My all-time-favorite Organizational Strategy for the Math Classroom (That it only took me 8 years to figure out).

What’s that old Einstein quote?…

…the definition of insanity is doing the same thing over and over again and expecting a different result? If this is truly the definition of insanity, I guess the leading adjective to define the organizational structures in my math classroom over the years must be “insane.”

( Fun fact: we all must be insane because it looks like Einstein never said this in the first place).

Anyway, without further ado,

Here is my FAVORITE Organizational Strategy for the Math Classroom (that makes me a little less insane each day):

Test your expo markers here- yunderstandmath.com

Give Them a Place to Test Those Expo Markers

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Who doesn’t hate a dried up (or almost dried up) Expo marker? No one… The answer is no one because EVERYONE hates this. Teachers hate this. Custodians who have to pick up lost Expo caps from the floor hate this. Students hate this. Everyone. I get it. So, I understand why students want to test their Expo markers before they use them.

However, this doesn’t stop it from being my biggest pet peeve. Every year. Without fail. For EIGHT long years. No matter what I did… move the Expo markers across the room… put Expo markers out at each table…hang large signs that say ‘PLEASE DO NOT TEST YOUR EXPO MARKERS ON THE WHITEBOARD’… no matter what, each day, at the end of the day, I would inevitably end up with large streaks across MY whiteboard left behind by well-meaning students who just didn’t want to suffer through the experience of having to write with a dried-up Expo Marker. And then every day, like clockwork, I would have to erase these streaks before I wrote up the homework, wrote out reminders for the class, demonstrated a solution, hung an anchor chart, or in any way used MY whiteboard.

Insanity.

No more. This year it finally clicked. I understand the student frustration and motivation. Wouldn’t I want a place to test these Expo markers too? Why not just provide them with a designated location to conduct said tests?

LIGHT BULB.

It worked. Like a charm. I didn’t even have to explain. Not once. All I did was tape a small handheld whiteboard to the supply shelf, labeled it “Test Your Expo Markers Here” and ta-da, no more streaks across MY whiteboard at the end of the day.

[Insert face-palm Emoji here]

A place for everything and everything in its place. Check out other ideas for the math classroom at yunderstandmath.com on Instagram @y_understandmath & on Twitter @yunderstandmath

(Now if only I could get them to THROW OUT the dried up markers instead of leaving them in the bin for someone else to find…).

<3, C

WhY are you Showing me Elementary and Middle School Resources?

We know, you thought that we advertised ourselves as being able to help you plan for your algebra instruction.  You’re right. We did. And regardless of all of the elementary content you see on our website, we would argue that we are.  

Differentiation.  Personalized Learning.  Enrichment. Intervention.  We get it. As a teacher, we are expected to be everything to everyone.  The expectations (as well as the educational jargon) can be a heavy weight to carry around.  

This is where we hope to help.  While understanding that there isn’t a silver bullet that will magically lift these expectations off of your back, we hope to be able to lighten the load by providing you with resources to help differentiate for the needs of the students who show up in your classroom each day with varied and vast mathematical experiences and background understandings.  

We started this month by identifying some common misunderstandings related to CCSS.Math.Content.HSA.SSE.A.1 and CCSS.Math.Content.HSA.SSE.A.2 (seeing structure in expressions).  During the second week, we worked backwards from an A.2 example problem [3(m - 3) + 2m - 1 + 6] and identified the elementary building blocks that were intertwined in the process of simplification.  During the third week, we built on the elementary building blocks and identified some foundational topics taught in middle school that lead to fluency in simplifying expressions.

Each week, we’ve highlighted five correlated skills/understandings (what we’ve been referring to as the building blocks of understanding).  For each correlated skill, we’ve found an instructional video that explains whY, and we’ve also identified instructional resources that you can utilize in a small group when planning for intervention, or with the whole class if you’ve identified a gap in understanding of the building blocks.  

Differentiation is whY we’re decomposing these algebra standards to their elementary and middle school roots.  Pre-assessment is how you can effectively identify which of the foundational skills you need to return to before pushing ahead in the algebra curriculum.  

