# Mathematics

YOU + DLS = GREATNESS!

Every student can be successful with the right support group. Our Department strives to meet the needs of the class as a whole and each student individually. This means meeting our struggling students at their current level of understanding and challenging all of our students to succeed beyond their expectations. We encourage critical thinking and incorporate problem-solving opportunities in all of our classrooms. We offer a variety of levels of classes that not only challenge the students but prepare their skill sets for college and the rest of their lives.

## Math Courses

- 310 - Intensive Math
- 312 - Algebra I
- 313 - Honors Algebra I
- 322 - Modern Geometry
- 323 - Hon. Modern Geometry
- 324 - Advanced Geometry
- 332 - Algebra II and Trigonometry
- 333 - Hon. Algebra II and Trigonometry
- 334 - Advanced Algebra II and Trigonometry
- 341 - Integrated Math
- 342 - Pre-Calculus
- 343 - Hon. Pre-Calculus
- 352 - AP Statistics
- 353 - AP Calculus AB
- 355 - AP Calculus BC

## 310 - Intensive Math

**Grade Offered:** 9

**Prerequisites:** None

To be successful in this course, students must demonstrate improvement in the following skill sets: Math facts, basic computational skills, number sense, speed, and accuracy. This course is meant to complement their Algebra 1 course, not replace it. By addressing basic math skills in this course, students who have struggled in mathematics in the past have the opportunity to address the root of the problem. When available, class time may be spent reinforcing topics in the Algebra 1 course. Students who need this course will not take a foreign language in their freshmen year. This is a pass/fail course that does not impact the grade point average calculations.

## 312 - Algebra I

**Grade Offered:** 9

**Prerequisites: **None

To be successful in this course, students should have a mastery of; addition, subtraction, multiplication, and division of integers, fractions, and decimals, the number line and properties of numbers, factors, divisibility tests, and prime factorization…and should have been introduced to; GCFs, LCMs, exponents, square roots, absolute value, scientific notation, ratios and proportions, percents, and order of operations. This course is intended for students to build a solid foundation of algebraic skills and concepts. By becoming proficient in these skills and concepts, the students can apply them confidently in further math courses. Topics covered include; solving equations, solving and graphing linear equations and inequalities, solving systems of linear equations, polynomials, rational expressions, radical expressions, quadratic equations, and algebra word problems.

## 313 - Honors Algebra I

**Grades Offered: **9

**Prerequisites: **Algebra I in 8th grade, HSPT and IFMPE scores, and approval of department leader.

To be successful in this course, students should have mastery of: addition, subtraction, multiplication, and division of integers, fractions, and decimals; exponents, absolute values, and order of operations; solving basic linear equations and linear inequalities. The incoming freshman is required to be proficient in the operations on the set of rational numbers and on the basic applications of these operations, i.e., percentage problems and simple equation solving. The student then proceeds to study variable and algebraic expressions from monomials to polynomials and the operations on them. Manipulative skills are emphasized in addition to developing kills in solving open sentences. Emphasized are single variable linear and quadratic equations and some of their applications. Also introduces are the concepts of irrational numbers and their operations, two variable sentences and graphing, functions and rational expressions. Time and ability to permit the introduction of right triangle trigonometry and its applications.

## 322 - Modern Geometry

**Grade Offered:** 9, 10

**Prerequisites:** Algebra I

To be successful in this course, students should have mastered the following: performing addition, subtraction, multiplication, and division with whole numbers, fractions, and decimals; solving linear algebraic equations; isolating variables in a function. This course will provide students with the knowledge and fundamentals continue to develop, and expand upon. It will emphasize the student’s knowledge of algebra and deductive reasoning applied to geometric properties. The geometric principles studied in this course are applicable to all of the sciences. The application of this course material is essential. Emphasis will be placed on: reinforcing basic concepts of Algebra, understanding geometric language, graphing and coordinate Geometry, measurements in two and three dimensions, applying algebraic properties to geometric principles, and applications of geometric properties.

## 323 - Hon. Modern Geometry

**Grade Offered:** 9, 10

**Prerequisites:** “A-” in Algebra I, approval of department leader.

To be successful in this course, the students should have already mastered the following: basic operations with integers, fractions, and decimals; solving simple algebraic equations; determine relationships between angles, polygons, circles, and three-dimensional shapes. Algebra and Geometry are united in a presentation of traditional geometric topics with a view toward coordinate Geometry. Algebraic concepts, such as systems of linear equations, word problems, and graphing serve as a unifying principle. Topics include logic, proof of fundamental theorems, congruencies, similarity, area, volume and quadratic equations.

