Gobbler’s Dilemma

I think every teacher struggles with keeping the kids engaged and learning during “short weeks” of school before breaks.  This year, my team of teachers at school seemed to have an extra challenge as not only did we have a two day school week but we also owed the kids a cross ball tournament as an incentive for winning the school’s annual food drive and I needed to give a common math assessment to every student on the team as well.  An idea was quickly born to have every teacher on the team (Math, Science, Social Studies, and Language Arts) give my math assessment in their 1st hour on Tuesday morning followed by the Mathalicious lesson Gobbler’s Dilemma in every class.

Gobbler’s Dilemma lends itself very easy to this plan as the math involved is very straight forward and easy and the focus is more on the logic and strategy involved in stores deciding if they should be open or closed on Thanksgiving.  I provided the lesson guide and student handouts to each teacher for their class and as a team we went through the lesson on our planning period to make sure everyone was ready for Tuesday.  Our team of students included 2 classes that are taught in a collaborative setting (2 teachers) due to special learning needs and 2 classes of Advanced Pre- Algebra and the lesson seemed to work equally well in both classes.

The basic premise of the lesson is for students to use the information given and logic to decide if their store should be open or not on Thanksgiving.  I did make some modifications for our collab class by creating the chart for Question 1 on the board in a lay out that was a little more easy to follow.  They seemed to really be struggling with the “matrix” style chart so we created more of a list on the board as a class and then they were able to fill in the matrix chart with fewer issues.  I also modified question 3 a bit to help with student focus.  Question 3 calls for students to engage with a partner in a strategy game to see how stores must make the decision to open on Thanksgiving or not without knowing what their competitors are doing.  Instead of having students do this in pairs we did it as a whole class.  The students were store A and I was store B.  I selected a class spokesperson who would poll the class about if they wanted to open Thursday or Friday while I was in the hall.  Both the class and myself would write their decision on a mini-white board and then would reveal our decisions when I came back in the room.    I really liked that modification the best.  It allowed the students to engage in the strategy game but also allowed me to help drive the discussion and  keep things on track on what was a high energy day for the kids.  They also loved playing against me and wanted to try and beat my store however they could.

This lesson is a great example of how engaged students can be when involved in a lesson that they view as important and worthwhile.  For the 65 or so minutes we worked on the lesson they were engaged and really thinking deeply about the math and how it impacted the decision making of stores nationwide.  It was also fabulous for the “non-math” teachers on our team to get to engage the kids in a mathematical discussion to show them that regardless of content area intelligent adults should be able to talk about math.  Below are some of the kids reviews of the lessons.  Excuse the misspellings I am typing them as the kids wrote them!

I liked this activity because it is using math with real work things that are interesting to 7th grade students.

It was fun because I’m very competitive and love things like this.

I liked it because it was competitive.  It was a fun way to spend time.  Questions were difficult to understand.

I did like this activity because it’s using math in real life situations.

Dear Mathalicious, I really enjoyed your lessons.  They led to great and interesting conversations.

The lessons Mrs. Powers reached today was interesting and I learned.

I like this lesson, the reason is because maybe I can stop stores from doing Black Friday on Thanksgiving with a good reason why.

I like this lesson because I like going to the mall, so I can relate to it.  And this is kind of cool because it gives you a little idea of how stye run the stores and make money.

I loved this lesson because it made me feel like I was real store owner.  Also that is changed the way I look at stores that open at Thanksgiving.

This lesson is cold and we should do it more.

I liked the lesson.  I think that the dision we made was good and we learned and had fun.

For me, the lesson was  a fantastic way to keep the kids engaged and talking about math on an otherwise chaotic day.  I am sure Gobbler’s Dilemma will be a part of our team Thanksgiving tradition from here on out.  Here’s hoping Mathalicious comes up with a great lesson ASAP for the day before Winter break!

He Said 2n-3

If you aren’t using Visual Patterns in your classroom please start tomorrow!  This amazing site developed by one of my “math idols” Fawn Nguyen has been one of the most amazing additions to my classroom this year.  We do Visual Patterns every Thursday for Tough Pattern Thursday and I would be lying if I said I haven’t wanted to throw in the towel on it more than once.

