I started out today's lesson with a "warm up that is also a hint." I wrote 2 and 9 on the board, and under that I wrote 7 and 8. I asked which ones were far apart and which ones were close together. I wanted them to be able to recognize a fraction like 1/20 has numbers that are far apart, so it is smaller than a half, and a number like 3/4 has numbers close together, so it's greater than a half. In the past when I asked my class "what do you notice about the numbers in the fractions," they would struggle, looking for odds and evens and other coincidences that weren't actually moving their thinking in a direction that would help them with this concept. With this warm up, they actually got the concept halfway through the lesson, and they OWNED it. They felt like they were discovering this on their own. Really powerful!
This was even after I made a joke and asked, "Which numbers are close together, and which are far apart. Not literally."
They thought it was funny.
The next step, after identifying those fractions that were equal to a half, was to identify fractions that are greater and smaller than half. I gave them another chance, and allowed students to get manipulatives to test out a few of the fractions on the page. They did a better job with the materials this time, maybe because their product was an individual one instead of a group one.
So once again, I asked students to memorize two fractions, this time one that was greater than a half and a fraction that was less than a half, write them on a poster and randomly stick them on the poster. Once again, I was able to rapidly sort them and once again, I asked them to figure out how I was able to do it. And once again, they made some impressive observations that I was able to commemorate in an anchor chart. They each copied their favorite method, and went back to work on their papers with a new found strategy and way to explain how they know what they learned.
As promised, I posted the coloring page they started the day before for you to download for free for a limited time.
Here are the finished results!
The kids had their quiz on fractions greater than, less than, and equal to a half, in preparation for moving on to, well, the rest of fractions, haha. Luckily we still get to "limit" the fractions that our fourth graders are exposed to. For example, 7ths, 9ths, 11ths, and pretty much anything over 12ths are not in the CCSS. That takes a lot of the pressure off of focusing on the algorithm as the only tried and true method of finding an equivalent fraction. I'm loving the more exploratory methods I'm "allowed" to focus on this year instead. There will be plenty of time later to multiply the numerator and denominator by the same number. Because for now, they seemed to deeply understand the concept of half, greater than half, and less than half; they all passed their quiz, woo! Next week I might post the quiz as a freebie too, but it's also hand written.