Becoming a Teacher

By far the question I get asked the most is “why did you become a teacher?”.  I have no good answer for that question.  I have made it clear that I never intended to be a teacher but once I stepped in front of a group of kids I began to fall in love with the profession for a lot of reasons.  With 100% honesty I can tell you that when I decided to become a teacher I didn’t think about:

  • Having summers off.  It truly never crossed my mind and it truly has never happened.  I work at STEM Camp in the summer, host a Back to School Math and Reading Clinic for incoming 6th graders, go to many PDs beyond the required 24 hours, spend weeks redoing my classroom, read all the education books that I don’t have time for during the school year, and make plans about how I need to improve on in the coming year in order to best serve my students.
  • Losing my pension.  When I relocated back to Kentucky to teach I knew their pension system was strong.  Perhaps I didn’t do enough research but I assumed that it would be there for me when the time came for me to retire.  It never once crossed my mind that the system I pay my share into monthly would falter or the agreement I entered into when I became a Kentucky teacher would be voided or changed.
  • Not collecting social security.  I had absolutely no idea that Kentucky teachers were not eligible for social security.
  • Teaching until I was 65 with 44 years of complete service.  I starting teaching at the age of 21.  In order to make it until 65 I will work 44 years before I can retire.  If you have ever been in my classroom you know it is a wild and crazy experience.  I literally spend my days standing on tables, jumping from chair to chair, laying on the floor and dramatically acting out real world math situations.  It is hard to imagine me doing any of those things at 65.
  • Being armed at school.  I truly had no idea that 13 years ago when I became a teacher that parts of the public would eventually want me to carry a gun at school.  I have to keep the safety of my student on my mind daily and I have numerous “plans” on what to do during an active shooter situation but none of them include me being armed.


I have never thought about any of those things to be honest until this year.  This year I have had to stand by and watch my profession be ripped apart by my elected officials.  I have had to hear that I am unsophisticated, lazy, greedy, misinformed, ignorant, and perhaps worst of all bad at my job.  I now have to think about all the things listed above on a daily basis.  I have to wonder what will happen to my career and my financial future when my legislators finally reach an agreement.  I have to feel like a bargaining chip in a political game rather than a valued and educated professional.  Even still, I get up every morning prepared to provide 120 students with the best math education I can.  I continue to do the very best I can at my job in spite of what I continue to hear about my profession in the media because:

  • All children deserve access to highly qualified educators that are passionate about what they do.
  • Although my legislators have no problem turning their back on me, I could never turn my back on the students I represent and serve.
  • For many students I (and their other teachers) am the only caring adult they come in contact with on a given day.
  • I had inspired, motivated and talented teachers for all 13 years I was a public school student and future generations of Kentuckians deserve the same.
  • Whether they realize it now our not, our legislators were once students who also benefited from the hard work and dedication of teachers.  Teachers influence the future well beyond the years they teach.
  • My heart lies in the classroom.


I am not really sure what the purpose of this post is except to say that I can promise you that teachers are not the monsters that our current Kentucky leaders are making us out to be.  We are parents, community members, volunteers, coaches, voters, and of course teachers that truly have the best interest of Kentucky students at heart.  We believe that Kentucky kids deserve the most educated, talented and passionate teachers standing in front of their classrooms each day (or in my case on a table!) each day.  The only way to achieve that is to ensure that we continue to keep our promised to past, present and future teachers.  Teachers have paid not only their financial part into the pension system but also their emotional part by investing in child after child that has come to their classroom.  It is time for our elected officials to pay their part.29197266_10105411006441640_6386232781327826944_n




The Magnet Game

Lots of people have been asking about some of the games we play in class that I have been posting on Twitter…I am going to do my best to do a short blog series on these as we head into spring time and I know lots of teachers will be looking for ways to review content and keep kids engaged!  For the record I don’t take credit for any of these!  I have had the pleasure of working with some brilliant people over the years that I have shared these with me and now I am glad to share them with you!

The Magnet Game is one of those games that I have to talk myself into playing due to the mass chaos that is causes in my classroom but the kids always rate it as one of their favorites and once we start playing it is one of my favorites too!

Materials needed: 

Magnets that will stick to your white board

Colored pieces of paper (amount of colors depends on how many teams you want, I usually do 5)  I generally create 8 slips from one sheet of paper.

