Numbers About Me

August 19, 2013, 3:30 am

≪ Previous: Interactive Notebook Table of Contents

This year, as a getting to know you activity, I had students complete a half-sheet entitled "Numbers about Me." Well, actually, the paper said "Numbers about __________________________," and students had to write their names in the blank. This was the perfect closing activity for the second day after my students had participated in the Marshmallow Challenge.

Numbers About Me Activity

Students were supposed to write five numbers that had special meaning to them and tell me the significance that number had in their lives. I was shocked by the number of freshman I had that did not know the meaning of the word "significance."

Last year, I had students do this on the first page of their interactive notebooks, but I didn't get a chance to read them until the first time I collected notebooks to grade. This way, I was able to engage each student in a conversation about one of their important numbers as I circulated the classroom and picked up the completed activity. Some responses were quite interesting, but I'm pretty sure nothing could top my Algebra 2 student who predicted the date he would die as one of his important numbers...

Now that we are seven days into the school year, I need to pull these back out and re-read them! This time, I should be able to put a face with the name...

If anyone is interested in using this short activity in their class, I have embedded the file I used below.

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Organizing Absent Work

August 21, 2013, 12:59 pm

≫ Next: Thankful....

≪ Previous: Numbers About Me

Box to Hold Absent Work

In a perfect world, every student would be in class every single day. Sadly, I don't teach in a perfect world. Last year, as I began teaching, I knew that I needed to have some way to organize the work that students missed. I ended up creating a "While You Were Out" Binder that turned out to be way too time consuming. After about a week, I stopped using it, and I resorted to a really lazy method. If a student was absent, they would need to come see me at an appropriate time and ask for what they had missed. This works okay *if* I can locate the papers they need in the mess that I call my desk, *if* they remember to come ask for them, and *if* students understand what constitutes an appropriate time to ask. That is way too many "ifs."

Absent Work Form "Today, You Missed..."

This year, I'm trying something new. We're not even a month into school yet, so I don't know that this works in the long run, but this new system is definitely working better than last year's system! On my cabinet, I have a hanging file box that says "Absent? Look here!" The first hanging file has a half-page form that I fill out for each student who was absent that day. I write their name, the date, and check off whatever they missed that day. If there are any handouts, I staple them to the back of the form. Since the amount of writing I have to do is minimized, I can get these done in a very small amount of time at the end of the day. Instead of dreading this end of day task, I actually look forward to it because it's one of the easiest things to mark off my to-do list!

When students come to me and say they were absent, all I have to do is point to the box. I can also easily check and see what students are not picking up the assignments they missed. If you are interested in the form I use, I have embedded it for your below to download!

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Thankful....

August 24, 2013, 6:43 pm

≫ Next: Algebra 1 Student-Made Foldables

≪ Previous: Organizing Absent Work

The school year is off to a pretty good start! I have yet to win over my current students. They just don't quite know what to think of me yet. A good number of them are currently in the stage of "I hate math. I hate this class. I hate you." Okay, maybe they don't hate me, but it certainly feels like it some days. Once we have our first test, I'm hoping that my students will start to see themselves as capable when it comes to mathematics.

Friday morning, one of my Algebra 1 students gave me this problem to solve. They decided that since I gave them problems to solve everyday, I needed to be given a problem to solve. I read it and smiled, but I didn't write anything.

I am so blessed to have students from last year drop by my classroom on a daily basis. Some of them come in for help with their math homework. But, most of them come in to just chat. I ask them how their life is going. We talk about their hobbies or extracurricular activities. They question me about why I'm changing the way I do some things in my classroom. Why do you sing to your students this year, but you didn't sing to us last year? Why do you have "Super Star Students" this year, but you didn't have them last year? These conversations remind me why I chose to stay in this school district. These students need me. I'm making a difference here.

The next hour, I come into my classroom after the bell rings to find this addition.

And, before long, my current group of students will come around, too.

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Algebra 1 Student-Made Foldables

August 27, 2013, 6:40 pm

≫ Next: Algebra 1 Unit 1 Interactive Notebook Pages

≪ Previous: Thankful....

I've been keeping my students super busy with their interactive notebooks. So far, my Algebra 2 students are loving the interactive notebooks. My Algebra 1 students HATE them. I still think they'll come around eventually...

Since I left both my camera and my interactive notebook at school, I'm going to share some photos of the interactive notebook pages that my Algebra 1 students created last year for their semester project. Yes, this post has been setting in my drafts since May...

I know that I am continually inspired by foldables and other creative creations I see online. It is my hope that one of these might serve useful as inspiration to you. Remember - these were created by students. Make sure you check these very carefully for errors before using with students!

Finding Slope from 2 Points

Airplane Method for Factoring Quadratics

Four Types of Slope

Domain and Range

Four Types of Slope

Solving Systems of Equations by Substitution

Solving Systems of Equations by Substitution - Inside

Absolute Value Foldable with Slider

Parallel, Perpendicular, or Neither Foldable

Parallel Lines and Perpendicular Lines

Lines That Are Neither Parallel Nor Perpendicular

Mean, Median, Mode, and Range Foldable

Domain and Range Graphic Organizer

Graphing Inequalities Foldable

Four Types of Slope Foldable

Domain and Range Foldable

Domain and Range Foldable - Inside

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Algebra 1 Unit 1 Interactive Notebook Pages

August 30, 2013, 6:49 pm

≫ Next: Algebra 2 Interactive Notebook Pages for Unit 1

≪ Previous: Algebra 1 Student-Made Foldables

My Algebra 1 students just finished up their first unit on Thursday. This year, I am attempting to model my Algebra 1 class on the Kagan Cooperative Learning Algebra 1 curriculum. As I'm getting to know my students, I have made some adjustments. Okay. I've made a ton of adjustments. My Algebra 1 students this year seem to be at a lower level than last year's students. Let's just say it's going to be an interesting year...

I'm so excited to share with you what my students' interactive notebooks consist of thus far! I've embedded the files for these pages at the bottom of this post. Hope these can be of some use to you!

Algebra 1 Interactive Notebook

Unit 1 Table of Contents

3 Requirements for a Good Definition

The Kagan curriculum I am using focuses on having students develop their own definitions for the vocabulary words for each unit. This is an entirely new approach to me. I'm used to just giving the students the definition and having them write it down. I'm kinda obsessed with the Frayer Model.

I'm enjoying the approach, however, of having students examine examples and counterexamples to determine what a word means for themselves. Time will tell if this leads to a higher level of understanding and recall. The first lesson of the year focused on what a good definition consists of. Our three requirements for a good definition were: 1) states the term, 2) states the nearest classification, and 3) states those items that make it unique.

We practiced a lot with this. I used some examples provided in the book to give my students the opportunity to practice writing a definition that had absolutely nothing to do with mathematics. Students were given a minute or two to examine the zingers and thingmabobs. Then, each student wrote their own definition based on the examples and counterexamples. Next, each person in the group shared their definition with the rest of the group. Each group discussed everybody's definition and combined the best parts of each definition into one group definition. Finally, we discussed the group definitions as a class and wrote one class definition. The process is very time consuming. But, it produces AMAZING discussions. So, I think it's worth it.

Writing Good Definitions Practice

Since I used images from this book, I cannot post these files to download. If you are interested in these resources, you may purchase the book here.

Unit 1 Vocabulary Foldables

My students repeated this process for our 10 vocabulary words for unit 1. They completed the "My Definition" section as homework. And, the entire next class period was spent creating group and class definitions. These were formatted as two book-type foldables that students glued in their interactive notebooks. I love that these foldables capture the process that students went through to write their own definition.

The Real Number System Graphic Organizer

We summarized the real number system using the graphic organizer that I created last year. It felt good to be able to reuse something from last year instead of creating something entirely new from scratch!

Exploring Rational and Irrational Numbers Foldable - Outside

This is a picture of a foldable that I created for my students to use as they walked through an exploration activity. This activity did not go as planned. I thought it would take one class period. After one class period, we had only started to scratch the surface. I ended up never finishing this activity with my students because I felt a need to move on. Still, I want to share this activity with you in the hopes that someone might be inspired to take this and make it better or at least give me insight on why it didn't quite work.

