Statement of Philosophy
The Mathematics Department offers a curriculum with topics, course content, instructional emphasis, and teaching methods that meet standards of the new century. The Department requires the use of hand held graphing calculator technology in all courses. The curriculum emphasizes experimental and exploratory problem solving and communication of mathematical ideas verbally and in writing. Students create and use graphs of data and functions to develop mathematical skills, to reason through problems, and to understand complex relationships.
Department Objectives
- Provide instruction in contemporary high school mathematics.
- Emphasize the student's role in the learning process.
- Emphasize modeling real world applications.
- Expose students to technology in mathematics and its applications.
- Provide individualized help.
- Offer a variety of teaching techniques that include cooperative learning and student participation.
- Challenge the best students with difficult problems and mathematics competitions.
Graduation Requirements
- Two years of mathematics is required of all students for graduation.
- Algebra II is recommended, as current standardized tests such as SAT/ACT, include this material.
- Three or four years are recommended to meet the entrance requirements of most colleges.
- A five-year sequence is available. Students with advanced skills may be
Course Descriptions
Algebra I
Target students: Grade 9-10
Pre-requisite: None
Number of times course can be taken: 1
Seating priority: None
Credit per semester: .50 per semester (full year course)
Meeting time: Daily
Description:
Algebra I is the study of mathematical patterns and ideas. It is balanced between learning skills, exploring concepts, and solving problems. Technology is used to gather, interpret, and represent data from real-world situations. Creating and using mathematical models is a theme throughout. Algebra is integrated with geometry, probability, and statistics. Topics covered include equations - linear, quadratic, and exponential - as well as systems of equations and inequalities, functions, and fractals.
Objectives:
- Identify relationships in real world settings
- Represent data in various forms that illuminate patterns
- Evaluate expressions; solve equations; apply these skills to decision making processes
- Recognize new problem situations; use algebraic and numeric concepts to aid in understanding
Student Performance:
- Presentation of problem solutions and/or activity results to the instructor and/or the class
- Participation in class discussions, small group activities, and group project/work sessions
- Completion of technology-based and/or online activities, labs, projects
Assessment:
- Completion of traditional and/or online homework
- Demonstrated ability to use technology to analyze and interpret algebraic relationships, and to prepare reports
- Successful performance on lab/activity reports, projects, quizzes and tests
Text/materials needed:
- Discovering Algebra 2nd Edition, by Jerald Murdock, Ellen Kamischke, Eric Kamischke
- Graphing Calculator (TI-84 or TI-83)
- Notebook and writing materials, Graph paper, Ruler
Geometry
Target students: All who meet pre-requisite
Pre-requisite: Algebra I
Number of times course can be taken: 1
Seating priority: None
Credit per semester: .50 per semester (full year course)
Meeting time: Daily
Description:
This course is investigation-driven and activity-based. It covers topics of Euclidean Geometry such as deductive proof, properties of polygons, circles, similar/congruent triangles, parallel lines, area and volume, the Pythagorean Theorem, basic concepts of right triangle trigonometry, and general ideas of transformations. Computer technology and traditional Geometry tools are used in all investigations. Applications of Geometry concepts to various arts areas are incorporated within the course.
Objectives:
- To use deductive reasoning to justify conjectures about geometric figures.
- To analyze problems and use geometric properties to solve them.
- To apply logical/visual thinking skills to study geometric figures and their properties.
- To evaluate the validity of statements concerning geometric figures and properties.
Student Performance:
- Presentation of problem solutions and/or investigation results to the rest of the class.
- Participation in class wide as well as separate group discussions.
- Completion and presentation of projects to class members and others.
Assessment:
- Completion of traditional and/or online homework (journaling.)
- Successful use of investigations to develop conjectures individually and in groups.
- Shown ability to apply geometric properties to solve problems.
- Shown ability to use deductive reasoning to justify conjectures.
Text/materials needed:
- Discovering Geometry, Fourth Edition by Michael Serra
- Graphing Calculator (TI 84 or 83)
- Compass, protractor, notebook and writing materials
Algebra II
Target students: Any grade level
Pre-requisite: Algebra I and Geometry
Number of times course can be taken: 1
Seating priority: None
Credit per semester: .50 per semester (full year course)
Meeting time: Daily
Description:
Algebra II is primarily the study of functions - linear, exponential, polynomial, and parametric - through the use of data. Introductory trigonometry, statistics, and probability topics are also explored. Students use calculators, computers, and data gathering devices to investigate all topics. Throughout the course students discover the sense behind the mathematics, rather than simply learn steps for solving problems. Small group work, discussion, and the real world interpretation of the mathematics are stressed. Applications to the arts are woven throughout the curriculum.
Objectives:
- To analyze unknown functions as transformations of simple functions.
- To identify linear and exponential relationships in real world situations.
- To apply and analyze functions in the context of everyday life.
- To evaluate new problem situations and apply numeric, algebraic, and graphical concepts to aid in understanding.
Student Performance:
- Presentation of projects and problem solutions to the rest of the class.
