
Mathematics DepartmentCoursesConstantly changing technology is influencing careers in all fields. To prepare our students for these new and exciting opportunities, the Bellefonte Area School District offers a mathematics program with a variety of courses combining traditional theory with practical application.
1.0 credit
Recommendations: Recommendation of their current mathematics instructor.
The goal of Prealgebra is to develop fluency with rational numbers and proportional relationships. Students will extend their elementary skills and begin to learn algebra concepts that serve as a transition into formal algebra and geometry. Students will learn to think flexibly about relationships among fractions, decimals, and percents. Students will learn to recognize and generate equivalent expressions and solve singlevariable equations and inequalities. Students will investigate and explore mathematical ideas and develop multiple strategies for analyzing complex situations. Students will analyze situations verbally, numerically, graphically, and symbolically. Students will apply mathematical skills and make meaningful connections to life’s experiences.
(02053) COMMON CORE ALGEBRA 1 (Part I)
1.0 credit
Recommendations: Successful completion of PreAlgebra or a B in 8^{th} grade Introduction to Algebra and recommendation of their current mathematics instructor.
This course provides the first half of the study of Algebra 1. The main goal of algebra is to develop fluency in working with linear equations. Variables and abstract systems are used to examine the set of real numbers, as well as its major subsets and properties. Students will extend their experiences with tables, graphs, and equations. Students will use technology and models to investigate and explore mathematical ideas and relationships and develop multiple strategies for analyzing complex situations. Students will analyze situations verbally, numerically, graphically, and symbolically. Students will apply mathematical skills and make meaningful connections to life’s experiences.
(02054) COMMON CORE ALGEBRA 1 (Part II)
1.0 credit
Recommendations: 73% in Common Core Algebra 1 (Part I) and recommendation of their current mathematics instructor.
This course provides the second half of the study of Algebra 1. The main goal of algebra is to develop fluency in working with linear equations. Students will extend their experiences with tables, graphs, and equations and solve linear equations and inequalities and systems of linear equations and inequalities. Students will generate equivalent expressions and use formulas. Students will simplify polynomials and begin to study quadratic relationships. Students will use technology and models to investigate and explore mathematical ideas and relationships and develop multiple strategies for analyzing complex situations. Students will analyze situations verbally, numerically, graphically, and symbolically. Students will apply mathematical skills and make meaningful connections to life’s experiences.
1.0 credit
Recommendations: “A” in 8^{th}grade Introduction to Algebra and recommendation of their current mathematics instructor.
The main goal of Algebra 1 is to develop fluency in working with linear equations. Students will extend their experiences with tables, graphs, and equations and solve linear equations and inequalities and systems of linear equations and inequalities. Students will extend their knowledge of the number system to include irrational numbers. Students will generate equivalent expressions and use formulas. Students will simplify polynomials and begin to study quadratic relationships. Students will use technology and models to investigate and explore mathematical situations verbally, numerically, graphically, and symbolically. Students will apply mathematical skills and make meaningful connections to life’s experiences.
Students who have successfully completed Common Core Algebra 1 (Part I) and Common Core Algebra 1 (Part II) may not take Algebra 1 for credit.1.0 credit
Recommendations: Successful completion of Algebra 1 (or Common Core Algebra 1 (Part I) and Common Core Algebra 1 (Part II) and successful completion of Geometry, as well as the recommendation of their current mathematics instructor. Students may also take this course concurrently with Geometry.
A primary goal of Algebra 2 is for students to conceptualize, analyze, and identify relationships among functions. Students will develop proficiency in analyzing and solving quadratic functions using complex numbers. Students will investigate and make conjectures about absolute value, radical, exponential, logarithmic and sine and cosine functions algebraically, numerically, and graphically, with and without technology. Students will extend their algebraic skills to compute with rational expressions and rational exponents. Students will work with and build an understanding of complex numbers and systems of equations and inequalities. Students will analyze statistical data and apply concepts of probability using permutations and combinations. Students will use technology such as graphing calculators. Students will analyze situations verbally, numerically, graphically, and symbolically. Students will apply mathematical skills and make meaningful connections to life’s experiences.
1.0 credit
Recommendations: 73% in Algebra 2 and recommendation of their current mathematics instructor. Students who take AMC as a second math class must have taken Honors Algebra or have 93% in Algebra 2.
This course begins with a review of the first two years of algebra. This is followed by the study of such topics as functions, determinants and matrices, graphing, the quadratic formula, radical equations, synthetic division and complex numbers, sequences and series, probability and statistics, logarithms, and conic sections. Students will analyze situations verbally, numerically, graphically, and symbolically. Students will apply mathematical skills and make meaningful connections to life’s experiences. This course should be considered by students who plan to attend college. Accelerated students who want to complete their knowledge of mathematics should schedule this course in addition to PreCalculus.
1.0 credit
Recommendations: Successful completion of Algebra 1 and recommendation of their current mathematics instructor. Students may also take this course concurrently with Algebra 2.
The main goal of Geometry is for students to develop a Euclidean geometric structure and apply the resulting theorems and formulas to address meaningful problems. Students will use experimentation and inductive reasoning to construct geometric concepts, discover geometric relationships, and formulate conjectures. Students will employ deductive logic to prove theorems and justify conclusions. Students will extend their preexisting experiences with algebra and geometry to trigonometry, coordinate geometry, and probability. Students will use dynamic geometry software, compass and straightedge, and other tools to investigate and explore mathematical ideas and relationships and develop multiple strategies for analyzing complex situations. Students will apply mathematical skills and make meaningful connections to life’s experiences.