This activity was created with N-RN.3 (3. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.) in mind. I had some blank sticker name badges in my desk. So, I took a Sharpie and wrote various rational and irrational numbers on each name badge. As students came in the classroom, they got to pick a random number from the pile. After a brief introduction to the TI-30 Scientific Calculator, students were instructed to partner up and fill out the first line of this chart. They would fill in their number, the classification of their number (rational or irrational), their partner's number, their partner's number's classification, and the operation of addition. Using the scientific calculator, students would add the two numbers together, record the result, and then determine whether the result was rational or irrational. Find a new partner. Repeat until the first five lines have been filled in.

Exploring Rational and Irrational Numbers Foldable - Inside

After completing five addition operations, we would have a class discussion. I was hoping that students would arrive at the fact (on their own) that a rational plus a rational is always rational, an irrational plus a rational is always irrational, etc. This went semi-well. Some of my classes struggled with this way more than others. None of my classes made it to division. One class barely made it through subtraction.

Rational and Irrational Number Name Badges

What I didn't account for was the sheer amount of time that it took for my students to partner up, do the calculations, and fill out this chart. This ended up feeling like an entire waste of a class period because it was a lot of work with very little to show for it. I ended up doing most of the talking and discovering during our discovery period which was frustrating.

I still want to put this idea out there, though. I think it's good to blog about the lessons that go well, the lessons that are just mediocre, and the lessons that don't go as planned.

And, yes, I'm the crazy teacher who wore a sticker around ALL DAY that read 3/8. I put it on during first hour because I had an odd number of students. So, I actually went through the activity with my students. I didn't take off my sticker because I figured I would just have to make another one to wear for third hour and sixth hour. Third hour, we had a fire drill. Of course, I got asked by everyone I saw why I was wearing a number on my shirt. The math teacher definitely came out in my answer as I explained that I wasn't just wearing any number, but a rational number. Conversation ensued about what a rational number was. Yes, I'm that teacher who takes every opportunity possible to teach my kiddos something mathematical!

Me with My Rational Number Badge

Later that morning, we had our tornado drill. As the students huddled in the stairwell, the teachers stood in the hall. The history teacher looked at me and said, "So, you're less than half?" Confused, I asked her to repeat the question. "So, you're less than half?" Still confused, I decided that I would just agree with the history teacher and go on down the road even though I had no idea what she was talking about. Luckily, she motioned toward my sticker, and I realized that she was referring to the fraction I was proudly wearing. The other teachers in my building are used to my crazy methods that I use to teach math by now, so they weren't that surprised.

What did surprise me was my statistics students. I have a class of 5 juniors who are taking statistics as their upper level math elective. Statistics is the only class that we offer our students above Algebra 2. These are our best and brightest math students who have chosen to take their math class at our school instead of our local Career Tech center. Of course, they had to ask about my lovely sticker that I was wearing. I explained why I was wearing it, and I told them about all the crazy conversations I had had that morning as a result. What do my students decide to do? They decide that they want to make their own stickers with numbers on them to wear around the school for the rest of the day. There are kids who love math, and I'm so thankful that I get the chance to teach them! (I'm thankful for my students who don't love math, too. But, that's another post for another day!)

Integer Operations Foldable - Outside

After using two-colored counters to derive the rules for adding, subtracting, multiplying, and dividing integers, I had my students create a four-door foldable to summarize the results of their findings.

Integer Operations Foldable - Inside

Inside, we wrote the rules for each type of problem and included several examples of each for students to refer to.

Order of Operations Graphic Organizer

The last topic covered in Unit 1 was the order of operations. I did not follow the approach laid out in the Kagan curriculum for this topic. I attempted to adapt last year's interactive notebook set-up for this topic. But, I added new activities and songs as an attempt to reach students that I felt like I had not reached during our work with integer operations. I'm hoping that I will have time this weekend to create a post of the resources I used from other blogs to teach each major topic for this unit. Next year, I'd love to be able to come back and find the links of all the resources I used the previous year.

Files are embedded below. If you cannot view these files, please make sure you have Flash/Shockwave installed. If you persist in having problems, please send me an e-mail. I'll be happy to attach them and send them to you directly.

Unit Table of Contents

Requirements for A Good Definition

The Real Number System

Exploring Rational and Irrational Numbers

Blank 4-Door Foldable for Integer Operations Foldable

PEMDAS Graphic Organizer

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Algebra 2 Interactive Notebook Pages for Unit 1

August 31, 2013, 4:00 am

≫ Next: An Algebraic Oath

≪ Previous: Algebra 1 Unit 1 Interactive Notebook Pages

This year, I have resolved to do a much better job at the interactive notebook in Algebra 2 than last year. Last year, we had 12 students in my entire school who were enrolled in Algebra 2. This year, that number is just under 40. This is both exciting and kinda terrifying. First of all, it means that more students are prepared and willing to take Algebra 2. At the same time, my Algebra 2 students this year are greater in number and much more varied in level. This presents many challenges. But, these are challenges I am excited to attempt to meet.

Our first unit in Algebra 2 is an introduction to functions, function notation, domain and range, intercepts, maximums and minimums, intervals of increasing and decreasing, finding solutions, and transformations. My goal is to create a foundation which I can build off of once we start linear functions. I am also working hard to prove to my students that they are capable of doing Algebra 2 level work. Many of my students have extremely low confidence. We are also learning how to use the graphing calculator. This is the first experience any of my students have had with a graphing calculator, and I am working hard to make it a positive one.

So far, my Algebra 2 students are loving our interactive notebooks. They thank me on an (almost) daily basis for making Algebra 2 visual, fun, and easy. I have some students who are complaining right now that Algebra 2 is too easy. I told them that they just had to wait. Before they knew it, we would be exploring logarithms, exponentials, conic sections, and all kinds of other exciting mathematical relations. After going on and on about how excited I was about everything we were going to be learning and studying this year, one student asked, "Do you like math?" I was a bit taken aback by this question. Are there math teachers who don't like math? Of course, I like math. I love math! I eat, breath, and sleep math.

As usual, I have embedded the files for these foldables at the end of the post. If you have trouble viewing them, please make sure that you have Flash/Shockwave installed. If that does not correct the problem, please send me an e-mail and let me know what documents you are needing. I will be happy to send them to you!

My Algebra 2 Interactive Notebook

Algebra 2 Unit 1 Table of Contents (Thus Far)

I have already blogged about the NAGS foldable I had my Algebra 2 students create here.

NAGS Foldable - Outside

NAGS Foldable - Inside

NAGS Chart

I still haven't found a better way to practice differentiating between function/not a function than this card sort. I blogged about this last year.

Function / Not a Function Card Sort

We also created a Frayer Model for the word "function."

Function / Vertical Line Test Frayer Model

I stole this coordinate plane foldable from Ms. Haley and her wonder Journal Wizard blog! I think this is a big improvement over the coordinate plane foldable I did with my students last year. I created a template for this foldable which I have embedded below.

Parts of the Coordinate Plane Foldable

Our notes over independent and dependent variables were less than exciting. Maybe next year I will come up with a card sort or something. Hmm...

Independent and Dependent Variable Notes

Last year, my students had a TERRIBLE time remembering the difference between domain and range. This summer, at the amazing Common Core Training I received from the Oklahoma Geometry and Algebra Project (OGAP), I was introduced to an amazing resource--Shmoop. They have amazing commentary for each and every high school common core math standard! I learned about the DIXROY acronym from their commentary on F-IF.1.

Domain and Range Notes - Interactive Notebook

DIXROY stands for "Domain - Inputs - X-Coordinates and Range - Outputs - Y-Coordinates."

DIXROY Acronym for Remembering Domain / Range

I was able to re-use the domain/range notation foldable that I created last year for my Algebra 2 students. My students were VERY confused by the different notations. I haven't yet figured out a way to introduce these notations without overwhelming my students. They recovered, eventually.

