this lesson! When I told them that I had lied to them at the beginning and told them all of the scales were balanced, they were not happy. In fact, they decided that I should have to give them all candy since I lied to them. That was my plan all along, of course.

Balanced Scale Problems

Solving Equations with Variables on Both Sides of the Equal Sign - Outside of Foldable

Solving Equations with Variables on Both Sides of the Equal Sign - Inside of Foldable

I still had some students who were getting their steps out of order when trying to solve equations. After a quick google search, I happened upon this solving equations flowchart foldable. I was instantly in love! You can download a copy of the foldable here from In Stillness the Dancing.

I referred to this as our flippy, flappy, foldy thing. I think this was one of our most-used foldables of the year so far. Our special education teacher loved it, too. I guess the reason why I love this so much is that it takes students step by step through the process of solving an equation. These are the same questions I would be asking a student if I was sitting by them and helping them. By giving all of my students this tool and modeling how it works, I am equipping my students to help themselves. (And, yes, my students remarked that I was WAY TOO happy about this foldable.)

Solving Equations Flowchart Foldable - Outside

Solving Equations Flowchart Foldable - Yes Flaps

Solving Equations Flowchart Foldable - No Flaps

Downloadable Templates:

If you are having trouble viewing the embedded files, please ensure that you have Shockwave installed. If you still cannot download the files, feel free to send me an e-mail. I would be happy to attach the files and send them to you.

Unit Table of Contents

Blank Frayer Models

Inverse Operations Graphic Organizer

Do/Undo Method of Solving Equations Foldable

Solving Equations with Variables on Both Sides of the Equal Sign Foldable

Today, one of my students asked me if I planned to continue teaching for the rest of my life or if I was planning to change occupations in lieu of more money. Teaching is all I have ever wanted to do. I was the kid who started keeping a list in middle school of all of the favorite activities I had done in school in every grade since the first grade so I could one day implement them in my own classroom. I know you are insanely curious about what activities made the list! My second grade teacher had a great method of practicing spelling words. My third grade teacher's memorable lesson about the first assembly line involved us assembling our own cars out of candy. In the fourth grade, I got to dye carnations using food coloring and make my own fossil of a sea shell using plaster of paris in an empty milk carton. My fifth grade experience was characterized by the amazing book report projects that we had the opportunity to complete. Plus, we got to do a lot of history projects and make teepees out of tortillas! I'll never forget my sixth grade homeroom teacher and the amazing classroom culture she created. I still have a piece of paper with a heart on it that is covered in affirmations from my fellow classmates. My sixth grade math teacher taught me that math could be taught effectively through fun and games. And, my sixth grade science teacher led us through the only dissection I ever enjoyed--a flower! There were more, but I think you get the picture. :) Looking back, I'm not sure exactly what type of teaching job I expected to have. I certainly can't think of a job that would allow me to do ALL of those things.

During my senior year of high school, I was incredibly blessed to be able to work with my AP English Literature teacher, Mrs. Elliott, to perfect a number of scholarship essays and my valedictorian speech. When most people found out that I planned on entering the education field, they would often do their best to discourage me. Many of my teachers told me that I should pursue something worthwhile like law school or medical school, not an education degree. I was told I was wasting my talent. My own high school principal advised me to go into "anything but education." Mrs. Elliott was different. She encouraged me to pursue my dream of becoming a teacher. We talked about the difference I would be able to make in the world. (Of course, I think she is still disappointed I am making a difference in the world by teaching mathematics instead of English!)

Just over six years ago, my senior English teacher helped me to take my feelings, my dreams, my desires and put them in more eloquent words than I could have ever imagined possible: "My goals keep me focused, eternally striving, and determined to overcome life's obstacles. Life is too transitory to waste in search of riches or celebrity status. I accept that teaching is not going to make me rich. Nor will it bring me fame. The self-fulfillment resulting from the knowledge that I have touched the lives of this country's future engineers, congressmen, doctors, lawyers, teachers, and astronauts will provide an intrinsic joy that cannot be found elsewhere. A teacher's profound influence may never be fully known, but unlike fleeting fame and wealth, it is immortal." And, those words still ring true today. Teaching has definitely not made me rich. And, I only have to deal with the fame of teaching when I go to Wal-Mart or the only grocery store in town.
But, my every action touches the lives of the 85 or so students who sit in my classroom on a daily basis. Add to that the 65 students that I was blessed to teach last year. I realize that doesn't sound like a lot. There are 7.125 billion people in the world, and I have impacted the lives of approximately 150 teenagers. I don't see the numbers, though. (What a shocking thing for a math teacher to say, right?) I see the faces. I see the face of the girl who won her first ever award for her performance in my Algebra 1 class. She was so shocked to hear her name called during the awards assembly that she didn't come up to the front to be recognized. I see the face of the student who passed her Algebra 1 EOI last year after failing Algebra 1 the previous year, Algebra Fundamentals the year before that, and 8th grade math the year before that. I see the faces of the parents who tell me that they had never heard their child say that they liked anything about school, or (gasp!) math, until they took my class. I remember the face of the boy who interrupted my lesson one day to say, "You make math fun!"

Sadly, these aren't the faces of this country's future engineers, congressmen, doctors, lawyers, teachers, or astronauts. These faces belong to students who have lived harder lives than I could ever imagine. These are students who I will never see walk across the stage, donning their cap and gown. They have dropped out, moved away, made irreversible decisions. But, I have still made a difference, an unquantifiable difference.

I get to spend my days surrounded by students. I teach them math, and in return, they teach me about life. They teach me about what it looks like to overcome unimaginable obstacles. They teach me about the power that a single word can carry. They teach me things without even realizing it. Joy punctuates my day. I laugh. I cry. I get way too excited about polynomials. I tell jokes to my students. They try their hardest not to laugh. Okay, not laughing usually doesn't require that much effort. We celebrate the good things that are happening in their lives. They are my students, my kids, my life.

So, to the student who asked but will likely never read this blog, no. No, I would not trade this job for a job I hated, even if the other job offered $2 million dollars. I can't imagine another job that could make me feel so fulfilled. Yes, there are the days that are characterized by stress and not so good parts of being a teacher. But, even those days are made better by my students.

Veterans Day was one of those days. I was stressed to the max, trying to get the PowerPoint presentation ready for that afternoon's assembly. After running upstairs to check and see if the Veterans Luncheon was going smoothly, I returned to my classroom to grab my lunch. I got the surprise of my life when I walked in the door. Two of my students had brought their lunches to eat in my classroom. This was not surprising. I often have students hang out in my classroom for all or part of their lunch period. No, I was surprised by the fact that they had pushed two desks together, covered them with a red table cloth, placed a glass vase on the table, set a "Reserved" sign on the table, and lit a tea candle. An origami flower ornament had been commandeered from my cabinet to set in their vase. And, there they sat with their lunchables, sweet tea, and dill pickle potato chips. I couldn't do anything but stop in the door way and laugh. Without realizing it, these two sweet girls had made my day. And, I can only hope that I do the same to someone else at least once a day.

A Lunchtime Surprise

We have been busy, busy, busy this year in Algebra 2! Now that we're on Unit 4, I decided it was time that I get our pages from Unit 2 and Unit 3 posted! Our first unit of the year covered the basics of functions. I posted the pictures of the rest of Unit 1's material here. But, I had yet to finish or take a picture of our function transformations foldable at that time. This foldable was created after students had explored function transformations using an activity I learned about this summer called Move the Monster. I got a paper copy of the handout at the OGAP Common Core Workshop I attended this summer. But, I found an answer key to the activity online that someone else had posted if you want to see what the activity is all about.

