explain the linear equation of solid
Answers
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In the first part of the lesson, students plot
ordered pairs, graph linear functions defined
by a variety of representations, and then
create two-dimensional figures using the lines as
boundaries. Students are asked to calculate the
perimeters and the areas of the bounded regions and
then to describe and sketch the three dimensional
figures formed when the planar regions are revolved
about a horizontal or vertical line. Students must
determine the dimensions of the solids based on
their understanding of how the shapes are created
and then calculate the volumes. As students
compare the volumes when the same planar region
is revolved about different lines, they develop a
deeper conceptual understanding about how the
change in the radius impacts the overall volume of
a solid. The activity, which includes an interactive
computer demonstration and a real-world model of
a custom bowling ball, provides an engaging setting
for students to practice and apply their skills with
graphing linear functions, as well as calculating
areas and volumes.
The lesson is designed to enhance student
understanding of the Common Core State Standards
by developing coherence and connections among
a variety of mathematical concepts, skills, and
practices. Each question in the lesson requires
students to incorporate several of the targeted and
reinforced/applied standards in new or non-standard
situations, including graphing linear equations,
recognizing two-dimensional bounded regions and
the three-dimensional figures they sweep out by
rotation, as well as calculating perimeters, areas, and
volumes.