Domain and Range Notation Foldable - Outside

Domain and Range Notation Foldable - Inside

I downloaded the domain and range cards from this blog post. There are 32 cards which give my students 32 opportunities to practice finding the domain and range!

Domain and Range Foldable

We made a tiny envelope to hold our 32 cards. Let me just say - having the students cut out all 32 cards took WAY too much time. I was about ready to pull my hair out. I think we might of spent half of a fifty minute class period just cutting these cards out. But, we used them a lot, so I think it was worth it.

I LOVED the envelope template that Kathryn (iisanumber.blogspot.com) posted earlier this summer. I downsized her template to the exact size needed to fit the domain and range cards I linked to earlier.

The Cutest, Tiniest Envelope to Hold our Domain and Range Practice Cards

Then, I took inspiration once again from Ms. Haley at Journal Wizard. She had her students create an interactive domain and range finder foldable.

Domain and Range Foldable (That sadly doesn't photograph well...)

As you can see, this foldable perfectly holds the domain and range practice cards from our handy-dandy envelope!

The foldable is made to perfectly hold our domain and range practice cards that are housed in the envelope.

Students fold over the domain tabs to help them determine the left-most and right-most points on the graph. If the graph goes approaches negative or positive infinity, the students leave the flap open where it reads positive or negative infinity. I wanted my treatment of domain and range to be much more hands-on this year, and I think this foldable does the trick!

After doing many, many cards together, I had students find the domain and range of all 32 cards as homework. They had to write the domain and range in both interval and algebraic notation. (And, the discrete graphs had to have their domain written in set notation.) The next day, I gave them an answer key to use the check their work.

The Domain and Range Foldable in Action

One of the main thing my students need to be able to do on their Algebra 2 EOI is to describe graphs. This foldable is an attempt to introduce my students to the concepts of x-intercepts, y-intercepts, relative maximums, relative minimums, increasing intervals, decreasing intervals, roots, solutions, and zeros.

Describing Characteristics of Graphs Foldable - Outside

Because there is so much information on this one foldable, this was a perfect opportunity to use COLOR WITH A PURPOSE. Each term was marked with a different color. And the corresponding part of the graph was marked with the same color. This is one of my favorite foldables that we have done this year!

Describing Characteristics of Graphs Foldable - Inside
AKA - Proof I LOVE color-coding!

I've posted some close-ups of the flaps if you'd like to see what I had my students write.

Close-up of Right Flaps

Close-Up of Left Flaps

Last year, my Algebra 2 students really struggled with the concept of an inverse. So, this year, I decided to start talking about inverses very early in the school year. This will allow us to revisit the concept over and over as we explore different types of function in a much more in depth manner. By the time the EOI rolls around, my students should no longer be scared when they see the word inverse!
This foldable was inspired by @druinok's post from February.

Inverse of a Function Foldable - Outside

I want my students to be able to find the inverse if they are given a set of points, a graph, or an equation. Since we have only just started exploring functions in general, the examples we went through were quite simplistic. We will explore much more complicated inverses as the year progresses!

A lot of my students were terrified when I told them that we would be learning about inverses. By the end of the lesson, they were amazed that inverses were actually quite easy.

Inverse of a Function Foldable - Inside

Inverse of a Function - Important Fact!

I still have to figure out how I want to introduce transformations to my Algebra 2 students. That topic should end our first unit. Hmm...

Embedded Files are Below:

Unit Table of Contents

NAGS Foldable

NAGS Chart

Coordinate Plane Foldable

DIXROY (Domain and Range) Graphic Organizer

Blank 3 Door Foldable for Domain/Range Notation Foldable

Interactive Domain and Range Finder Foldable (And Tiny Envelope Pattern from iisanumber.blogspot.com

Describing Graphs Foldable

Coming Soon!

Inverse of a Function Foldable

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An Algebraic Oath

September 6, 2013, 5:59 pm

≫ Next: Things Teenagers Say... Volume 1

≪ Previous: Algebra 2 Interactive Notebook Pages for Unit 1

I believe that my Algebra 2 teaching experience has made me a better Algebra 1 teacher. I see the misconceptions that my students enter Algebra 2 with. And, I'm striving to clear up as many of those misconceptions as possible with my current group of Algebra 1 students.

During our first Algebra 2 unit on functions, my students have been evaluating a lot of functions. They fully understand the concept of substituting in the given value of the variable. However, so many of my students do not place the value in parentheses when they substitute it into the function. Most of the time, they still end up with the right answer. But, they always end up missing problems such as find f(-2) if f(x) = -x^2 - 2x + 4. When they substitute in the -2 without parentheses, many of my students' first instinct is to change the two negative signs to a positive sign. This is bad. Very bad.

I don't know about you, but I have a terrible time convincing students that the way they have been doing algebra for the past few years is wrong. I can tell them it is wrong. I can hand back their graded papers that are covered with ink. We can review it as a class. But, for some reason, they seem to instantly tune me out as soon as they realize this is something they have already learned before, even though they did not learn it correctly in the first place.

This year, I decided that my Algebra 1 students were not going to follow in the footsteps of my current Algebra 2 students. When my students evaluated expressions or functions, they were going to always, always, always use parentheses. I asked myself, "How can I accomplish this?" I thought about the way I normally emphasize things in my classroom. I say them over and over and over. I write them in all caps with plenty of underlining on the Smart Board. I have my students write it in their notebooks. I repeat myself constantly.

That just didn't seem quite special enough. Those methods are just a normal day in my classroom. I emphasize a lot of stuff. So, how could I really emphasize something? How could I teach like a pirate? How could I give my students an experience instead of just another math lesson? The answer didn't come quickly.

In fact, it came as an epiphany about fifteen minutes before class was supposed to start. I wasn't going to just tell my students that they should always use parentheses when substituting values into an algebraic expression. No, my students were going to tell me that they would always use parentheses when substituting values into an algebraic expression.

I quickly typed up an oath: I, _______________________, do solemnly swear (or affirm) that I will always use parentheses when substituting values into an algebraic expression. To complete the experience, I printed the oath on gray card stock. I made lines for my students to sign and date. When cut out, the oaths would be conveniently wallet-sized so students could be reminded of this oath forever. (Students who were uncomfortable with taking an oath or swearing were given the option of affirming the statement instead. By saying that they affirmed the statement, they would be making an affirmation instead of an oath.)

Algebraic Oath Card

I used all of my acting skills to really play up this oath. I told the students how serious of a matter this was. I passed out the cards with the oath printed on it. I asked students to read the oath to themselves and see if they had any questions about the commitment they were preparing to make. Next, I made my students stand up. I chastised them for not taking this experience seriously enough. I had them raise their right hands. There were giggles and smart comments. Again, I reminded students that this was a very serious matter. I told them that the fact that they were not taking this as seriously as they should be was "crushing my heart."

In unison, we read the oath together as a class, and we signed our cards to commemorate the occasion. My students pointed out that there should have been a place on the card for a witness to sign... Some of my students suggested that we should have placed our hands on our interactive notebooks when we took the oath. I heard several students say that they felt like they had just joined a gang. Apparently, they now look at me as their ringleader.

There were the students who thought the entire thing was stupid. They told me that they were going to bring their cards to graduation and burn them in front of me. But, for the most part, I think my students really enjoyed it. I love the fact that sometimes the only help I have to give a student is to ask them, "Remember the oath that you took?" One of my students, when he turned in his homework, said, "I think I got all of my problems right because I remembered my oath."

I've embedded the pdf file for the cards below, but I'm not entirely happy with it. I whipped up these cards in less than five minutes, and it definitely shows. But, I think they served their purpose.

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Things Teenagers Say... Volume 1

September 15, 2013, 5:10 pm

≫ Next: Relations, Functions, and Dating Advice

≪ Previous: An Algebraic Oath

Year two of teaching has been a lot easier than year one was. Of course, this year has brought its own unique challenges. My Algebra 1 students, as a group, struggle much more with mathematics than last year's group. The number of students we have taking Algebra 2 has tripled since last year. I'm really excited about what this group of kids will be able to accomplish, but we have some major confidence issues to overcome in the next several months! I'm teaching statistics for the first time, and I'm learning as my students learn.