We advocate for the use of open-ended pre-assessments.  By leaving the questions open-ended, it allows us the space to identify fundamental misunderstandings within student solutions.  For example, one of the questions on our ‘Seeing Structure in Expressions’ pre-assessment asks students to simplify 5 + 3 (m - 3) + 2m - 1.  Each time I give a pre-assessment in my classroom, I scan student papers for their responses to each question one at a time. I don’t mark-up the papers, but simply sort the papers into groups based on similarities in their solutions.    As I was looking over this particular pre-assessment question, I noticed that some of my students were adding 5 and 3 before they distributed (ending up with something close to 8m - 24 + 2m - 1 before combining like terms). I was then able to sort my students into two groups.  With one group, I planned to help them use algebra tiles to identify why 8 (m - 3) is not the same as “five plus three groups of (m - 3).” When we worked in this small group, I remember that the use of the algebra tiles led to a great discussion about the order of operations and why it makes sense that we would have to distribute before we add in this expression.  With the students in my second group, I planned to push their thinking to show the distribution of a variable by an expression. This intervention and enrichment were both made possible because students had prior experiences using area models to multiply.

This is how it all ties together.  Understanding of multiplication as a representation of equal groups (and visualizing these products with an area model) is first taught in third grade (CCSS.Math.Content.3.OA.A.2). The concept of working within grouping symbols following the order of operations is first introduced in fifth grade (CCSS.Math.Content.5.OA.A.1) and then revisited in relevant contexts each year thereafter (check out the ‘Four 4s’ activity in our week 3 resources).  The distributive property is first introduced in third grade (CCSS.Math.Content.3.OA.B.5) as a way to break down a product into its friendly factors. Computation with negative integers is taught in seventh grade CCSS.Math.Content.7.NS.A.1 and CCSS.Math.Content.7.NS.A.2, but understanding of negative rational numbers is solidified in sixth grade. We could go on, but we think you get our point. All of these understandings are essential to being able to simplify 5 + 3 (m - 3) + 2m - 1.  

So, yes, we’ve highlighted a kindergarten standard on a blog that has marketed itself as a place for resources for algebra teachers.  But, we hope you can use the resources we’ve compiled to help your students build on their past experiences and fill in any gaps they may have in the understanding of the building blocks.  

Happy differentiation!

If you’re interested in the ‘Seeing Structure in Expressions’ pre-assessment we’ve described above, we’d love to share it with you!  It is attached as a PDF to the welcome e-mail you will receive if you sign up for our monthly newsletter here:

WhY Vertical Alignment is Essential

How am I Supposed to Have Time for This?

Although I am in my second year outside of the classroom, I remember the grind of being a classroom teacher. When you are in your classroom, you are constantly thinking: what’s best for my students? As teachers we spend countless hours planning lessons, collecting data, analyzing data, revising lesson plans, communicating with parents, researching materials and collaborating with teachers and colleagues in the building--among what feels like a million other responsibilities. The majority of these to-dos happen outside of our scheduled work days. So whY should we make the time to vertically align? The bottom line: vertical alignment IS what’s best for your students.  Fortunately, there are many resources out there that can be helpful in visualizing that vertical alignment, and we’re here to help streamline the process even more.


What is Vertical Alignment?

Let’s start out by defining vertical alignment. As a teachers, we already focus on horizontal alignment. We look at our grade level standards and determine what our students need to know and then think about how to get them there. But we know that isn’t where we should stop. It would be so helpful if we could know  what the students in our classrooms come in knowing, as well as where they are headed the following year. Knowing what our incoming students know or should be able to do allows us to build on mathematical concepts and strategies previously learned in order to meet the grade level expectations. Knowing what our students will be learning and what they should be able to do in the following grade level will allow us to bridge the gap and prepare our students for the next step.


What Resources are out There to Help Support Vertical Alignment?

Critics of the Common Core State Standards refer to these standards as “new math.” Here at Y Understand Math, we view the Common Core State Standards for what they truly are: a framework of logical, mathematical standards that conceptually build on each other in such a way that allows for a deeper understanding. As teachers, we often find it hard to find time to vertically align. Trying to collaborate with teachers in the grade level below or above can be time consuming. Locating the standards online and sifting through what they say; making sense of the domains and numbers, it can all be challenging and overwhelming--I mean, c’mon! Can’t addition and subtraction be the same NBT throughout all grade levels?! This would make ALL of our lives so much easier!

