LEARN NC

K–12 teaching and learning · from the UNC School of Education

Investigating fraction relationships with relationship rods

http://illuminations.nctm.org/LessonDetail.aspx?ID=L542

A lesson plan for Grades 3–4 Mathematics

Provider: National Council of Teachers of Mathematics

About this resource

Appropriate grades
3–4
Subjects
mathematics (number sense)
Provider
National Council of Teachers of Mathematics

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Students use relationship rods to explore fraction relationships, which lays the foundation for work with more challenging fraction concepts. Illuminations provides an activity sheet and a fraction bars applet for completing the lesson. After engaging students in conversation about relationship rods, the teacher offers them the opportunity to explore the manipulatives. When students understand the relationship of bars to numbers, they can use the Integer Bar applet to continue the activity.

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.

NCTM Standards and Expectations covered in this lesson include:

  • Recognizing and generating equivalent forms of commonly used fractions, decimals, and percents.
  • Developing understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers.

North Carolina Curriculum Alignment

Mathematics (2004)

Grade 3

  • Goal 1: Number and Operations - The learner will model, identify, and compute with whole numbers through 9,999.
    • Objective 1.01: Develop number sense for whole numbers through 9,999.
      • Connect model, number word, and number using a variety of representations.
      • Build understanding of place value (ones through thousands).
      • Compare and order.
    • Objective 1.05: Use area or region models and set models of fractions to explore part-whole relationships.
      • Represent fractions concretely and symbolically (halves, fourths, thirds, sixths, eighths).
      • Compare and order fractions (halves, fourths, thirds, sixths, eighths) using models and benchmark numbers (zero, one-half, one); describe comparisons.
      • Model and describe common equivalents, especially relationships among halves, fourths, and eighths, and thirds and sixths.
      • Understand that the fractional relationships that occur between zero and one also occur between every two consecutive whole numbers.
      • Understand and use mixed numbers and their equivalent fraction forms.
    • Objective 1.06: Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.

Grade 4

  • Goal 1: Number and Operations - The learner will read, write, model, and compute with non-negative rational numbers.
    • Objective 1.03: Solve problems using models, diagrams, and reasoning about fractions and relationships among fractions involving halves, fourths, eighths, thirds, sixths, twelfths, fifths, tenths, hundredths, and mixed numbers.
    • Objective 1.05: Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.