Yes, James. Fractions are hard, but they can be fun too!
I love my annual exploration of fractions with my fourth graders every spring. This is uncharted territory for them, as we intentionally delay introducing the concept of fractions until they have enough cognitive development to really appreciate and understand these strange numbers. I tell them from the start, “This is probably the hardest thing I’m going to ask you to do all year.” while I sip coffee from my 3 out of 2 people have trouble with fractions mug. We spend time thinking about what fractions mean, building fractions with manipulatives, making observations and looking for patterns. We look at equivalents to “benchmarks” like one-whole, one-half, one-third. All the while, building, drawing, observing, sharing ideas, asking questions and most importantly, letting my students set their course on this adventure.
After about a week of working with fractions, one of my girls asks today, “What about a fraction like eleven-twelfths?”
“What about it Alexa?” I ask.
“Well, it seems like you can get really, really close to one whole, but never get there.”
The rest of the class has been sucked into the intrigue by now, so I suggest we build all the fractions we can like what Alexa is talking about.
And then the magic begins!
One says, “She’s right, we’re never gonna get there!”
Another notices, “Look, the differences between the fractions are getting smaller!”
And, “Hey, even though the pieces are smaller, the bigger denominators are bigger fractions this time!”
After several minutes of playing around, I tell them what unit fractions are, and how we’re building numbers that are one unit fraction away from one-whole. Then it gets serious.
“Wait a minute, is one-whole a unit fraction?” and “Does this mean that ∞-1/∞ is really 1?”
These are the questions that get asked when your students are really thinking about the concept and they are really getting it. Pushing their understanding to the limits, joyfully, of their own accord.
To wrap things up, I asked them to think about fractions that were really close to one-half, but less than one-half and fractions that were really close to one-half, but greater than one-half. Now.This.Was.Fun!
Shouts from around the room, each trying to get closer to the mark than the other...
“Five hundred one - thousandths!”
I cannot wait until class time tomorrow morning. What uncharted territory will we explore? Only my students know. I look forward to the adventure.
Give your students room to play with concepts and the tools to do so, and they will dig deeper and learn more than any procedural instruction will provide them. Yeah, fractions are hard, but they’re really cool numbers too!