The sample material from Shapes and Geometric Reasoning consists of the two investigations from Lesson 3, "Parallelograms: Necessary and Sufficient Conditions." Parallelograms are defined and students are asked to prove the properties of parallelograms. Conditions that ensure a quadrilateral is a parallelogram are then considered. Finally, special parallelograms (rectangles, rhombuses, and squares) and their properties are introduced. In addition, students investigate and then prove the Midpoint Connector Theorem for Triangles and for Quadrilaterals.
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 common pattern as elaborated under Instructional Design.
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In Course 4, geometry and algebra become increasingly intertwined. Students develop understanding of two-dimensional vectors and their applications 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.
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