## 324 - Advanced Geometry

**Grades Offered:** 9, 10

**Prerequisites**: 9th Grade: Algebra I in 8th grade, HSPT and IFMPE scores, and approval of department leader.

Prerequisites: 10th Grade: “A” in Hon. Algebra I, and approval of department leader.

To be successful in this course, the student should have already mastered the following; fractions, decimals, percents, exponents, radicals, solving equations and inequalities, solving and applying proportions, solving and graphing linear equations, solving systems of equations, and factoring all forms of polynomials. In addition, he should have been introduced to basic geometric formulas, the quadratic formula, the Pythagorean theorem, data analysis and probability. This course is designed for those freshmen and sophomores who have demonstrated a strong proficiency in Algebra I. The pace and depth of this course is substantially greater than the Hon. Geometry. In addition, students will be involved with the following: constructions with a protractor and compass, some independent projects, several math competitions, concentrated problem solving, and an introduction to trigonometry and functions.

## 332 - Algebra II and Trigonometry

**Grade Offered:** 11

**Prerequisite:** Modern Geometry

To be successful in this course, the students should have already mastered the following: basic operations with integers, fractions, and decimals; solving simple algebraic equations; factoring algebraic expressions. This course requires a fundamental knowledge of Algebra I and Geometry. Through problem solving and theoretical discussion it strives to strengthen the student’s ability to manipulate algebraic symbols, solve complicated equations and simplify algebraic expressions. In addition, the course will help the student to deepen his understanding of the concepts of algebra and the structures and principles, which govern the manipulation of symbols, and how the symbols themselves can be used to record ideas and gain insights into problem solving situations.

## 333 - Hon. Algebra II and Trigonometry

**Grades Offered: **10, 11

**Prerequisites:** “B” in Hon. or Advanced Geometry and approval of department leader.

To be successful in this course, students should have mastered the following: perform operations with numbers comfortably and easily; evaluate expressions, with and without variables, using the order of operations; graph basic functions when given an equation or be able to make a table of values; work with and graph linear equations; solve linear equations and simple quadratic equations; factor simple linear and quadratic expressions; know how to work with special right triangles (30-60-90 and (45-45-90) and the Pythagorean Theorem. This course places an emphasis on developing mathematical thinking and problem solving. It begins with an intense review of the basic concepts of algebra. Special attention is placed on polynomial, trigonometric, logarithmic and exponential functions, and their graphs. At this level, we treat the calculator as an aid to understanding – not as the central feature of the course. Applications from all branches of science are used to show how mathematics is used to model real-life situations. Throughout the course, concepts are studied from an algebraic, geometric, numeric and verbal point of view. If time permits, a non-technical approach to such topics as sequences, statistics, and probability is presented.

## 334 - Advanced Algebra II and Trigonometry

**Grades Offered:** 10, 11

**Prerequisites:** 10th Grade: “B+” in Advanced Geometry, and approval of department leader.

Prerequisites: 11th Grade: “B+” in Hon. Algebra II or Advanced Geometry, and approval of the department leader.

To be successful in this course, students should have mastered the following: factoring quadratic functions, solving and graphing linear functions, representing information as a function, identifying the relationships of sides in special right triangles, using proportions to solve for sides of similar polygons. This Hon.level course is designed for those sophomores and juniors who have a strong background in algebra and geometry. Review is provided for topics from first- and second-year algebra. Advanced topics are then introduced to prepare students for the next course in the sequence, A.P. Calculus. Advanced topics include: Circular and Trigonometric Functions, Sequences and Series, Exponential and Logarithmic Functions, and Conic Sections. Supplemental topics will include introductions to Probability and Statistics, Matrices and Vectors, Limits, Derivatives and Integrals. Where possible, concepts are presented from four points of view: geometric (graphs), numeric (table), symbolic (formulas), and verbal (discussion). Upon completion, students should be able to solve practical problems and use appropriate models for analysis and prediction. Graphing calculators (TI 83+ or higher) are required and used throughout the course.

