LEARN NC

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

Expanding our pattern block fraction repertoire

http://illuminations.nctm.org/LessonDetail.aspx?ID=L346

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, patterns)
Provider
National Council of Teachers of Mathematics

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In this lesson, the students expand the number of fractions they can represent with pattern blocks by increasing the whole. Illuminations provides an activity sheet, links to related web resources, and instructions for completing the lesson. In small groups, students explore fractions using a virtual pattern block applet and a web resource that provides virtual manipulatives.

Students will:

  • Identify fractions when the whole (region) and a part of the region are given.
  • Represent the fractional relationship between the pattern block shapes using a standard form of the written notation (e.g., the green triangle is x of the blue rhombus).
  • Identify the fractions represented by various pattern blocks when "whole" is defined in different ways (e.g., 1 whole = 1 yellow hexagon; 1 whole = 2 or more yellow hexagons).

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 1.04: Use basic properties (identity, commutative, associative, order of operations) for addition, subtraction, multiplication, and division.
    • 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.

Grade 5

  • Goal 1: Number and Operations - The learner will understand and compute with non-negative rational numbers.
    • 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.