

Objectives
of the Unit

Sample
Overview
The sample student
material below is from Lesson 1, "Reasoning Strategies." In
this investigation, students examine arguments presented in differing
forms and using differing reasoning strategies. They are asked to judge
these arguments on the basis of how well the arguments convince them
that the asserted proposition is true. From these experiences, they are
asked to identify characteristics of arguments that make them convincing
and logically correct. This approach to developing reasoning abilities
is recommended in the Common Core State Standards for Mathematics within
the Standards for Mathematical Practice number 3: Construct viable arguments
and critique the reasoning of others. (Alignment
of CorePlus Mathematics with the Common Core State Standards)
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 3 Unit 3, Similarity
and Congruence, students will extend their ability to reason
formally in geometric settings. Deductive reasoning is used to prove
theorems concerning 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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