My goal was for students to discover the transformations for themselves. Then, we summarized these findings in a foldable for future reference. I'll be honest. My Algebra 2 kiddos struggled a lot with this activity. But, I would like to think that it was a productive struggle.

Function Transformations Foldable - Outside

Function Transformations Foldable - Inside

Unit 2 was a review of linear functions. Since linear functions are an Algebra 1 topic, we went through this very quickly. I covered rate of change, graphing linear functions, graphing linear inequalities, and graphing systems of equations and inequalities. We didn't create any INB pages over systems. Due to time constraints, I only reviewed how to solve systems graphically. Time will tell if that was a smart decision or not.

Unit 2 Table of Contents

Rate of Change Graphic Organizer

This year, I emphasized rate of change much more than I did last year. I used this as an opportunity to constantly review the difference between dependent and independent variables. Whenever students would struggle with interpreting the rate of change, I would direct them to this page a lot.

I also made the decision to teach my students about linear functions in the form y = a+bx instead of the typical y = mx+b. Let me tell you, this is a hard thing to do. First off, I've always taught y=mx+b before. When I took Algebra 1, I was taught y=mx+b. My Algebra 2 students who paid attention in Algebra 1 love y=mx+b. Okay, maybe they don't love it. But, the idea of changing from y=mx+b to y=a+bx did not set well with them at all.

I was told, however, at two separate conferences this summer that my students would do better with exponential functions of the form y=a(b)^x if I taught them linear functions in the form y=a+bx. We will see. We will definitely see.

There are some things I like about teaching y=a+bx. It does make more sense to tell students that we always graph the y-intercept first when it comes first in the equation. However, standardized test questions seem to always write linear functions in the form y=mx+b. This does give me an opportunity to remind students that it doesn't really matter what order we write the equation in as long as we make sure that the signs are correct and that the slope is the coefficient of the x.

Slope and Linear Functions INB Page

Outside of y=a+bx Foldable

Inside of y=a+bx Foldable

I am still in love with Slope Dude. I thought that I wouldn't need to show Slope Dude to my Algebra 2 students. But, my students who had me last year in Algebra 1 insisted that we HAD to watch it again. It was kinda funny. They talked up Slope Dude like crazy to their fellow students. "This is the best video ever." "It's so funny." Then, they kept making cryptic comments like "Puff Puff Positive" and "This is Zero Fun." Their classmates were SO confused and intrigued at the same time. So, I pulled up the video on YouTube. The audio isn't the loudest, so I made everyone stop talking. I started the video. The kids who had seen it before were cracking up. The kids who had never seen it before had a look on their faces that was priceless.

Seriously, if you haven't watched Slope Dude, it will be the best 2 minutes and 36 seconds of your day. I promise. I don't know what it is about this video, but every time I have ever showed it, my students were narrating Slope Dude's adventures by the end of the video. Be forewarned: your students will also never refer to the slope as positive again. It will be "Puff Puff Positive." And, there may be an audible gasp whenever you say the word "Undefined." After all, it is the worst curse word ever in mathematics.

Months later, my students still are talking about Slope Dude. Last week, our Geometry classes started reviewing linear functions. Some of my Algebra 1 students from last year came by to tell me about it. When the Geometry teacher reviewed the four types of slope, the students insisted on calling the slopes by their Slope Dude names. I hear that the Geometry teacher was not impressed...

Slope Foldable (When Closed)

Slope Foldable (When Open)

I used our lesson over linear vs non-linear graphs as graphing calculator practice. Students rearranged each equation to get y by itself and entered it in their graphing calculator. I downloaded this activity for free from TpT.

Linear / Nonlinear Card Sort

I also can't teach horizontal and vertical lines with HOYVUX!

HOYVUX - Outside of Foldable

I made a slight change this year. I added O/K to the horizontal lines slope and N/O to the vertical lines slope to emphasize that it is okay to have a zero in the numerator. The slope is just zero. But, you cannot have a zero in the denominator. Then, the slope is UNDEFINED! (And, yes, I apologize for my cursing.)

HOYVUX - Inside of Foldable

After making this foldable for the second time, I had an epiphany. I should have made this into two separate foldables. The HOY section should glue on the page horizontally. The VUX section should glue on the page vertically. I'll definitely be trying this out when I get to this topic with my Algebra 1 students!

Graphing Linear Inequalities

Many of my Algebra 2 students were very nervous about graphing linear inequalities. It was a topic that they hadn't really understood in Algebra 1, and they did not think they would be able to understand it. This was a lesson where my principal just decided to pop in for a formal observation. It ended up going well, though. I was worried at first. The students were telling me that this was going to be hard and that they wouldn't be able to get it.

Once we had worked through 3 problems together, one of my students announced to me, her fellow students, and the principal that "You have shown me the light!" Graphing linear inequalities quickly became one of my students' favorite parts of this unit.

We concluded our INB pages for Unit 2 by gluing in our two linear regression labs: Bouncing Tennis Ballas and Twizzlers. I posted about these two labs here.

Bouncing Tennis Balls Lab

Twizzlers Lab

PDF Templates to Download:

If you have trouble downloading these, please make sure that you have Shockwave installed. If you still cannot download these, please send me an e-mail. I would be happy to attach the files and send them to you.

Unit Table of Contents (PDF)

8 Door Foldable for Function Transformations (PDF)

Rate of Change Graphic Organizer Map (PDF)

y=a+bx Foldable (PDF)

HOYVUX Foldable (PDF)

Graphing Linear Inequalities Graphic Organizer (PDF)

Bouncing Tennis Balls Lab (PDF)

Twizzlers Linear Regression Lab (PDF)

Unit 3 was a weird one for Algebra 2. I wanted to cover exponential functions right after linear functions to see if teaching y=a+bx actually helped my students to graph y=a(b)^x. I also needed to review exponent rules with my students before we could move onto quadratic functions, radical functions, or logarithmic functions. And, I also needed to make sure that my students were solid on the distributive property, combining like terms, and factoring before we got any further into the semester. So, I sort of combined all of these into a hodgepodge Unit 3.

Unit 3 Table of Contents - I apologize for the fact that this was not up-to-date when I took the picture. Oops...

Exponential Functions Frayer Model

Exponent Rules

Ms. Hagan's Book of Exponent Rules worked so well with my Algebra 1 students that I decided to try it out with my Algebra 2 students.

Parts of a Power and Unwritten Exponents

Exponent Rules for Like Bases

Negative and Zero Exponents

You can read more details about how I taught exponent rules in this post.

Naming Polynomials Graphic Organizer

Combining Like Terms and the Distributive Property Foldable - Outside

Combining Like Terms and The Distributive Property Foldable - Inside

Introduction to Factoring Notes

If/when I ever do this again, I will type up the polynomials that are written in marker. Students will have to cut them out and decide if they are the factored version or the distributed version. Students will glue them in the appropriate places on the table and then come up with the corresponding version.

I used the same factoring graphic organizers with my Algebra 2 kiddos that I used with my Algebra 1 kids. You can read more about my approach to factoring this year here.

Factoring Quadratic Trinomials when a=1

Factoring Quadratic Trinomials when a>1

Factoring Difference of Squares

We closed out the unit with an exponential growth and decay of skittles lab, but that will have to be another post for another day!

PDF Templates to Download:

Unit Table of Contents (PDF)

Blank Frayer Models (PDF)

Naming Polynomials Graphic Organizer (PDF)

Factoring Quadratic Trinomials (a=1) Graphic Organizer (PDF)

Factoring Quadratic Trinomials (a>1) Graphic Organizer (PDF)

Factoring Difference of Squares Graphic Organizer (PDF)

October 21st was Celebration of Mind Day. Celebration of Mind Day is a holiday that honors Martin Gardner and his contribution to recreational mathematics. This was the first day my students came back from Fall Break. So, they had been out of school for five entire days. I decided this would be the perfect opportunity to expand their horizons and show them a side of mathematics that they maybe hadn't seen before.

