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?IMG_8202

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.)IMG_8205

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?IMG_8208

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: IMG_8207

  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



Creating Structure for Context in Math

What’s Your Teaching WHY?

This morning at the airport (At 5 fricking o’ clock! I need to fire my secretary for scheduling this flight. Oh wait. That’s me!) I was answering emails and a timid voice interrupted my thoughts.

Excuse me. Are you a teacher?

This always makes my heart happy. As a middle school teacher, you often believe the kids won’t think twice about you once they leave your room. Why would they, with all the distractions the world has to offer?!!

So when a former student not only remembers you from looong ago, AND takes the time to share her experiences and life journey with you, you tear up just a little. You remember that these precious moments are WHY you were born to be an educator.

My WHY is simple. I love seeing my peeps have the “click” in math. I love learning about these humans, with all their quirks and unique personalities. I love supporting them and inspiring them to do great things. I just love THEM.

What is your WHY? Ponder, remember, and remind yourself of this through the year.

Have a great 2019-2020! I KNOW it will be a year to remember! 💕

What’s Your Teaching WHY?

How Do Our Beliefs in Math Affect Our Students?

I was honored to work with amazing teachers this week. We took a survey from NCTM (National Council Teachers of Mathematics) on our beliefs regarding student learning and our instructional practices in mathematics. This, in itself, led to amazing discussions about what we truly believe math IS and how we interpret that into instructional decisions within our classrooms.

But then we took it further. We got into groups and discussed not so much whether we agreed or disagreed, but whether it was a productive or unproductive belief in respect to student access and learning.  Here are two to consider:

There were fantastic discussions about these particular ones, especially for educators of EL and SPED. We also considered how parents might respond to these. Powerful conversations around access, flexibility in thinking, understanding conceptual and procedural mathematical ideas, and yes, fluency.

Here was the point. Our beliefs, whether productive or unproductive, affect our attitudes towards mathematics and the children we are blessed to teach. Those attitudes affect the actions we take. Who gets to answer which questions? Who gets the “tough” tasks and who has to keep doing drill and kill worksheets? Who gets to explore puzzles and who has to retake tests or do homework (because their home life doesn’t lend itself to being able to do it at home)? And those actions MATTER. They affect the results you will get from your students.

Belief chart

So as you gear up for this school year, consider taking the beliefs survey yourself. Even better, have your team take it and REALLY dive in to what beliefs are productive an unproductive. The more we reflect, the more we can grow and be effective at what we truly want; to teach students to love, learn and understand mathematics. Have a great year!

For the beliefs survey: 2017_06_19_Holstrom_Grady_2BeliefsSurvey


How Do Our Beliefs in Math Affect Our Students?

That Moment You Realize Your Child Is Suffering

All who have multiple children know that each one is wonderfully different. You can raise ’em the same, yet they have their own amazing quirks and personalities, strengths and passions. This could not be more true of my two boys.

My youngest is now 5. He has always been the rough and tumble type. Everything is a competition to him. (Even last night he was standing on his tippy toes trying to be ‘taller’ when raising his hand at church!) He is funny, outgoing, and a firecracker. He is a joy.

Yet school stuff has not yet become his thing. He seemed disinterested in learning his letters, yet loved to be read to. He never wanted to sit with me and learn the components all say are so important for kinder. His preschool teachers said it would come; that he just was a busy bee and had other, more important things to care about. And honestly, I believed that too. He loves to create, tell stories, sing, build, and live outdoors. Who was I to take that away from him?

So when his amazing preK teacher suggested a hearing test, I was on board. No big deal; just go do it and cross it off as another thing we did. It came back inconclusive. Went for an ENT hearing test. The results were staggering; at least 30% hearing loss in each ear. The doctor said, “Think of being submerged underwater for 5 years of your life, trying desperately to hear what people are saying. That is what your son has lived through.” I am still teary thinking about this. I am a fricking educator! How did I not catch this?  I was in denial as well, until that very day driving home I asked my boy if he saw the cool tree. “Tree?” “Yes, the tree over there (I pointed out the car window.).” “Like, dessert?” And that is when it hit me. My child wasn’t hearing.

We started to notice. He said, “What?” almost every time you told him something.  He couldn’t hear the TV clearly; he was reading lips (which we now know why he would never answer us when watching TV; he was too focused on the screen to hear us). In preK, during circle time, he struggled to hear all the conversations and his body would just be exhausted from trying to listen that he gave up.  When listening to a story, he focused on the pictures for meaning versus our words. He was trying his best, his very best, and it was exhausting. My heart broke. My baby boy, sweet thing he is, was struggling under my teacher nose, and I hadn’t caught it.

Long story short, he is now hearing much more, with just a tweak of medication. He still has a hearing loss, and we will test every year to make sure it isn’t degenerative. He is learning how to deal with sounds he hadn’t heard before. (At church last night he couldn’t believe they played bells!) He begins speech therapy (I had no idea he would need that either) next week and they are excited to see his progress, as am I. And funny enough, he is now interested in learning his letters, sounds, words, etc. It all makes sense; for how can you be interested in something you never knew existed?

I bring this story up for one reason. We are not perfect. Even if we have our children’s best interests at heart, we may miss something. It takes a true village to raise our children. If you do not have a village to help, find one. If your children go to daycare or summer camp, get to know their counselors. Ask them questions. Find out what your children are doing, and how they are doing. Talk to your children’s teachers next year. Get to know them, because they see your children more often than you do! And listen, even when you don’t want to. In a world that is so negative right now, I feel strongly that we need to support, build, and nurture each other and our tiny humans in order to make them the best they can be.


That Moment You Realize Your Child Is Suffering

Developing Perseverance

giving upI don’t get it. Can you help me? My teacher didn’t explain it. I forgot. This is stupid.

We have all been there. We have all heard each of these when our child is working on math homework. The question is, how do we get him/her to stop being helpless? Here are a few ideas to start with.

Listen to their frustrations. Then move on. Look. Being frustrated is okay. We don’t want to say it isn’t. But being helpless is not okay. This is a life lesson. Not everything is easy, but we don’t get to give up.

Don’t do the math for them. That only lets your child know you will let them off the hook every time.

Help them find resources and look at them together. Some questions to help you out:

  • Where are your notes from today? Let’s review them and see if there is anything there we can use.
  • What are you learning? Let’s look up some videos ( is a great site for video lessons, but if you just go to utube or teachertube you will find others) and see if we can relearn it together.
  • Let’s look at your book and see if there are any examples that might help us.
  • Call/Facetime/text a friend and see if they can assist you. (Research shows that study groups truly help all students in mathematics!!!
  • Email the teacher and see if s/he has tutorials to help. (Many teachers put up videos, the solutions, etc on-line. Find out if yours does!)

Above all, let them know that it is okay to not know everything, but NOT OKAY to give up. This is a biggie. Most math worth doing  takes time. Students assume that if they don’t get the answer right away, they must have done it wrong (or don’t know what they are doing and are not good in math). So not true! Help your child use resources available to be successful, but they need to do the work and put in the effort.


Developing Perseverance