# Creating Structure for Context in Math

I was honored to facilitate lesson study with IM1 teachers today. Their students are struggling (due to high EL/SPED population) with solving word problems. I dug deeper, and we decided the struggle is really the first step: creating equations from situations.

We decided our goal as educators this year is to work on teacher clarity: making our lessons streamlined and very goal-oriented. If we know our goals for the lesson, then every move we make (every breath we take…) is for the goal. So how do we clarify translating context to equations?

We started from the end: the benchmark. We took a problem the students struggled with, and tweaked it several times, each time only altering only one component. Students had to work from the original version (which we used simple numbers to keep it accessible) for each new “version”. They discussed what changed from situation to situation and how that affected the prior equation.

Version 1: Troy works for an ice cream cart vendor. He receives \$10 for taking the cart out for a shift, plus a commission of \$2.00 for each item he sells. Troy worked a shift Saturday and earned \$60.  How many items did he sell?

Version 2: Troy works for an ice cream cart vendor. He receives \$15 for taking the cart out for a shift, plus a commission of \$2.00 for each item he sells. Troy worked a shift Saturday and earned \$60. How many items did he sell?

Version 3: Troy works for an ice cream cart vendor. He receives \$15 for taking the cart out for a shift, plus a commission of \$1.25 for each item he sells. Troy worked a shift Saturday and earned \$60. How many items did he sell?

Version 4: Troy works for an ice cream cart vendor. He receives \$25 for taking the cart out for a shift, plus a commission of \$0.10 for each item he sells. Troy worked a shift Saturday and earned \$52.90. How many items did he sell? (Problem from the benchmark.)

We used 3 scenarios. In each, we kept our questions as consistent as possible (again, clarity):

• Which part is varying (changing)? How do you know?
• Which quantity would be the coefficient? How do you know?
• Which quantity would be the constant? How do you know?
• (From version to version) What has stayed the same? What changed? How does the changed quantity affect our equation? Why?

Students were engaged, writing on their tables and willing to discuss with each other. They had many moments of “ohhhhhh” and “oops!” and learned quite a bit about the components of 2-step equations. They definitely need more time, and the teachers have committed to continuing the work as warm-ups or on modified days.

Oh! And did I mention this was a co-taught Special Ed class, with many English Learners?! Amazing!

So our major takeaways were:

1. Know your goal!
2. Keep your goal in mind when creating the tasks/lesson and questions for clarity and focus.
3. Breaking the situations into translating and solving (working on a single component) allows students to focus and interpret.

Below is our ppt. Hope it is useful! Happy Math-ing!

Linear Equations in Context LS 8.27.19

# Everything I Learned, I Learned From Teaching: The Resignation I Wish I Could Have Written

Just an FYI: This is not a blog for learning math. This one is to thank the many individuals who have shaped my being, both in and out of school.

So I am super bummed. I had to write a letter of resignation for a job I love. With that, it felt like I was writing a resignation for the CA portion of my lifetime. Though I still do some important work with amazing teachers in CA (Cuca peeps you aren’t getting rid of me yet!), I am no longer affiliated with a school, a set of students, or that place to call my teaching home base.

A bit of recap. My husband was given this amazing opportunity to make a difference in the lives of our Wounded Warriors. This is not something our family takes lightly, as I am pretty sure between the two of us we have had family in every branch of the military. So we took it on for two years. My district was generous in giving me a two-year leave of absence. However, we have fallen in love with our current location and the work we both are being able to do. So….We are taking a HUGE leap into the world of unknown and seeing where these opportunities take us.

Teaching is something I was born to do. I love learning and I love watching that ‘spark’ children get when they have an ‘ah-ha’ moment. Yet it is through the village who raised and sculpted me that I feel confident today in my teaching. Here are the top 5 lessons I have learned through teaching that have transcended my professional life and helped make me who I am today.

1.  “You will understand once you have your own children.” I had been teaching a whopping year when this got thrown at me. I was a middle school math teacher and thought I was a bad ass. I had a great rapport with most of the students, loved the curriculum, and was a fav with my colleagues. When parent-teacher conferences came about during my second year, I thought I had it down. A mother sat with me, listened to all I said about her child, and then responded with a knowing look this phrase. I was floored and was ticked off. How would I learn more just from having my own kids?! Wasn’t I great now? No, I was not. And yes, she was right. I am far more patient now. I understand when students don’t have their work done. I get it that there is (gasp!) more to life than math. And from the moment I had my first, I worked harder at creating young learners who cared about learning and each other rather than simply good seventh grade math kids.
2. “If you show you truly care, the mistakes you make will be forgiven.” After about 12 years of teaching, I became a curriculum specialist for our County Office of Ed. My mentor, Carol Cronk, is amazing. I could write novels about the lessons I take back to my classroom from her. The first few weeks I was able to just shadow and watch how she worked with teachers and administrators, and we would debrief after. After a Framework PD session, she told me some of the mistakes she had made, and that she knew the teachers knew she had made them as well. When I questioned her about it, this was her reply. And it’s true. If I made a mistake with my students (or teachers), they forgave me. Just as I have forgiven them. It’s the level of respect you have for one another. And I think it works in life as well. If you show you care (and really mean it), people are far more accepting. This lesson just hit me again as I watched so many different journalists report on Super Tuesday… How many of the candidates have my respect? How many of them can I forgive? How about you?
3. “You need to see it the way students do.” Ahhhh….Dr. Fischman. She has been the toughest on me, and I have probably learned the most from her. Let’s backtrack. I love numbers. See them everywhere and do fabulous things with them. When I was working with Dr. Fischman, procedural methods and ‘playing with numbers and formulas’ were indeed my strong suits. But that is not what we were teaching. I learned that there are other ways of thinking about mathematics. I learned to listen to my students and use what they knew to tap into the mathematics I needed to teach them. I learned to LISTEN, and not just be heard. (Still working on this one, though!)Thank you for that.
4. “Fake it Til You Mean it” So there are many things I love to learn about, technology NOT being one of them. I feel so helpless with technology, so I typically steer clear. However, after going back into the classroom, I was pushed kicking and screaming into SMART boards, responders, laptops, etc. My dear friend, Aly, would say to us during our tech trainings, to suck it up and literally, fake it til you get it. And I would. I would fake that I knew what was going on. And it totally worked! As I faked it, my confidence level rose, I tried new “stuff”, and so on. It really helped me get out of my phobia (well…still a bit fearful…). So thank you, Aly, for pushing me onward and not letting me drown in my fears.
5. “I Will End My Days Teaching” One of the teachers at my first middle school position was an Immersion teacher for English Learners, grades 3-8. Linda Chace is amazing (and I had her husband for fifth grade- small world!). However, I knew that she had been an administrator for several years prior to this position. I asked why she left the administrative side. She said she wanted to finish her time teaching. I still take this to heart. Do what you love. Do other things and learn from them, but always go back to what you are passionate about. Make a positive difference in the world, while enjoying what you do.
There are so many others I could add to this list. Yet these five nuggets of truth stick with me. Thank you for supporting me. Thank you for helping me grow. Thank you for making me be better for our children.
Jen