Wow those early weeks of patterns were tough with kids constantly focused on finding the common difference and then never being able to move forward into writing an expression that was always true for n number of steps.  There was so much productive struggle on those early days (I have decided to call it productive struggle to make myself feel better about life) that I didn’t know if we would ever get to a good place with patterns.  Each week on their weekly reflection when asked what they needed help with student after student kept writing Tough Pattern Thursday.  I thought about changing the warm-up, I really did but Tricky Model Thursday just didn’t have the same ring as Tough Pattern.  Instead we kept pushing through and miraculously week after week they started getting better.  Yes it took some guidance from me, some leading questions, some paraphrasing, and some modeling but they really started getting better.  Even more amazing was the fact that on their weekly reflection Tough Pattern Thursday started moving from what they needed help with most to their favorite part of the week.

And then came last Thursday when one of my students who I will call “Z” brought me to tears with his description of the pattern.  What you need to know about Z is that he is an English Language Learner who has been perpetually novice on state assessments and below grade level in both reading and math for as long as he can remember.  He gets frustrated in math, not as much because of the numbers but because of the reading and language involved.  I have remedied as much of it as I can for him.  I gave him a list of the numbers and their spellings to eliminate some of that frustration and we have focused on vocabulary as much as we can to try and make Z feel more successful in class.  I have watched him over the course of that last few weeks get more and more comfortable with the pattern each week and started to get the feeling something big was about to happen and then it did.  Last Thursday Z’s hand was the first in the air when I asked for thoughts on the pattern.  I wasn’t really ready to get at the algebraic part yet and was just looking for thoughts and ideas on how to break the picture apart but as soon as I saw his hand I knew I had to call on him.  I expected him to have some thoughts about what came next or how he was thinking about it but that isn’t what I got at all.  Instead in his still slightly broken English Z excitedly said “2n-3!  2n-3!”.  Without a doubt that is in my top 5 teaching moments thus far.  The look on Z’s face and his classmates face were priceless as we checked his expression for accuracy to find it was dead on.

Will Z finish the year on grade level in math this year and will he finally rise above the novice category on the state test I really don’t know.  However I do know that he will never forget 2n-3.  He will never forget the confidence that came out of math class that day.  He will never forget that he too can do and be successful at math.  And me, I will never forget that success is much sweeter when it doesn’t come easy.  Thanks Fawn for bring Visual Patterns to our classroom it has taught us about more than just math!

Their Hopes and Dreams Forever Changed Mine

A few weeks ago, Mr. Payne and I began to see a disconnect between a great deal of our students and ourselves. We both work hard to form relationships with every child and for the most part are very successful at the relationship piece. However, when we tried to talk to them about the future and college we were met with resistance each time especially with our students who are English Language Learners. As we talked to them about why they thought college wasn’t an option for them a heartbreaking misconception surfaced. Our students basically look at us as upper class “white people” and themselves as “lower class”. We kept talking with them and trying to flush out their thoughts to understand where the disconnect was. Over and over again the kids were basically telling us that we were successful and that they never would be. This was a startling revelation for both of us and we decided we had to do something to flip their view points.

On a whim one day I remembered that I had read an article about how the most powerful question you can ask students who are socio-economically disadvantaged is “what are your hopes and dreams?”. Last Thursday morning Mr. Payne and I stepped away from the content a while, shut our classroom door, and had a long talk with the faces looking back at us. I can’t tell you everything that we said or they said because I promised them that what happened in the room that day would remain confidential. We spent the next half our telling the kids more about ourselves, about how we were both first generation college students and about our own childhood circumstances. We worked to really convey to them that we didn’t always have it easy either but in the words of Kid President, we got a goal and we got a dream and then we got to work. The kids shared some of their own stories and circumstances and did a lot of nodding and agreeing as other people shared theirs. It was one of those magical classroom moments that I won’t forget.

To follow-up we gave each student an index card and asked them to write down their hopes and dreams. They quickly got to work and wrote more than this group of students ever does as they filled out their card. We assured them that no one would see them except us unless they gave us permission and promised that we would do everything in our power to help them achieve whatever dreams they wrote down. After the kids left Joe and I spent some time tearfully reading their responses and were amazed at what we found. These kids, the kids who fail every class, the kids who are behavior problems, the kids who don’t seem to care about anything have some amazing hopes and dreams. Flipping through those cards, what really jumped out at me first was that every goal was attainable. However the second thing that caught my attention was the fact that more than anything these kids just want to help others. They want to be police officers, teachers, and military personnel. They want better lives and to help their families but most importantly the undertone of them all was that they just want to have hope. Hope for a future and hope for a better life than what they have now.