We talked about who Martin Gardner was. He did not invent the hexaflexagon, but he did tell the world about it. I first learned about hexaflexagons when I was in the tenth grade. My sister was in the seventh grade at the time, and she got to make one in her math class. I was a tad jealous, and I was also extremely frustrated. I couldn't figure out how to make it work! And, she made it look so easy.

Last year, I made my first hexaflexagon with my Algebra 1 students, and I instantly fell in love. I could probably sit for hours and play with a hexaflexagon!

If you want to host your own hexaflexagon party, there are all the resources you could ever need here. And, here is a link to PDF templates to make your own trihexaflexagon or hexahexaflexagon.

We started our discussion of hexaflexagons by watching a Vi Hart video.

My students were amazed. Of course, they instantly wanted to make one. I printed off templates for a trihexaflexagon. I have found that the best way to ensure success is to tell students to cut out their template and to double crease (once each way) each fold. If students do this, they will be MUCH less frustrated. And, their teacher is, therefore, much less frustrated!

After showing students how to assemble their hexaflexagons, I got the amazing opportunity to show students how to make their hexaflexagons work. I always let students try to figure out how to work them on their own. After all, they have seen a video of how it works. But, most students need someone to show them where to pinch and how to open up the center of their hexaflexagon. My favorite thing to do is to watch students' faces the first time they are able to open up the center of their hexaflexagon. Their expression is PRICELESS. I want to find a way to see that expression more on a day-to-day basis as we are learning algebra.

After creating their hexaflexagons, we watched the Hexaflexagon Safety Guide because it shows a lot of cool ways to decorate your hexaflexagon. Plus, who wouldn't want to see a hexaflexagon made out of a tortilla?

The day after we made our hexaflexagons, one of my students came back to tell me that she had stayed up late watching all of Vi Hart's videos. Her words: "Math is fun!"

To those of you who will say that I wasted a day of instruction with my Algebra 1 and Algebra 2 students, I would beg to differ. I wasn't hired just to teach math. I was hired to change lives, to inspire students. I have a group of Algebra 1 students from last year who come to visit me multiple times a week. When they realized it was Hexaflexagon Day, they almost all told me that they still had their hexaflexagon from last year. This is something they will remember for a long time. I can't say the same about worksheet or a quiz.

My Hexa-Hexaflexagon and My Tri-Hexaflexagon

One of my Statistics students is an amazing artist. This was her creation. I am inspired by it, and I just had to share! Isn't this just gorgeous? She puts my hexaflexagon to shame.

Have you ever just made a tiny change to how you teach something and been shocked by the difference it made?

A couple of weeks ago, I was tutoring one of my Algebra 2 students after school. We were multiplying polynomials, and he was getting the multiplication correct. But, he was messing up when it came to combining the like terms. After trying the same problem multiple times, I decided to write it out on the dry erase board as he told me each step.

Usually, I have students put squares or circles around like terms or squiggles or lines underneath them. This usually does the trick. This time, however, I decided that I would line up all of the x cubed terms, x squared terms, etc. This way, when I went to combine like terms, I just had to add the coefficients instead of worrying about where all the like terms were. The student seemed to like this method. And, I was kinda impressed with myself for my last minute creativity. I had already been at school for almost twelve hours at this point, so I was a little brain dead.

I didn't erase the board before going home, so this problem was still up when my Algebra 2 class came in the next morning. A few of my students noticed it and mentioned how they really like this method of organizing your work.

I took a picture, but the problem had been up for multiple days by that time. So, the answer has been partially erased. Sorry about that! Maybe everybody else has been teaching this way all this time... Or, maybe this will be new to you as well. If this post helps or inspires one person, it was worth it.

Method of Organizing Work when Multiplying Polynomials

It's been over a month since my last edition of Things Teenagers Say. You can check out the previous crazy things that I have overheard in my classroom in Volume One and Volume Two.

Enjoy!

--

Me: Today we are going to be learning about polynomials! Aren't you guys excited?
Student: Why would we be learning about party animals? I'm confused...

--

Student: Doesn't the US cover all seven continents?
Me: No. Let's take a look at this globe.
Student: This globe must be wrong. My seventh grade geography teacher told us that the US was on all seven continents.

(I guess the globe my mom bought for my classroom did serve a purpose!)

--

Student: The worksheet I just turned in has Icy Hot on it. Sorry!

(Later the Same Day)

Another Student: I apologize that my homework I just put in the tray has tabouli on it.

(This is only something that would happen in Drumright. Tabouli is like a way of life here. It is served every single day in the cafeteria. I'd never even heard of it before moving here. I wasn't impressed the first time I tried it at, but it definitely grows on you!)

--

(During a Celebrity Age Guessing Game to Motivate Linear Regression in my Stats Class)
There is a photo of Clint Eastwood on the Smart Board. Students have to guess the name of the celebrity and their age.

Student 1: Isn't that the guy from all those westerns?
Student 2: Yeah - that's John Wayne, right?

--

Student discussing me with another student: "Of course she doesn't wear makeup. She's a vegetarian. They're against stuff like that."

--

Student: I don't understand why my teachers always count my answers wrong when I put a line through my Ts.
Me: Do you know how to write an F in cursive?
Student: No. Why?
Me: Well an F in cursive is a T with a line through it. So, when you write a T with a line through it, your teachers think you are writing an F.
Student: That makes so much sense now.

--

Student: What are you eating?
Me: An enchilada.
Student: Why are you eating an enchilada?
Me: Because I brought leftovers for lunch. My mom made enchiladas when I went to visit my parents this weekend, and she sent me back some leftovers.
Student: Are your parents Hispanic?
Me: No. Why do you ask that?
Student: Well, only Hispanic people eat enchiladas.
Me: Yeah, that's not quite a true statement. Do I look like my parents are Hispanic?
Student: Yes. You look like you are part Hispanic and part Jewish.
Me: (Awkward Silence. Yeah, I didn't have any words to respond to that.)

--

Student: Can we listen to some music today?
Me: Sure, who do you want to listen to?
Student: How about some Michelangelo?

--

(Upon entering my classroom on the first day that the desks went from groups of four to rows)

Student: Why is this set up like an actual classroom? I'm confused.

Monday, I was blessed with the opportunity to do a rare thing: celebrate my birthday on a school day! My birthday almost always falls on Thanksgiving Break or the weekend. So, I can count on one hand the number of times that I've been able to celebrate at school. This was my first birthday celebration at school as a teacher, and I was pretty excited.

I had been talking up my birthday for weeks. Well, I guess it was actually more of a lament. I lamented the fact that my age was no longer going to be a prime number. In fact, I was going to have to spend the next 1,826 days as a prime number. There were two typical responses. Response 1: What is a prime number? This response was quickly followed by an "I'm so glad you asked!" and a short math lesson. Alternately, Response 2: You love math way too much. To this, I just smiled. It's true. I do love math. And, I'm glad my students can see my passion for the subject through my words and actions.

The celebration started a little early on the Friday before my birthday. I found sweet messages like this one written on my dry erase board.

A sweet birthday wish...

On the morning of my birthday, I changed the date and holiday to match the occasion.

My Mathematical Birthday Celebration

I was quickly informed that my monthly celebration was a tad too restrictive. Apparently, other people are born in November, too. After going to the teacher's lounge to make some copies for the day, I returned to find a lovely birthday surprise.

