This sample material consists of the second investigation and homework (MORE) set from Lesson 2, which develops and reviews the concepts of measurement of two- and three-dimensional shapes. The sample investigation revisits the Pythagorean relationship by considering what the length of the diagonal of a television screen reveals about the shape of the screen. Perimeter, area, and volume concepts are revisited and extended in other investigations of this lesson.
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 2, students develop an understanding of coordinate methods for representing and analyzing relations among classes of geometric shapes and use coordinates to represent geometric transformations and to understand their effects and that of their compositions. Students also develop the ability to model and analyze physical phenomena with triangles, quadrilaterals, and circles and to use trigonometric relationships to solve problems.
In Course 3, students develop the 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, 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.
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