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2022 PA-GM-2-1

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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 cm².

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 cm², to express the surface area of rectangular prisms.

Student Actions	Teacher Actions
Develop Mathematical Reasoning when exploring and communicating reasoning strategies for decomposing and utilizing nets to determine the surface area in a variety of mathematical situations involving rectangular prisms Develop a Deep and Flexible Conceptual Understanding when discovering that the surface area of a 3-D shape is equivalent to the total area of its composite figure and that the measurement is in squared units.	Use and connect mathematical representations by providing a variety of 3-D 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 problem-solving in the context of real-world 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 three-dimensional 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 same-sized 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 three-dimensional figures (G.3D.1.1).