PA.GM.2.1
PA.GM.2.1 Calculate the surface area of a rectangular prism using decomposition or nets. Use appropriate measurements such as cm^{2}.
In a Nutshell
Students extend previous knowledge of representing surface area with components of nets to develop an understanding of how these components are related to the algebraic representation of 2(l x w) + 2(l x h) + 2(w x h). Students will use appropriate unit measurements, such as cm^{2}, to express the surface area of rectangular prisms.
Student Actions

Teacher Actions



Use and connect mathematical representations by providing a variety of 3D rectangular prisms for students to decompose into appropriate net models and explore the relationship among individual and composite areas of the faces.

Support productive struggle by allowing time and structural support for students to develop strategies for finding the surface area of decomposed rectangular prisms.
 Implement tasks that promote reasoning and problemsolving in the context of realworld situations, such as wrapping a present, for students to develop and apply processes for determining surface area and assess the reasonableness of solutions in context.

Key Understandings

Misconceptions


Use decomposition of the rectangular prisms to find the areas of each surface, then use those areas to find the total surface area of the prisms.

All rectangular prisms contain three pairs of equivalent faces containing the same area and can be expressed with the algebraic representation: 2(l x w) + 2(l x h) + 2(w x h).


Students may have difficulty visualizing the unseen faces of a threedimensional figure, making it difficult to create an accurate net representation and/or determine the correct surface area. Students may forget how to find the area of a rectangle.

Students may assume that they only need to find the area of the faces that are visible in a pictorial model.

Students may not recognize that a rectangular prism has three pairs of equivalent faces and repeat the areas for a pair of faces in place of another pair.

Students may not express total surface area in squared units or with the appropriate measurement.

Knowledge Connections

Prior Knowledge

Leads to


Develop and use formulas for the area of squares and parallelograms (6.GM.2.1).

Recognize that the surface area of a rectangular prism can be found by finding the area of each component of the net of that figure (7.GM.1.1).

Using a variety of tools and strategies, develop the concept that surface area of a rectangular prism can be found by wrapping the figure with samesized square units without gaps or overlap (7.GM.1.2).

 Represent, use, and apply mathematical models and other tools (e.g., nets, measuring devices, formulas) to solve problems involving surface area and volume of threedimensional figures (G.3D.1.1).

OKMath Framework Introduction
PreAlgebra Introduction
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