## 341 - Integrated Math

**Grade Offered:** 12

**Prerequisites**: Must have been in Algebra II as a junior placement-teacher recommended only

This course is designed to prepare students to take a college level math course. The goals of Integrated Math are to teach and enhance traditional algebra topics, build confidence and positive attitudes toward math, improve reasoning, critical thinking, and study skills, and encourage students to think mathematically so they will feel comfortable translating real-life problems into mathematical equations. Topics that are covered for this course consist of real numbers, equations, inequalities, exponents, polynomials, factoring, graphing, systems, and radicals.

## 342 - Pre-Calculus

**Grade Offered:** 12

**Prerequisites:** Completion of Algebra II and Trigonometry, endorsement of the teacher, and approval of department leader.

To be successful in this course, the students should have already mastered the concept of functions in various forms including linear, quadratic, polynomials, and exponential. This course begins by reviewing and reinforcing the students’ algebraic and geometric skills. Special attention will be paid to pointing out the connection between the algebraic and geometric interpretations of important concepts. The student is then introduced to functions and their graphs with emphasis on: polynomial, trigonometric, exponential, logarithmic, and rational functions. The student should be able to develop mathematical models and use them to interpret real-world problems.

## 343 - Hon. Pre-Calculus

**Grade Offered:** 12

**Prerequisites**: “B+” in Hon. Algebra II and Trigonometry, approval of the department leader.

To be successful in this course, students should have mastered the following: solving linear and rational equations, graphing linear and quadratic functions, factoring of second- and third-degree polynomials, understanding the meaning of domain and range, simplifying and rationalizing radicals, using a graphing calculator to graph a function, and identifying the relationships of sides in special right triangles. This course is intended for the college-bound senior. It provides an intense study of the topics, which are fundamental to the study of calculus. Emphasis is placed on functions and their graphs with special attention to polynomial, rational, trigonometric, exponential and logarithmic functions. Where possible, concepts are presented from four points of view: geometric (graphs), numeric (tables), symbolic (formulas), and verbally (discussion). Upon completion, students should be able to solve practical problems and use appropriate models for analysis and prediction. Graphing calculators are used throughout the course.

## 352 - AP Statistics

**Grades offered: **12

**Prerequisites:** Honors Geometry & Honors Algebra 2

AP Statistics is an introductory college-level statistics course that introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students cultivate their understanding of statistics using technology, investigations, problem solving, and writing as they explore concepts like variation and distribution; patterns and uncertainty; and data-based predictions, decisions, and conclusions.

## 353 - AP Calculus AB

**Grades Offered**: 11, 12

**Prerequisites:** “B+” in Advanced Algebra II and Trigonometry, endorsement of the teacher, approval of department leader.

To be successful in this course, the student should have a strong background in Algebra, Geometry, Functions, Trigonometry, the Unit Circle and the Graphing Calculator. The student should also have shown the ability to reason mathematically, to apply mathematical concepts and processes to solve complex problems, and be able to explain and justify the thinking underlying their work. The student is introduced to the concepts of differential and integral calculus. Differentiation and integration of algebraic and transcendental (trigonometric, exponential and logarithmic) functions is emphasized along with the fundamental applications of these operations. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. The focus of the course is neither manipulation nor memorization of an extensive taxonomy of functions, curves, theorems, or problem types. Through the use of the unifying themes of derivatives, integrals, limits, approximation, and applications and modeling, the course becomes a cohesive whole rather than a collection of unrelated topics.

## 355 - AP Calculus BC

**Grade Offered:** 12

**Prerequisites:** “B+” in Advanced Placement Calculus AB, endorsement of the teacher, approval of department leader.

To be successful in this course, students should have mastered the following: know the unit circle and basic trigonometric identities; basic integration and differentiation methods of most basic function types; know and be able to use basic approximation methods (such as local linear approximation); be able to work with functions analytically, numerically, verbally, and graphically; be comfortable with the use of a graphing calculator. This course is an extension of Calculus AB rather than an enhancement, intended to be both challenging and demanding. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed geometrically, numerically, analytically, and verbally. Topics include parametric, polar, and vector functions, and analysis of their curves, numerical solutions of differential equations using Euler’s Method, L’Hopital’s Rule, including its use in determining limits and convergence of improper integrals and series. In addition, methods of integration, logistic differential equations, polynomial approximations and series, and applications of integration, including arc length and finding the area of a region bounded by polar curves.