LEARN NC

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

Fun with fractions set model: Looking back and moving forward

http://illuminations.nctm.org/LessonDetail.aspx?ID=L342

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, probability, statistics)
Provider
National Council of Teachers of Mathematics

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This lesson gives students an opportunity to explore fractions using the set model and is integrated with other areas of the math curriculum including data analysis and statistics. Using data collected about colored candies, students learn to create and label graphs. Illuminations provides detailed instructions and links to a graphing web tool and a circle grapher.

Students will:

  • Demonstrate understanding that a fraction can be represented as part of a set.
  • Identify fractions when the whole (set) and part of the set is given.
  • Describe a set of objects based on its fractional components.
  • Identify fraction relationships associated with the set.
  • Identify equivalent fractions.
  • Identify relationships inherent in equivalent fractions.
  • Reduce fractions to their lowest terms.

NCTM Standards and Expectations:

  • Collect data using observations, surveys, and experiments.
  • Represent data using tables and graphs such as line plots, bar graphs, and line graphs.
  • Recognize and generate equivalent forms of commonly used fractions, decimals, and percents.
  • 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.
  • 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.

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 4: Data Analysis and Probability - The learner will understand and use data and simple probability concepts.
    • Objective 4.01: Collect, organize, analyze, and display data (including circle graphs and tables) to solve problems.

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.
  • Goal 4: Data Analysis and Probability - The learner will understand and use graphs, probability, and data analysis.
    • Objective 4.01: Collect, organize, analyze, and display data (including line graphs and bar graphs) to solve problems.
    • Objective 4.03: Solve problems by comparing two sets of related data.
    • Objective 4.04: Design experiments and list all possible outcomes and probabilities for an event.

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.
  • Goal 4: Data Analysis and Probability - The learner will understand and use graphs and data analysis.
    • Objective 4.01: Collect, organize, analyze, and display data (including stem-and-leaf plots) to solve problems.
    • Objective 4.02: Compare and contrast different representations of the same data; discuss the effectiveness of each representation.
    • Objective 4.03: Solve problems with data from a single set or multiple sets of data using median, range, and mode.