This unit, which is on the Law of Sines and the Law of Cosines, is presented as a guide for making connections to and transitioning from right triangle geometry and trigonometry to exploring and solving triangles of any type. The Law of Sines involves using proportions to solve triangles when given ASA, AAS or SSA of a triangle while the Law of Cosines is a generalization of the Pythagorean theorem and can be used to solve triangles when given SAS or SSS of a triangle. The unit focuses on actively engaging students in the development of mathematical understanding of some basic trigonometric concepts through problem solving using a variety of representations. The Geometer Sketchpad (GSP) program is utilized to provide a dynamical geometry environment (DGE) for investigation, conjecturing, and discovery. The ultimate goal is for students to gain the ability to explore, to conjecture, to reason logically, and to use a variety of mathematical methods effectively to solve problems.
Explicit attention is given to investigations in a dynamical environment
on a regular and sustained basis. Allocating an equitable amount
of time in the lesson plan to investigate the important components
of problem solving, problem posing, and mathematical thinking,
which include problem models, strategic processes, meta-processes,
and affective models, should improve students' understanding and
learning in mathematics.
The unit is appropriate to help meet the Georgia Performance Standards
(GPS) course curriculum and for the backgrounds and interests
of the students who have completed Mathematics 3. A student's
background should include knowledge necessary to understand the
problems that are posed in the instructional unit. This background
knowledge is a prerequisite and will be strengthened by the completion
of the unit.
Rather than feel duty bound to go through the textbook section-by-section
on a daily basis, teachers should use textbooks as one instructional
tool among many. The textbook should be supplemented in appropriate
ways. This unit seeks to present mathematical ideas in a variety
of ways to help students construct knowledge of trigonometric
concepts.