Lesson plan

6. Farming fractions: Comparing fractions with like denominators (C)

teaches Common Core State Standards CCSS.Math.Content.3.NF.A.3 http://corestandards.org/Math/Content/3/NF/A/3
teaches Common Core State Standards CCSS.Math.Content.3.NF.A.3d http://corestandards.org/Math/Content/3/NF/A/3/d
teaches Common Core State Standards CCSS.Math.Practice.MP8 http://corestandards.org/Math/Practice/MP8
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Lesson objective: Understand that when the denominators are the same we can use the numerators to compare the number of same-size pieces.

Students bring prior knowledge of understanding fractions from 3.NF.1 (Develop understanding of fractions as numbers). This prior knowledge is extended to reason about denominators as students work to compare fractions with like denominators. A conceptual challenge students may encounter is understanding that the larger the number is in the denominator, the larger the number of pieces there are in a whole, and the smaller the size of the pieces will be. For example, if the denominator is two, the piece will be larger than if the denominator is eight. 

The concept is developed through work with visual models, such as tape diagrams, which will provide visual models that help increase student understanding.

This work helps students deepen their understanding of equivalence because students must reason about the size of the pieces to determine if the fraction is greater than, less than, or equal to another fraction.

Students engage in Mathematical Practice #8 (Look for and express regularity in repeated reasoning) as they repeatedly reason about the size of the pieces and move towards more abstract understanding of the size of fractional numbers. 

Key vocabulary:

  • area model
  • compare
  • denominator
  • number line
  • numerator
  • tape diagram

Special materials needed:

  • fraction strips
  • paper
  • pencil