Before I start, let me just say that I CANNOT make the #sundayfunday blog deadlines. Like, ever. This is, like, two weeks late. However, better late than never!
Last week, I started my fractions unit with my 6th graders. My students come from all types of elementary school backgrounds, and their skill levels are all over the place. At the beginning of the fractions unit, we do three days of leveled stations, and I work with one group each day.
This year, working with the advanced group in both of my Math 6 classes, we got stuck on one of my favorite tasks, “Sum to One,” for the entire class period. Like, we never got to the activity I had planned. I had a ball. I got this task from Michael Fenton’s blog a while back and it can be accessed here: http://reasonandwonder.com/sum-to-one/.
We do this as a warm up, and the students reason through, as much as is 6th grade-brain possible, why we have found all the possible solutions. They were pretty quick to recognize that the highest fraction they could make was 1/2, and so that limited how large of a denominator they could make.
After they were sufficiently proud of themselves, we moved on to the next step of the task.
They jumped right in to this, writing solutions all over the white board. We are still new into the school year and the students don’t know each other well. However, they were applauding solutions, correcting one another, and building off the ideas of one another. I was so pumped, but I was trying to play it cool.
When it seemed to come to a lull, I challenged students to come up with solutions with denominators that I randomly threw out (i.e. 5, 10, 12). After we had several solutions up on the whiteboard, I asked them if they could find patterns in the solutions they’d found. This held their interest for about two minutes. In one class period, a student threw out that there had to be a limited number of solutions, so I challenged them to consider both problems (three unit fractions and four unit unit fractions) to see if they could determine the limit on the number of solutions. This intrigued some students, and some students…not so much. I also threw out the challenge of them finding the largest denominator possible that still created a feasible solution. This prompt really hooked all the students in both classes, so this is where we worked up through the end of class.
I did this task last year with some success, but not nearly as much engagement as I had this year. I also realize that I did this with both my “B” group and my “C” group, but my “A” group – the group with the least number of skills mastered – did not get an opportunity to do this task. Guilty as charged. While they may not have gotten as deep as quickly, they should could have engaged with this task and had the opportunity to rise to the challenge. Duly noted for next year’s lesson planning.
Full disclosure, I hate having to teach fractions, so this was definitely a bright spot in my unit!