I asked special permission to share this card on my blog. This student is the epitome of the kid teachers talk about as being “hopeless”. He doesn’t seem to care about school, never does his homework, rarely pays attention to what I am saying, and is hard to find meaningful consequences and incentives for. He is an english language learner and struggles with reading and writing tremendously. He is the kind of kid who most would think just doesn’t care but his hopes and dreams tell a different story. He cares a lot just not about all of the same things we do.

This entire process changed my life in a lot of ways.  It made me realize that no matter how much I try to build relationships with my students that there will always be parts of their lives I can never understand.  It made me realize that no matter how disengaged or uninterested a students seems they still have hopes and dreams but they may be different and much more selfless than mine could ever be.  Most importantly, these kids and their dreams changed mine.  I now dream of being an even more effective teacher, of pushing myself and these kids further than anyone ever believed possible, of helping every one of them achieve their goals.  After all, they changed my dreams now it is time for me to help them achieve theirs.

Here is a great summary of their dreams.  I can’t wait to see them come true.

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What Common Core Did to My Classroom

One of my favorite colleagues, Mike Fannin, always pushes me to be a better teacher by asking those really reflective questions that there is no right answer to.  Today Mike, a social studies teacher, sent me one of those really fun and irrational anti-Common Core articles and asked my thoughts.  Once my blood pressure returned to normal range I begin to really think about how to put into words what Common Core did for my classroom.

Before Common Core I was a typical math teacher.  I had my curriculum maps and and state standards which read like a skill and drill check list that I marked off one by one whether the kids understood them or not.  I used really “great” methods and math terminology like “butterfly method”, “keep switch flip”, “leave opposite opposite”, and so many more that I would love to forget.  I moved to Kentucky the year that KCAS (Kentucky’s Common Core) was adopted and thought “how different could it be?”  The answer to that question can be answered easily with a quick peak inside my classroom today.

Today, my classroom is cognitively busy and alive with excitement about numbers.  We no longer focus on skills, timed tests, facts, or catchy phrases to make students remember things that have no meaning to them.  Today, we do math talks, counting circles, estimating, and reasoning instead of direct instruction.  We take the time to understand numbers and their meanings rather than memorizing facts.  I don’t drill random formulas and information into students heads so that they can remember it long enough to pass a test rather than understanding it to a depth that can be applied to real life.

I really do understand the reason so many parents seem to get upset about the “new math” associated with Common Core. After all, it is change and change is difficult but here is what I know. I have talked to tons of adults and not one has told me that they have to take skill and drill tests daily at work or risk being fired. When I ask what they have to do at work I get a lot of answers but there is always a common theme, in real life we are no longer asked to use math as a check list of skills that we either know or don’t know. Instead real life is about using the math to solve real problems, to be a critical thinker, to reason, and actually understand what is happening around them. Those are all the things along with many more that Common Core has brought to my classroom.

As I hear about states repealing Common Core and more and more anti Common Core material being pushed out there I have thought a lot about what will happen to my classroom if Common Core is removed or replaced as my standards. The answer the that question is nothing. You see, Common Core has already forever changed my classroom. I will never be nor to do I want to be that teacher from 5 years ago that was more worried about test scores and a check sheet that student understanding. I can never go back to that boring dull classroom when I have seen kids come alive and get so excited about really understanding math for the first time. No amount of reform, or Facebook posts, or anti-Common Core rants can take away what Common Core has already brought to my classroom.

Properties of Exponents Activity

I thought I did a really good job teaching the laws of exponents in my Advanced Pre-Algebra class until it came time for the quiz.  There were SO MANY misconceptions still.  It seems as though a lot of them had been exposed to and memorized a lot of the properties without a lot of conceptual understanding of the topic which led to a lot of mistakes on the quiz.  I quickly came up with this Exponent Matching activity to quickly review and reinforce the concepts.  Each student received a card and then traveled around the room looking for the three classmates that had a card with an equivalent exponential expression.  Once everyone thought they had found the right spot we debriefed as a whole class.  Some groups ended up with too many people in them and others not enough so we talked as a class about those cards to find the right group for them.  A few students never found a group so we also evaluated their card as a class to help them find the right spot.  As a follow-up homework assignment students created their own set of four equivalent exponential expression cards.  Students shared that this follow-up homework activity was critical to their understanding.  Feel free to edit as needed to meet your classes needs, it really worked for us!

