Lesson plan

8. Understanding Volume as Additive (C)

teaches Common Core State Standards CCSS.Math.Content.5.MD.C.5c http://corestandards.org/Math/Content/5/MD/C/5/c
teaches Common Core State Standards CCSS.Math.Practice.MP7 http://corestandards.org/Math/Practice/MP7
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Lesson objective: Understand that volume measures are additive to find the volume of irregular solid figures.

Students bring prior knowledge of area as additive from 3.MD.C.7d. This prior knowledge is extended to three dimensions as students find the volume of irregular solid figures by decomposing into right rectangular prisms. A conceptual challenge students may encounter is thinking that the volumes of numerous right rectangular prisms are multiplied by each other. 

The concept is developed through work with an irregular solid figure, which can be decomposed into right rectangular prisms that students are capable of computing the volume. 

This work helps students deepen their understanding of operations because numerous volumes can be added together for a total volume and volume is found by multiplying the dimensions of a right rectangular prism. 

Students engage in Mathematical Practice 7 (Look for and make use of structure) as they connect the structure to multiplicative reasoning, recognizing the iteration of layers when computing volume. Students recognize the volume of right rectangular prisms can be added together to compose irregular solid figures. 

Key vocabulary:

  • area
  • associative property
  • iterate
  • right rectangular prism
  • volume

Special materials needed:

  • graph paper
  • isometric dot paper
  • unit cubes