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.

2017-05-18 – 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.

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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.

 

2017-05-17 – Day 7 – Clothesline Math & Goodbyes

Yesterday we spent time making sense of the ideas of Clotheslines Math, and we were able to get a few quick reps in. Today, we dove straight in, students were broken up into groups of four, each person was assigned a job, and the students were tasked with placing the trig functions in their appropriate sequence on their number line. Students were given 15 minutes to make this magic happen

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I had one group finish early, which was perfect, they became the “experts” and I shipped them out across the “country” to troubleshoot groups where the sequence was stalled. Once the 15 minutes were up, groups verified their sequences with others, and with their “experts” were given another 2 minutes to confirm their sequence. Each group would use their device to take a picture of their successfully completed sequence, and then we tried this process whole class, randomly chosen people were given a tent, two students were holding our much longer class sized chord, and we tried to place the tents in a proper sequence.

So a couple of things that I loved about this process: 1) Students understanding of how to construct a viable number line is sorely lacking from establishing benchmarks to proper scale and this is a powerful way to build it; 2) The multivalued aspect of the trig functions were highlighted in context, so some students made this connection; 3) The periodicity of the trig functions were brought to light when we connected all of our group together, and what did they notice and wonder.

We were able to get to try this in 8th grade today, as well, but with different algebraic based tents. Students in 8th grade were much more accepting and understanding of the process (tents were integers) but struggled with the tents that were given as variables. Students had no problem placing m, 2m, and m/3 in a variety of orders. So we will be addressing this misconception in the next period. I am thinking of having students draw a distance, then draw twice that distance, and a third of that distance. Then we place the tents m, 2m, and m/3 on their number line and see where the conversation goes.

On another note, today was the last day of a content specific course in mathematics for new teachers and I wanted to highlight some of these pieces in our last class together. So we started with a warm up on the sheet placing various terms in order. Our random groups were given an envelope with 3 linear equations, highlighting various slopes and y-intercepts and three fractions and asked to place in the correct sequence.

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The teachers seemed truly engaged in the process, and the attending to precision (MP6) evident everywhere. After teachers shared their thinking and we compared, we talked about how this might be used in their content areas. I do not know if I facilitated bringing to light the flexibility of this strategy, but I think the teachers found some value in it as another tool in the trade. The evening was our last class together, as half of them will be graduating with their preliminary credential in a few weeks, and half will be doing so for another year but will be graduating to summer soon, so our theme of the night was graduation.

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As per our traditional sequence, we like to have a group photo to commemorate the evening by, and this one was no different. In the spirit of the class, I showcased a family fail photo, to prompt our discussion and as a reminder for myself, and we tried to take an awkward family photo together, and I think we nailed that result.

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It was an epic end to a great sequence of classes and I hope the new teachers were able to get as much from this as they gave my partner in this class. I hate to end this amazing post on a down note, but I felt the night went well, we did spend too much time on the “speed dating” portion discussing our use of a strategy from Teaching Reading in Mathematics (TRIM) with a problem from Fostering Algebraic Thinking (FAT) book. We didn’t debrief their assignment as well as I would have liked, and I don’t think I facilitated the connects between all the classes well. In the sequence of the night, time moved too quickly and trying to do too many things got the best of me. The part that really gets me is that it felt like we had put our hearts into this class, each night had a theme, we tried to make every moment purposeful, connected, meaningful and engaging, the teachers seemed to indicate they were picking up what we were putting down, but their feedback indicates more to the contrary than I would have expected. This is to say that no matter how well you dress something up if the content isn’t good, people will notice and will not connect to it. I am going to have to do a lot of reflection on this class and use these failures as opportunities to grow, learn, and question.