Lesson plan

4. Splitting rectangles to solve for area (C)

teaches Common Core State Standards CCSS.Math.Content.3.MD.C.7c http://corestandards.org/Math/Content/3/MD/C/7/c
teaches Common Core State Standards CCSS.Math.Practice.MP5 http://corestandards.org/Math/Practice/MP5
teaches Common Core State Standards CCSS.Math.Practice.MP7 http://corestandards.org/Math/Practice/MP7
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Lesson objective: Understand that a rectangle can be decomposed into two smaller rectangles, and the area of those smaller rectangles can be added together to find the total area of the original rectangle.

Students bring prior knowledge of area from 3.MD.C.5, 3.MD.C.6, and 3.MD.C.7. This prior knowledge is extended to larger rectangles as students decompose one of the sides of a larger rectangle. A conceptual challenge students may encounter is decomposing rectangles in ways that will make it easier to find the total area of the original rectangle. 

The concept is developed through work with the area model, which shows students the square units of the original rectangle and the smaller ones of which it is composed.

This work helps students deepen their understanding of equivalence because it shows that the sum of the area of the two smaller rectangles is equal to the total area of the orginal rectangle.

Students engage in Mathematical Practice 7 (Look for and make use of structure) as they solve for the area of more challenging rectangles using the area model and figure out efficient ways of solving by splitting up the length of the rectangle.

Key vocabulary:

  • area
  • area model
  • equation

Special materials needed:

  • one inch tiles
  • grid paper