It's easier in that I'm teaching in the same school with the same administrators. I know exactly who to go to when I have a problem. I know the best time to use the copy machine. I know what to expect now when it comes to things like homecoming, prom, and graduation. When I go to a football game, I see a ton of familiar faces. I don't worry about what I'm going to say when I stand up in front of my students. I have a reputation for requiring a lot from my students. I also have a reputation for having a really fun class.

This year, it seems like my students are saying funnier things than normal. This probably isn't the case. What is more likely is that I am paying more attention to what my students are saying instead of being overwhelmed by the newness of everything. And, I've learned the importance of recording the good moments. If you don't record the good, it is very easy to become overwhelmed by the bad.

So, I present to you Volume 1 of Things Teenagers Say:

An actual phone conversation that occurred in my class:

Yes sir, I was calling in regards to renting a tiger for our homecoming float...$5,000 per hour...I don't think so. Thank you for your time.

I feel like God today.

(Said by a student who was wearing ALL white.)

I don't like how much homework you're giving us. I'm about to run out of money...at the teacher's credit union.

(I'm still not sure I quite understand this one...)

You have pretty handwriting. Your handwriting on the Smart Board does not look like this!

While making a concept map over "algebra:"

Ms. Hagan - how do you spell exciting?

E-X-C-I-T-I-N-G. I'm so glad that you find my class to be exciting!

There's another word before that word, isn't there?

Yeah - "non."

I've already missed 20 problems, and we're only on number 14.

At least you're not like most teachers who drain their students' blood to grade their papers with.

Ms. Hagan! Did you see them carry out the dead body?!?

Me: What is -3-5?

Student: -2

Me: No.

Student: 2

Me: No

Student: 8

Me: No

Student: (exasperated) Is it -8?

Me: YES!
Student: Well, I thought it was -8 at first, but then I decided that was too mainstream.

I feel like I'm in a haunted house whenever I come into your classroom.

Is "describe" spelled with an "L"?

Do penguins have ears?

Do you have a sister? Because I saw someone who looked EXACTLY like you on television.

What show were you watching?
What Not to Wear

Do you know what we should do in class today? We should find the end of pi!

I make it clear to my students that I am most definitely not an artist. But, I don't think they quite believe me until they see me draw for the first time. Then, that leads to conversations like this:

Did you draw that while an earthquake was happening?

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Relations, Functions, and Dating Advice

September 24, 2013, 5:44 am

≫ Next: Good Things is a Great Thing!

≪ Previous: Things Teenagers Say... Volume 1

I guess I shouldn't be surprised when my students give me dating advice. After all, I gave them some dating advice a few weeks ago, and they must be just returning the favor. If you want to know what your students really think of you, let them write you an online dating profile. But, more on that scenario and how it came to be at the end of this post.

After spending several days on relations and functions in Algebra 2, I put up this slide. Mathematical Dating Advice. Yes, the room will grow quiet. Conversations will cease, and all eyes will be on you. You will be shocked at the rapt attention that your students are capable of paying you.

When you are dating, you want to be in a functional relationship. Let the x-coordinate of the ordered pair be any person. In this case, the x-coordinate is Bob. Let the y-coordinate of the ordered pair be the x-coordinate's significant other. As you can see, Bob is dating both Jill and Sue. Therefore, this is not a functional relationship. And, unless you want to get your heart shattered in a million pieces, you need to get out of this relationship as fast as possible.

After this short conversation, I think I saw some light-bulbs come on. There was laughter, and I heard several girls discussing how they were going to ask the next guy they were interested in if he was a function or non-function. They decided this was problematic, though, because he wouldn't know what they were talking about if he hadn't taken Algebra 2.

As students were working on their function/not a function card sort, one group of students called me over for what I thought was help. Actually, they had been discussing my advice, and they had decided that one of the girls was currently talking to a guy who was definitely not a function. So, could I please tell their friend that she should stop talking to this guy?

Fast-forward to about 2.5 weeks ago, my Algebra 2 students are now working on distance vs. time graphs. We're doing graphing stories. We're writing stories to match graphs. And, this is leading to a lot of off-topic conversations. It's a Friday, and the class consensus is that we would all rather be at the beach than analyzing graphs of walks at the beach.

And somehow, one comment leads to another, and my class is soon discussing how I should describe myself if/when I try online dating. This is what they come up with: "I like taking long walks along the beach and graphing them. I love reciting the quadratic formula. And, I enjoy reading math books by a roaring fire."

I guess I should be thankful that they are concerned about my relationship status. But, I don't think I will be taking their advice any time soon...

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Good Things is a Great Thing!

September 26, 2013, 2:36 pm

≫ Next: Math Teachers' Circle Reflection

≪ Previous: Relations, Functions, and Dating Advice

Teenagers will never cease to surprise me! Just when I think I finally have them figured out, they shock me by hating something I was sure they would love and loving something I was sure they would hate.

For example, last Thursday was International Talk Like A Pirate Day. Every day, I post whatever holiday it is on my dry erase board below the date. I get my holidays from this site.

Pirate Day Bellwork for Algebra 1

So, on International Talk Like A Pirate Day, my students entered the classroom to find pirate-themed bellwork. Were they impressed? No. Could they care less? No. Did anyone try to talk like a pirate? No. My third hour has the tendency to be a little unruly, so I was able to quiet them down rather quickly by exclaiming, "Avast!" Of course, they told me the only reason they stopped and listened to me was because I sounded ridiculous. Whatever it takes...

In late August, my district brought in an elementary school principal from another school district to talk to the entire district on classroom management and building classroom culture. I was skeptical about the training because the same presentation was being given to all the faculty from pre-K through 12 at the same time. After introducing herself, the presenter put up a slide that read, "Good Things." It was subtitled, "Personal or Professional." The presenter modeled how Good Things works by (briefly) sharing something good that had happened in her life recently. Then, she asked for a few volunteers from the audience to share a good thing that had happened to them. Some of the things shared were funny. Others were serious. Some were school-related. Others were personal. I instantly fell in love with this activity.

Good Things

I know I've read about this classroom routine somewhere before, but I had never tried it. I feared it would take too much time, but the good thing about Good Things is that you decide how many students share. If you only have three minutes for this activity, you only let three students share before moving on.

I'm going to be honest. The first time I tried this out in my classroom, it was kinda awkward. I modeled how to share a Good Thing. And, there was dead silence. On top of that, my principal was in my classroom observing. Now that we've been doing this every Monday for almost a month, the students know exactly what to do when I put up the Smart Board slide that says "Good Things." Hands are raised, clamoring to be the first one to share their good thing. I'm learning things about my students that I would have otherwise never learned. Students who won't speak up in class will raise their hand to share a good thing that is going on in their life. Students get to see a different side of their classmates, and it's exciting to see them realize that they have shared interests with others.

I'll put it this way. My students LOVE Good Things. One class loves it so much that they've decided that Wednesday should be dubbed, "Bad Things Day." They told me that sometimes they just need an opportunity to vent. I'm just not so sure about whether that is a great idea or not. I'm thinking it's not a good idea. The goal of Good Things is to build a climate of positivity, caring, and sharing. And, hopefully, students will realize that I care and will know that they can come and talk to me about anything.

I've decided that Mondays are the perfect day for this activity. First of all, it's easy to be negative on a Monday because most everyone wishes it was still the weekend. And, most of my students get their inspiration for Good Things from their weekend activities. Not only am I getting to know my students better, but my students are getting to know me better. Last week, I asked for Good Things for the first time without first sharing my own good thing. My weekend had been less than exciting, and I just really couldn't think of anything noteworthy to share. After the students were done sharing, one table of students was quick to point out that I hadn't shared anything, and they wanted to know how my weekend was. It was a nice feeling to know that my students cared enough to want to hear about my weekend. I guess I shouldn't be surprised, though. This is the same group of students who took it upon themselves to write me an online dating profile description...