Birthday Cake!

A birthday cake! The giver was so sweet and apologetic: "I got you a birthday cake! They left off the Miss and misspelled your name. I'm so sorry, but I got you a cake!"

Here's a picture of me and my beautiful, thoughtful cake.

A student brought me a birthday cake!

See the birthday hat? I bought it myself. :) I went into Family Dollar on Sunday night, and I bought 3 bags of candy and a birthday hat. The cashier asked, "Are you going to a party tonight?" I just smiled and said, "Not quite." The candy was for my students to eat on my birthday. The birthday hat was for me to wear on my birthday. I've stopped even trying to explain my random purchases to cashiers. I've decided that weird looks from cashiers are just a part of being a teacher.

Soon, I was greeted by two more students bearing another birthday cake! My students sure know how to make someone feel special!

Homemade Birthday Cake - Complete with a Math Problem for My Age

See the math problem that equals my age? I have trained my students well! :) And, the decoration above the word "Happy" is a number line. We've been graphing one variable inequalities, so this was especially fitting. (Though, I didn't realize it was a number line. I thought it was one of those markings that you would find on a football. Of course, it wouldn't make any sense to put that on MY cake. I didn't figure out it was a number line until the girl who drew it was bragging about the awesome number line she had drawn on my cake to her friends. Oh, that's what that was. There weren't any numbers on it, so I couldn't tell. The longer dash in the middle of the number line was supposed to give it away. Oops...)

The second birthday cake also came with a card and a "Birthday Girl" ribbon. I was pretty excited about this!

My Birthday Girl Ribbon - I was so proud of this!

A Happy Birthday Card

Of course, the best way to celebrate your birthday is mathematically themed birthday bellwork. My Algebra 1 students have been working on compound inequalities. So, they found this problem when they entered my classroom: Someone who doesn't know Ms. Hagan well enough to know that today is her 24th birthday guesses that she is less than 30 and greater than or equal to 22. Write this statement as a single inequality, if possible. Is it an "and" inequality or an "or" inequality? Then, graph this inequality on a number line.

Algebra 1 - Birthday Bellwork - Compound Inequalities

This problem ended up leading to some great discussion! Half the class was convinced it was an "or" inequality, and the other half was equally convinced it was an "and" inequality. It was fun to see them realize that both "and" and "or" could be found in the problem. I love using the highlighters on the Smart Board to graph the intersection of two inequalities.

We spent the rest of the hour reviewing inequalities for our test the next day. One of my students decided to make fun of my birthday hat. "Are you sixteen? Because that's what sixteen year olds wear on their birthday." I'm pretty proud of my response. "Well, the package said "Ages 3 and Up" when I bought it. Why don't we practice writing this as an inequality?"

Inequalities to the Rescue!

And, just so you know, my age is in the solution set for this inequality!

My Algebra 2 students have been working with radicals. We've been using the birthday cake method to find the prime factorization of the radicand. So, their bellwork was to find the prime factorization of my age. I told them there would be a contest for the most beautiful birthday cake. My second period Algebra 2 class took this contest very seriously. My fifth period Algebra 2 class couldn't have cared less.

Algebra 2 Birthday Bellwork - Prime Factorization

Here are pictures of some of my favorite birthday cakes:

Prime Factorization Birthday Cake

One student didn't exactly follow the instructions. They just drew me a birthday cake without the prime factorization. I asked, "Where did the x squared come from? That isn't a prime factorization." "Oh, I just thought you wanted us to draw you a cake. I decided your cake should be decorated with something mathematical." I guess that works, too.

Another Birthday Cake

One of my 8th graders surprised me with a birthday cupcake!

A Birthday Cupcake

Me and My Birthday Cupcake!

All in all, it was a fabulous day. We had fun. We ate cake. We did math. We did lots of math.

And, I can't forget to write about my birthday presents from my family! They were appropriately themed. I received an infinity necklace, an infinity scarf, and some awesome math games! (There were non-mathy things, too.) I'm so excited to try these out!

Mathematical Birthday Gifts

My Algebra 1 students just finished up a mini-unit on graphing and solving one variable inequalities.

As usual, every new unit starts with a table of contents. Last year, I had students keep one table of contents at the beginning of their notebook. I like the individual unit table of contents SO much better! Almost all of my students keep them up to date!

Table of Contents

This foldable was inspired by a foldable I saw on Coffee Cups and Lesson Plans. I started this unit by drawing the different inequality symbols on my Smart Board. I wrote numbers above each symbol. Then, I asked a simple question, "Who can tell me which number is above the symbol that means less than?" Hands shot up in the air. Some students gave me the correct number. Others had confused the symbol for less than with the symbol for greater than. Still others had confused it for the less than or equal to symbol. One student argued that there was no way of knowing because there were no numbers for the alligator to eat.

Graphing Inequalities Foldable - Outside

Oh, the alligator. I remember learning about the alligator in elementary school. The alligator is a really hungry animal. He always chooses to eat the largest number of fish possible. I even did a project for my ed psych class in college where I taught a kindergartner about inequality symbols using the alligator. Now that I'm teaching algebra, I can't stand the alligator. The alligator doesn't help my students translate symbols into words. The alligator holds my students back. So, I told them that they had to take everything they ever learned about the alligator and throw it out the window. I thought there was going to be a revolt in my classroom. One student proclaimed, "That's half of my life! You can't expect me to just throw away half of my life because you don't like the alligator."

When I look at an inequality symbol, I just know its name. I guess I just memorized them somewhere along the way without realizing it. Last year, one of my college algebra students was having a terrible time remembering which symbol meant less than and which symbol meant greater than. One day, she had an epiphany. If you make an L with your hand, it looks like the less than symbol. Less than starts with L. This was perfect! So, making a backwards L with your hand creates the greater than symbol. If you are familiar with sign language, you could also make an argument that there are similarities between a sign language G and the greater than symbol. My student who discovered the hand trick was so proud of herself! Her exact words were "This just made my day!" And, she never had to ask me about what a symbol meant again.

Since then, I've been teaching this hand trick to my students. After a couple of days, they usually get to where they just know what they symbol is without thinking about Ls and backwards Ls.

Graphing Inequalities Foldable - Inside

I had my students create the examples for each inequality symbol. I would let one student pick the variable and another student pick the constant. Some students were pretty mad at me because they didn't get a chance to pick a variable for the class. We graphed each example and talked about the difference between open circles and closed circles. My favorite discussion was on how to graph s is not equal to 3.

I teach my students that the order you write an inequality in matters. Does it really? No. However, on standardized tests, inequalities are always (almost always?) written with the variable first and constant last. Of course, compound inequalities are the exception to this rule. But, more about them later. As soon as I passed out this half-sheet of paper, I had the full attention and curiosity of my students. Why are there flip flops on my paper? Don't you realize it's winter?

I know, it's a little corny, but I told that "If you have to flip flop the sides of the inequality (to achieve the correct order), you must also flip flop the inequality symbol." They affectionately called this the "Flip Flop Rule."

Inequalities INB Page: Order Matters - The Flip Flop Rule

This next page was attempt to modify the page I created last year for graphing two-variable inequalities. I don't like it quite as well, but I guess it did the job.

This probably isn't the best thing to admit, but I didn't teach my students why it was necessary to flip the inequality symbol when you multiply or divide by a negative last year. I mean, I taught them to do it. I just never explained why. This year, one of my Algebra 2 students asked. I wrote 2 < 4 on the Smart Board. Then, I divided both sides by -1. If we keep the inequality symbol the same, we get -2 < -4 which is a false statement. Light bulbs went off. It was a beautiful sight. I am constantly becoming a better teacher. I've heard before that experience is the best teacher. I don't think I quite realized how true that is until I started teaching.

