GEOM.MATH.10.A

Identify the shapes of two-dimensional cross-sections of prisms, pyramids, cylinders, cones, and spheres and identify three-dimensional objects generated by rotations of two-dimensional shapes.

Geometry · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

Standard Unwrapping

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Vocabulary
shapestwo-dimensional cross-sectionsprismspyramidscylindersconesspheresthree-dimensional objectsrotationstwo-dimensional shapes
Skills
  • identify (shapes of two-dimensional cross-sections of prisms, pyramids, cylinders, cones, and spheres) #dok2
  • identify (three-dimensional objects generated by rotations of two-dimensional shapes) #dok2
  • analyze (the relationship between three-dimensional solids and their two-dimensional cross-sections) #dok2
  • describe (the formation of three-dimensional objects from two-dimensional rotations) #dok2
Learning Targets
  • I can recognize and name the shapes formed by cutting through prisms, pyramids, cylinders, cones, and spheres. #dok1
  • I can describe the process of creating a three-dimensional object by rotating a two-dimensional shape. #dok2
  • I can identify three-dimensional objects that result from rotating two-dimensional shapes. #dok2
  • I can analyze how slicing different parts of three-dimensional figures creates specific two-dimensional cross-sections. #dok2
Big Ideas
  • Three-dimensional objects can be understood and explored by examining their two-dimensional cross-sections and by observing how two-dimensional shapes create solids through rotation.
  • The relationship between two- and three-dimensional figures provides insight into the structure, properties, and formation of geometric shapes.
Essential Questions
  • How can slicing a three-dimensional object reveal its structure?
  • What two-dimensional shapes could result from different cuts of the same three-dimensional object?
  • How do two-dimensional shapes generate three-dimensional objects when rotated?
  • In what real-world contexts do cross-sections and solids of revolution appear?
  • How does understanding cross-sections and rotations help us visualize and solve geometric problems?