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Lesson Plan

1. Extend understanding of multiplicative comparisons in different types of problems (C)

teaches Common Core State Standards CCSS.Math.Practice.MP4 http://corestandards.org/Math/Practice/MP4
teaches Common Core State Standards CCSS.Math.Practice.MP7 http://corestandards.org/Math/Practice/MP7
teaches Common Core State Standards CCSS.Math.Content.4.OA.A.2 http://corestandards.org/Math/Content/4/OA/A/2
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Lesson objective: Extend understanding that one of the factors in a multiplication equation tells how many times greater the product is compared to the other factor in order to find any unknown quantity.

Students bring prior knowledge of using the relationship between three numbers in a multiplication equation to figure out a missing amount that makes the equation true from 3.OA.A.4. This prior knowledge is extended to generalize that the meaning of multiplicative relationship does not change depending on the type of problem being solved as students find the unknown product, group size, and number of groups. A conceptual challenge students may encounter is identifying which amount is unknown when different types of problems are used. 

The concept is developed through work with equations and tape diagrams, which help students visualize how the product of a multiplication equation is a certain number of times greater compared to one of the factors.

This work helps students deepen their understanding of operations because multiplication shows how many times greater one quantity is compared to another quantity.

Students engage in Mathematical Practice 7 (look for and make sense of structure) as they recognize that the meaning of multiplicative comparison stays the same, and use this relationship to solve for any unknown.

Key vocabulary:

  • comparison
  • equation
  • factor
  • greater than
  • less than
  • product
  • tape diagram
  • times
  • unknown

Special materials needed:

  • colored pencils, if desired, for coloring in tape diagrams
  • graph paper, if desired, for creating tape diagrams

 

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Solving problems using multiplicative comparison

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