This lesson unit is intended to help teachers assess how well students are able to visualize two-dimensional cross-sections of representations of three-dimensional objects. In particular, the lesson will help you identify and help students who have difficulties recognizing and drawing two-dimensional cross-sections at different points along a plane of a representation of a three-dimensional object.

Tutorial videos on cross sections of 3D objects along with interactive practice problems.

The purpose of this task is to surface a variety of strategies for visualizing twodimensional cross sections of three-dimensional objects, and to identify and/or draw such cross sections. Students encounter cross sections when they slice a loaf of bread, a piece of cake, or a hard-boiled egg, or when they tilt a glass of water in different ways and examine the surface of the water. This task aims to formalize these observations by defining a cross section as the intersection of a plane and a three-dimensional object.

The purpose of this task is to develop skills for visualizing solids of revolution generated by rotating two-dimensional objects about an axis. Students should also begin to recognize that a solid of revolution can be thought of as a collection of circular disks, and that cross sections perpendicular to the axis of revolution will always be circular.

Interactive applet that allows users to explore cross sections of different 3D objects by manipulating the properties.

This lesson utilizes the concepts of cross-sections of three-dimensional models to demonstrate the derivation of two-dimensional shapes.

Brief written explanation, link to video, example and practice problems on creating a solid by rotating shapes around a line.

This activity is meant for students to visualize the cross-sections of regular solids.  The activity is a GeoGebra created one and students find it very useful in understanding the cross-sections created by different planes.

In this Khan Academy activity, students will identify which 3D objects will create a certain 2D cross section.

In this Khan Academy activity, students will identify which 3D objects will create a certain 2D cross section.

Students examine the relationship between a cross-section and the base of a general cone. Students understand that pyramids and circular cones are subsets of general cones just as prisms and cylinders are subsets of general cylinders.

Students are reintroduced to several solids as a lead into establishing the volume formulas for the figures. They also identify the three-dimensional object generated by the rotation of a rectangular region about an axis

Students consider what it means to build a three-dimensional figure out of cross-sections and discuss the criteria to build a good approximation of a figure. After some practice of drawing cross-sections, students watch a 3D printer in action and make a tie between how a 3D printer works and Cavalieri's principle.

A series of interactive applets that allows the user to rotate various shapes around a given axis to form a solid.

This lesson unit is intended to help teachers assess how well students are able to: choose appropriate mathematics to solve a non-routine problem; generate useful data by systematically controlling variables; and develop experimental and analytical models of a physical situation.

In this Khan Academy activity, students will rotate 2D shapes about a line and determine what 3D shape is produced.

In this task students examine another solid of revolution—a frustum—and create a strategy for finding its volume. They then use a variety of strategies to decompose a figure that consists of curved edges into cylinders, frustums and cones to generate a sequence of better and better approximations of the actual volume of the solid.

Students will work through a self-paced tutorial to learn some of the basics of Sketchup and produce a 3D design of a dog house incorporating their choices for materials and design. (Note: I have a collection of these tutorials that I am willing to share that build on student knowledge of Sketchup and introduce 1-2 new tools with each tutorial. This is just one of those tutorials.)