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.
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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.
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 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
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What are some signs of student mastery?
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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. |