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Math Teachers' Circle Reflection

October 5, 2013, 2:40 pm

≫ Next: Fun With Linear Regression Labs

≪ Previous: Good Things is a Great Thing!

I've been busy, busy, busy lately! I've got a lot of recent classroom action that needs to be shared, but it will have to wait. I promised @pamjwilson that I would blog about this, and I try to keep my promises! :) But first, I have to share a picture of a flower that one of my students brought me.

A Gift From A Student

So, Thursday, after school, I was in my classroom. One of my Algebra 2 students from last year is currently taking Pre-Calculus at our local technology center, and I was tutoring her. As we were working on determining the end behavior of functions, another student came bounding into my classroom. She presented me with this pipe cleaner flower and said, "I made this flower for you because you're so bright and cheery like this flower." I was smiling until I heard her say "Not really" as she skipped back out of my classroom. It's the thought that counts, right?

On Thursday night, I joined @druinok for the inaugural meeting of the Tulsa Math Teachers' Circle. This was a new experience for me, and I wasn't exactly sure what to expect. I had done some reading online about math teachers' circles, but everything I read gave me the impression that each circle is unique.

We met at my alma mater, the University of Tulsa. I saw several of my math professors from college at the meeting, but they introduced themselves to me like we had never met before. Our evening started off with a lovely dinner. I sat with @druinok, two lovely ladies who teach middle school math at a local private school, and my former Calc 1 TA from college. Over dinner, we discussed what each of us taught and shared some funny stories about what life is like as a teacher. We also were reminded of what a small world it is that we live in!

Our session was facilitated by Judith Covington, a math professor at LSU Shreveport. She is a member of the North Louisiana Math Teachers' Circle, and she did a great job of introducing the concept of a math teachers' circle to us all. The main focus of the night was learning to play the game of SET. I had heard about this game via several blogs, and I had even tried to teach myself to play once using the Daily Set Game. That lasted about fifteen minutes before I gave up, frustrated. So, I was excited to finally learn how to play.

Three out of the five of us sitting at the table were experienced SET players. Thankfully, these three ladies did an amazing job of being patient with the other newbie and me. They did exactly what a good teacher should do. They gave us time to look for sets on our own. They would tell us when they found a set, but they didn't point it out. Each time they did point out a set, they would take the time to explain how the number, color, shading, and shape were either all the same or all different. When we pointed out things that weren't actually sets, they used it as a teachable moment. What card would you need to make a set with those two cards? And, slowly but surely, I think I started catching on.

My Very Own SET Game!

I think it's going to take me a long time to be able to identify sets efficiently, but I at least understand what I am doing now. Friday morning, I completed my first Daily Set Game. It may have taken me 12 minutes and 36 seconds, but I finished it all by myself! I think this is going to become part of my morning routine when I get to school. If I record the amount of time it takes me each day, I wonder what type of function would best model it?

After playing the game for a while, we turned our conversation to how the game relates to mathematics. Our facilitator led us through a great exploration of how SET can be used to teach geometry. We defined points, lines, planes, and hyper-planes using SET cards. I have to admit, I got a little lost when we started talking about hyperplanes. I was reminded once again why I teach algebra and not geometry! Still, it was so refreshing to spend time exploring and discussing mathematical concepts with other mathematically-minded people. The evening was most fun and intellectually stimulating. More information on the mathematics and geometry of SET can be found here.

This brings me to the most important thing I learned about math teachers' circles. These Circles are not meant to be a gathering of teachers to discuss the best way to teach factoring or share lesson plans. Instead, the purpose of these meetings is to engage teachers in actually doing and discussing mathematics. If you learn nothing that you can use in your own classroom, that is fine. As teachers, we require our students to problem solve. We continually present them with new material and ask them to grapple with it. Yet, how often do we do that? How often do we explore math problems that we don't automatically know how to solve or even approach? I know my students are amazed by my ability to look at 7x + x - 3x and determine that the expression can be simplified to 5x, but performing that process requires no real mental effort from me. This summer, I spent 16 days at various conferences, learning how to be a better math teacher. And, I learned a lot. But, I'm also excited for this monthly opportunity to just do math, whether it applies to what I am teaching or not. I hope that I never forget what it feels like to struggle through a problem, to persevere, to try different approaches.

I <3 Nerds Pocket Protector Courtesy of OSSM

Other highlights of the evening include my very own pocket protector! I also got to meet one of my blog readers which was very cool! I know that when I write something on here that I am putting it out there for the entire world to read. But, I'm still amazed to know that others actually read and use what I share! I also stopped by Dollar Tree while I was in Tulsa. I picked up these awesome neon starbursts.

Neon Starburts from Dollar Tree

When I bought them, I wasn't exactly sure what I wanted to use them for, but I knew I had to have them. I ended up buying three packages. On Friday, I decided that these starbursts were the perfect size to write reminders of what various buttons on our calculators do. This was definitely inspired by this pin! I can't tell you how many times I have had to explain how to type in an exponent on our calculators since school started. I doubt this will solve the problem, but maybe it will help at least one student. So far, I have put up calculator reminders for my Algebra 1 students. I'm still debating on what buttons to focus on for my Algebra 2 students who are using TI-Nspires.

Calculator Button Reminders

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Fun With Linear Regression Labs

October 6, 2013, 4:00 am

≫ Next: Things Teenagers Say...Volume Two

≪ Previous: Math Teachers' Circle Reflection

My Algebra 2 students just finished with our second unit of the year on linear functions. The unit didn't exactly go as I had planned. Their prior knowledge of linear functions was shockingly low. They knew it had something to do with y=mx+b, but they couldn't tell me what m and b stood for. They knew there was some formula for slope that involved x1, x2, y1, and y2, but they could never remember the order.

So, I basically ended up starting from scratch with these students which took much more time than I had planned on devoting to this unit. I will share the interactive notebook pages and specific activities we did later, but I do want to share the linear regression labs I did with my students. I wish I could say that my students loved these, but they didn't. They regularly told me how boring algebra was. I think the day I heard the most complaints was the day we performed a linear regression on data we gathered by eating twizzlers. How can eating twizzlers in math class be anything but exciting?!?

Linear Regression Lab 1: Personality Test Results

To introduce my students to linear regression, I had them do the True Colors Personality Test that I wrote about this summer. I had wanted to do this with my students at the beginning of the school year, but after two days of getting to know you activities, I was ready to jump straight into some mathematics! So, I saved the activity for later in the semester. We spent about 2/3 of the fifty-minute class period taking the personality test and learning about or results. My kids got really into this! I may have encouraged their interest a little by telling them this personality test would help them better understand their boyfriend/girlfriend. I ended up having to make copies of what each color means to give to the students because so many of my students wanted to give the personality test to someone and interpret the results.

The last third of the class period was full of data collection and graphing calculator action. I made a table on the Smart Board. Number of People vs. Time. I asked one student to volunteer to use the stopwatch on their phone to time the students for this activity. The students at table one took turns saying their name and their color from the personality test. We stopped the time and recorded the number of students and total time. We repeated this with table one and table two. We repeated it again with the students at tables one through three. Eventually we got a time for the students at all five tables saying their name and color.

Next, we had a short discussion about which variable was dependent and which variable was independent. I have been making a HUGE deal about independent and dependent variables this year. This was our first time ever to explore the spreadsheet function on our TI-Nspires. We entered the number of people in column A and the amount of time in seconds in column B. My favorite thing about the TI-Nspire is the process that you have to go through to make a scatter plot. First, you enter your data in the spreadsheet. Then, you insert a new Data and Statistics page in your document. This will make the calculator place your data points randomly on the screen. Once you figure out what your independent variable is, you click on the x-axis and choose the independent variable. The data points will start dancing across the screen to their proper homes. Then, you click on the y-axis and choose the dependent variable. After some more dancing, your scatter plot is done! It's fun to watch, and I love that students really have to think about which variable belongs on which axis!

