##
* *Reflection: Developing a Conceptual Understanding
My Personal Pizza - Section 3: Closure

Using the fraction squares and circles really helped the students complete the activity. They could not have done it without having the fraction squares and circles as references. I expected it to be difficult because in previous lessons, the students started out having a difficult time dividing the whole into equal pieces. As I walked around to monitor, I noticed that the students used the 1 whole plastic fraction piece as the reference. As they selected fraction pieces to build their 1 whole, I noticed that most students laid out all of the pieces on top of the 1 whole before they began to cut out the pieces. However, I noticed that 1 student would select a fraction, then cut it out. This student did this without building the whole pizza first. This student had a difficult time completing the pizza because as this student went on, he found it difficult to find a piece that would fit perfectly. I sat with the student to ask questions that helped the student compare the sizes of the pieces. For instance, this student needed a piece smaller than 1/3 to complete his pizza. I asked, "Should you piece be larger than 1/3 or smaller than 1/3?" This got the student to thinking about the size of the fraction. We have already learned in class that the bigger the denominator, the smaller the piece. This led the student to find a smaller fraction that could complete the pizza.

I think that activities like this are enjoyable for the students, while at the same time, providing them with new perspective on a skill.

*Fraction Squares and Circles*

*Developing a Conceptual Understanding: Fraction Squares and Circles*

# My Personal Pizza

Lesson 9 of 22

## Objective: SWBAT create a pizza and name the different fractions for the slices by using fraction pieces.

*50 minutes*

#### Whole Class Discussion

*15 min*

In today's lesson, the students learn to compare fractions by using fration squares and fraction circles to create a pizza with different size slices. This aligns with **4.NF.A2** because the students are comparing fractions with different numerators and denominators and using fraction circles and squares to justify their answers.

Because we have been working on fractions for a while, I wanted to give the students the opportunity to be creative with fractions. Before we begin, I ask the students to tell me what they have learned about fractions: Some student responses: The numerator is at the top and the denominator is at the botttom; the numerator tells you how many pieces; the denominator tells you how many to cut it into; and the top number is sometimes bigger than the bottom number.

I let them know that they are correct. For this lesson, I want to challenge the students' thinking in a creative way to compare fractions. I am requiring the students to create their own pizza the way that they want. The slices does not have to be the same size. (I realize that this will puzzle some of them, but struggle is good.)

Scenario:

My mom baked a large pizza for the family. My dad said that he wanted 1/3 of the pizza. My sister said that she was not that hungry, so she only wants 1/6 of the pizza. I only want 1/4 of the pizza. My mom said that she will eat 1/4 of the pizza as well. My mom said okay, she will cut the pizza the size that we want. How is this possible? Let's find out.

I point out to the students that when a whole is cut into different size pieces, then that creates fractions with different denominators. If they are cut into pieces that are the same size, then the denominator is the same (common).

Look at the pizza. Which piece is larger, the 1/6 or the 1/3? I give the students a few minutes to think about the question. The students respond that 1/3 is larger than 1/6. How many 1/6 pieces will it take to equal 1/3? Most students yell out 2, but a few students say 3. I take my marker and divide the 1/3 piece in half. The students can clearly see that it takes two 1/6 pieces to equal 1/3.

We can compare fractions within the whole. In this pizza, the largest piece is the 1/3. The smallest piece is the 1/6. Remember that models are excellent to help you compare fractions.

Let's practice comparing fractions in an activity.

#### Resources

*expand content*

#### Skill Building/Exploration

*20 min*

For this activity, I give each student an activity sheet (My Personal Pizza.docx). The students will all complete the activity independently, but they will share resources, such as the fraction squares and circles **(MP5)**. The students must create their own pizza cut into any sizes that equal 1 whole, therefore, the students must be accurate with the fraction sizes in order to come up with a whole pizza **(MP6)**.