This year, I wrote 5, a large space, and a 7 on the board. Then, I asked, "Who can tell me what symbol should go between these two numbers?" The class agreed that a less than symbol belonged in the middle. Next, I asked for volunteers. Tell me something we could do to both sides of this inequality. Add 2. So, we added 2 to both sides. Guess what? The inequality symbol is still true. What else could we do to both sides of this inequality? Subtract 7. The inequality symbol is still correct. Give me something else we could do. Multiply by 2. The inequality symbol is STILL correct. By now, my students were convinced that the inequality symbol would always remain the same. So, I issued them a challenge. The first person to come up with an operation that would require us to change the inequality symbol would win a Tootsie Pop. I bribe my students with A LOT of candy...

It took quite a while to come up with multiplying or dividing by a negative, but I like to think it was time extremely well spent. I must have still been half-asleep when I typed up these notes because I called it The Golden Rule of Inequalities: Whenever you multiply or divide both sides of an inequality by a negative number, you must flip the inequality symbol. In retrospect, the name makes no sense. My kiddos didn't seem to notice, though.

Solving and Graphing Inequalities in One Variable

The last part of our unit focused on compound inequalities. I used the topic of Christmas presents to motivate the difference between AND and OR Compound Inequalities. After completing our bellwork, I sat down on my stool at the front of the classroom and announced, "Today we are going to talk about Christmas." I called on a student and asked them what was on their wishlist for Santa. There were snickers. I guess high school students are too cool for Santa Claus...

The first time I did this, I lucked out. The first student I called on said that he wanted a PS4 or an X-Box One for Christmas. I became incredibly excited and started peppering him with questions. What gaming system do you currently have? If you get this new gaming system, will you have to get all new games or will your old games still work? Finally, I asked him which system he was leaning towards. "So, all you want for Christmas is an X-Box One?" "You'd be happy if the only thing you got for Christmas was an X-Box One." See what I'm building towards here?

Does the gaming system do you any good if you don't have any games to play? So, I told him that what he really wanted was an X-Box One AND some games for Christmas. Another student said my statement should actually say "I want an X-Box One, some games, AND some controllers for Christmas." If you get the gaming system but no games, you will be disappointed. If you get the games but no gaming system, you will be really disappointed. The second time I did this during the day, I had to ask 3-4 students before I found someone that wanted a new gaming system for Christmas. With my last class of the day, I asked almost every single person in the class before I found someone who mentioned video games. That was a shocker!

Then, I wrote an OR statement on the board. I want an X-Box One or a PS4 for Christmas. We had a similar conversation. If this was your wish, would you be happy if you found an X-Box One under the tree? Would you be happy if you found a PS4 under the tree? What if you found both under the tree? With an AND statement, you had to get both of your wishes to be happy. With an OR statement, you only have to get one of your wishes to be happy. If you get both of them, you will just be ecstatic. This was the perfect transition for looking at AND and OR inequalities.

Compound Inequalities Foldable - Outside

The inside of this foldable didn't photograph the best where I wrote in pencil on this dark purple paper. Sorry about that!

Compound Inequalities Foldable - Inside

PDF Templates to Download:

If you cannot view these files, please ensure that you have Shockwave installed. If you still can't access them, send me an e-mail. I will be happy to attach the needed files and send them to you. Thanks!

Unit Table of Contents (PDF)

Graphing Inequalities Foldable (PDF)

Inequalities: Order Matters Flip Flop Notes (PDF)

Solving and Graphing One-Variable Inequalities Graphic Organizer (PDF)

We are currently learning about radicals in Algebra 2. I am loving this unit! I'm building this unit off of a short unit I did on radicals with my Algebra 1 kiddos towards the end of last year. After all, there's no need to reinvent the wheel... We're still working on this unit, so there will be more pages posted sometime in the future.

Radical Functions Table of Contents

I'm doing something else radical with this unit on radicals. I'm trying out SBG. To be honest, I was disgusted with my Algebra 2 students' performance on the previous unit. I have quite a few students who CANNOT factor a trinomial. They bombed their last test. But, they are still passing my class. Therefore, they have no motivation to actually learn to factor. I've always loved the idea of standards based grading, but I've always written it off before as too time consuming.

I take it all back. Do you know what is too time consuming? Spending almost an entire month on a unit and having students not master key concepts because your grading system tells them they don't have to. Grades in my class have become almost meaningless. I hate it. When I look at a students' test score, I don't know what they know well and what they don't know at all. I don't know if they completely mastered one topic and left another topic blank. Or, maybe they made little mistakes on all of the topics.

It's gotten to the point where I hate to grade. I let the pile of papers to grade sit there, growing, all week long. Eventually, I bite the bullet and have a marathon grading session. When I pass back papers and tests, very few students look to learn from their mistakes. I hear other teachers talk about writing comments all over their students' papers. I don't even do that. Why? I know they won't read them.

In a desperate measure, I threw this together in about an hour. I wrote 6 learning goals for our unit on radicals. I decided to grade on a scale from 0-4. Is this the best scale? I have no clue. This was totally last minute. Once a student achieves a 4 on a learning goal, they are exempt from questions that cover that learning goal on all future quizzes.

I had my students glue in a score tracking sheet on the page facing their table of contents for Unit 4. Every day, I pass back the previous day's quiz. Students update the sheet in their notebook. Then, I review the questions students have questions on. I like that this new method is forcing me to teach in layers, not lumps.

If a student doesn't get a 4, they immediately start looking for their mistake. I have rarely been writing comments on the quizzes. I just put a number. It makes students think. Where did I go wrong? How can I avoid making this mistake on today's quiz? They get mad at me when I give them a 3 for a tiny, tiny mistake. But, by forcing them to retake the quiz, I am ensuring that they will never make that mistake again.

This system is a work in progress. I'm liking it so far. And, my students are liking it, too. I still have a handful of students who aren't trying on the quizzes. I'm not so sure what to do about that. The only complaint from students is that now they can't get their name on the Star Student Bulletin Board for making an 85 or above on our unit tests since the quizzes are replacing the unit test.

I love looking through my grade book. I can scroll down the columns and instantly know who needs work with each aspect of the chapter. I'm still trying to figure out how to do homework with sbg. And, I'm toying with trying out SBG with my Algebra 1 kiddos during our linear functions unit. Decisions, decisions, decisions...

SBG Tracking Chart and Table of Contents

Before we could delve into simplifying radicals, I needed to refresh my students' memories regarding prime and composite numbers. We color-coded a hundreds chart to keep in our notebooks for reference.

On the sides of the chart, we wrote definitions for prime and composite numbers. Two of my students decided we should color our prime number definition the same color as our prime numbers on the chart and likewise for the composite numbers. Color With A Purpose. I like it!

Prime and Composite Numbers Chart

We used highlighters that I had ordered from Amazon. They worked well for this activity.

Highlighters!

I'm still in love with the birthday cake method for prime factorization. I've written before about why I like this method better than factor trees.

The Birthday Cake Method for Finding Prime Factorization

I typed out the steps for finding the prime factorization for my students to save time. We also did examples together in our interactive notebooks.

Prime Factorization Birthday Cake Examples

Vocabulary is a very important part of this chapter. When I started teaching algebra, I didn't know the terms index or radicand. I'm sure my algebra teacher taught those words to me, but I never had to use them. I will not let my students go down this same path. We are constantly talking about the index and radicand!

Parts of a Radical - Index, Radicand, Radical Symbol

For practice, students had to determine the index and radicand of these radicals. This further emphasizes the necessary vocab for this unit.

