LEARN NC

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

Exploring the value of the whole

http://illuminations.nctm.org/LessonDetail.aspx?ID=L347

A lesson plan for Grades 3–5 Mathematics

Provider: National Council of Teachers of Mathematics

About this resource

Appropriate grades
3–5
Subjects
mathematics (number sense, number theory)
Provider
National Council of Teachers of Mathematics

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This lesson focuses on the relationship between parts and the whole. These relationships were developed earlier and require the students to consider the size or value of the same fraction when different “wholes” are compared. This lesson promotes problem solving and reasoning as the students compare similar fractions with different “wholes.” Students develop communication skills as they work in pairs and share their understanding about the relationship between the value of a fraction and the whole. Illuminations provides an activity sheet and detailed instructions for completing the lesson.

Students will:

  • Identify the fractions represented by various pattern blocks when “whole” is defined in different ways.
  • Demonstrate an understanding that the area of equivalent fractions is relative to the whole.

NCTM Standards and Expectations:

  • 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 equivalent representations for the same number and generate them by decomposing and composing numbers.
  • Use models, benchmarks, and equivalent forms to judge the size of fractions.

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 1.01: Develop number sense for rational numbers 0.01 through 99,999.
      • Connect model, number word, and number using a variety of representations.
      • Build understanding of place value (hundredths through ten thousands).
      • Compare and order rational numbers.
      • Make estimates of rational numbers in appropriate situations.
    • 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 1.04: Develop fluency with addition and subtraction of non-negative rational numbers with like denominators, including decimal fractions through hundredths.
      • Develop and analyze strategies for adding and subtracting numbers.
      • Estimate sums and differences.
      • Judge the reasonableness of solutions.
    • Objective 1.05: Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.

Grade 5

  • Goal 1: Number and Operations - The learner will understand and compute with non-negative rational numbers.
    • Objective 1.01: Develop number sense for rational numbers 0.001 through 999,999.
      • Connect model, number word, and number using a variety of representations.
      • Build understanding of place value (thousandths through hundred thousands).
      • Compare and order rational numbers.
      • Make estimates of rational numbers in appropriate situations.
    • Objective 1.02: Develop fluency in adding and subtracting non-negative rational numbers (halves, fourths, eighths; thirds, sixths, twelfths; fifths, tenths, hundredths, thousandths; mixed numbers).
      • Develop and analyze strategies for adding and subtracting numbers.
      • Estimate sums and differences.
      • Judge the reasonableness of solutions.
    • Objective 1.03: Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.