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Comparing Fractions in the Common Core

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How did you learn to compare fractions? I learned to find a common denominator or change them to a decimal. Have you thought about other ways? Consider how the understanding of a unit fraction can create multiple ways for comparing fractions. The CCSS expects third grade students to understand unit fractions. Here are four possibilities:

  1. Common Denominator – This way is very familiar to most.  Compare 4/9 and 5/9. Use the logic that a person with 4 pieces that are one-ninth in size has less than a person with 5 pieces that are one-ninth in size.
     
  2. Common Numerators – Many of you may not have thought about comparing fractions by their numerator. Compare 3/5 and 3/7. Use the logic that a person with 3 pieces that are one-fifth in size has more than a person that has 3 pieces that are one-seventh in size.
     
  3. Distance from One – Compare 3/4 to 6/7. Use the logic that a person missing a piece that is one-fourth in size has less than the person that is missing a piece that is one-seventh in size.
     
  4. Distance from 1/2 – Compare 3/8 and 5/12. Use the logic that a person that is missing a piece one-eighth in size in order to have 1/2 would have less than a person that is missing a piece one-twelfth in size to have  1/2.

Ask students to compare fractions using unit fraction logic and share their thinking versus asking students to show their math work.

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