Which is bigger--1/2 of 12 cubes or 1/3 of 18 cubes?
I had the students glue the prompt into their notebooks and to decide on an answer and try to "prove it" with words, pictures, or by modeling.
I walked around to snoop, and I was a little surprised at what I saw. About 1/2 my kids (1/2 of 22 for those who are really in the fraction zone) got it instantly in their heads. The other 1/2 didn't even seem to know where to start. I asked the students to self-select groups--if they wanted help, they should join me up front in the room and if they were confident, I asked them to pair up and to try to write this type of problem for each other.
When I had my group, I poured out the cubes in a pile and we spent some time modeling this problem and talking through it. We reviewed key concepts and terms from the past few days and then worked for a while "telling stories" along this same line. "Which would be more--1/2 of 16 M&M's or 1/4 of 20?" and so on. Gradually, through modeling, more and more students left the group to go work with a partner to try more.
After a while, it was time to move on--it was Friday after all--so I decided to treat them to some edible manipulatives!
|Math is always better when it is filled with artificial colors and flavors, right?|
|Notice the "What fraction of your Skittles are brown?" This REALLY tripped them up! Even my first-ones-dones struggled with what the answer to that would be. Some even tried to count the purple ones as browns!|
|As the problems got trickier, a few students needed to pull out cubes or other counters to model.|
We are definitely in a better place with our fractional understanding--but a few students are still really struggling with the idea that if 1/4 of 20 is 5, 3/4 of 20 is 15 so next week we will do some more work with that. I did introduce a "drawing model" to some students--next week I will expand on that. I do think we are clear that a "whole" can be a "thing"--like a pizza, a pan of brownies, or a piece of paper but that a "whole" can also be a "whole bunch" or a set. More next week!
I did include the Skittles fraction sheet if you are interested. . .
This blog post is now a part of my comprehensive fraction unit available by clicking the image below. Hundreds of teachers have now used it to change the way they teach fractions!