A set of problems that you want to use during the game.  (I usually dump them into a SMART Board file or PowerPoint)


I randomly assign kids to “color” teams.  They don’t need to be sitting with members of their team (it is actually better if they aren’t).  I just walk around the room randomly handing kids stacks of one color of paper.  I make sure the teams are the same number of people on them.  (If there isn’t a number that is easily divisible I just do the best I can.  For example if is have 28 students I do 3 teams of 6 and 2 teams of 5 but make the maximum points a team can earn during a round 5.

I always start with enough magnets for each student in the class.  I display the first question, they answer it and then run to the board to place their answer under a magnet.  After the answers are in I quickly scan them and award one point to the teams for every correct answer.  (I usually have a student keep track for me on the board).

Before I display the second question I remove 2 or 3 magnets to make it a bit more interesting.  I continue to check for correct answers and reward points before removing a couple more magnets each round.  Eventually as the rounds progress it gets very interesting to get a spot under a magnet.


We always have so much fun playing this game and it is an awesome way to practice procedural fluency.  It requires very little prep work and materials that are readily available to my classroom!  I hope you will give it a try also, if you have question please ask!

Making Kids Feel Special


In my last blog post I talked a bit about going to the PLCs at Work Conference last fall and some of the math ideas I was able to generate as a result.  However, my head was also filled with lots of other ideas to improve our school culture as a whole.  A huge take away for me was on the importance of making kids feel special.  My own children are lucky to go to a wonderful elementary school that makes a huge effort to make students feel special.  Not only do the classrooms have weekly VIP recognitions for students who go above and beyond but there are also awards assemblies quarterly where every child is recognized for what they shine at.  As a parent, I love the way their faces light up when they have been recognized by their teachers or administrators and how genuinely excited they are when one if their classmates is recognized.  In my school we do recognize children as students of the month however with only two students selected per team out of a school of 1100 there are a great number of children who never receive this recognition.  There are also a lot of students who do amazing things from time to time but just can’t seem to keep their school life together enough to be recognized for this monthly achievement (sometimes 1 day is a long time for a kid to keep it together, much less 30!)

Upon arriving home, my colleague Erin Sienecki and I knew we wanted to make an effort to find a way to make more kids feel special.  We came up with the idea to recognize kids for “popping” up as leaders with popcorn on Fridays.  We settled in on the popcorn idea because:

  1. It’s cheap and with a budget of $0 that’s important
  2. We knew the smell of popcorn popping would fill the building and kids would know leaders were about to be recognized.

We created a bulletin board with the help of some very creative volunteers and slips for teachers to nominate students for a leadership award.  The goal was for teachers to recognize kids who went above and beyond in some way whether it be social or academic that wouldn’t necessarily earn them student of the month recognition.  We have had students nominated for things such as cleaning up trash that didn’t belong to them or for showing really high growth on an assessment.


On Friday mornings we have PTSA volunteers come in and pop the popcorn, place it in the bag and staple the leadership nomination on the bag.  We also make copies of the completed nomination forms so that we can add them to our bulletin board.  Near the end of the day, our administrators burst into classrooms to announce that there is a student leader in the room!  The students usually begin trying to guess who it is as the administrator reads their nomination form to the class and then presents the leader with the bag of popcorn.  The kids are always so excited for their classmates and cheer and clap and also hopefully resolve to work hard so that they may be recognized the next week.

Thus far, we have had some really positive feedback on the program from staff, parents, and students.  We have been recognizing around 70 students biweekly with this leadership program and can’t wait to expand it to a weekly program next school  year.  Personally, each student I have nominated for a leadership award has mentioned it to me privately and thanked me for seeing the good in them.  As a teacher, it does my heart so much good to know that for a brief moment I was able to help a student feel special.


And on a special side note, most of the credit for this program goes directly to my colleague Erin Sienecki.  Erin is champion of making kids feel loved and special and I am thankful for her leadership on this school wide initiative.

Homework vs. Practice

I had the opportunity to go to the PLCs at Work Conference last fall with some colleagues and one of the sessions rocked my math teacher world.  I have written a few different posts about homework over the years and boy have my philosophies changed from that first year when I assigned the ever famous #1-30 even book assignment.  Since that time, I have shortened up assignments, been more intentional about picking problems, and stopped assigning homework just for the sake of assigning it.  However, while at the PLC conference I had the chance to hear Tim Kanold speak and his presentation evolved my homework practices even more.


