There are challenges in your life as an educator that let you know you have really grown. Recently I had an opportunity to really challenge myself, learn, and grow.

Let’s set the stage.

- Let’s start with 71 fifth graders eagerly awaiting me like a school of pirañas.
- Let me decide to teach this on a Friday afternoon, before a 3 day weekend.
- I’ll time it so students have been on a morning field trip for half the day.
- I’ll choose two of most challenging topics that has not been seen by students before this lesson.
- Having chosen two of the hardest learning targets for the grade level, now I’ll present them both simultaneously.
- Oh, this is fractions and word problems together, and did I mention they haven’t seen either yet.
- Now, let’s add in some classroom disruptions built into the mix, so half the students will leave and come back in at random times for a play tryouts.
- The lesson plan calls for 90 minutes, essentially the second half of the students day.
- Did I mention there are 71 sugar filled 5th graders on the Friday afternoon before their first 3 day weekend in over 2 months attempting to tackle difficult material they haven’t seen yet…ok.

Now the stage is set for the challenges before me and I am excited about the opportunity. So what I have in my arsenal are three key weapons: 1. Notice Wonder 2. Numberless Word Problems 3. Relationships

My lesson starts out with a series of short animations (too fast in hindsight) showing the algorithm and a visual model for 5.NF.2. Students write a NoticeWonder statement, then pair share. Students will repeat this process four times, with the same videos (which is why I made them fast animations), each pass getting more specific with the content they are meant to pull out. I am testing if students can tell me how the algorithm works without me saying anything about it, and I am also testing if they can replicate the process with minimal instruction. I learned the animations were too fast to make this an accurate test, so I do not know yet.

Although I had a word problem to go through as well, as I was circulating and listening to student responses, I made decision to dive into their understanding of the algorithm. In general, we are attacking their understanding of fractional relationships with unlike denominators. Utilizing various visual models to aid this understanding, we had a great discussion about the various pieces, using pizza as an analogy because 100% of 5th graders love pizza.

Having students start with an agreement that two pizzas are identical, so this is our unit. Now the number of slices we cut the pizza into is our denominator, these are the equal sized groups. The numerator is how many slices we have left of the pizza. Students relate to this understanding because they have a context around it. The next question usually gets them, “Can we add these two pizzas with different sized slices together?”

After some discussion, the students agreed we could add them together, but we wouldn’t be able to fit them on the tray evenly since the slices were different sizes. Which brings context to why we need to find a common denominator, we’re just trying to make the pizza slices the same size. We can do this by cutting up the pizza slices from one size into as many slices as we made in the other and vice versa. For example, in our problem we had pizza A with 4 slices and pizza B with 7 slices, so each remaining slice of pizza A was cut into 7 equal sized slices and each remaining slices of pizza B was cut into 4 equal sized pieces.

We were at the point that around 65% of students were understanding the content of the above paragraph, and of that group 80% could tell us why the numerators also changed, and why the number was bigger. One student was rocking the denominator early, still had trouble with the numerator piece specifically, her strength is in the numerical understanding, not the visual model, so it’ll be interesting to bridge that gap with her. The great thing is you could see her making sense of the problem, and it bothered her it wasn’t clicking yet….I’ll be anxious to see what she uncovers.

Although, I didn’t get to the actual word problem, we had a wonderful conversation, and the students given the tremendous hurdles were highly engaged in the discussion. I was quite happy with the turnout, and I already know a couple of things that would make the lesson so much better. Five years ago, if you’d told me I was teaching a lesson with the setup mentioned, I’d thought you were crazy, but this is evidence of growth, maturing and understanding of how learners engage with content. All that to say, so much of this learning comes from being connected, both in my district and to my PLN, that make this a great learning experience.

P.S. My lesson in PDF format is here.