# 8. Splitting Rectilinear Shapes to Find Area (C)

teaches Common Core State Standards CCSS.Math.Content.3.MD.C.7d http://corestandards.org/Math/Content/3/MD/C/7/d
teaches Common Core State Standards CCSS.Math.Practice.MP8 http://corestandards.org/Math/Practice/MP8

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Lesson objective: Understand that the area of a rectilinear shape is additive.

Students bring prior knowledge of area of rectangles from 3.MD.C.5 a & b, 3.MD.C.6, 3.MD.C.7a. This prior knowledge is extended to shapes that are not quadrilaterals as students decompose the shape into rectangles of which they can find the area. A conceptual challenge students may encounter is looking at the sides of all the rectangles which make up the rectilinear figure.

The concept is developed through work with the area model, which allows students to decompose the shape to find the area of smaller rectangles and put it back together to find the total area.

This work helps students deepen their understanding of operations because addition of the area of the rectangles is used to find the area of a rectilinear shape.

Students engage in Mathematical Practice 8 (Look for and express regularity in repeated reasoning) as they use the area model to find the area of rectangles within a rectilinear shape to solve the total area of the rectilinear shape.

Key vocabulary:

• area
• area model
• square units

Special materials needed:

• graph paper
• square tiles
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