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5-GM-2-2

Page history last edited by Robbyn Glinsmann 6 years, 2 months ago

5.GM.2.2 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.

In a Nutshell

In objective 5.GM.2.2, students will be able to use the most efficient strategies to determine the surface area of a rectangular prism and the net of a rectangular prism. They must conceptualize the idea that different sized shapes can have the same surface areas, and this can be achieved through illustrations, construction, and manipulation of objects. This is their first experience with surface area. They should not be exposed to the surface area formula, but find surface area by finding the area of each component of the net.

Student Actions	Teacher Actions
Develop a Deep and Flexible Conceptual Understanding by finding the surface area of each component of a decomposed net to then determine the surface area of the whole three-dimensional figure. Develop the Ability to Make Conjectures, Model, and Generalize by recognizing 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. Develop Accurate and Appropriate Procedural Fluency by developing and utilizing formulas to determine areas of figures. Develop the Ability to Make Conjectures, Model, and Generalize by using a model or concrete manipulatives to find surface area to aid in the visualization of concepts and relationships. Example, deconstructing a cereal box.	Implement tasks that promote reasoning and problem solving by allowing the students to discover their most efficient way to determine surface area. Use and connect mathematical representations by modeling the decomposition of rectangular prisms into nets and asking students to explain their thinking as they also decompose a prism into a net. Build procedural fluency from conceptual understanding to become efficient in using the area algorithm, and then finding the total area of all surfaces.
Key Understandings	Misconceptions
Determine the surface area of a rectangular prism by adding the areas of each face. Justify the idea that rectangular prisms with different dimensions can have the same area. Deconstruct and construct a 3D shape into the proper net and assign the correct measurements to each face segment.	Confuse area and perimeter, surface area, and volume. Think if they can’t see it in the picture, the face or edge is not there. Think there is only one possible net for each figure. Think it has to be in a specific orientation for a net to be produced. Think if there is a missing side length, they can’t figure out the length based on other properties of the shape.