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

Pattern block fractions

http://illuminations.nctm.org/LessonDetail.aspx?ID=L345

A lesson plan for grades 3–5 Mathematics

Provider: National Council of Teachers of Mathematics


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In this that lesson builds on the previous two lessons, students focus on the identification of fractional parts of a region and record them in standard form. Students continue to develop communication skills by working together to express their understanding of fraction relationships and to record fractions in written form. Illuminations provides worksheets and links to virtual pattern block programs. After exploring relationships between shapes, students use pattern blocks to find relationships and to determine answers to guiding questions provided by the teacher.

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.
  • Identify the numerator in a fraction and understand that the numerator is the top number in a fraction and indicates the number of parts of the whole.
  • Identify the denominator in a fraction and understand that the denominator is the bottom number in a fraction and indicates the number of parts into which the whole is divided.

NCTM Standards and Expectations covered in this lesson include:

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