Student Actions

Teacher Actions

• Demonstrate a deep and flexible conceptual understanding of mathematical concepts by decomposing a rectangular prism to apply knowledge of area for squares and rectangles to find the surface area and discover that rectangular prisms containing faces of different dimensions can have the same surface area. 

• Develop the ability to make conjectures, model, and generalize by making predictions about the surface area of a given rectangular prism and creating mathematical models, including nets and decomposition, to develop conjectures for the surface area of a rectangular prism of any size.

• Develop the ability to communicate mathematically when using mathematical language to describe, discuss, write about, interpret, and model situations involving surface area of a rectangular prism. 

• Implement tasks that promote reasoning and problem-solving to allow students the opportunity to compare and develop efficient strategies for determining the surface area of rectangular prisms.

• Use and connect mathematical representations by providing opportunities for students to decompose rectangular prisms and make their thinking visible by modeling their mathematical decompositions

• Pose purposeful questions to support students in explaining and/or modeling their thought process in developing the concept of surface area. 

Key Understandings

Misconceptions 

• Deconstruction and reconstruction of a figure to calculate area.

• Surface area refers to how many square units it takes to cover all of the faces of a three-dimensional object.

• Surface area is expressed in square units since the surface area is the combination of the area of its faces.

• The surface area of a rectangular prism is determined by combining the areas of all 6 rectangular and/or square faces.

• Rectangular prisms containing rectangular and/or square faces of different dimensions will have the same surface area when the sum of the areas of the faces is equivalent.

• Assign side length measurements from a rectangular prism model to corresponding segment lengths within the 2-dimensional net representation.

• A rectangular prism can be deconstructed into a 2-dimensional model of six connected, but non-overlapping, rectangular, and/or square faces. 

• Students may confuse area and perimeter and incorrectly calculate the area of the faces of a rectangular prism.

• Students may think if a face or edge is not visible in the picture it does not exist in the net representation.

• Students may think a specific orientation of a rectangular prism has to be true for a net to be produced.

• Students may not recognize and/or use other properties or measurements in a rectangular prism figure to determine a missing measurement. 

• Students may not include the areas of all 6 faces in a net representation when calculating surface area. 

  Knowledge Connections

Prior Knowledge

Leads to 

• Recognize and draw a net for a three-dimensional figure (cube, rectangular prism, pyramid). (5.GM.1.3)

• Recognize that the surface area of a three-dimensional figure with rectangular faces with whole numbered edges can be found by finding the area of each component of the net of that figure. Know that three-dimensional shapes of different dimensions can have the same surface area. (5.GM.2.2)

• Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithms and finding unknown measures. (6.GM.2.1) 

• Calculate the surface area of a rectangular prism using decomposition or nets. Use appropriate units (e.g., cm²). (PA.GM.2.1)