In this lesson, students visualize solids of rotation created from rotating twodimensional figures using an axis of rotation. These visualization skills will be useful in later lessons when students need to analyze twodimensional figures that are cross sections of threedimensional figures. For example, sometimes it is necessary to consider vertical cross sections of cones or pyramids to solve problems involving volume. In future courses, these visualization skills will be applicable when using calculus to compute volumes or when using linear algebra in three or more dimensions.
As students describe characteristics of solids, they have the opportunity to use language precisely (MP6). When students visualize the relationship between two and threedimensional objects, they are thinking abstractly (MP2).
Lesson overview
 1.1 Warmup: Which One Doesn’t Belong: Solids (5 minutes)

1.2 Activity: Axis of Rotation (10 minutes)
 Digital applet in this activity
 Includes "Are you Ready for More?" extension problem

1.3 Activity: From Three Dimensions to Two (15 minutes)
 Digital applet in this activity
 Lesson Synthesis
 1.4 Cooldown: Telescope (5 minutes)
Learning goals:
 Determine the twodimensional shape that when rotated using a given axis generates a particular threedimensional solid.
 Identify and describe (using words and other representations) the threedimensional solid created by rotating a twodimensional figure using a linear axis.
Learning goals (student facing):
 Let’s rotate twodimensional shapes to make threedimensional shapes.
Learning targets (student facing):
 I can draw the twodimensional shape that creates a particular threedimensional solid when rotated using a given axis.
 I can identify the threedimensional solid created by rotating a twodimensional figure using a linear axis.
Required materials:
 Precut figures
 Tape
Required preparation:
 Devices are required for the digital versions of the activity Axis of Rotation and From Three Dimensions to Two.
 If using the digital versions, acquire devices that can run the GeoGebra applet, one for every 23 students.
 If using the paper and pencil version of the Axis of Rotation activity, cut out a set of shapes from card stock for each group of 3–4 students, with enough for at least 1 shape per student.
 Shapes can include rectangles, circles, and various kinds of triangles.
 If desired, find some honeycomb paper decorations to display to students to help them visualize solids of rotation in the Axis of Rotation activity.
Glossary:
 axis of rotation  A line about which a twodimensional figure is rotated to produce a threedimensional figure, called a solid of rotation. The dashed line is the axis of rotation for the solid of rotation formed by rotating the green triangle.
 solid of rotation  A threedimensional figure formed by rotating a twodimensional figure using a line called the axis of rotation. The axis of rotation is the dashed line. The green triangle is rotated about the the axis of rotation line to form a solid of rotation.
 Access the complete Geometry Course glossary.
Standards:
 This lesson builds towards the standard: CCSS.HSGGMD.B.4MS.GGMD.4MO.G.GMD.B.3MO.G.GMD.B.4
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