There are some quality resources out there to help map the transition between concepts at different grade levels.  One such resource is the Coherence Map at achievethecore.org.  However, we find that poring over these lists of standards can be mind-numbing. That’s where we come in! Just like how we work to make mathematical understanding visual for our students, Courtney and I are here to highlight common strategies taught within these vertical frameworks, you guessed it, in a visual way.  


WhY Should you Trust us to do This Work?

Courtney and I are uniquely positioned to look at vertical alignment from a bird’s-eye view.  Our opinion? Rather than living in a perpetual state of trying to diagnose why students cannot grasp complex algebraic concepts, why not look at how the skills students learn each year build on each other and support those more challenging math concepts in upper grades?  This week, we’ve tried to do just that.

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Last week, we took a deep dive in unpacking CCSS Algebra Standards A.2 and A.1: Seeing Structure in Expressions. This week, we will look at the underlying math concepts that are introduced in elementary school and add to students’ success and understanding in algebra. Think about this: how does skip counting--first introduced in kindergarten--serve as a fundamental building block for using the distributive property when simplifying an algebraic expression?? I’m sure you’re thinking, ‘it definitely doesn’t’, but we are here to tell you ‘it absolutely does!’ Crazy to think about!

-A


So, whY are we doing this?!

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Let’s start out by saying THANK YOU to each and every person supporting us on our journey of Y Understand Math. Whether it has been a personal text or a follow on instagram, we are excited for what’s next and feel thankful to have the support of so many people.

We wanted to start out by sharing the whY behind this side-project. To do this, we think it’s best to take a trip back to where it all began.


So, whY Courtney & Ashleigh? Who are we?

Ashleigh grew up outside of Baltimore, Maryland and always knew she’d be a Terp.  Courtney grew up in central New Jersey (yes, that exists), and although, admittedly, she never dreamt of being a Maryland Terrapin, her decision to attend Maryland ultimately led her to meeting her husband, her first job and her college basketball obsession. Both Elementary Education majors at the University of Maryland (UMD), we had several classes together and formed a friendship that involved working on assignments together, asking questions about teaching, and most of all, venting about the high-demands of student teaching in our senior year at UMD, while the rest of our friends were out...enjoying senior year. We went through student teaching together, we experienced our first snow days together and we, ironically, built our first websites together--our online teaching portfolios for graduation. We graduated from UMD and went off into our separate teaching positions, continuing the conversation about teaching, students and everything in between.

Courtney, Secondary Math Teacher

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As I’m sure you’ve already surmised, my name is Courtney.  Currently, I am a secondary math teacher in Arlington, Virginia.  My teaching journey has taken me from a student teaching position in fifth grade, to sixth grade for four years, back to fifth grade for a year, and three years ago, to my current role teaching sixth grade math, pre-algebra and ‘algebra, functions, and data analysis.’  In addition to classroom teaching, I also have my Masters in educational policy from the University of Virginia.

I spent my first five years teaching every subject.  Although I enjoyed history, science and language arts (that last one, in particular), my heart was always in graphing functions ;).  We were departmentalized as a school, and although we rotated responsibilities each year, I always made sure that I was teaching math (some years teaching two or three different levels).  When I decided that I wanted to make the switch to secondary school, I knew that it would be to be a math teacher.

As I mentioned before, my second love has always been reading/language arts.  When we are taught to be reading teachers, we are taught about the value of ‘think alouds’ and of modeling the thoughts of a fluent reader.  I’ve always wondered why it’s uncommon to think of teaching math with this same philosophy. Reading is presented as the art of making connections between your lived experience and the text. Conceptual understanding of math is often viewed as a mysterious, innate talent. It does not have to be this way. My goal is for math to be viewed as an art as well, the art of making connections between your experience and the visual nature of mathematical concepts.

Ashleigh, Math Facilitator

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Hi everyone! My name is Ashleigh and I am a math facilitator in Charlotte, North Carolina. I know what you are thinking: what on earth does that mean? The easiest way to put it is I am a teacher of teachers, or as we refer to it in my school: a coach. When I think about my journey in education, it honestly amazes me how much it has evolved. When I reflect on everything that led me to where I am today, it’s clear that I was always meant to be a math educator.

I spent my first two years of teaching at a Title I School in Alexandria, VA. I taught third grade reading and co-taught math with, my now dear friend, Beth Terry. It’s Beth who first sparked my love of teaching math. I always liked doing math, but Beth made teaching math exciting. I still implement so many of the strategies, games and best practices I learned from being in her classroom.