I Change My Teaching Philosophy Four Times a Day

I feel like I suffer from some sort of a multiple personality disorder that only teachers suffer from.  I hope I am not alone here but I truly feel like my teaching philosophy changes at least four times on a bad day and a lot more than that on a good day.  It isn’t that I want to be this way but I just can’t make myself commit to a teaching style.  In general whatever I am going right that second in my classroom is what I will tell you I am most passionate about.  The problem is that as soon as I start the next activity or method that will become what I am most passionate about.

I really admire and look up to the people that are much more dedicated to what they believe in than I am.  I want to be like Dan Meyer, Fawn Ngyuen, Kate Nowak, and so many other of my teaching “idols” but I just can’t do it.  I always going to be the kind of person to claim one day that teaching number sense is the most important thing I do and the next day swear to you that it is problem solving.  The minute I get done telling you that I never use direct instruction I will stand up and give direct instruction for 10 minutes because my kids seem to have some misconceptions that I can’t figure out how to address any other way.

In the end, like most teachers I think I just really try and do the best I can for every second that my kids are in my room.  Sometimes that means that four minutes into what I thought was going to be a really good lesson I throw the whole thing away because I got a really good idea or realized the kids needed something totally different.  And sometimes it means that a kid will ask me if I ever been tested for ADHD (which happened a couple of weeks ago) but in the end I am confident of two things:

1)  I do the best I can every day to reach every learner and leave no one behind

2)  Kids are truly always on their toes and never know what they are going to do in math class (even if it is because sometimes I don’t know either)

When Knowing 3 * 2 = 6 Isn’t Enough

We recently started our expressions unit where I introduced kids to the joy of Algebra Tiles and modeling expressions.  I was feeling pretty good about how things were going until it was time to begin the distributive property.  Out of pure curiosity at the beginning of class one day I asked the kids to grab some integer chips or Algebra Tiles and model two times three.  I would be lying if I said I wasn’t shocked about what they did.


This was by far the most common model.  The discussion went a little like this:

Me: How many chips are in front of you?

SS: Five

Me: But what is two times three?

SS: Six

Me:  Then why do you only have five chips in front of you?

SS: Because you said to model two times three.

Confused, we had a quick discussion about the meaning of multiplication being about making groups.  We talked about how two times three really meant either two groups of three or three groups of two.  They seemed to get it so I moved on like any other terrible teacher and later tweeted the picture.  Someone on Twitter challenged me to ask them another modeling question the next day but this time with a fact they didn’t know.  I said challenge accepted, I mean after all I had just told them what multiplication meant they surely would get it right tomorrow.

The next day I asked them to model fourteen times eight.  On a positive note there were kids who completely nailed the model this time and I would have thought I was really good teacher…

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Except the other half of the models looked like these:

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Now interestingly enough, even the kids who made these models incorrectly got the correct answer because off to the side of their table they had worked the problem out using the standard algorithm but still really not knowing that 14 times 8 actually means 14 groups of 8 or 8 groups of 14.  We did some more investigations into this using both multiplication and later division until it seemed like we had a good grasp of what was going on.  The kids conversations during this time were priceless:

S1:  Did you know that is what multiplication meant?

S2: No but do you think it is weird she is teaching this to us?

S1: Kind of but I think she might be teaching it the right way.

Later I tweeted a lot more of the modeling frustrations to mixed reviews.  Of course math teachers were mainly supportive but others questioned why a kid needed to know why 2 * 3 = 6 as long as they memorized the fact.  I guess for me that just isn’t enough.  I think kids need conceptual knowledge of what they are doing in math class rather than just blind trust that the facts they memorized are correct.

These are the kids that when asked to model 2x end up modeling x +2 as they do not understand the difference in the two.  I see kids hit the wall with this a lot with the distributive property.  If they do not understand multiplication as an area model they almost always struggle with understanding how to distribute which I am sure if how we ended up with teachers asking kids to memorize FOIL rather than really asking kids to visualize what is happening.

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Trust me when I say that I have a lot left to learn as a math teacher, probably more than is possible before I retire.  But I do know and believe that pushing kids to understanding mathematics conceptually rather than blindly memorizing facts and rules is where my heart lies.  I don’t think I would or could be a teacher if 2 * 3 = 6 was good enough.