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- picture form of fractions

2. mathematical/logical- reducing fractions, comparing fractions, finding equivalent fractions, finding the least common multiple
3. interpersonal- they must interact in the assessment in both pairs and then as a whole class to order the fractions from greatest to least
4. bodily/kinesthetic- the students will be physically lining up from greatest to least in their assessment

Materials: worksheet, overhead projector, index cards

Grouping: whole class instruction; individual work, become partners in assessment

Universal Design:

ESL/EC: the first problem on the worksheet will have the steps written out with blanks to fill in (then the remaining problems they will have to fill it out fully)

EC: I will address misconceptions at the beginning of the lesson to avoid further confusion

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

AIG: Students who finish the worksheet early will have the option to use dominoes; they can pick 2 dominoes at a time and make their own fraction problem with them

Procedures:

1. I will use the overhead I used yesterday as the sample way to find a common denominator and explain to students that as soon as they find the new denominator to set up both equations immediately "2/5 = ?/15 and 1/3 = ?/15." Students will then know they are not supposed to just multiply both fractions by the same number. I will tell them NOT to multiply both fractions by the same number, they will be different numbers. The denominators are the same, not the number you multiply by.
2. I will hand out the worksheet with the first problem guided with blanks. I will explain to students that they will be expected to show every step of the work as they were yesterday in their groups. I will circulate the room to look for any problems and to answer questions.
3. I will go over the last problem with the class doing the step-by-step process for reinforcement. I will ask the students to guide me through it. What do I do next? What number am I using to multiply the numerator and the denominator? etc.

Assessment:

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 think the students needed individual practice comparing fractions with the same process we had used the day before in groups. I was able to work with students on individually as they worked on the worksheet. The worksheet was also for documentation of them learning to compare fractions. The first problem that was already laid out for them really guided them through the process. Some students still struggled to make the transition in number two, where they had to do the whole process by themselves. I could have made smaller transitions between each problem by slowly taking away one guided step at a time; universal design might have been met even better by slowly taking away the steps. Once I explained to some of the confused students individually what I was expecting them to do, they were able to move on through the rest of the problems with ease.

I think they enjoyed finding their equivalent fraction after having to do the worksheet. They were contrasting activities and allowed different levels of energy. Tomorrow, I will not be able to teach because the students will be involved in so many specials. Instead, I will be developing a computer program to use during my center time during the last lessons I teach. Mr. Cain is the technology specialist at North Graham and he has agreed to help me make a program. I was really pleased at how willing he was to help! On Friday, I’ll be going in to teach my first lesson on adding fractions with unlike denominators.

Which fraction is the smallest? Go through steps a, b, c, & d with each problem.

1. 2 1

d) which fraction is the smallest?

2. 4 3

6 , 5

3. 5 3

*4. 10 7 (you don’t have to go through steps a-d if you can explain why

3 , 11 one of these fractions is obviously smaller)

5. 2 5

7, 11

6. 11 9 4

12 , 10 , 5

7. 4 4 1 5

10 , 5 , 2 , 12

8. Arena, Rolando, and Carissica are running a relay! Arena will run 2/5 of the distance. Rolando will run 4/15 of the distance. Carissica will run 1/3. Arrange the relay team in order from shortest distance to longest distance.