Tim argues that homework should truly be seen as independent practice.  I know as math teachers we always think of homework as independent practice but are we really treating it that way?  When a sports team or musician practices they make mistakes, receive feedback and get better.  No one bails them out by saying hey it’s ok that you can’t do that, here let me just do it for you, or nope you can’t try that again you should’ve done it right the first time.  Yet that is exactly what we do with homework.   We assign homework and then hand out zeroes when it isn’t done, go over it in class, and then put it behind us.  We give kids the answers to the homework as we go over it but never help them address or practice the skills that caused them to get the answer wrong or not even attempt it to begin with.   I always end up spending 10 minutes or more at the beginning of every class going over the homework and then answering questions about it but according to Tim’s presentation that is just me bailing out the kids that didn’t try…his recommendation was for me to give out the answers ahead of time to make sure they were making the most of their practice.  That way they could self-check, self-monitor, and self-grade as they did the homework rather than after the fact.

I decided that I might as well give that a try and immediately started providing all of my classes with the answers to the homework ahead of time.  I made it pretty clear to the kids that we would try it for two weeks and then talk about if they thought it was helping or hurting them in regards to their understanding of the material.  At first they were so excited, I think they thought “hey I can just copy down the answers and do none of the work”.  I really focused on setting the expectation of it being practice and that they were responsible for completing their own practice.  I may not be at their “practice” with them but I would certainly be watching their “game” through formative and summative assessments and monitoring their performance to determine if the homework answers were helping or hurting their understanding.

I am definitely a data driven teacher but do not have any quantitative data at this time that shows any significant increase or decrease in their assessment scores since I have started giving them the answers ahead of time.  What I can tell you is that as a teacher I have taken back 10 or more minutes of my class time by eliminating the need to spend a lot of time going over every single homework problem.  Instead, I let the kids ask questions at the beginning of class if there were any problems that they just couldn’t figure out but in general they have worked at home to refine their practice until they arrive at the correct solution.  I also have lots of thoughts from my students about whether receiving the homework answers helps or hurt them in math class.  Some of their comments are below:

  • Even though she gives us the answers to our homework we still have to show work and the answers help me check my work and see what I did wrong.  I have the choice to cheat but that won’t help me in the long run.
  • Getting the answers to the homework helps me a lot because when I am stuck on a problem that I don’t get it makes it easier because you know what answer you are working toward and when I get it wrong I can fix it on my own.
  • I love how I can check and correct my own work at home.  Also we don’t have to take ten minutes out of class to check it which is usually boring and I don’t pay attention anyway.
  • It helps me check over my work so I know I am doing it right.  Also it helps me figure out how I’m wrong.
  • It saves time in class and helps me figure it out when I am stuck on a problem.

I asked all of my classes for feedback on receiving the answers ahead of time and there were truly no negative responses in any of the classes.  Even some parents have sent messages that it helps them provide their child with more help.  It can be overwhelming for parents to try and help their child review and correct homework (I know it is for me, sometimes I am just not sure what the teacher is looking for on assignments and I am a teacher!) since they have the correct answers ahead of time.  As a parent and a teacher, I am all for making homework time as easy as I can on parents because I know for me it can be very frustrating at home to try and get it done!

For now the homework as a true practice method is working in my classes so I plan to continue it to see how it effect student learning in the long run.  Thanks Tim Kanold for further helping me develop as a teacher…I am always ready to get better!  As a side note, Tim also recommended that homework never be more than 6 to 8 problems (that was the one thing I was already doing) and that of those 3 to 5 be from the standard you learned that day and the rest from previous lessons.  As you know in my Math 7 classes we are using the Illustrative Math Curriculum and that is exactly how each of their practice sections are set up!  Having the constant spiraling back of content preplanned for me has been wonderful and has kept the “big ideas” of Math 7 at the forefront all year!  I am excited that they had the vision to incorporate best homework practices along with best instruction practices.  Using Tim’s recommendations for problem selection has been considerably more difficult in my Algebra I class as it uses a traditional text book and requires quite a bit more planning to incorporate his strategies.  I do continue to try and follow his plan the best I can!  Practicing isn’t an option for athletes, musicians, or artists and in my room it is no longer an option for mathematicians either.  Practice over homework everyday!


