PRECALCULUS CURRICULUM - Newtown Public Schools

15 downloads 260 Views 103KB Size Report
Demana, Waits, Clemens, 1994 pgs. 3-21, Chapter 13 ... that are nonlinear. Resources: Precalculus Mathematics, Demana, Waits, Clemens, 1994 Chapter 10.
PRECALCULUS CURRICULUM

NEWTOWN SCHOOLS NEWTOWN, CT. August, 1996

MATHEMATICS PHILOSOPHY − We believe mathematics instruction should develop students' ability to solve problems. − We believe that the study of mathematics should prepare students with the skills necessary to interpret the multiple uses of numbers encountered in the real world. − We believe that representing, discussing, reading, writing and listening to mathematics are vital parts of learning. − We believe that students experience mathematics as sensible, logical and enjoyable when they are actively engaged in the learning process. − We believe that students should be encouraged to appreciate the power of mathematical structures. − We believe that mathematical strands should be connected to each other. − We believe that mathematics education should be integrated with other curricular areas or disciplines. − We believe that mathematics education should open opportunities for students to perform successfully in our scientific/technological/informational society. − We believe that instructional strategies in mathematics should meet the learning needs and styles of all students. − We believe that mathematics instruction should be a blend of concrete and abstract, application and theory, skills and concepts. − We believe that assessments are essential tools for students' learning, growth and achievement.

MATHEMATICS GOAL Students will gain mathematical power as they learn to: − Value mathematics. − Become confident in their ability to do mathematics. − Become mathematical problem solvers in theoretical and practical situations. − Communicate mathematically. − Reason mathematically. − Demonstrate their ability through learning activities and assessments.

PRECALCULUS CONTENT STANDARDS Students will be able to: − Use the graphing and calculator computer to augment their study of precalculus. − Use the vocabulary of functions and functional notation to describe the characteristics of linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions and their inverse. − Apply the vocabulary and laws of trigonometry. − Use parametric equations and polar coordinates. − Use matrices to solve systems of equations and inequalities. − Identify sequences and series.

Content Standard Students will be able to use the graphing and calculator computer to augment their study of precalculus. Objectives: Students will be able to: − Study the behavior of functions and relations including conic equations, parametric equations, and polar equations. − Deepen understanding and intuition about a wide variety of functions and relations and to provide a foundation for the study of calculus, statistics, and higher mathematics. − Determine graphically the number of solutions to equations and systems of equations, to solve equations, systems of equations, and inequalities graphically with accuracy equal to any numerical approximation. − Determine relative maximum and minimum values of functions graphically with accuracy equal to any numerical approximation. − Investigate graphically and determine the solution to "real world" problem situations that are not normally accessible to precalculus students. − Provide geometric representations for problem situations and to analyze their connections with algebraic representations for problem situations. Suggested Instructional Strategies and Classroom Activities: Four graphing calculator activities - Compound Interest, Graphs & Viewing Rectangles, Solving Equations, and Screen Coordinates. Resources: Graphing Technology Manual. Demana, Waits, Clemens, 1994 pgs. 3-21, Chapter 13

Content Standard Students will be able to use the vocabulary of functions and functional notation to describe the characteristics of linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions and their inverse. Objectives: Students will be able to: − Determine the domain and range of a function. − Identify different types of functions from their equations and from their graphs. − Determine the composition of two or more functions. − Graph a function using critical values and any extreme that exist using a graphing calculator. − Find the zeros of a function and interpret their meaning graphically and algebraically. − Extend the concept of zeros to an inequality and interpret its solution. − Solve systems of equations involving functions and interpret the result both algebraically and geometrically. − Provide solutions to "real world" problem situations that are modeled by functions. Resources: Precalculus Mathematics , Demana, Waits, Clemens, 1994 Chapters 1 - 6.

Content Standard Students will apply the vocabulary and laws of trigonometry. Objectives: Students will be able to: − Understand the proof of the law of sines and the law of cosines and use their computational applications to solve a variety of problems. − Express complex numbers in trigonometric form and interpret the result geometrically. − Determine powers and roots of complex numbers both algebraically and geometrically. − Use the computational applications of trigonometric functions to solve a variety of problems in a right triangle. − Apply the arithmetic of vectors and use the concept of vectors to solve "real world" problem situations. Resources: Precalculus Mathematics, Demana, Waits, Clemens, 1994 Chapters 7-8.

Content Standard Students will use parametric equations and polar coordinates. Objectives: Students will be able to: − Define a curve and graph it parametrically. − Translate among rectangular coordinates, parametric equations and polar coordinates and explain the geometric connection. − Graph curves in polar coordinates using a quick sketch and a graphing calculator. − Describe the polar form of the conic sections. − Graph quadratic forms using a graphing calculator. − Solve "real world" problem situations modeled by quadratic forms. Resources: Precalculus Mathematics, Demana, Waits, Clemens, 1994 Chapters 9-10.

Content Standard Students will use matrices to solve systems of equations and inequalities. Objectives: Students will be able to: Solve systems of equations algebraically. Use matrix methods to solve and interpret systems of linear equations. Solve a system of equations using matrix methods. Write algebraic representations of the conic sections and find graphs of rotation transformations. Use graphical methods to solve systems of equations and inequalities that are nonlinear. Resources: Precalculus Mathematics, Demana, Waits, Clemens, 1994 Chapter 10.

Content Standard Students will identify Sequences and Series. Objectives: Students will be able to: − Define a sequence, either by formula or recursively, and identify the first several terms and the n"1 term of a sequence. − Identify and solve problems about arithmetic and geometric sequences. − Understand sigma notation and use some of the basic summation formulas to find finite sums. − Find the sum of an infinite geometric series and use a graphing calculator to obtain a visualization of a geometric series. − Demonstrate graphically that functions such as sin x, cos x, Vx+1 can be approximated on a given interval by a polynomial expression. − Use the principle of mathematical induction to prove mathematical generalizations. Resources: Precalculus Mathematics, Demana, Waits, Clemens, 1994 Chapter 11.