My students don’t understand fractions. They hate them, they don’t get them, etc. They know plenty of the “rules” but they don’t why they’re doing anything or how it actually works. We’re currently in the midst of Number Sense, and this is how we’re doing fractions. A huge thanks to my sister for her work on this individually and with WISME and CCLM in Wisconsin (for, um, fourth grade math). I’m not comfortable posting the powerpoints here, but am willing to share them.
Fraction Screener. 20 minutes to mostly model fractions in various models, representing things like sharing items equally, sharing items with a remainder, equivalence and partitioning.
Start fraction strips. We cut a rainbow of paper strips (9 colors), as well as spare “practice” strips from scrap paper (yay! Another use for all that blank-on-one-side mental math!) My sister said to cut waaaaaay more than you need, and it still wouldn’t be enough. True. I did and it wasn’t. I asked the students if they could work on folding for homework, and they gamely said yes. [If you do something like this: no writing on the strips, with the exception of blacking in the fold lines to make them easier to see/count. That’s how you find which one is which–counting, not looking at a number.]
While some students made a lot of progress over the weekend, many of the students came in Tuesday with several still-flat strips. We walked around and helped (and so did some of the already-finished students) and I had some very eye-opening conversations. “I need help with ninths.” “Ok. …any ideas which strip ninths might have a relationship with?” “….eighths? tenths?” and the like. Same thing with tenths. This is an on level ninth grade math class, and if anything my students have impressed me so far both with their ability and their willingness to try things. I don’t think this is unique. My students aren’t the only ones dying to blindly multiply by the other denominator ad nauseum because someone told them to.
We took a couple quick pauses in here for:
- How many numbers is a fraction? (Consensus: probably two. Bizarre: the two kids who said “something else”)
- How many folds did you make on each strip?
After that, we had the students fold each strip so that one unit was showing. We used the phrasing, “One share of size one-half” and so on, first with single shares, then moving into fractions like 3/4 (way harder to say–try it! Its tongue-twisty!). I tried to stay away from the technical language of numerator and denominator because I felt like students would be more likely to approach this in a new and different way (as opposed to multiply-all-the-things) if they were using different language.
Then we moved through some practice problems having students fold the strips and use them to represent and then talk about different comparisons. Some other discussion worked its way in there nicely, such as when one student said that more shares is bigger and was paused to develop some counterexamples.
I had already done this in my Honors class, and the show in Honors went something like this:
Do three comparisons using fraction strips. resist models. get annoyed. everyone’s frustrated.
This was a lot better. Students are still uncertain, but are trying their fraction strips, willing to trust us and hopefully ready to summarize comparison rules tomorrow (we’re calling it the Big 4).
A few notes on this and the posts that will follow: I’m not going for how-to-compare-every-last-fraction you can make up. I want my students to understand that thirds are larger than fifths because a unit is being split into equal pieces. I realize sometimes, you do need to multiply. But a lot of the time you don’t, and a basic comprehension of a number as being closer to 1 or 0 would go a long ways.
Do you teach fractions? Do you get annoyed when your students resist what you want them to do? Have you ever folded fraction strips?