**Subject Area:**Mathematics

**Grade:**912

**Domain-Subdomain:**Geometry: Geometric Measurement & Dimension

**Cluster:**Level 2: Basic Application of Skills & Concepts

**Cluster:**Visualize relationships between two-dimensional and three-dimensional objects. (Geometry - Additional Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

**Date Adopted or Revised:**02/14

**Date of Last Rating:**02/14

**Status:**State Board Approved - Archived

**Assessed:**Yes

**Assessment Limits :**

Items may include vertical, horizontal, or other cross-sections.Items may include more than one three-dimensional shape.

**Calculator :**Neutral

**Clarification :**

Students will identify the shape of a two-dimensional cross-section of

a three-dimensional object.Students will identify a three-dimensional object generated by a

rotation of a two-dimensional object**Stimulus Attributes :**

Items may be set in a real-world or mathematical context.A verbal description of a cross-section or a three-dimensional shape

may be used.**Response Attributes :**

Items may require the student to draw a line that shows the location

of a cross-section.

**Test Item #:**Sample Item 1**Question:**A rectangle and a horizontal line segment are shown.

What is the resulting object when the rectangle is rotated about the horizontal line segment?

**Difficulty:**N/A**Type:**MC: Multiple Choice

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Original Student Tutorial

## Problem-Solving Tasks

## Virtual Manipulatives

## MFAS Formative Assessments

Students are given the coordinates of the vertices of a rectangle and asked to describe the solid formed by rotating the rectangle about a given axis.

Students are given the coordinates of the vertices of a right triangle and asked to describe the solid formed by rotating the triangle about a given axis.

Students are asked to identify and draw cross sections of a rectangular prism and to describe their dimensions.

Students are asked to identify and describe two-dimensional cross sections of three-dimensional solids.

Students are asked to sketch, describe, and compare three horizontal cross sections of a cone.

Students are given a solid and asked to determine the two-dimensional shape that will create the solid when rotated about the *y*-axis.

## Original Student Tutorials Mathematics - Grades 9-12

Learn how to determine the shape of a cross-section created by the intersection of a slicing plane with a pyramid or prism in this ninja-themed, interactive tutorial.

## Student Resources

## Original Student Tutorial

Learn how to determine the shape of a cross-section created by the intersection of a slicing plane with a pyramid or prism in this ninja-themed, interactive tutorial.

Type: Original Student Tutorial

## Problem-Solving Tasks

Reflective of the modernness of the technology involved, this is a challenging geometric modeling task in which students discover from scratch the geometric principles underlying the software used by GPS systems.

Type: Problem-Solving Task

This task is inspired by the derivation of the volume formula for the sphere. If a sphere of radius 1 is enclosed in a cylinder of radius 1 and height 2, then the volume not occupied by the sphere is equal to the volume of a "double-naped cone" with vertex at the center of the sphere and bases equal to the bases of the cylinder

Type: Problem-Solving Task

## Virtual Manipulatives

Using this resource, students can manipulate the measurements of a 3-D hourglass figure (double-napped cone) and its intersecting plane to see how the graph of a conic section changes. Students will see the impact of changing the *height* and *slant* of the cone and the *m* and *b* values of the plane on the shape of the graph. Students can also rotate and re-size the cone and graph to view from different angles.

Type: Virtual Manipulative

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.

Type: Virtual Manipulative

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.

Type: Virtual Manipulative

## Parent Resources

## Problem-Solving Tasks

Reflective of the modernness of the technology involved, this is a challenging geometric modeling task in which students discover from scratch the geometric principles underlying the software used by GPS systems.

Type: Problem-Solving Task

This task is inspired by the derivation of the volume formula for the sphere. If a sphere of radius 1 is enclosed in a cylinder of radius 1 and height 2, then the volume not occupied by the sphere is equal to the volume of a "double-naped cone" with vertex at the center of the sphere and bases equal to the bases of the cylinder

Type: Problem-Solving Task