# Mathematics

YOU + DLS = GREATNESS!

Every student can be successful with the right support group. As a department we strive 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 will not only challenge the students but prepare their skill sets for college and the rest of their lives.

## Freshman Classes

## 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.

## 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.

## Freshman/Sophomore Classes

## 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, on which their future math classes will depend, 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 to the teaching of the class. 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.

## Honors 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, on which their future math classes will depend, 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 to the teaching of the class. 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.

## Advanced Geometry

**Grades Offered: **9, 10

**Prerequisites (Ninth Grade): **Algebra I in eighth grade, HSPT and IFMPE scores, and approval of department leader.

**Prerequisites (10th Grade):** “A” in Honors Algebra I, and approval of department leader.

To be successful in this course, the student should have already mastered the following from Algebra 1; 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.

## Sophomore/Junior Classes

- Algebra II & Trigonometry
- Honors Algebra II & Trigonometry
- Advanced Algebra II & Trigonometry
- IB Mathematics SL 1
- IB Mathematics HL 1

## Algebra II & 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.

## Honors Algebra II & Trigonometry

**Grades Offered: **10, 11

**Prerequisites: **“B” in Honors 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.

## Advanced Algebra II & 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.

## IB Mathematics SL 1

**Grades offered: **11:

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

This course will have an emphasis on statistics, modelling and use of technology. This course is appropriate for those with an interest in the applications of mathematics and how technology can support this, and is aimed at students who will go on to study subjects such as social sciences, natural sciences, medicine, statistics, business, some economics courses, psychology, and design. This course will develop: a curiosity and enjoyment of mathematics, and appreciate its elegance, beauty and power; develop a deep, lifelong understanding of the concepts, principles and nature of mathematics; communicate mathematics clearly, concisely and confidently in a variety of contexts; develop logical and creative thinking, and patience and persistence in problem-solving to instill confidence in using mathematics.

## IB Mathematics HL 1

**Grades offered:** 11

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

This course will have an emphasis on calculus appropriate for pure mathematicians, engineers, scientists, economists, those with an interest in analytic methods. This course is aimed at students who will go on to study subjects with substantial mathematics content such as mathematics itself, engineering, physical sciences, or some economics courses. This course will develop: a curiosity and enjoyment of mathematics, and appreciate its elegance, beauty and power; develop a deep, lifelong understanding of the concepts, principles and nature of mathematics; communicate mathematics clearly, concisely and confidently in a variety of contexts; develop logical and creative thinking, and patience and persistence in problem-solving to instill confidence in using mathematics.

## Senior Classes

- Pre-Calculus
- Honors Pre-Calculus
- IB Calculus AB
- IB Calculus BC
- IB Mathematics SL 2
- IB Mathematics HL 2

## 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.

## Honors Pre-Calculus

**Grade Offered: **12

**Prerequisites: **“B+” in Honors 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. 353 – AP CALCULUS AB

## IB 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 national Advanced Placement syllabus is followed. 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. A pre-course (summer) reading and writing assignment is required.

## IB 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. It is 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.

## IB Mathematics SL 2

Grade Offered: 12

Prerequisites: Enrolled in IBDP and Honors Algebra 1 & Honors Geometry.

The Math SL course is a standard level course intended for motivated students with knowledge of basic mathematical skills and concepts. Students enrolled in this course should be able to apply mathematical techniques correctly, appreciate the usefulness of math, and will develop logical, critical, and creative thinking. Students are expected to apply their knowledge to solve realistic problems. Topics in this course include: Algebra, Functions and Equations, Trigonometry, Matrices, Vectors, Statistics, Probability, and Calculus. During the course, students will also write a math inspired paper on a topic of their choice, and take two external examinations at the end of the course.

## IB Mathematics HL 2

**Grade Offered: **12

**Prerequisites:** Enrolled in IBDP and Advanced Geometry & Advanced Algebra 2.

The IB DP higher level mathematics course focuses on developing important mathematical concepts in a comprehensible, coherent and rigorous way, achieved by a carefully balanced approach. Students are encouraged to apply their mathematical knowledge to solve problems set in a variety of meaningful contexts. Development of each topic should feature justification and proof of results. Students should expect to develop insight into mathematical form and structure, and should be intellectually equipped to appreciate the links between concepts in different topic areas. They are also encouraged to develop the skills needed to continue their mathematical growth in other learning environments. Topics in this course include: Algebra, Functions and equations, Circular functions and trigonometry, Vectors, Statistics and probability, Calculus, Sets, relations and groups, and Discrete mathematics