Geometry (& GT)
Unit 4: Extending to Three Dimensions
Students’ experience with twodimensional and threedimensional objects is extended to include informal explanations of circumference, area and volume formulas. Additionally, students apply their knowledge of twodimensional shapes to consider the shapes of crosssections and the result of rotating a twodimensional object about a line.
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What will my child learn?
Students will:
Visualize the relation between twodimensional and threedimensional objects.
G.GMD.B.4
Identify the shapes of twodimensional crosssections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects.
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).
G.GMD.A.3
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems (SAT® Content  ATM.08).
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)
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).
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).
Students will:
Visualize the relation between twodimensional and threedimensional objects.
G.GMD.B.4
Identify the shapes of twodimensional crosssections of threedimensional objects, and identify threedimensional objects generated by rotations of twodimensional objects.
 Check for Understanding: Cross Sections of 3D Objects
 Review/Rewind: Rotating 2D Shapes in 3D  Slicing a Rectangular Pyramid
 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).
 Check for Understanding: Geometric Descriptions of RealWorld Objects
 Review/Rewind: Volume of a Cone
 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).
 Check for Understanding: Volume Word Problems with Cones, Cylinders, and Spheres
 Review/Rewind: Volume of Triangular Prism and Cube  Volume of a Sphere
 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: Properties of Shapes
 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
 Review/Rewind: Density Word Problem: Blimp
 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?

Tools & Technology
Shodor Interactive (Cross Section Flyer)  provides an interactive platform for exploring mathematical concepts Math Interactives  allows users to explore concepts of surface area, volume, 3D shapes, and nets 
More 4 U
Volume and Surface Area 