Standards:
GGMD.A.1 Give
an informal argument for the formulas for the circumference of a circle, area
of a circle, volume of a cylinder, pyramid, and cone. Use dissection
arguments, Cavalieri’s principle, and informal limit arguments.
GGMD.A.2 (+)
Give an informal argument using Cavalieri’s principle for the formulas for
the volume of a sphere and other solid figures.
GGMD.A.3 Use
volume formulas for cylinders, pyramids, cones and spheres to solve problems.^{★}
GGMD.B.4 Identify
the shapes of twodimensional crosssections of threedimensional objects,
and identify threedimensional objects generated by rotations of
twodimensional objects.
GMG.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).^{★}
GMG.A.2 Apply
concepts of density based on area and volume in modeling situations (e.g.,
persons per square mile, BTUs per cubic foot).^{ }^{★}
GMG.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).^{ }^{★}
Focus Standards of
Mathematical Practice:
MP.1 Make sense of problems and persevere in
solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the
reasoning of others.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated
reasoning.
Instructional
Outcomes:
Full Development of the Major Clusters,
Supporting Clusters, Additional Clusters and Mathematical Practices for this
unit could include the following instructional outcomes:
GGMD.A.1
 I can recognize crosssections of
solids as twodimensional shapes
 I can recognize formulas for area and
circumference of a circle and volume of a cylinder, pyramid, and cone
 I can use the techniques of dissection
and limit arguments
 I can recognize Cavalieri’s principle
 I can decompose volume formulas into
area formulas using crosssections
 I can apply dissection and limit
arguments (e.g. Archimedes’ inscription and circumscription of polygons
about a circle) and as a component of the informal argument for the
formulas for the circumference and area of a circle
 I can apply Cavalieri’s Principle as a
component of the informal argument for the formulas for the volume of a
cylinder, pyramid, and cone
GGMD.A.2(+)
 I can calculate the volume of a sphere
and other solids using Cavalieri’s principle.
GGMD.A.3
 I can utilize the appropriate formula
for volume depending on the figure
 I can use volume formulas for
cylinders, pyramids, cones, and spheres to solve contextual problems
GGMD.B.4
 I can use strategies to help visualize
relationships between twodimensional and threedimensional objects
 I can relate the shapes of
twodimensional crosssections to their threedimensional objects
 I can discover threedimensional
objects generated by rotations of twodimensional objects
GMG.A.1
 I can use measures and properties of
geometric shapes to describe realworld objects to solve geometric
problems
 I can, given a realworld object,
classify the object as a known geometric shape; use this to solve
problems in context
GMG.A.2
 I can define density
 I can apply concepts of density based
on area and volume to model reallife situations (e.g., persons per
square mile, BTUs per cubic foot)
GMG.A.3
 I can describe a typographical grid
system
 I can 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
system based on ratios)
