Here’s a Massachusetts teacher comparing the MA standard for teaching manipulation of fractions to the equivalent Common Core standard. She discusses the specific standards and how the improved Common Core standard changed her teaching for the better.
In the years before the Common Core was adopted by Massachusetts, I used direct instruction to teach operating on fractions. Specifically, I taught dividing fractions only using the standard algorithm. I would present the steps to divide fractions, as a class we would come up with a way to remember the steps (KCF- Keep, Change and Flip), practice as a group, and then students would spend a day or two proving they were proficient with the computation. My students were masters of precision, rulers of proficiency. But, my students often struggled to determine if a word problem inferred division because they only had practice computing with fractions, and not understanding or applying division of fractions. The picture of the assignment is from a classwork I gave just a few years ago.
Prior to shifting instruction towards the Common Core I noticed that my students never fully mastered division concepts. They were unsure how to set up or read division expressions, cannot determine the dividend or divisor in a problem, and cannot differentiate between the types of division problems. Overall, they had a very narrow understanding of division.
Knowing this, my students now spend more time looking at various types of division word problems.
I was very nervous when I first introduced modeling division of fractions using visuals. Having taught strictly procedure in previous years, this was an uncomfortable change for me. But now, it completely makes sense, and gives students who struggle with precision an access point and provides all students a way of understanding what division of fraction accomplishes and how it works.
I am excited that the Common Core is a chance for me to improve both my teaching and help my students truly “get it,” rather than just “doing it.” Students can now not only use the standard algorithms to perform operations with fractions, but they understand how it works. I have found that making these moves to address the Common Core State Standards pushes students to be persevering problem solvers, compute accurately and efficiently as well as understand what they are doing.
see the whole post at Division of Fractions Before and After Common Core | Transitioning to the Common Core.