Illuminations: Fun with Fractions

# Fun with Fractions

## Investigating Equivalent Fractions with Relationship Rods

 Students investigate the length model by working with relationship rods to find equivalent fractions. Students develop skills in reasoning and problem solving as they explain how two fractions are equivalent (the same length).

### Learning Objectives

 Students will: demonstrate understanding that a fraction can be represented as part of a linear region describe part of a linear region using fractions identify fraction relationships using different "wholes" as a reference identify equivalent fractions identify the fraction in lowest terms

### Materials

 One set of relationship rods per student (may be purchased commercially or made by printing the Relationship Rods in color) Investigating Equivalent Fractions Activity Sheet Fraction Bar Applet

### Questions for Students

 When you used the brown rod as the unit (whole), what equivalent fractions did you identify? [Students should line up other colors (end to end) to make lengths equivalent to the brown rod. After lining up various rods, students should identify the following equivalent fractions: 2/8 (2 white rods) = 1/4 (1 red rod), 4/8 (4 white rods) = 2/4 (2 red rods) = 1/2 (1 purple rod), 6/8 (6 white rods) = 3/4 (3 red rods).] From each set, which fraction is in lowest terms? [Students should know that when comparing equivalent fractions, the group with the smallest number of rods represents the fraction in lowest terms. Therefore, when comparing 2/8 and 1/4, 1/4 is in lowest terms. When comparing 4/8, 2/4 and 1/2, 1/2 is in lowest terms. When comparing 6/8 and 3/4, 3/4 is in lowest terms.] When you used the orange rod as the unit (whole), what equivalent fractions did you identify? [Students should line up other colors (end to end) to make lengths equivalent to the orange rod. After lining up various rods, students should identify the following equivalent fractions: 2/10 (2 white rods) = 1/5 (1 red rod), 5/10 (5 white rods) = 1/2 (1 yellow rod), 6/10 (6 white rods) = 3/5 (3 red rods), 8/10 (8 white rods) = 4/5 (4 red rods).] From each set, which fraction is in lowest terms? [When comparing 2/10 and 1/5, 1/5 is in lowest terms. When comparing 5/10 and 1/2, 1/2 is in lowest terms. When comparing 6/10 and 3/5, 3/5 is in lowest terms. When comparing 8/10 and 4/5, 4/5 is in lowest terms.] When you used the blue rod as the unit (whole), what equivalent fractions did you identify? [Students should line up other colors (end to end) to make lengths equivalent to the blue rod. After lining up various rods, students should identify the following equivalent fractions: 3/9 (3 whites) = 1/3 (1 light green), 6/9 (6 whites) = 2/3 (2 light greens), 9/9 (9 whites) = 3/3 (3 light greens) = 1 (1 blue).] From each set, which fraction is in lowest terms? [When comparing 3/9 and 1/3, 1/3 is in lowest terms. When comparing 6/9 and 2/3, 2/3 is in lowest terms. When comparing 9/9, 3/3, and 1, 1 is in lowest terms.] When you used the dark green rod as the unit (whole), what equivalent fractions did you identify? [Students should line up other colors (end to end) to make lengths equivalent to the dark green rod. After lining up various rods, students should identify the following equivalent fractions: 2/6 (2 white rods) = 1/3 (1 red rod), 4/6 (4 white rods) = 2/3 (2 red rods), 3/6 (3 white rods) = 1/2 (1 light green rod), 6/6 (6 white rods) = 3/3 (3 red rods) = 2/2 (2 light green rods) = 1 (1 dark green rod).] From each set, which fraction is in lowest terms? [When comparing 2/6 and 1/3, 1/3 is in lowest terms. When comparing 4/6 and 2/3, 2/3 is in lowest terms. When comparing 3/6 and 1/2, 1/2 is in lowest terms. When comparing 6/6, 3/3, 2/2, and 1, 1 is in lowest terms.]

### Assessment Options

 At this stage of the unit, students should be able to do the following: demonstrate understanding that a fraction can be represented as part of a linear region describe part of a linear region using fractions identify fraction relationships using different "wholes" as a reference identify equivalent fractions identify the fraction in lowest terms Examining student recordings on the Investigating Equivalent Fractions Activity Sheet can be helpful in making instructional decisions about students’ understanding of fraction relationships.

### Teacher Reflection

 Which students understand that a fraction can be represented as part of a linear region? What activities are appropriate for students who have not yet developed this understanding? Which students can describe part of a linear region using fractions? What activities are appropriate for students who have not yet developed this understanding? Which students can identify fraction relationships using different “wholes” as a reference? What activities are appropriate for students who have not yet developed this understanding? Which students can identify equivalent fractions? What activities are appropriate for students who have not yet developed this understanding? Which students can identify the fraction in lowest terms? 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 3-5Develop 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.
 This lesson was developed by Tracy Y. Hargrove.

1 period

### NCTM Resources

Principles and Standards for School Mathematics

### Web Sites

 More and Better Mathematics for All Students
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