During this lesson, students will investigate relationships among fractions. Students will use cut out pizzas and fraction circles to compare equivalent fractions. First, they will exchange fractional parts of construction paper pizza circles in an attempt to use as many different fractional parts as possible to obtain a whole pizza. Next, they will assemble different fractional parts of fraction circles in order to be able to make a complete circle. Finally, students will compare various equivalent fractions with the help of manipulatives. This lesson will take two to four class periods.
The Eddie Files #104C: Fractions: Any Way You Slice It

Students will:
• find and record as many different ways as they can to create complete circles out of their various fraction circles.
• determine equal fractions by comparing fractions that take up the same area.
• record on paper strips all possible equivalent fractions they can find with their fraction circles.

• class set of large construction paper circles for pizzas (enlarged from enclosed attachments)
• 9" x 11"construction paper to cut out pizza
• toppings - about 3 pieces of paper per topping
• one fraction circle set per student or various colored copies of the attached fraction
• circles which have been enlarged and copied on construction paper
• one pencil per student
• paper for each student
• glue sticks
• a pair of scissors per student
• adding machine tape or strips of paper to list equivalent fractions - 8 strips per group of 3 - 4 students

Divide the class into groups of 3 - 4 students per group. Hand each group several sheets of a particular color of construction paper. Assign each group a pizza topping to cut out which matches the shade of their paper. Explain that these pieces will be used in a lesson on fractions.
Elicit from students verbally or in written form what they know about fractions. (For example: they are part of a whole, they have a numerator and a denominator, etc.) Discuss terms such as fair shares and equal fraction pieces.
Ask students to observe during the viewing of the video why some of the students were unable to reassemble a complete "fraction pizza".

You will use segments from The Eddie Files: Fractions: Any Way You Slice It to stimulate an investigation of fractions. PAUSE after each activity is introduced. Using your remote control, FAST FORWARD through Eddie's introduction. CUE segment where Miss Toliver comes to class dressed like a chef, tossing the pizza dough. Push PLAY and view the video until Miss Toliver has the children glue the pizza toppings onto their pizzas. PAUSE before she gives the students the task to cut the pizzas into fractional parts. Ask students to describe what is occurring in the video.
Hand out the large construction paper circles with the predrawn lines to show how they should be cut as pizza crusts. Distribute "paper toppings" to each group. Each group of students should have the same size fraction to cut. Have each student create his or her own pizza, but emphasize that they are not to glue on the side that has the predrawn lines.
After each student has created a fraction pizza, press play and resume the video tape. Watch until the students have completed their task of reassembling their pizzas using fractional parts borrowed from their classmates.

Hand each group a piece of paper with a fraction that matches the predrawn lines on the "pizza crusts". For example 4/4, 8/8, 12/12 . Explain that they are to cut their pizzas into as many pieces as the fraction on their piece of paper, just like the students in Miss Toliver's class. Then, they are to label their pieces with the appropriate fraction. (For younger students it may help to model how to label the fractional parts or to label the bottom of the "crusts" in advance.)
Once students have completed this task, have them trade fraction pieces with other classmates within a given amount of time, as the students in Miss Toliver's class had done.
Some ground rules may want to be considered here such as: no running, no grabbing pieces away from people, make sure you give and receive fair shares - shares that match the pieces you give up, etc.
When a given amount of time has passed, students will take out their math journals and assess how successful they were in obtaining a complete circle once again. Direct students to describe which fractional parts they used and to respond to the following quick write question. Were they able to complete the pizza circle once again? Why were they able or unable to do so?
After they have completed their reflections on the activity, students will glue the their new complete or incomplete pizzas on a piece of paper together with their writing. Collect their pizza projects and use as a preassessment for of the students' understanding of fractions.
Distribute to each group of students a set of fraction circles or the construction paper fraction circles. Direct students to label the fraction circles with their appropriate fractions. For example: a circle cut into four equal pieces should be labeled 1/4 - 1/4 - 1/4 - 1/4 and so on.
Next students should order the fraction circles from largest to smallest size fraction pieces, 2/2 being the largest and 12/12 being the smallest. Each group of students will build and record on a group paper as many ways as possible to build one full circle. Students should take turns within the group at building, drawing and recording their findings.
Discuss groups' findings. Guide discussion toward comparing fractions. Introduce the term equivalent fractions and explain that these are fractions that name the same amount such as 1/2 and 2/4. Trading equivalent fractions has enabled the students to receive fair shares.Did any of the students notice that some of the fractions they used named the same amount, even though the denominators were not the same - as in 1/4 and 2/8 for example? Have students look at their group's paper and see if they can find any more of those equivalent fractions.
Now, prompt groups to build and record as many equivalent fractions as they can come up with for each piece in the set. They are to draw and write each equivalent fraction set on paper strips. For example: 1/2 = 2/4 = 3/6 = 4/8 = 5/10 = 6/12 on one strip, then 1/3 = 2/6 = 4/12 on another strip and so on. Have groups report their findings to the class.
At this time return pizzas and writings to students. Discuss the students' findings. Were some students able to trade their fraction pieces for two equivalent pieces? For example: one student may have traded 1/4 for 2/8 or 1/2 for 2/4 or 1/4 and 2/8.

Challenge students to design their own fraction set using materials from home. They can use a variety of materials or objects, paper strips for example.
Hold a competition with another class to find and record many ways to assemble complete fraction circles. Organize the results on a chart.

Art:
Create a drawing using equivalent fractions.

### Master Teacher: Gerlinde Wirzfeld-Olvera

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