## Comparing and Ordering Fractions

### Brenda LazarusColleges and Universities - Florida

#### Description

Students are introduced to the comparison of fractions and the ordering of fractions.

#### Objectives

The student compares and orders commonly used fractions, including halves, thirds, fourths, fifths, sixths and eighths, using concrete materials.

#### Materials

-Computers with Internet acess
-Projection device
-Poster
-Paper
-Markers
-One set of manipultive fraction parts for each student
-Paper Fraction Model (See associated file)
-Teacher set of fraction parts that can be displayed on a projection device

#### Preparations

1. Gather needed materials.
2. Arrange for computer availability on day 2 of lesson).
4. Familiarize yourself with the website and the contents of the Identifying Equivalent Fractions segment and the practice activities on the site.

#### Procedures

Pre-requisite: Students should have already been introduced to basic fractions and combining basic fractions with common denominators.

1. Introduce the activity with a brainstorming activity. Ask: What are some everyday uses for fractions?

2. Record responses on chart poster paper.

3. If students do not give examples of everyday fractions that make use of comparing fractions and equivalent fractions, add some examples yourself, for example, cooking, doubling a recipe, making something from wood, and sewing a curtain.

4. Use the overhead projector to give students problems, such at 1/2, 4/6, 1/3, 3/5, 3/4, and 2/8 with the fraction pieces.

5. Show students the following sets: 2/2, 3/3, 4/4/ 5/5, 6/6, 8/8 with manipulatives on the overhead projector. Start from whole to part.

6. Next, show students 1/2, 1/3, 1/4, 1/5, 1/6, and 1/8 in order. Ask the students: What do you notice about the pieces? (Elicit that the larger the piece, the smaller the denominator or a similar concept statement.

7. Next, mix up the parts starting with just 1/2, 1/3, and 1/4. Ask students to choose the same pieces for themselves from their manipulatives and place them in order from the largest to the smallest fraction.

8. Show students 1/2 piece, two 1/3 pieces, and three 1/4 pieces. Write out the fractions you have created as a model for the students.

9. Ask the students to choose the same pieces for themselves and place them in order from largest to smallest fraction. Ask them to write out the fraction they have created on paper.

10. Let the students work alone, or with a partner, to create some similar problems on their own.

11. Students may move from concrete materials to the paper fraction model activity at this point (download from attached file). Students arrange the cut pieces on their desks.

12. Hold up one piece and inform students that because there are twelve pieces, one piece would represent 1/12 in a fraction. Place it back together to make the whole again.

13. Then ask the students what could be taken away to make 1/2 of a whole. Have volunteers come to the overhead and make that happen by removing six of the twelve pieces.

14. Demonstrate to the students by pulling the pieces apart and together from each other slightly that 1/2 is also equivalent to 6/12, 3/6, etc.

Day 2
1. Locate the Website AAAMath (see Weblinks)and save it on your desktop.

2. Go to the section of the Website on Equivalent Fractions and use the section Identifying Equivalent Fractions to review the concept of equivalent fractions with the students.

3. Go through the Equivalent Fractions Activity with the class to model how to use the site.

4. Ask students to give their responses as you work the problems.

5. Encourage students to use their sets of manipulatives to help them solve the problems.

6. Have students work in pairs, or by themselves, to do the practice activities on their own.

7. Demonstrate the use of the paper fraction model to the students and have them create some of the equivalent fractions and comparison of fraction problems that were worked on in part one of the lesson.

#### Assessments

It is important to monitor the students' use of the manipulatives early on to ensure that the students are correctly making their models with the manipulatives and writing the abstract numerical fractions correctly.

After the demonstration and practice activities, ask the students to take out a piece of paper and write the answers to ten fraction problems shown on the overhead using concrete materials.

Circulate and formatively assess students as they use the technology tools. Provide assistance for students who are experiencing difficulty and monitor accordingly.

#### Extensions

The length of this activity will depend on how many computers you have available to you. Day two may be set up as a learning center if you only have one or two computers. It could be a whole group activity if you will be using a computer lab for this activity.
The lesson can be extended through the use of the website to progress as student understanding of fractions increases. The next section after comparing fractions would be converting fractions.