

Objectives
of the Unit

Sample
Overview
The sample student
material below is from Lesson 1, Investigation 3. In Investigations 1
and 2, students created shapes using geometry software, developed the
distance and midpoint formulas, and considered how the slope of lines
can be used to determine whether or not lines are perpendicular. This
knowledge was then used to identify special triangles and quadrilaterals,
such as isosceles triangles and parallelograms. In the third investigation,
students learn how to represent circles in a coordinate plane with equations.
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.
View the
Unit Table of Contents and Sample Lesson Material
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How the
Geometry and Trigonometry Strand Continues
In Course 2 Unit 7, Trigonometric
Methods, students develop an understanding of trigonometric functions
and the ability to use right triangle trigonometry to solve triangulation
and indirect measurement problems.
In Course 3 Units 1 and 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. Circular functions (sine and cosine) are used to model
periodic change in Unit 6, Circles
and Circular Functions.
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 reliefs; 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. They also 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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