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.
- Check for Understanding: Cross Sections of 3D Objects
- Review/Rewind: Rotating 2D Shapes in 3D | Slicing a Rectangular Pyramid
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 Real-World Objects
- Review/Rewind: Volume of a Cone
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
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
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
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
What are some signs of student mastery?
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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 |