4.2 Fraction Equivalence and Comparison

Unit Goals

  • Students generate and reason about equivalent fractions and compare and order fractions with the following denominators: 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Section A Goals

  • Make sense of fractions with denominators 2, 3, 4, 5, 6, 8, 10, and 12 through physical representations and diagrams.
  • Reason about the location of fractions on the number line.

Section B Goals

  • Generate equivalent fractions with the following denominators: 2, 3, 4, 5, 6, 8, 10, 12, and 100.
  • Use visual representations to reason about fraction equivalence, including using benchmarks such as $\frac{1}{2}$ and 1.

Section C Goals

  • Use visual representations or a numerical process to reason about fraction comparison.
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Glossary Entries

  • common denominator
    The same denominator in two or more fractions. For instance, \(\frac{1}{4}\) and \(\frac{5}{4}\) have a common denominator.
  • composite number
    A whole number with more than 1 factor pair.
  • denominator
    The bottom part of a fraction that tells how many equal parts the whole was partitioned into.
  • equivalent fractions
    Fractions that have the same size and describe the same point on the number line. For example, \(\frac{1}{2}\) and \(\frac{2}{4}\) are equivalent fractions.
  • factor pair of a whole number
    A pair of whole numbers that multiply to result in that number. For example, 5 and 4 are a factor pair of 20.
  • multiple of a number
    The result of multiplying that number by a whole number. For example, 18 is a multiple of 3, because it is a result of multiplying 3 by 6.
  • numerator

    The top part of a fraction that tells how many of the equal parts are being described.

  • prime number
    A whole number that is greater than 1 and has exactly one factor pair: the number itself and 1.