

Objectives
of the Unit

Sample Overview
In Lesson 1
Investigations 13, students used combinations of side lengths
and angle measures to create congruent triangles and quadrilaterals.
They investigated properties of these figures by experimenting and
through careful reasoning. Then they used those properties to study
the design of structures and mechanisms to solve problems.
In
Investigation 4
(the sample material), students revisit the Pythagorean Theorem that
they studied in middle school. Students provide an argument that justifies
the Pythagorean Theorem by finding the area of a square in two different
ways. They construct triangles and use careful reasoning to verify
the converse of the Pythagorean Theorem in a specific case and then
use similar reasoning to establish the general case.
Instructional
Design
Throughout the curriculum,
interesting problem contexts serve as the foundation for instruction.
As lessons unfold around these problem situations, classroom instruction
tends to follow a fourphase cycle of classroom activities—Launch,
Explore, Share and Summarize, and Apply.
This instructional model is elaborated under Instructional
Design.
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Material
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How the Geometry
and Trigonometry Strand Continues
In Course 2,
students develop an understanding of coordinate methods for representing
and analyzing relations among classes of geometric shape and proving
geometric properties. They use coordinates to represent geometric transformations
and to understand their effects and that of their compositions. Students
also develop an understanding of trigonometric functions and the ability
to use trigonometric methods to solve triangulation and indirect measurement
problems.
In
Course 3,
students extend their ability to reason formally in geometric settings.
Deductive reasoning is used to prove theorems concerning parallel lines
and transversals, angle sums of polygons, similar and congruent triangles
and their application to special quadrilaterals, and necessary and
sufficient conditions for parallelograms.
In
Course 4:
Preparation for Calculus, geometry and algebra become increasingly
intertwined. Students develop understanding of twodimensional vectors
and their application and the use of parametric equations in modeling
linear, circular, and other nonlinear motion. In addition, students
intending to pursue programs in the mathematical, physical, and biological
sciences, or engineering extend their ability to visualize and represent
threedimensional surfaces using contours, cross sections, and topographic
profiles; and to visualize and sketch surfaces and conic sections defined
by algebraic equations. They also extend their understanding of, and
ability to reason with, trigonometric functions to prove or disprove
trigonometric identities and to solve trigonometric equations. Finally,
students geometrically represent complex numbers and apply complex
number operations to find powers and roots of complex numbers expressed
in trigonometric form. (See
the CPMP Courses 14
descriptions.)
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