Berger- Student work week 5

These past two weeks we have been working with fractions. We have been teaching how to reduce fractions to the lowest terms, how to compare fractions, and how to add and subtract fractions with like and unlike denominators. A main components of these topics is knowing how to find factors and multiples of numbers. A lot of the students often confuse when they are supposed to be finding the factors and when the are supposed to find multiples to find the answers of the problems. In class today, we reviewed how to add fractions because that is what they were working on the past two days. We used today to catch up on all of the aspects of fractions we have been teaching to see where the students are at, what they understand and what they are still confused about. The first set of problems they were told to figure out where 6 problems that they had to write the fractions to lowest terms. In order to do this, the students were supposed to find the factors of the numerator and denominator and then find the greatest common factor, so that they could then divide the numerator and denominator by this common factor in order to provide them with their answer, in lowest terms. Many of the students began by trying to find multiples for both the numerator and denominator. I think this was because we had just done a few addition problems, with unlike denominators, so they had to find the multiples in order to find common denominators. 

I examined one student's work and saw that this was the case and when I asked him to explain what he was doing, he realized that he wasn't adding or subtracting fractions like the past two days. He had to think for a minute what we had done last week and at the beginning of the week.  With a little assistance he realized what he should be doing. The problem was to write the fraction 16/28 in lowest terms. So I continued to watch him and instead of writing all of the factors for the numerator and denominator, he divided them by 2, which resulted in 8/14. I asked him why he decided to do that and then he said, "well two goes into 16 and 28." I then explained that even though 2 goes in to both of those numbers, that doesn't necessarily mean that it's the biggest number that does, and it might not give you the fraction in lowest terms. I asked him to recall that we had said at the beginning of the week, if the numerator and denominator are both even numbers, then you did not reduce the fraction to the lowest term possible. He looked back at the problem and saw that 8 and 14 could both be divided by 2 again, giving him 4/7, which he said was the fraction in lowest terms. I told him that although he did come up with the right answer, I want him to write all of the factors for each number and then find the greatest common factor, so that he doesn't have to go through the process of dividing more than once. I showed him how he could have just done 16/4 and 28/4 giving him 4/7 right away. Throughout the next few minutes I came back and checked on his work and he was doing the work in the manner that we had explained, correctly.

My mentor teacher and I really tried to organize this unit in an effective manner for the students' benefit. The textbook had adding fractions a few chapters after reducing to the simplest form, and then mixed numbers came before addition and subtraction, and it just really did not make sense to us. So we re-organized the fraction unit in a way that we felt made sense. I think that we could have done a better job in realizing all of the little aspects that the students would need more work on such as finding factors and multiples. This is where a pre-assessment would have been helpful, because we assumed that the students were aware of these terms because they had been learning it for a few years now, according to the teachers and some students that brought in old notebooks. I think that the students were getting really confused with the idea of when to use factors and when to use multiples, so today, while they were doing workbook problems, I wrote key points on the board for when they should be using them and how to use them. I think that this clarified it a bit for the students, but again I believe that we could have organized the unit better. My mentor teacher and I were also supposed to go on to adding and subtracting mixed numbers today but realized that since many of the students are having a hard time understanding addition/subtraction of the proper fractions, this would not be a good idea. So, we spent all class reviewing the information from the past two weeks of fractions. I think this was beneficial for the students. Next week we will be going on to addition and subtraction of mixed numbers so I think what I will do is begin the class by asking them if they think we will need to find factors or multiples and have them explain why.