## Eggsactly with a Dozen Eggs

3-5
1

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.

Introduce the set representation by having each pair of students examine an egg carton filled with plastic eggs (or some other marker if plastic eggs are unavailable or cost prohibitive.) Ask students how many eggs are in the set. [12.] Suppose six are used to bake a cake. Have students remove six eggs. Students should record their egg configuration on the Eggsactly Eggs Activity Sheet.

Have students participate in a gallery walk examining other students’ egg cartons to see all the different ways students might have removed six.

• Ask students what all the egg cartons have in common. [There are six remaining.]
• What fraction of the entire set is 6? [6/12; accept 1/2 or other equivalent fractions.] If students do not make the connection between equivalent fractions, e.g., 6/12 = ___, they have an opportunity to develop these relationships in later lessons.
• What fraction was removed? [6/12 or 1/2] Have students label their recording sheet as 6/12. Some students may choose to label their sheet with an equivalent fraction, such as 1/2. If so, this provides an excellent opportunity to introduce equivalent fractions.

Continue removing varying numbers of eggs. For example, suppose this time that we need eight eggs to bake our cake. Have students remove eight eggs. Students should record their egg configuration on the Eggsactly Eggs Activity Sheet. Have students go on another gallery walk to see all the different ways students might have removed eight.

• Ask students what all the egg cartons have in common. [There are four remaining.]
• What fraction of the entire set is 4? [4/12; accept 1/3 or 2/6.]
• What fraction was removed? [8/12, 2/3, or 4/6.] For the remaining eggs, have students label their recording sheet as 4/12. [Accept 1/3 or 2/6.]

Have students investigate the different ways they can arrange their eggs when given the fraction. For example, ask students to show 1/4 of a dozen? (Use the Eggsactly Eggs Activity Sheet to have students represent several different configurations all equivalent to 1/4 of a dozen.) Have students identify fraction relationships associated with the set (e.g., 6 of the set of 12 eggs is the same as 6/12 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).

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 Eggsactly Eggs Activity Sheet and the sheet should be labeled according to the fraction. For example, students might use several images of the egg carton on the activity sheet to record all the ways to show x of a dozen.

Have students investigate the different ways they can arrange their eggs when given the fraction. For example, ask students to show 1/4 of a dozen? (Use the Eggsactly Eggs Activity Sheet to have students represent several different configurations all equivalent to 1/4 of a dozen.) Have students identify fraction relationships associated with the set (e.g., 1/2 of the set of 12 eggs is the same as 6/12 of the set, OR when the numerator stays the same and the denominator increases, the fractions become smaller, e.g. 1/3 is smaller in area than 1/2).

Convene the whole class to discuss the activities in this lesson. The guiding questions may be used to focus the class discussion as they were used to focus individual student’s attention on the mathematics learning objectives of this lesson.

Assessment Option

1. At this stage of the unit, it is important to know whether students can:
• Demonstrate understanding that a fraction can be represented as part of a set
• Identify fractions when the whole (set) and part of the set are given
• Identify fraction relationships associated with a set of twelve
2. Student recordings can be used to make instructional decisions about students’ understanding of fraction relationships. Areas needing additional work can be developed during subsequent lessons. More challenging experiences can be provided for those students who need them. You may choose to use the Class Notes recording sheet to make anecdotal notes about students’ understandings.
3. Collect students' Eggsactly Eggs Activity Sheets. Use the Eggsactly Eggs Answer Key to check student responses to the questions on the activity sheet.

Extension

Move on to the next lesson, Eggsactly with Eighteen Eggs.

Questions for Students

1. What do you notice about the relationship between 1/2 of a dozen and 1/4 of a dozen?

[Students should be able to tell from their recordings that 1/4 is half of 1/2.]

2. What do you notice about the relationship between 1/3 of a dozen and 1/6 of a dozen?

[Students should be able to tell from their recordings that 1/6 is half of 1/3.]

3. What can you tell about the size of the fraction when the numerator is the same for both fractions, e.g., 1/4 and 1/6?

[The smaller the denominator, the larger the fraction.]

4. What can you tell about the size of the fraction when the denominator is the same for both fractions, e.g. 2/5 and 3/5?

[The smaller the numerator, the smaller the fraction.]

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 Eighteen Eggs

3-5
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.

### 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, such as one fourth is one half of one half.

### 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.