Together as a class, the students walked through the process of performing a linear regression of the form y=a+bx. This summer, I went to two separate week-long workshops that told me that I should stop teaching y=mx+b and start teaching y=a+bx. The first time I heard that, I wrote it off as crazy talk. After all, y=mx+b and I have been friends since middle school. But, the second time I heard that, I started to think that there might be some merit to the idea. This year, I am experimenting with teaching y=a+bx for the first time. I'm still not quite sure how I feel about it, though. I guess time will tell. (I also would have never thought that I would have given up my trusty TI-84 for a TI-Nspire, but that has also happened. I was helping a student with their TI-84 on Friday, and it was such a weird experience. I've started to forget where some of the buttons are already!) We discussed the slope and the y-intercept and their meaning in this situation. We also discussed reasons why our data was not perfectly linear. The bell rang before we could delve much deeper into it.

I have also done this activity without having the students share results. At one workshop, we called this "Pass the Buck." The presenter took a dollar bill out of his wallet and gave it to someone sitting at the first table. That person said their name and passed the buck to the next person. We stopped at the end of the first table and recorded the time. The buck made it's way back to the original person, and we timed the amount of time it took to pass the buck to the end of the second table. This process continued until the buck had made it to every table.

Linear Regression Lab 2: Bouncing Tennis Balls

Bouncing Tennis Balls Lab

This lab was another activity that I learned about through the OGAP Common Core Training I attended this summer. It is based on an Illuminations activity from NCTM. Students are given a tennis ball to bounce for two minutes. Every ten seconds, the number of bounces is recorded. I learned a lot from doing this activity for the first time.

1. When you teach in a building that was built in 1919 and your room is on the second floor, it's not a good idea to do this lab in your classroom. The science teacher whose classroom is directly beneath you will send a student upstairs to ask you to stop doing whatever you are doing because it is distracting them. Oops... I guess five bouncing tennis balls can make quite a bit of racket. We ended up going down the hall to the auditorium and doing our bouncing on the stage.

2. Do not hand out the tennis balls to the groups until the last minute possible. Otherwise, students will start their practice bounces before you demonstrate the proper way to bounce a tennis ball for this lab. Then, you will find yourself in a scenario like this.

Student - Can we have another tennis ball?
Me - What did you do with the tennis ball I just gave you?
Student - We might have lost it?
Me - How could you lose it? I just gave it to you a few seconds ago!
Student - Well, I only bounced it once, but...

Immediately, all eyes in the classroom were drawn to the ceiling. Other perks of working in such an old building are that there are incredibly high ceilings and random pipes running EVERYWHERE. Okay, maybe only one of those is a perk. I looked up above the light fixtures to see the tennis ball resting on some pipes. If you look closely, you should be able to see it.

I told the students that they would not be given another tennis ball. If they could get the tennis ball up there, they could find a way to get it down. Eventually, one of the students stood on top of their desk and used an umbrella to dislodge the tennis ball.

3. Even if you show students the proper way to bounce a tennis ball so their data is linear, they will not listen.

4. The provided table asks students to count the number of bounces in each ten-second interval. Then, afterwards, they are supposed to fill in a third column with the cumulative number of bounces. This will confuse students INCREDIBLY. Have students mark out the middle column and ONLY record the cumulative number of bounces.

5. Yes, having each student collect their own set of tennis ball data sounds like a great idea. But, you will be much saner if you have each group collect one set of data. That was a lesson learned the hard way!

Here is the handout I created to use with my students. I took the activity a step farther than Illuminations did and used it as an opportunity to review a lot of the concepts that we had started working with in Unit 1. Students were asked to classify variables as dependent and independent, calculate the rate of change between various intervals, classify a scatter plot as linear or non-linear, determine if the produced scatter plot is a function, describe the relation as increasing or decreasing, perform a linear regression using their calculator, interpret the meaning of the slope and y-intercept in this particular situation, and use the regression equation to make predictions. Once students were done with the lab, their page could be folded in half and glued in their interactive notebooks.

Linear Regression Lab 3: Twizzlers!

Twizzlers Linear Regression Lab

The Twizzler Lab was not an original idea. I stole the idea from here and modified it to fit my group of students and their needs. The idea is simple. Give students a twizzler to eat. Before students take a bite from their twizzler, they measure its length. After each bite, they remeasure the twizzler until they have eaten the entire thing. They use this data to create a scatter plot and perform a linear regression.

I used almost the exact same set of questions from the tennis ball lab with the twizzlers lab. I was surprised by the number of students who claimed to not like twizzlers. I mean, I don't like twizzlers, but I figured most teenagers did. I'm more of a chocolate person myself! I told those students who didn't like twizzlers to have someone else eat their twizzler for them. But, they still had to participate and take the measurements.

The file for the Twizzlers Lab is also embedded below.

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Things Teenagers Say...Volume Two

October 7, 2013, 4:00 am

≫ Next: Finally Arrived...

≪ Previous: Fun With Linear Regression Labs

Today, I present to you Volume 2 of Things Teenagers Say. In case you missed Volume 1, you can check it out here.

"What year was it last year?"

--

Student: Would you kill your kid for 5 million dollars?
Me: First, I don't have a kid. And, no, I wouldn't kill my child if I had one.
Student: But, it's five million dollars!

--

Student: You'll never guess what the other math teacher just said!
Me: What did he say?
Student: Well, another student asked him "What's up?" And, he said, "My blood pressure."

--

Student: Ms. Hagan, can I tell you about my dream?
Me: Well, we're kind of in the middle of a lesson right now. Can it wait?
Student: I guess, but you were in my dream. So, I really need to tell you about it.
Me: Remind me about it when I get done explaining today's lesson. Then, you can tell us all about your dream.
<Five minutes later>
Me: Everyone should be working on their assignment now. If you have any questions, make sure you check your notebook first before asking for help.
Student: But, you never let me tell you about my dream.
Me: Okay, tell us about your dream.
Student: Well, I dreamed that you were in a psycho hospital.
Me: Lovely...

(The student then proceeded to tell us her entire dream. It involved two of my students coming to visit me in the hospital. But, they stopped at a bridge along the way, and one of my students fell off the bridge and died. The other student was so distraught that she returned home without visiting me. A while later, she and another friend decided to come visit me again. But, they stopped at the bridge to honor the memory of their dead friend. While at the bridge, the second friend was possessed by the spirit of the dead friend. This possessed child then came to the hospital and helped me to escape. Somehow, I'm pretty sure we all ended up back at the bridge, dead. I cannot make these things up.)
--

I wish my mind was a printer so I could always show my work.

--

While pointing to a three-hole punch that is setting on my desk:
"Is this a stapler or a hole punch?"

Apparently three-hole-punches are a thing of the past?

--

"Don't touch this." - Written near a pool of dried blood on a student's homework assignment. I wish I was making this up!

--

Don't say "quiz"! You're hurting my best friends that are on the side of my face.

--

Student: Where are you from?
Me: I grew up in Coweta.
Student: What state is that in?
Me: Oklahoma. It's only a little over an hour away from here.
Student: Oh. You don't sound like you're from Oklahoma. You have an accent.
Me: I have an accent?!?
Student: Yeah. You have a Wisconsiny accent. I have family in Wisconsin, and you sound exactly like them.

After this conversation, I felt a need to question my statistics students the next hour.

Me: Guys, do I have an accent? One of my students last hour said that I have an accent.
Student: I wouldn't say you have an accent, but you do have a specific way of saying things.
Me: Oh. This students said I don't sound like I'm from Oklahoma. She said I sound like I'm from Wisconsin.
Student: I've met people from Wisconsin, and you don't sound like them. But, you don't sound like you're from Oklahoma. Maybe that's because you speak properly.

