We continued working on multiplying fractions this week and introduced dividing fractions on Tuesday. The students were relieved when this topic replaced working on subtraction because it has fewer steps to follow and overall, I think it is an easier concept to grasp. A few things that I noticed were that when the students are cross canceling, they get confused with which numbers the can cancel with one another. I think this is because they first have to cross cancel and then the next step is to multiply horizontally (numerators with numerators and denominators with denominators). Another common error with cross canceling was that instead of crossing out the given number and replacing it with the quotient that you receive once dividing both numbers by that common factor, the students would write the number that they are dividing both numbers by. For example after switching signs and getting the reciprocal, 4/5 x 10/2. The students would change both the 4 and the 2 to 2s. They would then change the 10 to a 5 and the 5 to a 5. By talking to individual students and explaining the correct way to do this method, I think that my mentor teacher and I clarified this process to most of the students. One last interesting thing that a bunch of the students were doing was that they were changing some of the numbers in the fractions to 1s. When I talked to a few students about why they were doing this, some of them said "well 5 can go into 7 one time". So although at first it may seem like a random act, they actually do have reasoning. They were getting cross dividing confused with long division, which is what we do at the end of the problem if it is an improper fraction. Overall, the students mostly understand how to multiply and divide fractions. They also seem to enjoy dividing a lot more than subtracting. One thing that we need to work on this week with the students is long division. We didn't realize that many students didn't know how to divide before coming into the 5th grade. Most of them are picking it up really quickly but we do need to focus on long division in the next few days. Tomorrow I plan on having the students work in their table groups (3-4 students) and write down all of the steps for dividing fractions. Then we will come together and make a class list of all of the steps. From there we will review how to cross divide, then how to do long division and finally bring it all together to do some independent division of fractions.
The questions that I have involve your basis for concluding that the students "understand" fractions or "enjoy" dividing. Although I am not disputing your judgement here, and although this is merely a short blog post, I think it is important to think about how / on what you are basing your evaluations. Again, this matters less in this blog post than it does in larger projects (like the unit plan or parent-teacher conferences). But try to think about what you are basing your conclusions on. This is important in the unit plan in the sense that you will want to make sure that your summative assessment lines up with your objectives and goals and that you have thought about what different results on your formative assessments might tell you about student understanding.
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