Students Work to Manipulate Fractions
In order to demonstrate how I handle a unit, I decided to showcase a math lesson, and how I assess students work. This first paper is how I started the students working with improper fractions. We started a chapter on fractions, so the class has had experience with fractions before this concept was started. My goal is to have them be able to add and subtract mixed number fractions. This first paper is just so they can get used to changing improper fractions in to mixed number fractions. The emphasis was more on getting how to change the fraction and not so much on making sure the fraction will reduce. You can see that when you look at problems 8 and 14. This particular student seemed to understand the concept very well.
This next paper is after I had introduced adding and subtracting mixed number fractions. A majority of the class at this point has shown that they are able to change improper fractions to mixed number fractions. They started to understand that when you add two fractions together and get an improper fraction you must add that improper fraction to the whole number in the problem. They can also see why you are supposed to borrow from whole numbers in order to increase a fraction amount to be able to subtract fractions in which the first fraction is less than the second. Again, my emphasis is on the ability to work with this concept, and not in reducing fractions. I should note that the class in its entirety knows how to find equivalent fractions, therefore I do not believe that reducing will be a problem when they are totally comfortable with all that they are currently trying to learn. The problems in this paper comes entirely from simple multiplication or subtraction errors.
At the end of each week I collect the classes math journals. Throughout the week I make sure that they work in their journals at least twice. I do this for two reasons. The first reason is so that I can get a grade from an area that I believe they should be able to work with somewhat ease. I am not trying to make it too easy, but if we have been working on finding equivalent fractions, and I know that they should all be that far, I will have them do a page in their books that highlight that discipline. The second reason is that I want to be able to see how each student is dealing with the new math concept for that week. This is a part of their journals that I grade, but do not give a score. It is a way for them to go through what I have written down and see where they need to work. It is a lot of work to do that for each classmate, but I have gotten excellent feedback from my pupils. They like seeing that my red pen is not just for negative marks. It is there to help them grow. I also leave a note for each student trying to encourage them by letting them know where their strengths are, and then what they can work on to get better. Here are examples of a couple of journal entries.
You should now be able to see how I am asking them to start reducing their work in to its simplest form. They have been dealing with this same area of curriculum for a while, and now that I think that they are getting much more comfortable with it, I am asking them to go just a little further to strengthen their answer. After the chapter is over, I give the class an exam to see where the class is as far as skill is concerned. When you look at the second question, notice that this student was able to see that 6/30 is equivalent to 1/5 without having to write the problem out.
Not everybody in the class is as successful as my example here. I must say though that I did have more than a couple of students really grasp on to what I was teaching them, and how I was teaching them. One student in particular really needed all the help that she could get. One day, after instructing the class on their next assignment, I noticed this student walk up to turn in her paper. For a second I had thought that she had just gotten frustrated with trying to subtract improper fractions, wrote something down real quick, and turned it in. As it turns out, she got it, and was able to do all the problems with no errors. Still one of my happiest moments this semester.
