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

Parts of a square

http://illuminations.nctm.org/LessonDetail.aspx?ID=L307

A lesson plan for grade 3 Mathematics

Provider: National Council of Teachers of Mathematics


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Students investigate the ways shapes can be divided into equal pieces with one or two cuts. It provides a review of the following vocabulary terms: square, triangle, and rectangle; congruent, one-half, and one-fourth. The other lessons in this unit build on this introductory lesson. Illuminations provides helpful activity sheets and resources and detailed directions for completing the lesson.

Students will:

  • Explore ways to divide a square into two equal parts with a single cut.
  • Explore ways to divide a square into four equal parts.
  • Use geometric and fractional terms to name the parts.

NCTM Standards and Expectations:

  • Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes.
  • 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 and generate equivalent forms of commonly used fractions, decimals, and percents.

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 1.05: 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.
  • Goal 3: Geometry - The learner will recognize and use basic geometric properties of two- and three-dimensional figures.
    • Objective 3.01: Use appropriate vocabulary to compare, describe, and classify two- and three-dimensional figures.

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.