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Understanding Rational Numbers and Proportions

http://illuminations.nctm.org/LessonDetail.aspx?ID=L284

A lesson plan for grades 5–7 Mathematics

Provider: National Council of Teachers of Mathematics


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In this lesson from Illuminations, students use real-world models to develop an understanding of fractions, decimals, unit rates, proportions, and problem solving. The activities in this investigation center on situations involving rational numbers and proportions that students encounter during a fictitious trip to a bakery. These activities involve several important concepts of rational numbers and proportions, including partitioning a unit into equal parts, the quotient interpretation of fractions, the area model of fractions, determining fractional parts of a unit not cut into equal-sized pieces, equivalence, unit prices, and multiplication of fractions.

North Carolina Curriculum Alignment

Mathematics (2004)

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.

Grade 6

  • Goal 1: Number and Operations - The learner will understand and compute with rational numbers.
    • Objective 1.01: Develop number sense for negative rational numbers.
      • Connect the model, number word, and number using a variety of representations, including the number line.
      • Compare and order.
      • Make estimates in appropriate situations.
    • Objective 1.03: Compare and order rational numbers.
    • Objective 1.04: Develop fluency in addition, subtraction, multiplication, and division of non-negative rational numbers.
      • Analyze computational strategies.
      • Describe the effect of operations on size.
      • Estimate the results of computations.
      • Judge the reasonableness of solutions.
    • Objective 1.07: Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.

Grade 7

  • Goal 1: Number and Operations - The learner will understand and compute with rational numbers.
    • Objective 1.01: Develop and use ratios, proportions, and percents to solve problems.
    • Objective 1.02: Develop fluency in addition, subtraction, multiplication, and division of rational numbers.
      • Analyze computational strategies.
      • Describe the effect of operations on size.
      • Estimate the results of computations.
      • 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.