11. Compare and order fractions

Big Ideas:

1. Students can learn about math and their world through individual activities as well as social interaction
2. Mathematics is something we use in our everyday lives.
3. Students can learn according to their level with differentiated, enriching activities that are learner-centered.
4. The world does not always come in "wholes."
5. The same fraction can be represented in many different ways.

Objectives:

1. TSW put fractions in order from a mixed list both least to greatest and greatest to least.
2. TSW find equivalent fractions.

Multiple Intelligences:

1. visual/spatial- manipulatives, picture form of fractions

2. mathematical/logical- reducing fractions, comparing fractions
3. interpersonal- work in groups to practice the skills and they must interact in the assessment

Materials: markers, chart paper, overhead projector

Grouping: whole class instruction; work in groups of four when practicing skills, become partners in assessment

Universal Design:

ESL/EC: each time the fractions are compared, they will be shown pictorially on the board; there will be stronger students in each group to help when students are working on problems

EC: the assignments in the cooperative groups will be recorders for those students who are having more trouble with the process; they will get practice by writing out the process and they will not be passive onlookers in the group

Procedures:

1. I will first instruct the students in the process of finding a common denominator and will write the step-by-step procedure on the overhead.

1. draw a picture of both fractions to guess which fraction is larger
2. write a list of multiples for each denominator
3. circle the least common multiple
4. make equivalent fractions using the least common multiple by multiplying both the denominator and the numerator by the same number
5. compare the fractions with like denominators and choose which is greater; decide which amount you would rather have and why

1. I will model this process with 4/9 and 5/12.
2. I will leave the overhead example there for students to use as a reference.
3. I will assign a role for each person in the five groups. There will be a recorder, reporter, monitor, and drawer. The drawer will make the initial drawing to allow students to make an educated guess on which amount is bigger. The recorder will write the rest of the process. The monitor will make sure everyone is participating and everyone understands what is going on. The reporter will be responsible for explaining the answers and anything the group has written.
4. I will wander around the classroom putting "tokens" in the group cup if the students are working well together (this is part of Ms. Bateman’s management systems). I will also look at the progress of the work and ask questions to make sure everyone is engaged.

GROUND RULES for Groupwork

1. Everyone must perform their assigned role.
2. Each student in the group MUST understand the material once you are done.
3. Everyone must be nice to one another. No name-calling. You have to be patient!
4. Groups where everyone is contributing, everyone is being nice, and all the answers are well-written out will get a treat!

The Problems:

(these problems are written on a piece of chart paper at the front of the classroom)

1. The candy shop owner wants to know if you would rather have 4/7 or 3/5 of a pound of chocolate!

2) The fresh juice maker wants to know if you would rather have 1 4/9 or 1 1/3 cups of prune juice!

3) The baker wants to know how much cookie dough you want. Do you want 2/5, ¾, or 3/10 of a pound?

 Assessment:

Most of the assessment is postponed until day 4 because they will be working individually on the process and then there is a class activity to make sure all the students are understanding. During this lesson, there will be some assessment though. As I go around between the groups, I will listen for the input of the students. I will also ask questions about why they are doing certain things. The finished chart paper will be something I can physically take with me to look over afterwards.

Reflection:

I was generally pleased with how this lesson went today. The students liked having a particular role in their group and they also enjoyed using the chart paper. I needed these positive aspects to counteract what they felt to be a boring process of finding a common denominator. I talked to my dad, who is now a seventh grade teacher, the night before my lesson. He reminded me of the need for ground rules for the groupwork. I felt that by addressing what I expected of them and being able to use Ms. Bateman’s management system of giving tokens for positive group work really aided the success of this lesson. I also felt that by a weaker student being the recorder really helped them understand the process better. The other students were able to guide them through the process without them having to be singled out as not understanding; it was simply their job to write down what the other students were sharing. If the job had been given to some of my stronger students, I think they would have gone through the work without involving the other students. My strongest student, who is significantly ahead of all the other students, started recording the information when he became frustrated. I went over to the group and said that I expected a different recorder and he explained how the recorder didn’t understand. I expressed that instead of taking over, the process would have to be explained to the recorder. When I returned, they were working much better as a group. The strong student was peer-teaching rather than taking over.

The other problem with the group work was that there are more weak students than there were recording positions. In some of the groups, as I walked around I switched roles for the third problem so that another weak student would get the opportunity to write. The group work took longer than I expected, so I had to postpone further activities and assessment until tomorrow. I think they now need to go through the same process individually. I could tell that the "lightbulb" had gone off in many more students today while walking around between the groups. They were able to understand the system since it was broken down into steps for them. I think they also enjoyed being able to draw the fraction and guess which was larger. Tomorrow I will address with them, why drawing a picture is a good beginning but cannot be trusted completely. The only way they can be sure one fraction is larger is by making common denominators.

I also found through working with the individual groups that a misconception needed to be addressed. Many students want to multiply both fractions by the same number rather than keeping the same denominator. I will address this misconception when I begin tomorrow’s lesson. In the worksheet, I will also have the first problem filled out with some "fill in the blanks." The guidance of the blanks will make sure students do not just multiply both fractions by the same number, but use the common denominator.