MA19.3.15

Mathematics (2019) Grade(s): 3

MA19.3.15

Explain equivalence and compare fractions by reasoning about their size using visual fraction models and number lines.

Unpacked Content

Knowledge

Students know:
  • Fractions with different names can be equal.
  • Two fractions are equivalent if they are the same size, cover the same area, or are at the same point on a number line.
  • Unit fraction counting continues beyond 1 and whole numbers can be written as fractions.
  • Use a variety of area models and length models to show that a whole number can be expressed as a fraction and to show that fractions can be equivalent to whole numbers.
  • Comparing two fractions is only reasonable if they refer to the same whole.
  • The meaning of comparison symbols , = .
  • Reason about the size of a fraction to help compare fractions.
  • Use a variety of area and length models to represent two fractions that are the same size but have different names.
  • Use a fraction model to explain how equivalent fractions can be found.
  • Use a variety of area models and length models to demonstrate that any fraction that has the same nonzero numerator and denominator is equivalent to 1.
  • Use models to show that the numerator of a fraction indicates the number of parts, so if the denominators of two fractions are the same, the fraction with the greater numerator is the greater fraction.
  • Use models to show that the denominator of a fraction indicates the size of equal parts a whole is partitioned into, and that the greater the denominator, the smaller the parts.-Determine when two fractions can not be compared because they do not refer to the same size whole.

Skills

Students are able to:
  • Explain equivalence of two fractions using visual models and reasoning about their size.
  • Compare two fractions with same numerators or with same denominators using visual models and reasoning about their size.
  • Express whole numbers as fractions.
  • Identify fractions equivalent to whole numbers.
  • Record comparisons of two fractions using , or = and justify conclusion.
  • Explain that the whole must be the same for the comparing of fractions to be valid.

Understanding

Students understand that:
  • A fraction is a quantity which can be illustrated with a length model or an area model.
  • Two fractions can be the same size but have different fraction names.
  • A fraction can be equivalent to a whole number.
  • Any fraction that has the same nonzero numerator and denominator is equivalent to 1.
  • The numerator of a fraction indicates the number of parts, so if the denominators of two fractions are the same, the fraction with the greater number of parts is the greater fraction.
  • The denominator of a fraction indicates the size of equal parts in a whole, so the greater the denominator, the smaller the size of the parts in a whole.

Vocabulary

  • Equivalence
  • Visual fraction model
  • Number line
  • Numerator
  • Denominator
  • Reasoning
  • Conclusions
  • Comparison
  • Point
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