1.0 credit
Recommendations: 73% in Algebra 2 and Geometry, as well as the recommendation of their current mathematics instructor.
The main goal of Precalculus is for students to gain a deep understanding of the fundamental concepts and relationships of functions. Students will expand their knowledge of quadratic, exponential, and logarithmic functions to include power, polynomial, rational, piecewise, and trigonometric functions. Students will investigate and explore mathematical ideas, develop multiple strategies for analyzing complex situations, and use graphing calculators and mathematical software to build understanding, make connections between representations, and provide support in solving problems. Students will analyze various representations of functions, sequences, and series. Students will analyze bivariate data and data distributions. Students will apply mathematical skills and make meaningful connections to life’s experiences. Precalculus is highly recommended preparations for students who plan to continue their formal education beyond high school in the mathematics and/or science fields.
(02110HPC) HONORS PRECALCULUS
1.0 credit
Recommendations: Successful completion of Honors Algebra and recommendation of their current mathematics instructor.
This course continues the Honors mathematics curriculum which began with Advanced Algebra. Students will study the same topics as in PreCalculus, but experiences will be enriched and expanded. The main goal of PreCalculus is for students to gain a deep understanding of the fundamental concepts and relationships of functions. Students will expand their knowledge of quadratic, exponential, and logarithmic functions to include power, polynomial, rational, piecewise, and trigonometric functions. Students will investigate and explore mathematical ideas, develop multiple strategies for analyzing complex situations, and use graphing calculators and mathematical software to build understanding, make connections between representations, and provide support in solving problems. Students will analyze various representations of functions, sequences, and series. Students will analyze bivariate data and data distributions. Students will apply mathematical skills and make meaningful connections to life’s experiences.
1.0 credit
Recommendations: Successful completion of PreCalculus and recommendation of their current mathematics instructor.
This is a college preparatory course that explores the theories and applications of differential and integral calculus. This course begins with a review of elementary calculus principles. Concepts, results, and problems presented in this course are expressed geometrically, numerically, analytically, and verbally. Technology will be used regularly to reinforce the relationships among the multiple representations of functions and to confirm written work, to implement experimentation, and to assist in interpreting results. Unifying themes in the class are functions, graphs and limits, derivatives, and integrals.
(410) ADVANCED PLACEMENT CALCULUS AB
1.0 credit (1.07weight)
Recommendations: Successful completion of Honors PreCalculus or an A in PreCalculus and recommendation of their current mathematics teacher. Advanced Math Concepts is strongly recommended. Students must apply for admission into this course.
Students enrolling in this course experience a collegelevel Calculus course in preparation for the national AP Calculus AB examination. The AP syllabus covering both differential and integral Calculus drives the instruction in this course. Concepts, results, and problems presented in this course are expressed geometrically, numerically, analytically, and verbally. Technology will be used regularly to reinforce the relationships among the multiple representations of functions and to confirm written work, to implement experimentation, and to assist in interpreting results. Unifying themes in the class are functions, graphs and limits, derivatives, and integrals. This course covers the same material as a first semester college calculus course. Participants must be selfmotivated and prepared to adhere to the expectations and requirements necessary for successful completion of the course. Students in AP courses are expected to take the national AP exam.
(02125CBC) ADVANCED PLACEMENT CALCULUS BC
1.0 credit (1.07weight)
Recommendations: Successful completion of Honors PreCalculus and recommendation of their current mathematics teacher. Advanced Math Concepts is strongly recommended. Students must apply for admission into this course.
Students enrolling in this course experience a collegelevel Calculus course in preparation for the national AP Calculus BC examination. The AP syllabus covering both differential and integral Calculus, as well as Taylor and Maclaurin series, drives theinstruction in this course. Concepts, results, and problems presented in this course are expressed geometrically, numerically, analytically, and verbally. Technology will be used regularly to reinforce the relationships among the multiple representations of functions and to confirm written work, to implement experimentation, and to assist in interpreting results. Unifying themes in the class are functions, graphs and limits, derivatives, and integrals, and series. This course covers all of the material in AP Calculus AB with additions, covering the first two semesters of college calculus. Participants must be selfmotivated and prepared to adhere to the expectations and requirements necessary for successful completion of this rigorous course. Students in AP courses are expected to take the national AP exam.
(02201) PROBABILITY AND STATISTICS
1.0 credit
Recommendations: Successful completion of Algebra 2 and recommendation of their current mathematics instructor.
This course provides an elementary introduction to probability and statistics with applications. Topics include: basic probability models; combinatorics; random variables; discrete and continuous probability distributions; statistical estimation and testing; confidence intervals; and an introduction to linear regression. This course is highly recommended preparation for students who plan to continue their formal education beyond high school in the social sciences.
1.0 credit (1.07weight)
Recommendations: Successful completion of Trigonometry and recommendation of their instructor. Students must apply for admission into this course.
Students enrolling in this course will be introduced to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Students are exposed to four broad conceptual themes:
1. Exploring Data: Describing patterns and departures from patterns
2. Sampling and Experimentation: Planning and conducting a study
3. Anticipating Patterns: Exploring random phenomena using probability and simulation
4. Statistical Inference: Estimating population parameters and testing hypotheses
Participants must be selfmotivated and prepared to adhere to the expectations and requirements necessary for successful completion of the course. Students in AP courses are expected to take the national AP exam.