The students are provided with the necessary materials: construction paper, scissors, glue, fraction squares or circles, and an activity sheet. The students use the fraction squares or circles to help them create a proportional pizza that equals 1 whole. First, the students take the 1 whole fraction square or circle and trace it on construction paper. The students cut out the 1 whole piece. The students determine what toppings they want, as well as how much of it they want. As they create their pizza, they must identify the name of the fractions. As they use the fraction squares or circles to lay out for the different pieces, this is allowing the students to see the different fractions and see how they compare to each other in size. For example, if they create their pizza using 1/2, and 2/3, the students will need to determine what other fraction can be used. As they do this, they see that it must be a smaller than 1/2 and 1/3. They then see that 1/6 is a fraction that they can use. Once the students have the desired pizza made up of fractions pieces that equal 1 whole, they must trace the fraction pieces onto construction paper and then cut out the pieces. The students glue the pieces onto the 1 whole to make their pizza (Student Working2). Last, the students glue the pizza onto their activity sheet and label the fractions.

As the students work side by side, they are guided to a conceptual understanding through questioning by their classmates, as well as by me. Even though they are working on individual products, the students always talk and discuss what they are doing. (Especially, when it is an activity that they enjoy.)

As they work, I monitor and assess their progression of understanding through questioning.

1. Which toppings covers the largest amount of the pizza? What fraction is it?

2. Do the fraction squares validate that your pizza equals 1 whole?

3. What is the smallest fraction on your pizza? How do you know?

Any groups that finish the assignment early, can go to the computer to practice the skill at the following site until we are ready for the whole group sharing: http://www.math-play.com/math-fractions-games.html

*expand content*

#### Closure

*15 min*

To close the lesson, I have one or two students share their answers. This gives those students who still do not understand another opportunity to learn it. I like to use my document camera to show the students' work during this time. Some students do not understand what is being said, but understand clearly when the work is put up for them to see.

I feel that by closing each of my lessons by having students share their work is very important to the success of the lesson. Students need to see good work samples, as well as work that may have incorrect information. Samples of student work can be found here, as well as in the resources (Student Work - Pizza.jpg were the students used 1/6 cheese, 1/6 sausage, 1/4 peppers, 1/6 hamburger, and 1/4 pepperoni) and (Student Work - Pizza 2.jpg were the students used 2/6 cheese, 1/4 hamburger, 1/3 pepperoni, and 1/12 other.)

At the end of the lesson, I display the homework assignment on the board for the students to copy.

Assignment:

Write to Explain: How can you use fraction circles to help build a pizza that equals 1 whole?

*expand content*

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- UNIT 1: Fractions
- UNIT 2: Skills Review
- UNIT 3: Algebra
- UNIT 4: Geometry
- UNIT 5: Patterns & Expressions
- UNIT 6: Problem-Solving Strategies
- UNIT 7: Decimals
- UNIT 8: Measurement and Data
- UNIT 9: Multiplication and Division Meanings
- UNIT 10: Place Value
- UNIT 11: Adding and Subtracting Whole Numbers
- UNIT 12: Multiplying and Dividing

- LESSON 1: Is it 1 or more than 1? (Improper Fractions and Mixed Numbers)
- LESSON 2: Name that Fraction
- LESSON 3: Number Lines and Equivalent Fractions
- LESSON 4: Comparing Fractions
- LESSON 5: Explain Your Answer (Fractions)
- LESSON 6: Equivalent Fractions
- LESSON 7: Who has the largest fraction? (Ordering Fractions)
- LESSON 8: What's Another Name For Me?
- LESSON 9: My Personal Pizza
- LESSON 10: Fraction Game Day
- LESSON 11: Adding and Subtracting Fractions with Like Denominators
- LESSON 12: Adding Fractions with Unlike Denominators
- LESSON 13: Subtracting Fractions with Unlike Denominators
- LESSON 14: Decomposing and Composing Fractions
- LESSON 15: Teresa's Pizza (Fraction Decomposition)
- LESSON 16: Modeling Adding and Subtracting Mixed Numbers
- LESSON 17: Adding Mixed Numbers
- LESSON 18: Subtracting Mixed Numbers
- LESSON 19: Using Shapes to Model Fractions as Multiples of Unit Fractions
- LESSON 20: Multiplying a Fraction by a Whole Number
- LESSON 21: Fractions Review
- LESSON 22: What I Learned about Fractions Using Voki