Parts of a Radical Examples

I also typed out the steps for simplifying radicals. Last year, I had students write this out by hand, and it took WAY too long.

Steps for Simplifying Radicals

Then, we did examples of simplifying radicals in our notebooks.

Simplifying Radicals Examples

After simplifying radicals, we moved on to adding and subtracting like radicals.

Adding and Subtracting Like Radicals Notes

And, this was soon followed by multiplying radicals.

Multiplying Radicals Notes

We still have yet to cover dividing radicals, rationalizing the denominator, and converting between radical form and rational exponent form.

PDF Templates to Download:

Unit Table of Contents (PDF)

SBG Tracking Sheet for Interactive Notebook (PDF)

Prime and Composite Numbers Chart (PDF)

The Birthday Cake Method for Prime Factorization Notes (PDF)

Parts of a Radical Notes (PDF)

Steps for Simplifying Radicals (PDF)

Adding and Subtracting Radicals Notes (PDF)

Multiplying Radicals Notes (PDF)

Due to the Thanksgiving holiday, we only had two days of school this week. Needless to say, my students were not very excited about having to come to school on Monday and Tuesday. Several of the schools around us took the entire week off, so that made the week seem even more torturous to my students.

My statistics students were especially restless. We're in the middle of our unit on probability. Monday, we looked at some probability word problems. On Tuesday, I wanted to do something fun and interesting but still related to probability. I did a quick google search of probability activities, and I ran across a net of a cuboctahedron. Isn't that just a fun word? Cuboctahedron. Cuboctahedron. Cuboctahedron. It just makes me smile.

The activity instructed students to assemble their own cuboctahedron. (The net is on page 4 of the linked PDF document. I'm also intrigued by the probability activity on page 5 that involves acting out a Russian fable that predicts who will get married within the next year.) Then, they were to toss the cuboctahedron 100 times and count how many times it landed on a square face and how many times it landed on a triangular face.

Assembled Cuboctahedron and Net Pattern

I let my students each pick a sheet of cardstock from the cabinet, and I quickly ran off nets for them to cut out and assemble. The cutting and gluing process was more time intensive than I realized. This activity took the entire 50-minute period. Since it was the day before Thanksgiving break, this was perfectly fine. Most of my students ended up opting for tape because the net was so hard to put together. I used glue, and it works fine if you have enough patience to let the glue dry a little between steps.

My Class' Finished Cuboctahedrons

The cuboctahedron consists of 6 square faces and 8 triangular faces. Students were asked to predict the probability that the cuboctahedron would land on each type of face BEFORE tossing it 100 times.

As a class, they decided that 6/14 of the faces were squares. Therefore, the probability of landing on a square face was approximately 0.43. 8/14 of the faces were triangles. Thus, the probability of landing on a triangular face was approximately 0.57. '

Our Class Data

In 299 trials, the cuboctahedron landed on a square face. In 91 trials, the cuboctahedron landed on a triangular face. So, the experimental probability of landing on a square face was approximately 0.77, and the experimental probability of landing on a triangular face was approximately 0.23.

My students were intrigued by this data. I'm not sure what the authors' motivation was in writing this activity. Were we supposed to get these surprising results? We had a discussion of the difference between theoretical and experimental probability. What is the reason behind this discrepancy? Is it related to the differing areas of the faces? Or, is it as one student suggested related to the way that the cuboctahedron lands? It often hits on a corner, and when this happens it almost always favors the square faces for landing.

I liked this activity because it got my students thinking and talking about math on a day when they didn't feel like doing any math. It's a rare thing when I give my students a problem I don't already know the answer to. I need to do this more often! Does anyone know more about this perplexing polyhedron probability problem?

Remember the pictures I posted of my Algebra 1 INB pages over polynomials and factoring? That was the end of our second unit of the year. It looks like I never got around to posting the beginning of our second unit. Oops...

Unit 2 was simply titled "Expressions."

Unit 2 Table of Contents

We started Unit 2 by writing our own definitions of some very important vocabulary words. I got these examples/counter examples from the Kagan Cooperative Learning book for Algebra 1. I like the process of having students reason through the examples and non-examples to write their own definitions. However, I think I will break down the vocab and do it throughout the unit instead of trying to do all the vocab at the beginning of the unit. I think my students will retain the vocabulary better that way.

Unit 2 Vocabulary

We created these foldables to emphasize the parts of an expression. I stole/modified these from some foldables I found on A Sea of Math blog.

Parts of an Expression INB Page

Constant and Variable - Outside of Foldable

Constant and Variable - Inside of Foldable

Coefficient, Factors, Equivalent Expressions - Outside of Foldable

Coefficient, Factors, Equivalent Expressions - Inside of Foldable

We then moved onto translating expressions from words to math and from math to words. This foldable was created to summarize which words go with which mathematical operations.

Translating Expressions - Outside of Foldable

Translating Expressions - Inside of Foldable

The rest of the unit included exponent rules, polynomials, and factoring.

PDF Templates to Download:

Unit Table of Contents (PDF)

Parts of an Expression Foldables (PDF)

Four Door Foldable for Translating Expressions (PDF)

Yes, I realize it's December. We have successfully celebrated Thanksgiving. My classroom has now been turned into a Winter Wonderland (pictures to come)!

But, today I'm going to blog about Halloween. Why? Well, I haven't blogged about it yet. And, if I don't blog about something, I will forget about it. To be honest, I will still forget about it. But, if I blog, I will be reminded about it whenever I look back over old blog posts.

Warning: There isn't any math involved in this post. We didn't do any cool Halloween-related math projects. We just did math and ate candy. I still wanted to share these pictures with you, though.

One of the students who has a locker right outside of my classroom decorated her locker for Halloween. I would have never thought of doing this when I was in high school. Isn't it just precious?

A Halloween Decorated Locker

I had a pumpkin full of candy to share with my students for Halloween. We all know that teenagers do not get enough candy on Halloween. :) I know I ended up eating WAY more candy than I should have during the week of Halloween!

Halloween Candy

I think my students were more excited, though, by the Halloween stickers that I offered to let them choose from. Some of these stickers made their appearance on the locker that I showed you the picture of earlier. High school students LOVE stickers.

Halloween Stickers

My secret pal surprised me with a Halloween tumbler, filled with candy.

On the day after Halloween, I found a pile of candy on my desk that was left by a group of my students. Isn't that just sweet? (Pun definitely intended!)

Candy from My Students

Oh, and I can't forget to share pictures of the pumpkins that my students carved in their Family and Consumer Science classes. I was very impressed by their creativity. If I remember correctly, the green pumpkin pictured below was the winner. Directly behind it, you will see a recreation of Miley Cyrus' Wrecking Ball. I had to have a student explain that one to me. I was so confused. This happens a lot. I am constantly reminded just how out of touch I am with pop culture!

Carved Pumpkins

In college, I was always taught to begin my lesson plans with an anticipatory set. I always struggled with these. I couldn't quite remember my teachers ever using them when I was in school. How in the world would I be able to come up with one of these for every lesson that I teach?

I wish I could say I have mastered the anticipatory set. I haven't. Most days, the thought doesn't even cross my mind. But, I've certainly become more creative. My goal is that when students enter my classroom that their curiosity is piqued. What are we doing today? Why are there tennis balls on your desk? Why are the desks arranged differently? Or, today, "Why are there flies everywhere? That's just weird." To this, I responded, "Flies? Sorry, I haven't noticed any."

Flies on the back of chairs

A fly on the air conditioner

Flies perching on posters

A fly on the dry erase board

Flies are everywhere!

