## Eggsactly with Eighteen Eggs

3-5
1

Students continue to examine fractions as part of a set. This lesson helps students develop skill in problem solving and reasoning as they examine relationships among the fractions used to describe part of a set of eighteen.

Use the Eggsactly Eggs Overhead to review fractions as part of a set of 12.

For example, ask students how to show 1/2 of a dozen. Accept equivalent fractions (6/12, 3/6, etc.) and all the arrangements of six eggs in a carton that holds twelve eggs.

For the main lesson, students will investigate how their fractions would change if the egg carton holds 18 eggs instead of 12. Have students remove varying numbers of eggs to represent a fraction of the carton that remains. Students should also be given the fraction and asked to model using 18 eggs. The 18 Eggs in a Carton Activity Sheet should be used as students discover the different representations for each of the fractions.

Ask students how many eggs are in the set. [18.] Suppose nine are used to bake a cake. Have students remove nine eggs. Students should record their egg configuration on the activity sheet. Have students participate in a gallery walk examining other students’ egg cartons to see all the different ways students might have removed nine.

• Ask students what all the egg cartons have in common. [There are nine remaining.]
• What fraction of the entire set is nine? [9/18; accept 1/2 or other equivalent fractions. If students do not make the connection between equivalent fractions, e.g., 9/18 = 1/2, they will have an opportunity to develop these relationships in the next lesson.]
• What fraction was removed? [9/18 or 1/2.] Have students label their recording sheet as 9/18. [Some students may choose to label their sheet with an equivalent fraction such as 3/6. This provides an excellent opportunity to work with equivalent fractions.]

Continue removing varying numbers of eggs. For example, suppose this time that we need twelve eggs to bake our cake. Have students remove twelve eggs. Students should record their egg configuration on the 18 Eggs in a Carton activity sheet. Have students go on another gallery walk to see all the different ways students might have removed twelve.

• Ask students what all the egg cartons have in common. [There are six remaining.]
• What fraction of the entire set is twelve? [12/18; accept 2/3 or 4/6.]
• What fraction was removed? [6/18 or 1/3 or 2/6.] Have students label their recording sheet as directed by the activity sheet.

Have students investigate the different ways they can arrange their eggs when given the fraction. For example, ask students to show 1/3 of eighteen eggs. (Use the 18 Eggs in a Carton Activity Sheet to have students represent several different configurations all equivalent to 1/3 of eighteen eggs.)

Have students work in pairs to continue the investigation as different numbers of eggs are used. Students should be given time to investigate the variety of ways in which the eggs can be arranged. These arrangements should be recorded on the and the sheet should be labeled according to the fraction. For example, students might use several pictures of egg cartons on the 18 Eggs in a Carton Activity Sheet to record all the ways to show 1/3 of eighteen eggs.

Identify fraction relationships associated with the set (e.g., 1/2 of the set of 18 eggs is the same as 9/18 of the set, OR when the numerator stays the same and the denominator increases, the fractions become smaller — 1/3 is smaller in area than 1/2).

Assessment Options

1. At this stage of the unit, it is important for students to know:
• that a fraction can be represented as part of a set
• how to identify fractions when the whole (set) and part of the set are given
• fraction relationships associated with a set of eighteen
2. Collect the students' 18 Eggs in a Carton Activity Sheets to assess their thinking about fractions. Use the 18 Eggs in a Carton Answer Key to check student responses to the questions on the activity sheet.
18 Eggs in a Carton Answer Key

Extension

1. Continue the activity by changing the size of the egg carton. [You can create larger cartons by cutting the desired number of egg-cups and gluing them to other cartons.] For example, have students investigate how their fractions would change if the egg carton holds 6 eggs, or 24 eggs.
2. Move on to the next lesson, Eggsactly Equivalent.

Questions for Students

1. Have students think about the fractions that were constructed using a 12‑egg carton and the fractions that were constructed using an 18‑egg carton. Were any of the same fractions used?

[For example, we were able to show ___ of 12 as well as ___ of 18. How did the parts represented by these fractions differ?]

2. We have worked with egg cartons that serve as models for fractions with denominators of 2, 3, 4, 6, 9 and 12. How many slots would an egg carton have to have in order to work with fractions such as 5/8? What about 3/5?

[Have students generate other fractions they might like to model.]

3. What fraction relationships were you able to identify in this lesson?

[Student responses may vary.]

Teacher Reflection

• Which students understand that a fraction can be represented as part of a set? What activities are appropriate for students who have not yet developed this understanding?
• Which students can identify fractions when the whole (set) and part of the set is given? What activities are appropriate for students who have not yet developed this understanding?
• Which students/groups can articulate relationships between fractions?
• What parts of the lesson went smoothly? What parts should be modified for the future?

### Eggsactly with a Dozen Eggs

3-5
Students begin to examine fractions as part of a set. This lesson helps students develop skill in problem solving and reasoning as they examine relationships among the fractions used to describe part of a set of 12.

### Eggsactly Equivalent

3-5
Students use twelve eggs to identify equivalent fractions. Construction paper cutouts are used as a physical model to represent various fractions of the set of eggs, for example, 1/12, 1/6, and 1/3. Students investigate relationships among fractions that are equivalent.

### Another Look at the Set Model using Attribute Pieces

3-5
The previous lessons focused on the set model where all objects in the set are the same size and shape. Students also need work with sets in which the objects “look” different. In the real world, we are often faced with fraction situations where the objects in the set are not identical. For this lesson, students use fractions to describe a set of attribute pieces. Students develop skill in problem solving and reasoning as they think about their set and how to create new sets given specific fractional characteristics.

### Class Attributes

3-5
During this lesson, students create their own classroom survey or use previously generated questions to study the class and describe the set [class] in fractional parts. This lesson requires that students identify fractions in real-world contexts from a set of items that are not identical. This lesson is integrated with other areas of the math curriculum, including data analysis and statistics.

### Another Look at Fractions of a Set

3-5
This lesson gives students another opportunity to explore fractions using the set model. This lesson is integrated with other areas of the math curriculum including data analysis and statistics.

### Learning Objectives

Students will:

• Demonstrate understanding that a fraction can be represented as part of a set, given a set of identical items (eggs).
• Identify fractions when the whole (set) and part of the set is given.
• Identify fraction relationships associated with the set (for example, 1/3 of 18 is 6).

### NCTM Standards and Expectations

• Use models, benchmarks, and equivalent forms to judge the size of fractions.
• Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers.
• Recognize and generate equivalent forms of commonly used fractions, decimals, and percents.

### Common Core State Standards – Mathematics

Grade 3, Num & Ops Fractions

• CCSS.Math.Content.3.NF.A.1
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

• CCSS.Math.Content.3.G.A.2
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

Grade 4, Num & Ops Fractions

• CCSS.Math.Content.4.NF.A.2
Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Grade 5, Num & Ops Fractions

• CCSS.Math.Content.5.NF.B.3
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

### Common Core State Standards – Practice

• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.