Math = Love: October 2013

Sunday, October 13, 2013

What Can I Do With This?

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

Saturday, October 12, 2013

A Mathematical Breakfast

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

Friday, October 11, 2013

Student Perceptions

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!!!

Thursday, October 10, 2013

Recent Stats Happenings

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

Wednesday, October 9, 2013

Ms. Hagan's Book of Exponent Rules

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!"

(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
I always laminate activities like this so I can reuse them year after year after year.  Let's face it.  Teenagers are rough on pretty much anything you put in their hands.  Here's the laminator I own and recommend:

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.

Tuesday, October 8, 2013

Finally Arrived...

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?

Monday, October 7, 2013

Things Teenagers Say...Volume Two

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.
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."

Sunday, October 6, 2013

Fun With Linear Regression Labs

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.

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.

Files can be found here.

Saturday, October 5, 2013

Math Teachers' Circle Reflection

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.

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