G.3D.1.1
G.3D.1.1 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 (prisms, cylinders, pyramids, cones, spheres, composites of these figures).
In a Nutshell
Students will extend their knowledge of nets, measuring devices, and formulas for the surface area and volume of basic rectangular prisms and cylinders. Students will now explore processes for surface area and volume of more complex prisms as well as pyramids, cones, spheres, and composites of these figures.
Student Actions

Teacher Actions


Develop strategies for problemsolving by examining diagram models or descriptions of 3D objects to determine appropriate formulas and/or strategies for situations involving surface area and volume.

Develop a deep and flexible conceptual understanding by recognizing similarities and differences among properties of various threedimensional shapes for knowing how and when to apply corresponding dimensions to surface area and volume.

Develop accurate and appropriate procedural fluency by using efficient and accurate algebraic processes to manipulate and/or solve appropriate surface area and volume formulas.


Use and connect mathematical representations by presenting mathematical problems that include various models of threedimensional objects from different orientations and perspectives.

Implement tasks that promote reasoning and problemsolving by allowing students to explore properties of surface area and volume for a variety of threedimensional objects and developing strategies for solving for unknown values.

Key Understandings

Misconceptions


Solids have surface area and volume.

Composite solids are composed of different solids that are connected.

Surface area is a twodimensional idea and volume is a threedimensional idea

The surface area and a net of a figure are connected in that a net is a twodimensional representation of the surface area for a threedimensional figure.

The net of a solid can be used to visualize and build a physical model of the solid and a solid can be deconstructed into a net.

Surface area of any solid is the sum of the areas of all of its faces.

Volume of any solid is the product of the area of a solid's base and its height

The volume of a cone contains 1/3 the volume of a cylinder and the volume of a pyramid contains 1/3 the volume of a prism.


Students use diameter instead of the radius when determining surface area and/or the volume of a cylinder.

Students do not understand the difference between answers that are left in terms of 𝝅 and answers that are given as a decimal approximation.

Students cannot identify the base of the solid

Students use the volume and surface areas interchangeably

Students use units incorrectly when dealing with surface area and volume. For example, using square units instead of cubic units for volume

Students are not able to differentiate between height and slant height in pyramids and cones.

Students may include the areas of adjoining faces when determining the surface area of composite figures.

Students may incorrectly simplify a formula when evaluating for surface area and/or volume.

Knowledge Connections

Prior Knowledge

Leads to



OKMath Framework Introduction
Geometry Grade Introduction
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