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.

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.

2017-05-18 – Day 8 – Rich Task Routines & Fraction Splats

One of the charges my district has taken on requires that we work toward improving math instruction at the 5th-grade level – this grade level has been identified as a severe turning point in the performance and mindset of learners toward mathematics. We are working on ways that will improve instruction and learning experiences so students feel differently about mathematics and themselves.

One of our approaches is incorporating rich tasks for our students to access. The Rich Tasks provide both a better math experience and promote a growth mindset in mathematics.

FullSizeRender

The process I am testing is trying to tease out if the students can make connections between their thinking and others. In addition to sharing their thinking and being able to perform some complex mental arithmetic with everyones’ favorite F-word, fractions. I was gifted with two extraordinary teachers that let me try this approach with the amazing Steve Wyborney’s Fraction Splats. I have had huge success in grades 3 through 12 with the fraction splits, so I knew that wouldn’t be an issue, but the questioning and format may be a challenge. The results shown in the video below show the comparison of previous Rich Task Routines with the new version. What do you #NoticeWonder?

Overall, the day felt very successful, the students seemed highly engaged in their learning, and sharing out their thinking. The valuable conversations and having students point to and demonstrate their thinking is huge. The connecting to other people’s thinking may need some direct instruction on, and multiple reps before students are reliably able to tackle this piece.

 

2017-05-12 – Day 2 – Guest Presenter Steve Wyborney!!

Our special guest today, Mr. Steve Wyborney, delivered a fun and interactive learning experience for my Integrated Math 3 course. The students got to experience a variety of wonderful questioning strategies, they were enabled to challenge their teacher and integrated deep mathematical thinking into the whole process.

Mr. Wyborney’s incredible sense of creating engaging and powerful learning experiences was on display today, challenging the students to think differently and to understand things in a variety of ways.

The learning was deep, the conversations were rich, and the time flew by, a perfect ending to a rather long week. On that note, I am also learning to use SnapChap to capture the learning, which is why I’m continuing this video sequence. I like that every 10 seconds you have to finish your thoughts, forcing you to be more concise and embeds the idea of practice perfect. I also like the idea of the silly filters, as it helps me get past the weirdness I feel when taping myself. Combining this with my desire to blog more, I’ve created a snowball of learning experiences for myself, and with Day 2 in the bag, I’m excited that I just might make it.