of the Unit
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 Core-Plus Mathematics with the Common Core State Standards)
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 four-phase cycle of classroom activities—Launch, Explore, Share and Summarize, and Apply. This instructional model is elaborated under Instructional Design.
Unit Table of Contents and Sample Lesson Material
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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 two-dimensional 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 three-dimensional 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 1-4 descriptions.)
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