Standard 7 : Polyhedra and Other Solids (Archived)



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Describe and make regular and nonregular polyhedra (cube, pyramid, tetrahedron, octahedron, etc.). Explore relationships among the faces, edges, and vertices of polyhedra. Describe sets of points on spheres, using terms such as great circle. Describe symmetries of solids, and understand the properties of congruent and similar solids.

General Information

Number: MA.912.G.7
Title: Polyhedra and Other Solids
Type: Standard
Subject: X-Mathematics (former standards - 2008) - Archived
Grade: 912
Body of Knowledge: Geometry

Related Benchmarks

This cluster includes the following benchmarks
Code Description
MA.912.G.7.1: Describe and make regular, non-regular, and oblique polyhedra, and sketch the net for a given polyhedron and vice versa.
MA.912.G.7.2: Describe the relationships between the faces, edges, and vertices of polyhedra.
MA.912.G.7.3: Identify, sketch, find areas and/or perimeters of cross sections of solid objects.
MA.912.G.7.4: Identify chords, tangents, radii, and great circles of spheres
MA.912.G.7.5: Explain and use formulas for lateral area, surface area, and volume of solids.
MA.912.G.7.6: Identify and use properties of congruent and similar solids.
MA.912.G.7.7: Determine how changes in dimensions affect the surface area and volume of common geometric solids.


Related Access Points

This cluster includes the following access points.

Independent

Access Point Number Access Point Title
MA.912.G.7.In.a: Identify and describe three-dimensional solids, including sphere, cylinder, rectangular prism, and cone in the environment using mathematical names.
MA.912.G.7.In.b: Identify a plane that divides a sphere in half.
MA.912.G.7.In.c: Measure rectangular prisms to find the volume using the literal formula: length x width x height.
MA.912.G.7.In.d: Compare volumes of three-dimensional solids using physical and visual models.
MA.912.G.7.In.e: Identify the effect of changes in the lengths of the sides of cubes or rectangular prisms on the volume using physical and visual models.

Supported

Access Point Number Access Point Title
MA.912.G.7.Su.a: Identify properties of three-dimensional solids, such as sphere, cylinder, cube, and cone in the environment, when given the common name.
MA.912.G.7.Su.b: Compare volumes of three-dimensional solids in real-world situations.
MA.912.G.7.Su.c: Identify that changes in the lengths of sides of cubes or rectangular prisms will make the volume smaller or larger using physical models.

Participatory

Access Point Number Access Point Title
MA.912.G.7.Pa.a: Identify objects or pictures with three-dimensional solids in real-world situations.
MA.912.G.7.Pa.b: Match two or more objects with three-dimensional solids based on a given feature, such as the number of faces or overall size, in real-world situations.


Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Lesson Plans

Name Description
Cylinder Volume Lesson Plan:

Using volume in the real world

Relating Surface Area and Volume:

Students will recognize that while the surface area may change, the volume can remain the same. This lesson is enhanced through the multimedia CPALMS Perspectives Video, which introduces students to the relationship between surface area and volume.

Unit/Lesson Sequence

Name Description
Three Dimensional Shapes:

In this interactive, self-guided unit on 3-dimensional shape, students (and teachers) explore 3-dimensional shapes, determine surface area and volume, derive Euler's formula, and investigate Platonic solids. Interactive quizzes and animations are included throughout, including a 15 question quiz for student completion.

Virtual Manipulatives

Name Description
Cross Section Flyer - Shodor:

With this online Java applet, students use slider bars to move a cross section of a cone, cylinder, prism, or pyramid. This activity allows students to explore conic sections and the 3-dimensional shapes from which they are derived. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

A Plethora of Polyhedra:

This program allows users to explore spatial geometry in a dynamic and interactive way. The tool allows users to rotate, zoom out, zoom in, and translate a plethora of polyhedra. The program is able to compute topological and geometrical duals of each polyhedron. Geometrical operations include unfolding, plane sections, truncation, and stellation.



Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

Virtual Manipulatives

Title Description
Cross Section Flyer - Shodor:

With this online Java applet, students use slider bars to move a cross section of a cone, cylinder, prism, or pyramid. This activity allows students to explore conic sections and the 3-dimensional shapes from which they are derived. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

A Plethora of Polyhedra:

This program allows users to explore spatial geometry in a dynamic and interactive way. The tool allows users to rotate, zoom out, zoom in, and translate a plethora of polyhedra. The program is able to compute topological and geometrical duals of each polyhedron. Geometrical operations include unfolding, plane sections, truncation, and stellation.