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Geometry (& Geometry GT)

Unit 4:
Extending to Three Dimensions

Students’ experience with two-dimensional and three-dimensional objects is extended to include informal explanations of circumference, area and volume formulas. Additionally, students apply their knowledge of two-dimensional shapes to consider the shapes of cross-sections and the result of rotating a two-dimensional object about a line.

NOTE - The "Background Info. and Guided Practice" links require a free registration to use the LearnZillion content. Parents can create a free "Teacher" account here. Once logged in you can access the "Background Info. & Guided Practice" videos without interruption.

What will my child learn?

Students will:

Visualize the relation between two-dimensional and three-dimensional objects.  
G.GMD.B.4
Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
  • Background Info.
  • Check for Understanding: Cross Sections of 3D Objects
  • Enrichment Tasks: Tennis Balls in a Can | Global Positioning System I  

Explain volume formulas and use them to solve problems.  
G.GMD.A.1
Give an informal argument for the formulas for the volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments (SAT® Content - ATM.08).
  • Background Info. 
  • Check for Understanding: Geometric Descriptions of Real-World Objects
  • Enrichment Tasks: Circumference of a Circle | Area of a Circle  

G.GMD.A.3
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems (SAT® Content - ATM.08).
  • Background Info.
  • Check for Understanding: Volume Word Problems with Cones, Cylinders, and Spheres
  • Enrichment Tasks: The Great Egyptian Pyramids | Volume Estimation  

Apply geometric concepts in modeling situations (These standards are to be embedded throughout all units of instruction.). 
G.MG.A.1 
Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder)
  • Check for Understanding: 2D Geometric Models
  • Enrichment Tasks: Toilet Roll | How Thick is a Soda Can II? 

G.MG.A.2 
Apply concepts of density based on area and volume in modeling situations (e.g. persons per square mile, BTUs per cubic foot).
  • Check for Understanding: Surface and Volume Density Word Problems
  • Enrichment Tasks: A Ton of Snow | Indiana Jones and Golden Statue

G.MG.A.3 
Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
  • Check for Understanding: 2D Geometric Models
  • Enrichment Tasks: Ice Cream Cone | Satellite 

What are some signs of student mastery?
  • Uses volume formulas to solve mathematical and contextual problems that involve cylinders, pyramids, cones and spheres.
  • Uses dissection arguments, Cavalieri’s principle and informal limit arguments to support the formula for the circumference of a circle, area of a circle, volume of a cylinder, pyramid and cone.
  • Identifies the shapes of two-dimensional cross-sections of three-dimensional objects and identifies three-dimensional objects generated by rotations of two-dimensional objects.
More 4 U
Looking for clarification on some of the vocabulary used in the Geometry course? A slight variation in units, click here to download the MD State Department of Education's (MSDE's) geometry glossary.

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