## But That's Not FAIR!

### Barbara Johnson

#### Description

Students solve problems using fractions through hands-on activities and appropriate literature.

#### Objectives

The student uses concrete materials to model equivalent forms of whole numbers and common fractions.

#### Materials

-Louise Mathews. GATOR PIE. Sundance Publishers, 1995.
-Paper plates as thin as possible (2 per student with extras)
-Scissors
-Markers or colored pencils or crayons
-Round, individually-wrapped snack cakes (one per student)
-Plastic knives and closable plastic bags (for cakes)
-Computers to access online Student Web Lessons--Fabulous Fractions and Flowering Fractions

#### Preparations

1. Secure a copy of Louise Mathews' GATOR PIE.
2. Purchase snack cakes and plastic knives for each student.
3. Gather supplies and have the centers ready with materials and instructions.
4. Check computer connectivity to access Fabulous Fractions and Flowering Fractions, online Student Web Lessons available from the Beacon Learning Center.

#### Procedures

Note:
This lesson requires some prior knowledge for students. They should have been introduced to fractions and understand the terms, numerator and denominator.

Summary of the book, GATOR PIE: Two alligators, Alice and Alvin, find a pie in the swamp. They decide to divide it and are pleased to see how much they will each receive. An alligator with a nasty look comes out of the swamp and demands pie, so they have to cut it into thirds. The story progresses with more alligators coming out of the swamp and demanding part of the pie. Alice divides it into fourths and then eighths. Dividing the pie is making each slice smaller and harder to divide equally. When alligators continue to come out of the swamp, Alice finally has to divide it into 100 pieces. She is worried they won't all be the same size, so Alvin jumps up on the table and tells all the alligators to pick their own piece. There is an awful fight because the pieces are not equal. While the other alligators are fighting, Alice and Alvin grab the pie and run away to share the pie equally with fifty slices or half of the pie each.

Procedures:
1. Tell students that they will complete three workstations after a whole-class introduction today that reviews fractions and equal parts. Briefly explain all three stations, divide the class into three groups for the rotation, and review class rules for working in stations.

2. Introduce the lesson by asking students to demonstrate and predict in their math journals using the following prompts. (Print the prompts on the board or the overhead. Encourage students to use complete sentences.)

--Draw a diagram to show how you would you divide a pie for 2 people, 3 people, 4 people, and 8 people.
--Predict what will happen to the pieces of pie if you were to continue to divide it among more people.
--Next to each pie you have drawn, shade in the amount one person would get. With a different color, shade in the amount 2 people would get.
--After shading the amount each person would get, write the fraction it represents. Write the fraction for the amount that 2 people would get.
--What happened to the pieces of pie as you divided the pie into more and more pieces?
--What happened to the denominator of the fraction as you divided the pie into more pieces?

3. Allow 15 minutes for the students to complete their journal entries, then read aloud the book, GATOR PIE.

4. Have the students begin their workstation rotations. Workstations should be set up as follows:

A) Workstation #1: Before students go to this workstation, model how to divide a paper plate by folding the plate in half, counting the number of pieces (2). Have students use a marker and draw a line on the fold to indicate halves. Then fold it in half again and count the pieces (4). Have students model the way to divide a pie equally by using a paper plate. The instructions at the workstation should ask them to fold the plate in half, count the number of pieces, shade one in, and write the fractional part. Then, the students should fold the plate in half again, count the pieces, shade one in, and write the fractional part. Students make four folds--up to 16 pieces. On the back of the plates, ask students to record their predictions about what will happen if they fold their plates a 5th time. Have students write down how many pieces were in 1/2 of their pies when they folded it twice, then four times, then five times. Their names should also be written on the backs of the plates. (These directions should be printed at the workstation for students.)

B) Workstation #2: Give each student one round snack cake on a paper plate and a plastic knife. Ask, -How many fair shares can you create with this cake?- Everyone divides his or her cake into fair shares. Discuss in the workstation with other members of the group what happened to the cake. Compare it to what happened to the pie from the book, GATOR PIE. Store the cake in a plastic baggie to be enjoyed later. Students should record in their math journals under the day's date, how many fair shares they could create and why they couldn't make any more. They should also tell what fraction of the cake each fair share is. This entry should be written in complete sentences. (These directions should be printed at the workstation for students.)

C) Workstation #3: Students complete Fabulous Fractions, and Flowering Fractions, online Student Web Lessons available from the Beacon Learning Center. (These lessons should be bookmarked on the computers for students and printed directions for student behavior as well as computer instructions should be at this workstation.)

5. Meet as a whole group and go over what was done at the workstations. Emphasize that 1/2 of the pie plate was the same or equivalent no matter how many times the pie was divided. Demonstrate the concept on the board for students, then use a paper plate. Make sure that students understand that 1/2=2/4=4/8, etc.

6. Enjoy the cakes.

#### Assessments

Formatively assess the journal entry from the whole-class activity. Make sure students are:

1. Writing fractions correctly.
2. Explaining their predictions.

Formatively assess the folded paper plates from Workstation #1. Check for:

1. Correct labeling and shading of fractional parts.
2. The number of pieces in 1/2 of the pie each time it was folded.
3. A prediction that 5 folds increases the number of equal fractional parts. Students may or may not accurately predict how many equal pieces 5 folds will make (32).

Formatively assess the journals for the information from Workstation #2. Students should:

1. Accurately describe how many pieces the cake was divided into.<
2. Explain that the smaller the piece, the more difficult to divide it.
3. Check to see that the fractions are written correctly.

Observe students at Workstation #3 to make sure that they are participating in the online Student Web Lessons. Students who seem to have difficulty can be paired with those who demonstrate understanding of the fraction concepts practiced in these lessons.

#### Extensions

1. Explore other fractional representations using the Fair Share Shape Template (See Associated File).

2. Using the information from Workstation #1, have students create a chart to show the pattern concerning the number of folds and how many pieces it equals.