In grade 7, students described the twodimensional figures that result from slicing threedimensional figures. Here, these concepts are revisited with some added complexity. Students analyze cross sections, or the intersections between planes and solids, by slicing threedimensional objects. Next, they identify threedimensional solids given parallel crosssectional slices. In addition, they revisit solid geometry vocabulary terms from earlier grades: sphere, prism, cylinder, cone, pyramid, and faces.
Spatial visualization in three dimensions is an important skill in mathematics. Understanding the relationship between solids and their parallel cross sections will be critical to understanding Cavalieri’s Principle in later lessons. Cavalieri’s Principle will be applied to the development of the formula for the volume of pyramids and cones. Students use spatial visualization to make sense of threedimensional figures and their cross sections throughout the lesson (MP1).
Lesson overview
 2.1 Warmup: Slice This (5 minutes)

2.2 Activity: Slice That (20 minutes)
 Digital applet in this activity
 Includes "Are you Ready for More?" extension problem

2.3 Activity: Stack ‘Em Up (10 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 2.4 Cooldown: Sketch It (5 minutes)
Learning goals:
 Generate multiple cross sections of threedimensional figures.
 Identify the threedimensional shape resulting from combining a set of cross sections.
Learning goals (student facing):
 Let’s analyze cross sections by slicing threedimensional solids.
Learning targets (student facing):
 I can identify the threedimensional shape that generates a set of cross sections.
 I can visualize and draw multiple cross sections of a threedimensional figure.
Required materials:
 Clay
 Coins
 Cylindrical food items (Approximately cylindrical food items that can be easily sliced. Examples include carrots or cheese sticks.)
 Dental floss
Required preparation:
 Obtain several cylindrical cake snacks or other cylindrical food to cut with a plastic knife.
 Devices are required for the digital version of the activity Slice That.
 If using the paper and pencil version, prepare various solids from clay or play dough, such as cubes, spheres, cones, and cylinders.
 Each group of 34 students should have access to a threedimensional solid to analyze.
 Alternatively, you might consider getting food items from the grocery store with interesting cross sections or threedimensional foam solids from a craft store, and plastic knives to slice the solids.
Glossary:
 cone  A cone is a threedimensional figure with a circular base and a point not in the plane of the base called the apex. Each point on the base is connected to the apex by a line segment.
 cross section  The figure formed by intersecting a solid with a plane.
 cylinder  A cylinder is a threedimensional figure with two parallel, congruent, circular bases, formed by translating one base to the other. Each pair of corresponding points on the bases is connected by a line segment.
 face  Any flat surface on a threedimensional figure is a face. A cube has 6 faces.

prism  A prism is a solid figure composed of two parallel, congruent faces (called bases) connected by parallelograms. A prism is named for the shape of its bases. For example, if a prism’s bases are pentagons, it is called a “pentagonal prism.”

pyramid  A pyramid is a solid figure that has one special face called the base. All of the other faces are triangles that meet at a single vertex called the apex. A pyramid is named for the shape of its base. For example, if a pyramid’s base is a hexagon, it is called a “hexagonal pyramid.”
 sphere  A sphere is a threedimensional figure in which all crosssections in every direction are circles.
 Access the complete Geometry Course glossary.
Standards:
 This lesson builds on the standard: CCSS.7.G.A.3MS.7.G.3MO.7.GM.A.3
 This lesson builds towards the standard: CCSS.HSGGMD.A.1MS.GGMD.1MO.G.GMD.A.1
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