After we wrapped up our summary of how to compare fractions, we moved in to equivalency.
Everyone unfolded all their fraction strips and started finding where they had matching folds. By this time, everyone was pretty clear on how to use their strips and has a better understanding that all of our strips are the same size for a reason. After about thirty seconds, we choose one volunteer to tell us one match they had found. They picked /5 and /10 and the class helped list every fraction that matched on that list. From there we introduced equivalent and had the students spend about 15 minutes in their groups using their strips to list as many matching fractions as they could.
After all of the resistance to this kind of work in my Honors class, this class’ attitude was really refreshing. Neither of us saw any lists of multiplied numbers; they really worked with trying to find matching pairs visually*. We listed a few more on the board at the end of the time, and then go into defining equivalence and multiplying by a whole with any factor.
Then we introduced some other models. I really struggled with when was the appropriate time to do this–I didn’t want to tie students to the strips, but I also didn’t want to have so many things going on that students couldn’t focus on the important conceptual understanding. Ultimately, I decided to put it here, after comparison and wrapping up equivalency. We first did tape diagrams/fraction bars, and then moved on to number lines. We did a little the day before around partitioning number lines, but I saved most of it for today. Its definitely harder to work with eyeballing your own partitions, so we actually first flipped our notebooks sideways so we could make an 8″ + long line that worked with the fraction strips. It was a nice bridge between using something that was already the correct size (the strips) and emphasizing that the placement on the number line needed to be accurate.
I’m out for Day 4 at a training, but hopefully they’re doing their best at ordering fractions on a number line. (Although I already am thinking we could have done better by very intentionally choosing fractions that all use the same partitions for more problems to really get into that idea before making them need several different kinds of partitions (/5 and /8 on the same line). There’s always next year!
How do you help your students order fractions? Any ideas beyond “multiply all of the things”?
*I don’t have any problem with multiplying by a whole, but most of my students don’t have any idea why they’re doing it or what it means.