2017-09-25 Visual Multiplication of Fractions with Reducing

Recently, I was on a Sunday run when I received a compelling question I couldn’t wait to dive into. The question asked how would I teach the multiplication of fractions with reducing.

The teacher provided some background information to frame the situation. The students had been instructed on how multiply fractions and reduce. When the lessons were over, the students all showed they were competent in both skills on their formative assessments; however, when this teacher gave them a summative assessment, the shock of students’ performances afforded me this opportunity.

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To get started, I didn’t quite know if I understood what the teacher had tried to explain. Luckily the teacher shared images of the student work to shed some light on the situation. Being curious about the student work, without making any inferences was my first order of business.

Next, I thought if this was my student, what would I try with them, given where they are at?

The student’s work made me think a visual model might illuminate the concept, inferring from the student work might be one of the missing concepts.

If I’m going to a visual model, how might I represent this such as the student will tell me their #NoticeWonder statements?

The #NoticeWonder strategy is my go to when trying any learning experience with students. My mentor once said, “Never tell a student something they can tell you….” and creating opportunities for your students to tell you something about their learning is very powerful. I also created a video explanation of the visual strategy and an animation of the visual strategy that the students #NoticeWonder about.

Using the progressions for mathematics and comparing to the California frameworks, I wanted a visual representation that is both flexible and powerful that goes across multiple grade levels. Although, the use of the area model is a strategy students should be familiar with by the time they are done with second grade, the full power of this model may not be fully understood until much later. Utilizing it for how to decompose and multiply fractions seems a natural fit to build upon.

I am always curious when creating a lesson how it will go over with actual students, not just the idealized math lovers we all have hidden inside us. Presenting this lesson with some enthusiasm and, as Dave Burgess says, some sort of hook. I have a steak here that can be prepared so well, but when it’s cooked it gets ruined, so I’m thinking about how to hit that sweet spot of a juicy medium rare in terms of proper delivery. 

What are your thoughts? Would you try it with your students and let me know what changes you made to make it better?

Thanks for helping us all get better together.

2017-09-04 Numberless Word Problems

There are two things that I learned about toward the end of last school year that got me so excited I couldn’t wait to try them, Numberless Word Problems was one of them. One of my #eduheroes, Brian Bushart (@bstockus on Twitter), created this idea some time ago, and I was just learning about them. So, I wanted to get a couple reps in ASAP, and I was able to get a couple of reps in before the end of the year, and it confirmed my initial excitement.

With this school underway, I want to jump in early and often to get everyone on board with this idea, exposing all students to this opportunity and making it an ever growing area of powerful learning. On this journey last year, I was able to modify this into a sequence of learning events, where we start with a #NoticeWonder activity that builds the Numberless Word Problem the students create. Since students create the word problem, whether or not there are numbers is there choice, and it is so interesting what they come up with. The students smash their questions together to make a new question, and then they answer their question (or switch with another group and answer theirs) four ways.

Once the students have shared their answers and we’re all on board with the questions and answers, we compare our information to the state standards example(s). Students are always surprised that their questions are much harder than the state examples and think the state question is easy. Compared to previous times when given the state question, they typically shut down because it’s “too hard,” I’d say this is an amazing outcome.

Anyway, it’s still a work in progress and I’m super excited about it. Thanks Brian for sharing and making us all a little better.

2017-06-02 – Day 23 – Last Day

The combination of working on so many things, being pulled in so many directions meant the beginning of summer was especially important to pull back and refill. The last day of school with students, while I would miss our good times together, I have to admit, I was all like….


Especially considering we have an epic road trip planned to return us to the great northern reaches of this continent that I haven’t been to in over 16 years. So this summer….


….epic road trip is going to be amazing! I wish everyone a happy summer, I will be off the grid for most of that time, and be all like…



2017-05-15 – Day 5 – #Sketch50

I almost missed the journey, the idea is called #Sketch50 on Twitter and following various messages. I see the idea more like…


which forces you to…


And in order to do this, we need to realize…


Understanding that I would never spend 50 days drawing different ideas, but knowing that in order to stretch oneself getting in those reps is so important. The public display and daily demand cause one to formulate a habit around this idea. The result of this #sketch50 has extended to my blogging once a day until the end of school, knowing that writing, reflection, and expression of ideas through these various formats help us get better. With the terminus day 50 of #sketch50, I wanted to reflect on the journey, so the last 26 of my days are shown in the slide deck below (I’m working on getting all 50 into the deck). Love to hear your thoughts.