Letting Go of What I Thought I Knew

I have always been pretty open about the fact that I felt my “creativity” couldn’t be confined by me being tied down with a text book.  I have written numerous posts about it, tweeted it more times than I can count and told just about anyone who would listen that I didn’t need a textbook.  Turns out I just was right and wrong.  While a traditional textbook may not have been right for me; I have fallen in love with the Illustrative Math curriculum materials this year.

The EdReport on Illustrative Mathematics 6-8 Math Curriculum was released this week, making it the highest scored math program available on the market which only confirmed what I have seen in my classroom this year; the IM curriculum is a game changer for math education in this country.  I have been pretty vocal about my IM experiences this year, shared countless student work samples, videos, and pictures but I thought it was time to give other teachers a glimpse of what IM has done to my classroom performance.  I am definitely a data driven educator and as much as I have loved using the materials, it means very little if students do not see growth during the course of the year.  As you examine the results below please keep the following in mind :

  1. My class make-up this year is very similar to last year.  For the last two years I have taught two math 7 classes (one is a collaborative class for students with disabilities where I have a co-teacher).  The percentages of students from each sub-group is nearly identical for each of the last two years.
  2.  I am not a professional researcher.  I am a classroom teacher in every way.  I simply feel it is imperative I keep as much data as I can in order to make the best decisions I can for students on both a short and long term basis.
  3. I don’t work for Open Up Resources or Illustrative Math.  I have a passion and a heart for providing all students with access to the best math education possible regardless of geography, socio-economic status or other outside factors.

Unit Two Assessment Data:

Unit 2 focused on Proportional Relationships. The following data compares this year’s results with the Ratio & Proportions Part 1 Unit Test from 2016-1017 which most closely aligned with the content for 2017-2018.Unit Two Assessments

Unit Three Assessment Data:

Unit 3 focused on Measuring Circles. The following data compares this year’s results with test questions from the 2016-2017 Geometry Part 2 Assessment that focused on circles.

Unti Three

I was excited for those results but decided to play devil’s advocate and look at if from a more cynical point of view.  Last year’s data was based upon teacher written assessments and this year’s were the assessments that came with the Illustrative materials.   Although the IM tests are very rigorous and require a great deal of deep thinking I began to wonder how students would do on a more traditional standardized like assessment.  We are required to give semester finals in my district so I used that as an opportunity to see how the IM curriculum would transfer to a standardized test.  I used our district created final exam questions that were on the content covered during our first four IM units.  These were entirely multiple choice and very much like released items from our state K-Prep assessment.  The results were astounding.

Highlights from the fall final exam:

  • Average score was an 83% compared to 67% last year
  • The average score in my collaborative class was only 3% lower than the general ed class nearly eliminating the achievement gap between the two classes
  • There we NO NOVICE students in my collaborative class (I have never had that happen in 13 years of teaching

I feel pretty confident in saying that the kids will do just fine on our state test this year.  The best part was the kids comments about the test.  In years prior, students finished the assessment and said things like, “man that was so hard” or “I know I failed”.  This year they had comments like “do kids in other schools just take tests like that all the time?  It was so easy”.  I truly believe that due to the depth of thinking required in each and every Illustrative lesson, practice problem, and assessment that once students had to take a traditional assessment the cognitive load required was so much less that it presented no challenge to them.

As I said in the beginning of this post, I was concerned about letting go control of my teaching creativity and following a curriculum program but I couldn’t have been more wrong. I have more time to be creative because Illustrative has taken the curriculum design and planning off of my plate so I can find ways to make the workbook come alive for students.  Last week we watched a Ferris Bueller clip to understand why distance can’t be negative and then my favorite four minutes of Cosby Show when Theo is learning about being a “regular person” and money before we started looking at integers in the context of money.  I was sure that my kids would be lost on the concept of integers without using manipulatives like integers chips.  I gave the IM lessons my best shot though, and even though it is embarrassing to admit it, I even understand subtracting integers better after the thoughtfulness and context of the lessons using number lines and elevations.  I was able to improve their fluency with some of my favorite games, but the conceptual piece was done in a way far greater than I could have ever done and this teacher is thankful.  We took a formative assessment yesterday to see who needed some remediation time with me on adding and subtracting integers…in two classes there were noly two students who didn’t master the concept on the first try.   Although I don’t have the data in front of me, I am almost positive that last year I had more than two students at the end of the year that still hadn’t achieved mastery on that skill and this year after one attempt they had it.