Following teaching in Alexandria and a short stint in Los Angeles, the opportunity to move to Charlotte, North Carolina came next. I applied to almost every elementary school in the district, with little to no idea what teaching in North Carolina was like. I landed at a Title I school where I have been ever since. I spent my first two years teaching all subjects in 4th Grade. I always felt more successful when teaching math. I was more excited about teaching students math concepts and planning my math lessons. At the end of my second year teaching 4th Grade, my principal approached me with the opportunity to loop with my students.

Teaching 5th Grade math was a pivotal point in my journey. I already knew the majority of the students, so I could truly focus on my math instruction. I had one subject to focus on and give my undivided attention. My amazing co-teacher, Danielle Carlsen, had experience teaching 5th grade math and could support me in the learning process. We were a dynamic duo. One of our instructional assistants referred to us as Scottie Pippin and Michael Jordan. Just a few weeks into the school year, I realized the value that each of us brought to our 5th Grade math team. Danielle knew the 5th Grade content like the back of her hand and I knew the 4th Grade content like the back of my hand. In our planning sessions, she knew exactly where the students needed to go, and I knew exactly where they were coming from. Together we could support any gaps in grade level content and work together to develop lessons that built on what students already knew, in order to get to what they were expected to learn.

At the end of that school year, my principal approached me about the next step in my journey. This is my second year in my role facilitating math instruction and to say I love it would be an understatement. Working with adults is so different than working with children, but the impact of working with multiple grade levels and consequently more students is irreplaceable. I work with my teachers weekly on instructional planning. We start our planning sessions with the same process each time we meet. First, we look at what the students need to know, think about how we are going to teach them and whY these mathematical procedures work. It is this backwards design process that ensures we plan our lessons with the end in mind. During my time as a facilitator, my passion (some would say obsession) with math instruction is evolving by the minute. I love my job, I love the students and teachers I support, and I love, love, love math.


Courtney & Ashleigh

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A lot of time has passed since May 2011 when we graduated from UMD.  As our individual lives demanded more of our time and attention, we drifted apart a bit, but we have always had a common thread to hold us together: teaching. When together, we find ourselves sharing instructional ideas, talking about data and new ways of supporting students and sharing about the great things happening in our schools. It’s always positive. It’s always reflective. It’s always exciting, filled with joy and leaves us both feeling rejuvenated in our profession.

Sometime in September 2018

We were one month into our school year in our separate states. We honestly didn’t even remember the last time we had talked. Ashleigh was sitting on the couch watching Netflix after three days off of school due to a hurricane. Courtney was driving from her school after a long, exhausting school day and on the way to a tutoring session. Her mind was racing. She was feeling negative and ineffective and needed someone to bounce ideas off of. Although they hadn’t spoken in months, Ashleigh answered and listened attentively as Courtney spilled her thoughts.  

That was the afternoon that Y Understand Math was born (kind of).  This passion-project grew out of a desire to have a community to bounce ideas off of, a community of educators engaged in conversation about ‘math as an art.’

The whY

After a few months of brainstorming ideas, countless text messages and phone conversations and a few face-to-face meetings over coffee, we are ready to share our plan! We have realized that the two of us are uniquely positioned to have a ‘birds’ eye’ view of the vertical alignment of the math curriculum. With Courtney’s experience in upper elementary and secondary math and Ashleigh’s facilitator experience in elementary school, we have access to instructional strategies and materials ranging from kindergarten through Algebra II. We love digging into how one concept builds from one grade level to the next. We (embarrassingly) really enjoy noticing the connections between fundamental early-elementary concepts and topics covered in middle and high school classrooms.

We are advocates for the use of visual models, the development of conceptual thinking and the focus on ‘the whY behind the what.’ Our experiences and educational journeys have us equipped with the ability to vertically align: a practice that is so critical in education, but often hard to find time to do alone. We may be dorks, we may be crazy math ladies, and we may think about math on the weekends, but we want to create a community of educators who think about math in the same ways that we do.  Our framework will take a look at the underlying concepts that students learn K-8 that lead to algebraic understanding. Our goal is to help build awareness of the importance of the ‘whY behind the what’ when teaching math. We invite you to join our conversation and thank you for listening!