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2022 PA-GM-2-1

Page history last edited by Brigit Minden 10 months ago

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). 

 

OKMath Framework Introduction

Pre-Algebra Introduction

 

 

 

 

 

 

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