I have felt the need to share this data for a while but not for attention or kudos.  I truly believe the Illustrative Math curriculum is what is right for kids.  All kids deserve the chance to truly understand, comprehend, and enjoy math and this program provides that opportunity in an easy to use format.  It is a game changer in grades 6-8 mathematics.  A free, accessible, and differentiated curriculum seems to good to be true, but this isn’t just good it is phenomenal.  Thank you IM for chaining math instruction for both me and my students, I am beyond grateful.


Being Thankful

“You choose a thankless job, you can’t be upset when nobody thanks you. Don’t start chasing applause and acclaim. That way lies madness.” ~ Ron Swanson

I don’t know of a teacher who decided to get into the education profession for the acclaim, applause, recognitions or awards.  All of the teachers I have the pleasure to work with are selfless and giving people who you will ever have the chance to meet.  They are the people who buy extra granola bars and Goldfish weekly because their school backpack program is in need, the people who excitedly buy extra hats and gloves when they are on sale so they can hand them out to the kids who need them most, and the people who on snow days like my district had today are worried sick about who is home alone, who is without heat and who is hungry.  Teaching for all of us is about the feeling we get when a kid who has struggled with a concept has a light bulb go off, a former student comes by to update us about what they are doing now, or we feel like we really knocked it out of the park with a lesson we designed.

A week ago today I got to experience a feeling that I wish every educator got to experience once.  I sat in what I thought was to be a “boring” assembly about state testing and then heard my name announced as a Milken Education Award winner.  I got to see a student on the first row yell “that’s my math teacher!” and a gym full of kids chant my name.  I got to hear appreciation and recognition for the work that teachers just like me around the country do every single day.  In all honesty, it still hasn’t set in for me.  I will forever be thankful the opportunity that the Milken Foundation gave me that day, it is something that will never be forgotten in my lifetime.

As thankful and humbled as I was to have been chosen by Milken (I will never be sure how they found this Kentucky girl) I am just as thankful to the hundreds of people who have led me to where I am now.  I have had the opportunity to work with some amazing people and each and every one of them had a hand in molding me into the teacher I am today.  One night in a weekly #msmathchat I heard Justin Aion use the term involuntary collaboration to describe taking the best ideas you could find and making them your own.  I can comfortably say today that without involuntary collaboration from the best and brightest math teachers in the country that I wouldn’t be where I am today.  When people come into my classroom and see kids excited about learning math that isn’t just me.  It is Andrew Stadel and his Estimation 180, Fawn Nguyen and her Visual Pattern site, John Stevens and Would You Rather, and so many others that deserve recognition.  Those are the people and the things that have allowed math to come alive for my students.  I think, or I hope, my colleagues would be the first to tell you that I come out of my room about half of the time and say “man that was a real disaster”.  The truth is sometimes I have more lessons that fall flat than inspire kids to own the math but my Beaumont colleagues, administration, district math team, and MtBos community picks me up, makes me shake it off, and try harder the next day.

Perhaps most importantly I am thankful to the 1,500+ students that have given me the opportunity to be their teacher.  It can’t always be easy to have a teacher like me, that is so loud that my pod mates have to shut their door to drown out the noise or that is always trying a crazy idea that may or may not work but yet let me have fun with them for an hour each day (and most days they at least pretend they are having fun and enjoying math too!).  I will always be thankful to them for laughing at my stories and making a job seem like a lot more than a job.

The bottom line is I am thankful to be a classroom teacher. I am also thankful to the Milken Foundation for recognizing teachers across the country and promoting teacher leadership in such a positive and life changing way.  Since Tuesday I have heard more times than I can count, “well at least now you will be able to get out of the classroom”.  That statement has shaken me some I won’t lie.  I have had opportunities to leave the classroom each year for the last three or four years but I have inevitably chosen to return to room 406 for another year of professional growth and learning at the hands of 120 twelve and thirteen year olds.  The time may come at some point for me to leave the classroom but it certainly won’t be a decision I take lightly or that I look as a way “out” of teaching kids.  If I ever leave the classroom (and I am not sure I ever could leave it full-time)  it will be because I feel like I can positively impact more kids by helping teachers on a larger scale.  In the mean time I will remain thankful that I get to be a classroom teacher.26231627_10155833084391399_6181977321355652278_n (1)


