Common Core Geometry Unit 4 Starting Points
Unit 4: Extending to Three Dimensions
Essential Questions:
● How can a real-world object be modeled by a three-dimensional figure? How can
this be helpful in solving real-world problems related to the object?
● How can the formulas for volume, area and circumference be explained using
various tools and visual or tactile representations?
● How can the cross-section of a three-dimensional figure be described or sketched?
Are all cross-sections the same for a given three-dimensional figure?
● What will be the three-dimensional result of rotating a two-dimensional figure
about a line?
Curriculum Standards:
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.
Explain volume formulas and use them to solve problems.
G.GMD.A.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve
problems.
Apply geometric concepts in modeling situations.
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).
Apply geometric concepts in modeling situations. (Note: This standard will be
embedded throughout the unit)
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).
Approximate Length: 20-25 days (15-20 G/T)
Standard(s)
Days
Notes
G.GMD.B.4
Big Ideas:
3-5
G.MG.A.1
Identifying geometric figures from real-world
objects.
This document represents one sample starting points for the unit. It is not all-inclusive and is only
one planning tool. Please refer to the wiki for more information and resources.
Identifying cross sections in three-dimensional
objects.
Describe what three-dimensional objects are
generated by rotating two-dimensional objects.
Resources:
 Lesson: Cross Sections of 3D Figures
Assessment Items:
 Illustrative Mathematics: Tennis Balls in
a Can
 Illustrative Mathematics: Global
Positioning System II
G.GMD.A.1
G.MG.A.1
5-7
Big Ideas:
Derive formulas for volumes of cones, spheres,
pyramids, and cylinders.
Explore and derive Cavalieri’s principle.
Resources:
 Lesson: Cavalieri’s Principle
Assessment Items:
 Illustrative Mathematics: Use
Cavalieri’s Principle to Compare
Aquarium Volumes
G.GMD.A.3
G.MG.A.1
5-7
Big Ideas:
Solve real-world problems using cones, spheres,
pyramids, and cylinders.
Resources:
 Task: Fish Tank Decoration
Assessment Items:
 Illustrative Mathematics: Centerpiece
 Illustrative Mathematics: Doctor’s
Appointment
G.MG.A.3
G.MG.A.1
3-5
Big Ideas:
This document represents one sample starting points for the unit. It is not all-inclusive and is only
one planning tool. Please refer to the wiki for more information and resources.
Design a three dimensional structure to meet
criteria (include minimizing materials used or
maximizing volumne).
Resources:
 Task: Design It
 Lesson: Geometry Virtual Tour
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs
3.0 Unported License.
This document represents one sample starting points for the unit. It is not all-inclusive and is only
one planning tool. Please refer to the wiki for more information and resources.