Equivalent Fractions

  • Exploring Equivalent Fractions

    3rd grade


    Name fractions and develop an understanding of equivalent fractions using multiple models, including fraction strips, Cuisenaire rods, and number lines.


    Read aloud the book Fraction Fun by David Adler & Nancy Tobin.

    Give students a paper plate and have them discuss how to fold the plate to show ½, ¼, and ⅛. Have them color ½ in one color, ¼ in another color and ⅛ in a third color. Tell them that this activity is just a warm up to the ideas. They will participate in 4 lessons that will give them more experience naming fractions and finding equivalent fractions. This will lead nicely into the engage for lesson 1.


    Lesson 1 of 4

    Create and use fraction strips to discover name fractions and compare two unit fractions.

    Lesson 2 of 4

    Use Cuisenaire rods to explore fractional relationships. This lays the foundation for work with challenging fraction concepts like equivalence.

    Lesson 3 of 4

    Students generate and explore equivalent fractions using Cuisenaire rods.

    Lesson 4 of 4

    Reason and develop an understanding of how to place equivalent fractions on a number line.

    ARC Assessement

    There is an opportunity to assess if students can determine if two fractions are equivalent (equal) using multiple models, including fraction strips, Cuisenaire rods, and number lines, at the end of lesson 4 of this ARC. The assessment uses Cuisenaire rods and an activity sheet with a series of number line tasks. Students are asked to use Cuisenaire rods to generate number lines for halves, fourths and eighths, and determine which fractions are equivalent.

    Technology Resources

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  • ARC Global Essential Question(s)

    How can you determine if two fractions are equivalent (equal) using multiple models, including fraction strips, Cuisenaire rods, and number lines?


    equivalent fractions, relationship rods, Cuisenaire rods, fraction strips, number lines


    • fraction(s)
    • equivalent
    • equivalence
    • numerator
    • denominator


    CCSS, Content Standards to Domain Level

    • 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.NF.A.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.
    • CCSS.Math.Content.3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
    • CCSS.Math.Content.3.NF.A.3.a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
    • CCSS.Math.Content.3.NF.A.3.b Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
    • CCSS.Math.Content.3.NF.A.3.c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.

    CCSS, Standards for Mathematical Practices

    • SMP 3 Construct viable arguments and critique the reasoning of others.
    • SMP 4 Model with mathematics.
    • SMP 7 Look for and make use of structure.


    Original Source: Lessons 1–3: Illuminations Lesson: Making and Investigating Fraction Strips
    Original Author: Lessons 1–3: Tracy Y. Hargrove, Lesson 4: Dr. Dittika Gupta
    New Editors: Annie Fetter, Barbara Wood, Marrie Lasater, Nick Pyzik, Sherri Martinie