Seeing the Light of Conceptual Understanding

As a student, I was always great at memorizing formulas and processes.  A couple of good cram sessions never failed me before a big test and always kept my grades in the acceptable range at home.  That was a solid plan for me until Algebra II and Pre-Calculus hit and I found myself unable to understand any of what was going on without the basic foundation of number sense and algebraic reasoning required for such advanced mathematics.  As a result, I have always claimed to be a proponent of conceptual teaching.  I always gave my kids the obligatory 20 minutes of playing around with a concept before I said “ok let’s down to business” and pushed that conceptual piece straight to fluency and procedural skill in order to check off another standard on our curriculum map.

I teach a grade level Math 7 course, a collaborative math 7 course and Advanced Algebra I for 7th graders daily and although the content may be very different amongst them I have seen the same pieces of conceptual understanding missing over the course of the last week.  In Math 7 we are working on understanding scale factor and as a result have had many conversations on why dividing by 2 is the same as multiplying by 1/2 or dividing by 2/3 is the same as multiplying by 3/2.  It is a conversation we have had almost daily it seems as we work on thinking of scale as a multiplicative relationship and understanding how the value of the scale factor changes the size of the scale copy.

In my Algebra I class we are solving equations and inequalities but yet this understanding of the equivalence between dividing by a fraction and multiplying by its reciprocal is a barrier for many of my advanced students as well as we begin moving into solving more complicated and challenging equations.  The whole experience has really pushed me to ask myself where this conceptual understanding has been lost along the way.  The students I teach come from 5 or more different elementary schools and had a variety of teachers all of whom I have no doubt worked incredibly hard to teach this concept and so many others but yet like so many other concepts the students remain in the procedural rather than the conceptual world.

As teachers we all want 100% what is best for the students in our classroom.  We want them to feel successful, to learn the content, and to feel like we have taught them everything listed in our District Curriculum maps and state standards.  However, I think often times it is the conceptual understanding that gets lost amongst the ever growing list of things we need to cover and complete over the course of 177 days.  As I said, I have always worked to give my kids “time” to work on conceptual understanding, but was it ever really enough?  Conceptual understanding is hard…it requires time, perseverance, some creativity, and a lot of patience all of which can be hard to find time for in a 60 minute class.  When my learners struggle I often find myself showing short cuts or breaking things down to simpler steps so that they can find success and comfort in the procedure rather than pushing them until they reach conceptual understanding.

My work with Core Advocates and MTBoS mentors have certainly pushed me and inspired me to dwell more in the conceptual and I have continuously improved as a teacher, however this year I seem to see the light more than ever.  This year I’ve been lucky enough to get to pilot the new Illustrative Math curriculum from Open Up Resources and it has truly already challenged me in every way imaginable.  I have really seen over the course of the last few weeks how much conceptual understanding opportunities I have taken from my students at times so we could get to the big idea.  There have been lessons in the first unit that I thought to myself “are they ever going to get to the point” however I have held my feet to the plans provided.  We are wrapping up that first unit now and here is what I’ve seen…the kids do eventually get there.  I have given them the time to reason, struggle, make mistakes, draw pictures, and talk out their ideas and now here at the end of the unit I truly believe they know the procedure pieces better than they ever have.  They now OWN why they are doing what they are doing instead of simply doing what I said they needed to do.  When I posed a scale copy problem today, some kids grabbed a ruler and started measuring, others grabbed a piece of tracing paper and checked angles, others went for a protractor or index card, and some used simple reasoning but they all on their own found a way to prove two images weren’t scale copies.  The time spent allowing them to really grasp the math was far more productive than any time I could have spent trying to procedurally teach how to identify scale copies or scale factor.

I get while writing this that it sounds much  simpler than it is.  If I knew conceptual understanding was key for years, why did it take this long to really embrace it?  I think until this point I believed I was giving kids enough opportunities to struggle with the conceptual piece and until I really experienced an entire unit built around conceptual understanding first I couldn’t grasp how much time I really needed to give these ideas to develop and form in their head.  I am excited now to see how their ideas continue to develop over the course of the year.  The next IM unit is proportional relationships which will allow them to extend their understanding of scale directly to understanding proportional relationships as well.  I am more excited to see their understanding and reasoning continue to develop than I have ever been.  I am so excited I got to see the light.