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# Locating and Ordering Equivalent Fractions on the Number Line

### Collection Developed by:

Collection Credits

### Collection Funded by:

Funding for the VITAL/Ready to Teach collection was secured through the United States Department of Education under the Ready to Teach Program.

## Resources for this Lesson:

Connections

Everyday Math (2004)
Teacher Lesson Guide, pp. 541-548
Student Reference, pp. 47-50
Math Journal pp. 207, 356-357

Investigations/Scott Foresman (2006)
Different Shapes, Equal Pieces,
Investigation 1, Session 5: pp. 19-21.
Investigation 2, Sessions 3 and 4, pp. 29-37
Investigation 3, Sessions 1 and 2, pp. 41-45

Standards

to:

Not yet reviewed.

### Overview

Students are asked to find ways to share different-sized items equally between 2 people. They are asked to find equivalent fractions on a number line and to order those fractions by size. This CYBERCHASE activity is motivated by a video clip in which the CyberSquad has to find a way for Pan and Pin to share their different-sized bars of gold equally before the goat-boys will take the CyberSquad across the river in their boat.

3-6

60 minutes

### Materials

Handout 1: Equal Amounts of Gold
Handout 2: Equivalent Fractions
Assessment: Level A
Assessment: Level B
Three pieces of adding machine tape (20" each) for each pair of students, index cards

### Part I: Learning Activity

1. Distribute Handout 1: Equal Amounts of Gold . Have students work in pairs to complete the activity.

2. The handout shows a diagram of 15 pieces of gold of different sizes. Students should label the gold with either a P or a V so that the amount of gold labeled with P is equal to the amount of gold labeled with V.

Note to teacher: The handout is intentionally ambiguous as to whether the students should pay attention to the number of pieces , which are odd and hard to share, or to the size of the pieces. If they ask for a ruler, you can provide one.

3. Tell students that they will watch a video clip in which the CyberSquad solves the same problem.

4. Show students the Equal Amounts of Gold Video .

5. Ask the students to compare their methods to that of the CyberSquad.

6. Distribute Handout 2: Equivalent Fractions and three 20-inch pieces of adding machine tape to each pair of students.

7. Fraction denominations are: 1/2, 1/4, 1/8, 1/3, 1/6, 1/9, 1/5, and 1/10.

8. The handout guides students through constructing several sets of common equivalent fractions, with each piece of adding machine tape representing a whole unit.

### Part II: Assessment

Assessment: Level A (proficiency): Students are given a number line labeled with several unit fractions, and are asked to label the number line with several fractions equivalent to the unit fractions. 2) On another number line, labeled in eighths, students are asked to label the number line with various equivalent fractions, and to determine the largest of those equivalent fractions.

Fraction denominations in this assessment are 1/2's, 1/4's, 1/8's, 1/3's, and 1/6's.

Assessment: Level B (above proficiency): Students are given several strips marked with several different fractions. They are then asked to use index cards as an aid for determining the size of unit fractions on those strips, and asked to find fractions that are not marked on the strips.

Fraction denominations in this assessment are 1/2's, 1/4's, 1/8's, 1/5's, and 1/10's.