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.

Screen Shot 2017-09-24 at 4.01.41 PM

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.

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