Geometry
National Council of Teachers
of Mathematics
Standards 2000
URL: http://standards.nctm.org/document/chapter6/geom.htm
For all grades, NCTM standards focus
on students being able to: "analyze characteristics
and properties of two- and three-dimensional geometric
shapes and develop mathematical arguments about
geometric relationships; specify locations and
describe spatial relationships using coordinate
geometry and other representational systems; apply
transformations and use symmetry to analyze mathematical
situations; use visualization, spatial reasoning,
and geometric modeling to solve problems "
In grades 6–8 all students
should—
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understand relationships among the angles,
side lengths, perimeters, areas, and
volumes of similar objects; |
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create and critique inductive and deductive
arguments concerning geometric ideas
and relationships, such as congruence,
similarity, and the Pythagorean relationship; |
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draw geometric objects with specified
properties, such as side lengths or
angle measures; |
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use
two-dimensional representations of three-dimensional
objects to visualize and solve problems
such as those involving surface area
and volume; |
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use geometric models to represent and
explain numerical and algebraic relationships.
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Pi Machine 1-IV
(click on image for larger view)
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The Problem: Students approximate
pi by estimating the ratio of darts, thrown
randomly at a dartboard, that land inside
the circle to those that land outside.
Where's the Math: Investigations
explore the relationship between radius
and area in circles and spheres.
NCTM Standards: Geometry, measurement,
number & operations
Components: AgentSheets, logoscript,
HTML viewer, text editor, swing slider,
simple number table, number entry
Pi Machine 1
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Click on the links above to learn more about
the problem series, the math involved, sample
solutions, and developers' assessment
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In the Dark with an Elephant
(click on image for larger view)
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The Problem: Students investigate
how the appearance of a graph changes, based
on the scale of the graph and the region
being viewed.
Where's the Math: This problem
gives students experience in manipulating
graphs by changing domain and range values
for the viewing window, which can easily
be carried over to more powerful tools such
as graphing calculators. It also allows
students to become familiar with the Cartesian
coordinate system. The questions encourage
thought about how the shape of specific
areas of a graph are not necessarily representative
of the shape of the entire graph.
NCTM Standards: Algebra, geometry
Components: SimCalc, ImageView,
FunctionEntry, NumberEntry, Data Recorder,
Standard Swing components (buttons and labels)
Learn
more about the problem, the math
involved, sample solutions, and developers'
assessment
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