Magic Number

I taught a disastrous lesson about two step equations in my 1st hour collab class one day.  Painful really isn’t even strong enough to describe it.  It was too much too soon.  I tried to lead with some real-world type situations to get the kids to discover more of using two step equations on their own and it flopped.  The kids left confused and I left frustrated with both myself and them.  I have about 4 minutes between 1st and 2nd hour so I used it to revamp the entire lesson in hopes of salvaging the day.  I can’t tell you how thankful I am for the MTBOS as I remembered reading Julie Reulbach’s blog on magic numbers which led me to Sadie’s blog on the same topic.  I have absolutely no idea why it took me so long to jump on this band wagon.  I guess I always thought my kids were getting it using traditional instruction but this year they most definitely weren’t.  Those 4 minutes between classes were some of the best planning I have done all year.

I started class by telling the kids we were going to take a little break from math and do some magic tricks.  I was going to secretly pick a number and give them some clues to help them guess it.  The first person to guess the number would get 100 e-bucks (our team money incentive system).  I started out with simple things like I take a number multiply it by 2 and add 2 to get ten, what is my number?  A couple hands go up and say “four”.  Great.  We step it up a bit.  I take a number and divide it by 9 and add 12 to get 15, what is my number?  More hands go up than the first time with a correct guess of 27.  I start to think maybe we are on to something here.  I kept making up examples on the fly with more and more hands going up each time.  When I see I have nearly everyone I ask them to jot their own magic trick down on their table and miraculously they all do it with no complaining.  They were hooked.  I started letting them guess each other’s numbers until it seemed they had it down backwards and forwards.  We started discussing their methodology and how they were guessing these numbers.  Almost everyone said they worked “backward” if the clue said multiply by two add four get 10, they subtracted 4 and divided by two to get the magic number.  I knew that was my window to move on.

I handed out these Steps sheets and started guiding students through turning their magic tricks into equations.  Some of their work is below:

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All the kids did beautiful work and once their equations were written they quickly began to see the connection between “working backward” and finding their magic number.  I began selecting their equations and we began solving them using the equality properties rather than just “magically”.  The transition was so smooth for them it was hard to believe…why did I wait to so long to try this?!

Here are a few of the kids comments:

It made me understand the equation.  It made it so easy.

This helped me because its easier.

I like it because it helps me learn hard math.

I like magic number because you have to think really hard and it is also really fun.

I like magic number because it helped me understand how to get the answer through the steps.

It helped me because when we did examples of it it started to get to me.  When we did it into steps it made sense like adding or subtracting the opposite.  Then once we got it, it finally made sense!

I understand it more now than yesterday.

I like it because it is fun to figure out and challenges my brain which I love.  It helped me a lot!

Thanks MTBOS for the inspiration and “involuntary collaboration”!

What I Can Do

To be honest I have been in a funk lately.  The kids I teach this year have touched my heart in so many ways but that has come with its own consequences.  I have been too focused on what I haven’t and may not be able to do for these kids.  I cannot fix their home situations.  I cannot fix the things their young eyes have already seen and the problems they have dealt with.  I cannot fix years of bad school and math experiences that have left them hating school, math, and themselves.  I cannot fix the fact that some of them feel unloved, unwanted, and unimportant.  All of that and more has left me feeling ineffective and overwhelmed by the challenges that face these kids and myself as I spend the rest of the year with them.  My lesson first hour today totally fell apart in so many ways and I ended the class frustrated and ready to give up.  But then 2nd hour started , I adjusted, we moved on and I realized that just like I tell the kids I have to stop focusing on what I can’t do and start focusing on what I can.

I can greet these kids with a smile and a kind word everyday knowing that it may be the only one they hear all day.  I can give them an hour a day of a positive math experience for 177 days this year.  I can praise them for the little things they do right instead of only mentioning the big things they may do wrong.  I can cry with them when their parents have had a fight or they just found out they have to move because their family can no longer pay the rent.  I can send food home with them over long breaks because I know their cupboards are empty.  I can make sure that everyday they feel loved, cared for, and safe when they are with me.  I can be their cheerleader, their biggest fan, their advocate, and their safe place.

And for me they can continue to me my motivation and inspiration to never stop trying to change the world.

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.
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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!