- Participation in small group and/or class discussions
- Appropriate use of technology to aid in exploration and presentation of work
Assessment:
- Completion of homework from textbook and other sources
- Lab reports applying or exploring algebra concepts
- Demonstrated ability to interpret mathematical results in real world context
- Demonstrated ability to solve problems using multiple representations
Text/materials needed:
- Discovering Advanced Algebra 2nd Edition, by Jerald Murdock, Ellen Kamischke, Eric Kamischke
- Graphing Calculator (TI 84 or 83)
- Notebook and writing materials, Graph paper, Ruler
Advanced Placement Statistics
Target students: 11-12-Post Graduates
Pre-requisite: Algebra II required, Advanced Mathematics preferred
Number of times course can be taken: 1
Seating priority: None
Credit per semester: .50 per semester (full year course)
Meeting time: Daily
Description:
This course introduces the students to the basic concepts of one of the most important fields of mathematics most people ever encounter. Statistics is about data, and data are numbers with a context. Students learn to make statements of facts and inferences and to state a level of confidence in their inferences. They become proficient in accurately communicating statistical concepts, including methods of data collection and valid interpretations of data. The course follows the topics outlined in the Advanced Placement curriculum in preparation for the AP Test in May.
Objectives:
- Students learn to collect valid data.
- Students learn to describe and display data and recognize patterns and departures from patterns.
- Students learn the role probability plays in collecting and analyzing data.
- Students learn to make inferences about populations based on samples.
Student Performance:
- Students become proficient in accurately communicating statistical concepts through mathematical and graphical presentations.
- Students use appropriate reasoning as a critical aspect of gaining statistical expertise.
- Students use graphing calculators and computers to develop skills in descriptive statistics, simulations, and inference.
- Students write with increasing precision as they focus on the necessity of relating problems to a context.
Assessment:
- Traditional homework from textbook and instructor handouts
- Course projects including simulations, experiments, surveys and extended writing assignments
- Quizzes and Tests
Text/materials needed:
- The Practice of Statistics, Third Edition by Yates, Moore, and Starnes
- Graphing Calculator (TI 83 or 84)
- Notebook and writing materials
Advanced Mathematics
Target students: 11-12-Post Graduate
Pre-requisite: Algebra II
Number of times course can be taken: 1
Seating priority: None
Credit per semester: .50 per semester (full year course)
Meeting time: Daily
Description:
This course is designed to serve students who are preparing for Calculus or further work in mathematics. As a pre-calculus course, it offers an analytical, graphical and numerical approach to understanding polynomials, exponential functions, logarithms, and a wide variety of trigonometry topics. Additional topics may include polar graphs, conic sections, matrices, sequences, and series. Real life applications and data interpretation are integral parts of this course of study.
Objectives:
Recognize and explore various families of functions
Apply transformations to functions to study their properties and graphs
Grasp the foundations of trigonometry, including the unit circle, right triangles, graphs, and identities
Realize functions as models of real-life data
Student Performance:
- Presentation of problem solutions and/or activity results to the instructor and/or the class
- Participation in class discussions, small group activities, and group project/work sessions
- Completion of technology-based and/or online activities, labs, projects
Assessment:
- Completion of traditional and/or online homework
- Demonstrated ability to use technology to analyze functions and create models of real-life data
- Successful performance on lab reports, projects, presentations, quizzes and tests
Text/materials needed:
- Precalculus with Limits: a Graphing Approach, 4th ed., by Larson, Hostetler and Edwards
- Graphing Calculator (TI-83, TI-84, or TI-86)
- Notebook, ruler, and writing materials.
Advanced Placement Calculus
Target students: Those that meet pre-requisite
Pre-requisite: Advanced Math (Pre-Calculus)
Number of times course can be taken: 1
Seating priority: None
Credit per semester: 0.5
Meeting time: .50 per semester (full year course)
Description:
This course covers approximately one and one half semesters of college calculus. Students completing the course are prepared to take the AP Calculus AB exam. Topics studied include limits, continuity, derivatives and definite integrals along with their applications, indefinite integrals, separable differential equations, and improper integrals. The course material is explored through class discussions, small group lab investigations, and individual study of challenging problems. Students who wish to take the BC level exam are assisted with additional work outside of class.
Objectives:
- To analyze functional relationships using the derivative.
- To use the definite integral to solve problems involving accumulation.
- To synthesize the connection between the branches of calculus to inform the solutions to problems.
- To gain insight on everyday situations through the evaluation of calculus concepts involved.
Student Performance:
- Presentation of problem solutions to the rest of the class.
- Participation in class discussions
Assessment:
- Completion of homework from textbook and online sources
- Lab reports applying or exploring calculus concepts
- Demonstrated ability to combine concepts to solve problems unlike those presented in class
- Demonstrated ability to use graphical, numerical, symbolic, and verbal methods to answer questions involving calculus
Text/materials needed:
- Calculus: Graphical, Numerical, and Algebraic by Franklin Demana, Bert K. Waits, Daniel Kennedy, Ross L. Finney
- Graphing Calculator (TI 89 or 84 or 83)
- Notebook and writing materials.
