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.
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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.
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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.
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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.
Advancing New Hampshire Public Education 
I don’t think anyone of good will can find fault with this great teacher’s discovery of a more effective method of teaching fractions. Not in the least. And if the greater clarity and focus of the Common Core standards have aided in this discovery, hats off to the most recent effort to improve teaching and learning on a wide scale.
But please give teachers in general more credit for professionalism. The Common Core is not the light switch you often portray it to be, implying that teachers have been manacled in the darkness of past standards and only now have been freed by the light of the CCSS. If you had been observing good teachers over the past 20 years, you would understand that a light switch is clearly not an apt metaphor for what is more accurately a “fade-in” of better teaching as reflected in the ongoing interaction of research and classroom practice.
For example, look at the following and, as you read, guess when and where it was written:
“Problem solving is both a means of developing students’ knowledge of mathematics and a critical outcome of a good mathematics education. As such, it is an essential component of the curriculum. A mathematical problem, as distinct from an exercise, requires the solver to search for a method for solving the problem rather than following a set procedure. Mathematical problem solving, therefore, requires an understanding of relevant concepts, procedures, and strategies. To become good problem solvers, students need many opportunities to formulate questions, model problem situations in a variety of ways, generalize mathematical relationships, and solve problems in both mathematical and everyday contexts.”
A description of the Common Core? Well, yes…but it comes from the introduction of the Massachusetts Math Framework of 2000, which grew out of research recommendations going back years earlier. If one studies a crosswalk of Massachusetts’ standards of today and a decade ago, one will find not night and day but a progression of thought about how best to organize instruction to result in the kind of mathematical ability we’d like to see in our children. As the Massachusetts’ Framework of 2000 put it: “All of the curriculum frameworks are subject to continuous review and improvement, for the benefit of the students of the Commonwealth.”
Why is this point such a big deal? By placing the emphasis on a mere document and not on the ongoing inquiries of thoughtful educators, there is a great danger of what happens in many other circumstances when the essential inspiration for improvement succumbs to the mechanistic tools of standardization. In short, the life goes out of it, say what you will about how “enlightened” the new goals and strategies. The difference is that today, not only does the life eventually go out of it for teachers, but also the motive for improvement becomes fixed on market interests that have little to do with the value of learning fractions.
The most common comment I get is, “This is just good teaching,” which is a great comment on CCSS…meaning, so what could possibly be the problem. Just get over it.
Just put the emphasis on what good teachers do and have always done to the best of their ability — and not on the silver bullet of the CCSS – and I’ll get over it. Why, for example, do you think the CCSS has drawn such fire, especially from the right with a tendency to see governmental conspiracy, but also from the left with a tendency to see corporate collusion. Certainly not because of “good teaching,” which you could just as well have illustrated in how a good teacher taught fractions fifteen years ago. I know that you can’t get entirely away from putting a name on the latest round of standard-setting, but let’s at least be more humble about it. Do we really believe that we’ll see no further rounds in the relatively near future? The point I’ve been trying to make is that when the CCSS is made to seem responsible for the “good teaching” you observe today, it helps to create the illusion that something outside the schools and teachers that parents have grown familiar with – often with nostalgic reverence – has swooped in to roost and to stay just as long as it wants, or perhaps just until it can be driven away. So why do I not just get over it? The irony is that I’d like to see the CCSS stick around for a while and not get inadvertently driven away, and i say this with the intended wider scale of the effort in mind. Let’s remember also that preaching to the choir will eventually cause even the best of singers to “forget” how to sing.