--

A few weeks ago, my Algebra 1 students BOMBED a distributive property quiz. I was incredibly frustrated and ready to move on, but my students weren't. So, I printed off an Algebra with Pizzazz worksheet. I'm not the biggest fan of these worksheets. My math teachers in middle school and high school used them, and it seems like the first person to finish always announces the answer to the joke. Then, the other students write down the answer to the joke and don't actually have to do the math. I still use them sometimes because I love that they allow students to continually check their work, but I do make a big point of telling students that NO WORK = NO GRADE. The worksheet we were doing that day had a particularly cheesy joke that my students did not find humorous at all. I, however, found the joke to be quite amusing. It was one I had never heard before, and it made me chuckle.

Upon discovering this, I was told, "You need to update your sense of humor."

↧

Finally Arrived...

October 8, 2013, 4:00 am

≫ Next: Ms. Hagan's Book of Exponent Rules

≪ Previous: Things Teenagers Say...Volume Two

I pretty sure I have finally arrived as a teacher! Why? I am now the proud owner of my very own EZ Grader!

I've been wanting one of these since I was in at least the fourth grade. A couple of weeks ago, I was at my parents' house, and I saw this sitting in a box of stuff to donate. My parents were in the process of cleaning out one of their rental properties that had been abandoned, and my mom had boxed up some teacher stuff to donate. I made it pretty clear that this was not to be donated. This was mine!

I finally got a chance to use it last week with my Algebra 2 tests. And, the entire process of selecting the number of problems and finding the students' grade just makes me giddy! I'm not sure the novelty of this handy gadget will ever wear off...

Can you tell that I love what I do?

↧

Ms. Hagan's Book of Exponent Rules

October 9, 2013, 4:00 am

≫ Next: Recent Stats Happenings

≪ Previous: Finally Arrived...

Confession time. I am terrible at teaching exponent rules. Correction. I know how to teach them. I am terrible at getting students to see that most of their prior knowledge of exponent rules is wrong. A few weeks ago, I had someone ask me what superpower I would love to have. After thinking about it for quite a while, I decided that I would choose the power to be able to erase parts of the minds of others. If I have to take the time each year to reteach integer operations, the order of operations, and exponent rules to my Algebra 1 students, I would much prefer to teach these to them from scratch. Because as soon as I start reteaching something that they have heard before, their minds shut down and start ignoring me. I guess they are thinking, "I don't have to listen. I already know this!" But, the problem is that they don't know this. They think that a negative exponent means that you need to change the fraction to its reciprocal to make the exponents positive. In some cases, this works. But, they are overgeneralizing. They've been told that two negatives make a positive. So, -3 + (-5) must be +8. Again, they've taken a rule for multiplication and division and overgeneralized it. And, don't even get me started on the order of operations. No matter how many times I say that multiplication and division must be performed from left to right, I have a student who will argue with me that multiplication comes before division in PEMDAS so we must always do it first.

The same students who have been struggling with all of the above have been rocking our last few lessons on naming polynomials and multiplying polynomials. Why? My current theory is that multiplying polynomials is something they've never been exposed to before. So, they actually found it necessary to listen to my explanation...

I know some of you will criticize me for the following. And, I'm okay with that. I know this isn't perfect. It definitely isn't ideal. My teaching of exponent rules this year relies on a lot of tricks. I tried last year to have my students discover the rules for themselves. I used the amazing worksheets provided by Don't Panic, The Answer is 42. We went through each scenario by itself. On the product rule worksheet, my students rocked the product rule. On the quotient rule worksheet, my students rocked the quotient rule. After a week of exploring and discovering each rule separately, I challenged my students to look at a problem and figure out which rule they were supposed to use. They were lost. They could do each rule in isolation, but they couldn't figure out what rule to use in a given problem. I probably ended up spending two weeks on exponent rules, and I still had a group of students who just didn't get it.

This year, I spent three days on exponent rules.

Day 1 - We played a game that I found on Nathan Kraft's blog. Without telling the students what we were doing, I told them all to go write their name on the dry erase board and draw four x's below. First hour, one of my students raises their hand and asks, "Couldn't we have just written x to the fourth power below our names?" I almost died of happiness in that moment. I guess my continual emphasis that x squared means x times x and x cubed means x times x times x has paid off!

I put a problem on the board. I gave students 30 seconds or so to solve it. They held up their individual dry erase boards with their answers. The students who got it right got to go and erase an x from under someone's name. On the Smart Board, I demonstrated how to write out the powers in the problems as multiplication to derive the answer. We repeated this process. Slowly, we worked through almost all of the types of exponent problems. Yes, there were some complainers. "But, you've never showed us how to work out a problem that looks like this. This isn't fair!" To this, I told them to try their best. I believed in them!

When a student ran out of x's, that student became a zombie. Zombies could still take others out if they continued to get the problems right. One of my students in third period decided from the very beginning that he wanted to be a zombie. He was practically begging people to erase his x's. When no one would, he started erasing his own x's.

I called this "The Game of Grudge," and my students loved it. It sparked so many amazing conversations that wouldn't have happened otherwise. Could we have a negative exponent? Could we have an exponent on our exponent? Could you raise pi to a power? Could you raise pi to the power of pi?

Day 2 - The students wanted to know if we were going to play the game again. They were quite devastated when I told them we would be taking notes.

I've been wanting to make one of these books since I learned about them during a professional development workshop while I was student teaching. I've heard them called magic books and poof books. Basically, you take a sheet of letter sized paper and fold it into a cute little book with the help of a pair of scissors and some magic. Instructions on making the book can be found here.

Here are our notes in the form of a poof book:

Exponent Rule Book Cover

This is my copy of the book, so it is titled "Ms. Hagan's Book of Exponent Rules." My students titled their books with their own names.

Exponent Rules - Page 1 and Page 2

Our first two pages of the book feature some important vocabulary. I needed to make sure that all of my students knew what we were talking about when we mentioned the exponent, base, or power.

Exponent Rules - Page 3 and Page 4

I had never seen exponent rules presented using P->M->A before Mrs. D left a comment back in February on a post I made during my student teaching.

Here's what she wrote:

"I am currently student teaching. This is what I shared with my algebra students. I write P M A down the side of a piece of paper.

Product -> (2^3)^4 = 2^(3*4) = 2^12
(draw an arrow down to multiply) "look down a line to remember what to do with exponents. I see I need to multiply them."

Multiply -> 2^3 * 2^4 = 2^(3+4) = 2^7
(draw an arrow down to add) "look down a line to remember what to do with exponents. I see I need to add them. Also keep in mind the bases need to be the same!"

Add -> 2^3 + 2^4
(draw an arrow down to... blank space) "look down a line to remember what to do with exponents. Wait, there's nothing there. I cannot do anything with the exponents.""

I changed the P to mean Power to a Power. And, I explained it to my students like this: The arrow tells us what to do to the exponent rules. In a power to a power problem, the arrow points to multiply, so we multiply the exponents. In a multiplication problem, the arrow points to add, so we add the exponents. In an addition problem, the arrow points to nothing, so we do nothing to the exponents.

One of the things I am determined that my students will leave my classroom knowing this year is the word "vinculum." It's one of those things that I use on a daily basis that I didn't know the name for until a year or so ago. You know that bar you put above a repeating decimal? It's a vinculum. You know that bar you put between the numerator and denominator of a fraction? It's a vinculum. You know that top line of a radical symbol? It's a vinculum. I've emphasized this word so much this year, my eighth graders found it necessary to correct their science teacher for not referring to the vinculum by its proper name when learning about the density equation. Is this word critical to my students' success? No. I earned a degree in pure mathematics without knowing what the word meant. But, I do think it goes to show my students that they shouldn't be scared by new vocab words just because they sound scary.

I teach my students to remember that the vinculum looks like a giant subtraction sign. Thus, we subtract the exponents when dividing powers with like bases.

Exponent Rules Page 5 and Page 6

For negative exponents, I use "cross the line and change the sign of the exponent." We didn't have time to explore why this works, but I will cover it more in depth with my students when they reach Algebra 2. We also discussed why anything raised to the zero power is equal to 1.

