Lesson plan

8. Multiplicative comparisons with fractions (C)

teaches Common Core State Standards CCSS.Math.Content.4.NF.B.4b http://corestandards.org/Math/Content/4/NF/B/4/b
teaches Common Core State Standards CCSS.Math.Content.4.NF.B.4c http://corestandards.org/Math/Content/4/NF/B/4/c
teaches Common Core State Standards CCSS.Math.Content.4.OA.A.1 http://corestandards.org/Math/Content/4/OA/A/1
teaches Common Core State Standards CCSS.Math.Practice.MP1 http://corestandards.org/Math/Practice/MP1
teaches Common Core State Standards CCSS.Math.Practice.MP6 http://corestandards.org/Math/Practice/MP6

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Lesson objective: Understand that we can compare quantities using multiplication (such as "one quantity is n times as much as another quantity"),  whether the quantities are whole numbers or fractions.

Students bring prior knowledge of multiplicative comparison from Grade 4, Unit 7, when they worked with whole numbers (4.OA.A.1). This standard is revisited and prior knowledge is extended to multiplicative comparisons involving a fractional amount as students solve word problems where one of the amounts in the comparison is a fraction.  A conceptual challenge students may encounter is assuming that multiplication "makes bigger" or that we cannot make a multiplicative comparison between 4 and 7 because "there is no number we can multiply by 4 to make 7. 

The concept is developed through work with a number line, which reinforces the understanding that fractions are numbers that can be iterated multiple times to show a comparison.  Tape diagrams are also used in order to build on the understanding of multiplication as comparison that students developed in unit 7.

This work helps students deepen their understanding of operations because students extend their understanding of multiplication with whole numbers as comparing how much greater one amount is than another to include fractional amounts.

Students engage in Mathematical Practice 7 (look for and make use of structure) as they incorporate fractions into their understanding of multiplicative structures.

Key vocabulary:

  • compare
  • comparison factor
  • product
  • tape diagram
  • value