Illuminations: Fun with Fractions

Fun with Fractions

Unit Overview

Lesson 1

Lesson 2

Lesson 3

Lesson 4

Lesson 5

Lesson 6

Eggsactly Equivalent

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.

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 equivalent fractions
identify relationships inherent in equivalent fractions (e.g., 1/2 can be multiplied by 2/2 to get the equivalent fraction 2/4, or 2/4 can be divided by 2/2 to get the equivalent fraction 1/2.)

Materials

An egg carton designed to hold 12 plastic eggs (or 12 markers) for each pair of students
Construction paper cut to fit various fractions of an egg carton (1/12, 1/6, 1/4, 1/3, etc.)
Eggsactly Eggs Overhead

Instructional Plan

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

Eggsactly Eggs Overhead

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

Give students paper cutouts that cover various parts of the egg carton, e.g., 1/12, 1/6, 1/4, and 1/3 (see the illustration below). Students need enough cutouts of each fraction to represent the whole. For example, students will need two 1/2s, six 1/6s, four 1/4s, and so forth.

Have students investigate each cutout and identify the fraction that is represented by each. Guide students to label each cutout with the appropriate reduced fraction. For example:

Prompt students to begin looking for fractions that cover the same area, i.e., equivalent fractions. For example, ask students how many 1/12 pieces are needed to cover 1/6 [2]. Have students record 1/6 = 2/12 on notebook paper. Ask students how many 1/6 pieces are needed to cover 1/3 [2]. Have students record 1/3 = 2/6 on notebook paper.

Have students work in pairs to continue identifying as many equivalent fractions as possible. Groups should record all equivalent fractions on notebook paper. When finished, have groups take turns reporting the equivalent fractions to the whole class. If any groups did not find the equivalent fraction being shared, they should add the new set to their list. Ensure that all of the following are identified:

1/6 = 2/12
1/4 = 3/12
1/3 = 2/6
1/3 = 4/12
1/2 = 2/4
1/2 = 3/6
1/2 = 6/12

Have students explore relationships between the equivalent fractions. For example, students might notice that dividing the numerator and denominator by the same number results in an equivalent fraction. Along the same lines, multiplying the numerator and denominator by the same number also results in an equivalent fraction.

It is important to note one common misconception at this stage. Students assume that multiplying a fraction by 2, for example, will generate an equivalent fraction. That is not the case. Multiplying a fraction by 2/2, for example, will generate an equivalent fraction, because 2/2 is the same as one whole. Be sure to note any students who confuse these concepts so you can address their misconceptions.

Questions for Students

What do you notice about the relationship between 1/2 of a dozen and 6/12 of a dozen?

[Students should be able to tell from their recordings that 1/2 and 6/12 are equivalent fractions.]

What do you notice about the relationship between 1/3 of a dozen and 4/12 of a dozen?

[Students should be able to tell from their recordings that 1/3 and 4/12 are equivalent fractions.]

What do you notice about the relationship between 1/4 of a dozen and 3/12 of a dozen?

[Students should be able to tell from their recordings that 1/4 and 3/12 are equivalent fractions.]

What do you notice about the relationship between 1/6 of a dozen and 2/12 of a dozen?

[Students should be able to tell from their recordings that 1/6 and 2/12 are equivalent fractions.]

What other equivalent fractions did you identify using 12 eggs?

[Student responses may vary.]

What relationships do you see in the equivalent fractions identified in this lesson? Do you notice any patterns when you multiply a fraction's numerator and denominator by the same number?

[An equivalent fraction results.]

Assessment Options

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 the set including equivalent fractions (e.g. 1/2 of the set of 12 eggs is the same as 6/12 of the set)

Extensions

Continue the activity by using the egg carton that holds 18 eggs. Have students model and record all equivalent fractions. Have students investigate how their fractions would change if the egg carton holds 6 eggs or 24 eggs.

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 a 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 the fractions? What activities are appropriate for students who have not yet developed this understanding?
Which students/groups can identify equivalent fractions? What activities are appropriate for students who have not yet developed this understanding?
What parts of the lesson went smoothly? What parts should be modified for the future?

NCTM Standards and Expectations

Number & Operations 3-5

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.
Use models, benchmarks, and equivalent forms to judge the size of fractions.

This lesson prepared by Tracy Y. Hargrove.