The flies were kinda hard to miss. There were twenty of them. And, that was the point. I wanted my students to be wondering what today's lesson was going to be about.

Have you figured it out yet? I don't know how true this story about Descartes and the invention of the coordinate plane is, but I don't really care. I like the story, and I had a blast sharing it with my students. I told them that this story was from long ago, long before they had anything like electricity. "Do you mean this story is from 19 years ago?" Ummm...electricity had been invented nineteen nears ago.

I pieced together my version of the story from several different versions I found online. Rene Descartes was a sickly child. He was smaller and weaker than his peers. His father sent him off to boarding school. The school master was worried about Descartes. His theory was that if Descartes slept more, he would become stronger. So, Descartes was forced to remain in bed until late in the morning. He would lay in bed and ponder life and all things scientific and mathematical.

This habit carried over into his adult life. He often stayed in bed until almost noon. One day, Descartes noticed a fly on the ceiling while he was laying in bed. He watched it buzz to and fro, to and fro. And, he started to wonder. What if I wanted to share the exact location of the fly on my ceiling with someone else? After thinking about this for sometime, he determined that the location of the fly could be determined with precision if you knew the distance of the fly from two walls. From this epiphany, the idea of the coordinate plane system was born. Descartes never actually graphed on a coordinate plane, but he made it possible. The end.

"Oh, so that's why there are flies on the wall."

Next, I brought out my new favorite algebra teaching tool.

Life-Sized Coordinate Plane Made out of a Shower Curtain Liner, Duct Tape, and Electrical Tape

Over Thanksgiving Break, I pulled out my copy of Teach Like A Pirate to help me infuse some creative ideas into this unit on relations and functions in Algebra 1. One of the questions you should ask yourself when planning a lesson is if there is anyway you can get the students moving around. Can they act out the process?

I was reminded of my 8th grade Algebra 1 class in middle school. I remember walking down the hall with my class to stand in front of the auditorium. We used the grid lines on the linoleum floor to practice walking out various slopes. I actually remember it most for being incredibly confused about the entire process. But, I definitely have to give my teacher points for trying to make it more hands-on and kinesthetic.

I started to think of ways in which my students could graph points and later explore slope. My school was built in 1919. My classroom is carpeted. The hall outside my classroom is small 1-inch tile. There is some linoleum right outside the elevator, but I think my kids would disturb all of the other classes on that hall if I tried to have class in the hall. Where could I build a life-sized coordinate plane?

My sister suggested that I make my coordinate plane on something that could be picked up and moved like a shower curtain. I liked the idea. I went to Dollar Tree and purchased a 70" by 72" shower curtain liner and four rolls of electrical tape for $3.00.

Coordinate Plane Supplies. Grand Total: $3

With the help of my mom and sister, we laid out the shower curtain liner and marked the center of each side. We placed the rows of electrical tape 6 inches apart to make a grid that extended from -5 to 5.

Laying Out and Marking the Coordinate Plane

Starting the Grid

Finishing the Electrical Tape Grid

We used colorful duct tape to form an x- and y-axis for the coordinate plane.

Finished Product

It's definitely not perfect. There are lots of little wrinkles. The grid lines aren't all perfect straight. But, I love it. It's a coordinate plane. You can walk on it. I can fold it up and store it when I'm not using it. Plus, it's just cute.

When I pulled out my coordinate plane after discussing the invention of the coordinate plane, my students had incredulous looks on their faces. I'm surprised that I can do anything nowadays that will still shock them. "Did you make that?" Yes. They, of course, wanted to know what it was made out of.

I laid the coordinate plane in the floor and instructed my students to get out their interactive notebooks. We created a foldable about ordered pairs and a foldable about the parts of the coordinate plane. I have attached PDF templates of each at the bottom of this post.

Graphing Ordered Pairs Foldable - Outside

Graphing Ordered Pairs Foldable - Middle

Graphing Ordered Pairs Foldable - Inside

Parts of the Coordinate Plane - Outside of Foldable

Parts of the Coordinate Plane - Inside of Some Flaps

Parts of the Coordinate Plane - Inside

The parts of the coordinate plane foldable was stolen from the Journal Wizard blog. I always teach my students that the quadrants are numbered like the letter "c" is drawn.

After taking notes, my students were ready to do some coordinate graphing on their own. I invited the students to look around the room and pick their favorite fly "But they're all the same." "I don't care. Just pick your favorite fly." I pulled up a random name generator that I have saved in my favorites that I have already typed my class rosters into. I let the computer randomly pick a name. That student was tasked with taking a fly down from the wall. On the back of each fly is an ordered pair to graph. The student had to stand on the origin and walk through the process of graphing the point on the coordinate plane. The next person chose another fly from the wall and graphed it.

My students had a blast! We ran out of time for all the students to have a turn, and some of my students insisted on staying after the bell rang to have their turn. Of course, there were some students who acted like they were too cool to stand on the coordinate plane and graph. Nobody made any comments about it being too elementary. I loved it!

Even though the coordinate plane isn't the sturdiest or toughest, I think it stood up fine today after being used by three sections of Algebra 1. I'm definitely looking forward to using this new resource throughout the rest of this year.

PDF Templates to Download

Set of 20 Flies / Ordered Pairs (PDF)

Print on regular copy paper. Fold each page in half and laminate.

Ordered Pair Foldable (PDF)

Parts of the Coordinate Plane Foldable (PDF)

Last year, my classroom's Christmas decorations were rather insubstantial. I had a tree. Okay, I had a magnetic tree. I even put it up again this year.

Magnetic Tree on my Dry Erase Board

This year, I made some new additions. I hung garland above my dry erase board.

Garland Around My Dry Erase Board

I hung garland over the door to my classroom.

Garland Around my Door

You cant see them that well in this picture, but I put Christmas lights around my bulletin board. Sometimes, I plug these in and they blink. Sometimes, I plug them in and they don't blink. I have yet to figure them out.

Christmas Lights Around My Bulletin Board

Tiny snowflakes adorn my bulletin board of calculator posters.

Snowflakes on My Bulletin Board

Last year, my sister decided I needed a Charlie Brown Christmas Tree for my classroom. She bought me one on Christmas clearance. My kids all in two groups. There are the kids who have seen A Charlie Brown Christmas. They proclaim that my tree is "cute" or "adorable." Then, there are the kids who have never seen A Charlie Brown Christmas. "You need a better tree." "What's wrong with your tree?" "You need to get some more ornaments for your tree.""I'm sorry, but that's a wimpy tree." "Your tree has problems." I'm pretty sure my tree is going to have a complex by the time this holiday season is over. I love it, though.

A Charlie Brown Christmas Tree On My Desk

I wrapped more garland with lights around the edge of my desk.

Garland Around My Desk

I still have snowflake window clings and giant plastic snowflakes to hang, but those require a ladder to be hung. And, I have yet to find the time to tote a ladder up the stairs and risk my life in order to bring Christmas cheer to all. It will happen, though.

I've been playing Christmas music, too. I just love this season! My classroom is WAY more decorated than my house. But, I guess this is where I spend most of my time...

I'm gonna be honest. My students and I have way too many conversations about my current relationship status. I'm not married, and that bothers them. Students have stopped me in the Wal-Mart parking lot to tell me who they think I should be dating. They interrupt class to give me dating advice. I'd love to think that this is because they care so much about me. But, sometimes I think they'll talk about anything if it gets them out of talking about math.