Day 3 - Our last day on exponent rules was spent playing the Karuta game from Dont' Panic, The Answer is 42. I already had the cards cut and laminated from last year, so this was an easy lesson to implement. I started out by pairing the students up and having them match the exponent rule question cards with the exponent rule answer cards. After checking their answers, I had them switch decks and repeat. After each group was finished with the matching process, we played the karuta game.

Exponent Rules Karuta Cards

Basically, Karuta is a cross between Slap Jack and War. I tell the students to lay out either the question cards or the answer cards from their decks. Depending on which cards I had them lay out, I write either an answer or a question on the board. The first person to slap the correct card that corresponds with it gets to keep the card. The player with the most cards at the end wins. This game gets very competitive and VERY violent.

I had a lot more fun teaching exponent rules this year than last year. Plus, I'm estimating that I saved seven days of instructional time. I think it was a good mix of exploring the reasons behind the rules, memorizing the rules, and having fun.

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Recent Stats Happenings

October 10, 2013, 4:00 am

≫ Next: Student Perceptions

≪ Previous: Ms. Hagan's Book of Exponent Rules

This post will be short and sweet. I just wanted to post some pictures of what my statistics students and I have been up to lately. Sometimes I wonder what my principal think I am teaching in statistics. The last time he walked in my stats class unannounced, my students had the desks pushed apart, and they were in the floor, catapulting gummi bears. They offered to let him catapult a gummi bear, but he refused.

A couple of weeks before that, my principal's wife (who runs our library) walked down the hall while we were carrying out an experiment on paper air planes and the effect of wingspan on distance traveled. She didn't say anything, but I can only imagine the conversation that probably ensued between her and her husband regarding my unique teaching methods...

I learned so much about my students' current understandings of statistics by eavesdropping on their conversations while working through these data collection activities.

Our Supplies

We tested the catapult on varying stacks of books to determine if that made a difference in the distance traveled.

Measuring the gummi bear's distance

Our Airplanes to Test

Measuring the Distance Traveled. I try not to post pictures of my actual students. But, I think this one turned out blurry enough that I'm safe!

Unexpected Results

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Student Perceptions

October 11, 2013, 4:00 am

≫ Next: A Mathematical Breakfast

≪ Previous: Recent Stats Happenings

I am continually intrigued by the perceptions students have of their teachers. My students are especially frank and honest. If they love a teacher, I hear about it. If they hate a teacher, I hear about it even more. Working in a small school, everybody knows everybody VERY well. We have two teachers per core subject area (Math, History, English, Science), one teacher per elective (Computers, FACS, Agricultural Education), one special education teacher, one counselor, and one principal. So, when students complain about or praise a teacher, I know exactly who they are talking about. Sometimes the points they make are valid and/or insightful. Other times, they have received some sort of misinformation, or they lack the maturity to truly understand the situation. I require a lot from my students, and I am sure that this is reflected in how students view me and speak about me to others.

Yesterday, two students decided that they were going to challenge each other to a drawing contest. One of the students would pick something to draw, and both girls would have to draw it. Then, they would see whose drawing was the best. The subjects for their drawings ranged from the Mona Lisa to Hitler to an Egyptian Person to a pear to each other to ME! I was a little scared to look at their pictures of me.

I snapped pictures of their Mona Lisas and their portraits of me. I'm not quite sure there are words to describe how I feel about these...

First, I present to you my students' renditions of the Mona Lisa:

Mona Lisa

And, now, my students' portraits of me. I think I fared a bit better than Mona Lisa. Though, I'm still not quite sure what to think...

How Students See Their Math Teacher

I guess I'm most intrigued by the thought bubbles. Obviously, my students still need some more work on how to spell pi. And, then there's the fact that one plus two does not equal three pi. One pi plus two pi equals three pi. Is this what they meant? Or, did they just mean 1 + 2 = 3? And, they just threw in the word "pie" for good measure??? And, math is definitely something to get excited about! YAY!!!

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A Mathematical Breakfast

October 12, 2013, 4:00 am

≫ Next: What Can I Do With This?

≪ Previous: Student Perceptions

This week, I've been going through all of the pictures that are on my computer. I know there are a ton of things I've meant to blog about but haven't. So, I'm looking for blogging inspiration in my pictures.

This summer, my sister was tasked with making pancakes while we were at church camp. One of the other adult helpers challenged her to make a Z-shaped pancake for our smallest camper who was still in preschool. This Z-shaped pancake for "Zachary" led to an S-shaped pancake for "Sarah." Of course, my sister couldn't stop there. She made me a heart-shaped pancake, a pi-shaped pancake, and a right-triangle pancake. So, my breakfast spelled out, "Sarah loves pi."

I don't know if the best part was hearing the 3rd-6th graders talk about how they recognized the pi symbol from their math classes or eating apple pie filling on top of my pi pancake...

Mathematical Pancakes

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What Can I Do With This?

October 13, 2013, 4:00 am

≫ Next: Ms. Hagan's Museum of Art

≪ Previous: A Mathematical Breakfast

Okay guys. I need some help. My parents are amazing. They have supported me every step of the way in my teaching endeavor. They helped me move to Drumright. They helped me set up my classroom. They painted the walls. They installed a dry erase board for me. They built me bulletin boards. My mom is always on the lookout for cool things that I can use in my classroom. Sometimes, though, she buys me things to use even if she can't think of a use for them.

This is one of those things. An ice cream bucket full of pink and blue foam washers. I've had these for months now, and I still haven't figured out what to use them for. So, I'm asking you! What can I do with these?

Foam Washers

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Ms. Hagan's Museum of Art

November 16, 2013, 7:47 am

≫ Next: Rock, Paper, Scissors Math Tournament

≪ Previous: What Can I Do With This?

Okay. It's been over a month since I last wrote a blog post. It's funny. I stopped blogging for a few days because I felt like I had run out of anything to say or share. Then, I kept not blogging because I felt like I had too much to say or share, and I didn't know where to start.

But, I'm back! This past month has been busy, busy, busy. This past week, I finally got my copy of our Algebra 1 and Algebra 2 interactive notebooks up to date, so there should be lots of posts of new foldables and old foldables and lots of fun stuff in the next few days. (My copy of our notebooks was so out of date that my students told me that if I was taking my own class, I would be failing!) I've taken the pictures. I've uploaded the templates to box.com. Now, all I have to do is write the posts. If you don't see them posted in the next few days, feel free to barrage me with e-mails and comments.

About two and a half weeks ago, I had a couple of students draw pictures on their dry erase boards and display them on the wall. The fad has continued, and sometimes I feel like I have my own art museum in my classroom. Pretty soon, I'm not going to have enough boards left for all my students to have one to do work on, though. So, the art museum will have to come down. But, I did take some pictures. And, I thought I'd share these pictures with you. When students take pride in their work and want to display it, it makes me happy. Now, I only need to find a way to make this carry over into mathematics.

Sir Tweet started the entire thing. T-Rex is probably the newest edition to the art museum.

After seeing Sir Tweet, another student thought he could do a better job. So, another bird was added to the museum. Debate ensued for days about which bird was better.

The creator of Sir Tweet told me a fictional story one day about a giraffe, an elephant, a boy, and a girl who went on a double date. It was a rather involved story involving going to the movies and traveling to Narnia. Another girl provided this illustration of the story.

I have two students who sometimes come into my room during my planning period to work on homework. Inspired by the picture of the giraffe and elephant's date, they decided to draw a picture of the baby produced by the giraffe and elephant. I tried to explain that this was biologically impossible, but I was told that it was cute and that is the only thing that matters.

Maybe the reason I am so impressed by my students' artwork is that I am a terrible artist myself. My sister, on the other hand, is an amazing artist. She's currently in college to become an elementary school art teacher. The only drawing I do is to illustrate math problems. (And, to provide comic relief by doing so.) Here's a recent drawing I did while tutoring a student. This student is taking Pre-Calculus/Trig at our local technology center, and they have been working with angle of elevation and angle of depression problems.

Can you tell that is a light house and a boat? I was told that it looks more like a candle and a banana...

My Attempt at Illustrating a Math Problem

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