NCSOS:

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."

Objectives:

1. TSW put fractions in order from a mixed list both least to greatest and greatest to least.
2. TSW find equivalent fractions.
3. TSW use the manipulatives to represent fractions visually.

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

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

AIG/EC: I will give the assessment index cards according to ability level; the fraction will be more difficult for the advanced students; when students are trying to compare the fractions from least to greatest strong groups will be interspersed

Procedure:

1. I will review the previous lesson by asking questions about what we covered. A) What are equivalent fractions?

If we wanted to find an equivalent fraction for 1/3, what would we do? If we had the fraction 4/8, how could we find equivalent fractions? We can find the GCF to show 4/8 in its simplest form. I will ask a student to list factors of 4, then another student to list factors of 8. Another student will be asked to choose the GCF. I will divide both the 4 and the 8 by the GCF. I will write this whole procedure on the board.

What did we do last time to decide which fraction is larger?

2. I will write on the board " ½ , 6/8." We need to decide which fraction is the largest. How do they compare?

1. Last time we used the fraction circles to help us compare fractions. Now we are going to use least common multiples to help us compare. When we don’t have fraction circles around, we can use this method. Sometimes fraction circles don’t have the fraction we need.
2. We have two different denominators (bottom numbers): 2 and 8. We can list the least common multiples for 2 and then 8. (have a student give 4 multiples of 2 and then 8). What is the least common multiple? (8)

***this whole procedure will be written on the board

3. I will then explain how we are making an equivalent fraction for ½. Since the common denominator is 8, 2 had to be multiplied by 4. Now the numerator (top number) has to be multiplied by 4 as well. I will draw a representation of the fractions on the board as a way to check. I will ask students to look at their fraction circles to make sure ½ is equivalent to the new fraction we made and how it compares to 6/8.
4. I will follow the same procedure with {5/6, 2/3, ¼ } (add a question if it was 2 5/6, 2 2/3, and 2 ¼ ? and then compare {10/3, 7/9}.
5. I will repeat the procedure with more examples depending on how well the students seem to be understanding it. {4/9, 4/5, ½, 5/12}
6. I will then have problems on the overhead. I will ask them to work on them in their groups. Students will share their answers and reasoning.

1. Find 2 equivalent fractions for 1/5
2. Compare 2/4 and 3/6.
3. Compare 2/3 and 3/7
4. Compare 5 1/5, 5 1/3, and 5 4/15

Assessment: (postponed until later in the unit due to time constraints and the students having difficulty with the concepts)

1. I will introduce that everyone will receive an index card with a fraction written on it. It is their job to think of many equivalent fractions by using fraction circles or paper/pencil method.
2. I will give an example if I was given the fraction 1/8 what I would do and then 15/25.
3. I will hand out the index cards to the students (I will give a specific card that I have already designated to their ability).
4. They will search for their partner after they have thought of a number of equivalent fractions.
5. The students will announce to the class what their equivalent fractions are and explain how they know this is true.
6. I will ask the pairs to put away one of the fractions because their new job will be putting the fractions in order from least to greatest.

Reflection:

I felt my lesson went pretty badly today. I was disappointed in the fact that the students did not seem to make a connection with the use of the least common multiple with finding a common denominator for fractions. After I had explained how to go through the process of finding a common denominator, I looked at their faces and I could tell it just wasn’t clicking. I felt it might partly be because they needed to be more active; I thought the direct instruction might be draining them. So I moved on to the part of the lesson where they would work together on solving the problems. From the pre-test I gave, I knew that there were students who had experience with comparing unlike fractions. I thought the intermixture of the students would allow some peer-teaching. Instead the students are too focused on getting their work done. They did not work amongst each other as I have in math classes before when we were allowed to work together. I did not realize they lacked experience in this atmosphere. The students were also rebelling against having to work through such a long process of finding the common denominator. They wanted to just "eyeball" the fractions to decide which was larger. I did not do the assessment activity because the group work had become assessment enough. I went over the answers and how to arrive at the answers with them. So instead of continuing any further today, I decided I would need to revamp my approach for tomorrow.

I think my new approach will have them working in groups, but this time there will only be one recorder. I think this will promote them actually sharing information with each other. Also, I plan to make it a step-by-step process that must be fulfilled to compare fractions. They will have to complete all the steps rather than just stumbling upon the answer they feel "looks" correct. I also need to incorporate a real world idea to comparing the fractions. This lesson plan lacked that aspect. I think when they compare the fractions for tomorrow it will be amounts of different food or drink. (Would you rather have 1/3 or 2/15 quart of plum juice?)

Even though, I struggled through the lesson today, I think I did a good job at interacting with the students. I asked them questions to explain how they solved problems rather than accepting just the answer. I also appreciate the support you and Ms. Bateman gave me. It was disheartening after my first lesson going so well, to see my second lesson be unsuccessful. You both gave me some helpful feedback and reassurance to prepare for another day!