Last week, I was walking down the hall during my planning period when a student in the office called out my name. This was a student I had last year for Algebra 1. I have students I get along with extraordinarily well. This student is not one of them. We tolerate each other, and that's about as far as it goes. Last year, he made it very clear, through his actions, that he did not want to be in my class. I walked in to the office, and this is the conversation that followed:

Student: Do you still eat lunch with the science teacher every week?
Me: Ummm... I've never eaten lunch with the science teacher.
Student: Yes, you have. I've seen you.
Me: No, I haven't. I promise.
Student: Well, maybe you should start. Where do you eat lunch?
Me: I eat lunch in my classroom by myself.
Student: Why?
Me: I've got things to do.
Student: Well, you're never going to find a boyfriend that way!

The conversation took a turn after this. Much to my surprise, this student expressed excitement over the fact that he was going to get to have me for Algebra 2 next year. "You are going to teach Algebra 2 next year, right?" "I am going to get to have you next year, right?" "You are going to still be here next year, right?" "If you're not here next year, I'm going to hunt you down and find you." I'm going to take that threat as a compliment. This is proof that students do come around. He isn't the first student this year to come to me and tell me, in retrospect, how much he enjoyed my class last year. This is important because it seems like I have a lot more haters this year. There's hope, though. They may just come around, too.

So, enough of that tangent. Let's talk about some math. Remember the cuboctahedrons? In the same document that I found the cuboctahedron net in, I also found a reference to a Russian fable that predicted whether a young lady would get married in the next year. It seemed like an interesting probability problem.

Last week, I posed the problem to my statistics students. Apparently, in some Russian villages, they use a certain method to determine which girls will be married in the next year. Fold three long blades of grass in two. Have someone hold them so he loose ends are hanging down. Tie the ends together in three knots. The person holding the blades of grass lets go. If your knots have led to the formation of one large loop, you will supposedly be married in the next year.

Is this true? I have no clue. Either way, it still makes for an interesting problem. First off, what is the probability that you will end up with a large loop? I wish I had had my students write down their gut instinct regarding the probability before making any calculations. To me, the likelihood that a large loop would be formed was quite slim.

Predicting the Future...

I set my students loose on this problem, and they were quickly frustrated. During this time, I had been cutting some pieces of clothesline rope (the only thing I could find in my cabinet that would work!) to model this scenario. A pair of students acted out the ritual. And, amazingly, a large loop was formed! Wedding bells would be ringing! Another pair of students acted out the ritual. Wow, another large loop! Maybe this is more likely than we thought...

I only have five statistics students. After five trials, we had 3 successes and 2 failures. It was my turn. A student held the pieces of rope for me. I tied the ends together in three separate knots. By this time, I had made a probability tree model and knew that the probability was over 50 percent that I would be married in the next year. (I won't give away the actual probability in case you want to try out this problem on your own.)

What was my result? I know you are DYING to know.

My Future

Not surprisingly, I am supposed to be wed in the next 51 weeks according to this piece of rope.

We'll see...

I ended up having to walk my students through how to make the tree diagram for this problem. We haven't done much work with tree diagrams because they aren't presented in our textbook. If I ever teach statistics again, I will introduce tree diagrams and then have students walk through this problem with the instruction of making a tree diagram.

One student wondered if this is where the term "tying the knot" originated. I did some googling, and it doesn't seem so. But, I thought that was very creative thinking!

Alternately Titled: Crazy Conversations With My Students

(See Volume 1, Volume 2, and Volume 3 for more craziness.)

--

Me: You may use your notebook on this quiz. You may not use a friend on this quiz.
Student: What if my notebook is my friend?

Best Interactive Notebook Compliment Ever. End of Story.

--

Me: What did you have for breakfast?
Student: Oatmeal.
Me: I had Cheerios. I know you were wondering.
Student: What did you have for breakfast?
Me: I just told you. I had Cheerios. Were you not listening to me?
Student: I heard you. I just thought it would be impolite to not ask you since you asked me.

--

Student: You seem like the type of person who would have a guy trapped in their basement.

Creepiest Comment Ever. Do I really give off these vibes?!?!

A week later:

Me: He's not my boyfriend.
Student: Yeah, he's your hostage.

--

A student said something rude to me, and his punishment was to say two nice things about me in return.

"You have nice cheekbones."

How many teenage boys comment on people's cheekbones???

--

What did the dinosaur get when it jumped in the pool?
Wet.

--

What did the robot say to the centipede?
Stop being a centipede.

I think my students take after me in the joke department.

--

Student: Are you positive?
Me: Yes.
Student: What are you having?
Another Student: Who is the daddy?
Yet Another Student: Don't you know you're never supposed to say yes if someone asks if you are positive?

All I could do was shake my head and try to move on with the lesson...

--

Student: What's your favorite movie?
Me: It's a toss-up between Sweet Home Alabama and How To Lose A Guy in 10 Days.
<Hysterical Laughter from Multiple Students>
Me: Guys, what's so funny?
Student: What was the name of that second movie?
Me: How to Lose A Guy in 10 Days
<More Hysterical Laughter>
Student: Isn't that a movie about how to avoid stalkers? Why would that be your favorite movie?
Me: You've never seen How to Lose A Guy in 10 Days, have you?
Student: Why would I watch a movie about avoiding stalkers?

Finally, another student spoke up and agreed with me that it was a really good movie that was NOT about avoiding stalkers.

As a teacher, I know I'm not supposed to have favorites. But, there are those students who go out of their way just to make you smile. There are those students who notice the extra things that you do. There are those students who ask you how your day is and truly take the time to listen. There are the students who bring you cake on your birthday. There are the students who laugh at your jokes and tell you new jokes. There are the students who put forth effort on every assignment, who ask for help when they need it. There are the students who come to visit you just to say hi. There are the students who invade your classroom before school, at lunch, and after school to talk, to listen, and to be heard. There are the students who come to you for hugs, band-aids, and advice for their future.

I love all my students, but there are some who have earned a special place in my heart. These are the students I will remember always. These are the students who are more than my students. They have become my friends.

Yes, I know they taught me in college to never become friends with my students. There is supposed to be that clear line between teacher and student. But, they weren't exactly honest with me in college. They didn't tell me how hard teaching was going to be. They didn't tell me about the politics that come with working in a school. They didn't tell me about the drama. They didn't tell me how much my life would be impacted by high stakes testing and teacher evaluation programs. They didn't tell me about how much I would grow to care for the students that call me Ms. Hagan. They didn't tell me that some days there would be more important things than achieving the objective that I spelled out on my lesson plan. They didn't tell me how emotional teaching was. They didn't tell me what it would feel like to constantly give of yourself, with no guarantee of anything in return.

So, maybe I am breaking the rules. Maybe I will regret this some day. But, then again, maybe not.

Last Week's Holiday

Most days, the holiday I research and write up on the board goes largely unnoticed. But, some days, my students surprise me. This was one of those days:

A note from a friend...

Encouragement From A Friend...

Rock, Paper, Scissors Math Tournament

Algebra 1 INB Pages - Polynomials and Factoring

Algebra 1 INB Pages - Solving Equations

Why I Teach

Algebra 2 INB Pages - Function Transformations and Linear Functions

Algebra 2 INB Pages - Exponential Functions, Exponent Rules, and Factoring

Celebration of Mind Day (aka Hexaflexagon Day)

A Tiny Change

Things Teenagers Say...Volume Three

Two Cubed Times Three: How a Math Teacher Celebrates Her Birthday

One Variable Inequalities INB Pages (Algebra 1)

Radical Radicals

Cuboctahedrons: A Perplexing Polyhedron Probability Problem

Parts of an Expression and Translating Expressions Foldables

Halloween 2013

Help! My classroom has been taken over by flies!

Walkin' In a Winter Wonderland...

The Probability of Marriage

Things Teenagers Say...Volume Four

Those Students...