Course+Decription




 * Below you will find the course descriptions for the courses taught at Ludlow High School.**

**MATHEMATICS DEPARTMENT** The mission of the Mathematics Department is to provide every student with the mathematical skills that will afford them the opportunity to be successful in society. In this area, students concentrate on making mathematical connections and using principles of mathematics to communicate reason and solve problems. Students engage in projects, which require them to apply number systems, operations, and forms in real-world contexts. "The vision of the Massachusetts Mathematics Curriculum Framework is that all students in the Commonwealth achieve mathematical power through problem-solving, communication, reasoning, and connections." Guiding principles for the Mathematics Framework: Students explore mathematical ideas in ways that maintain their enjoyment of and curiosity about mathematics help; they develop depth of understanding and reflect real-world applications. All students have access to a high quality mathematics program. Mathematics instruction both connects with other disciplines and moves toward integration of mathematical domains. Working together in teams and groups enhances mathematical learning, helps students communicate effectively, and develops social and mathematical skills. Technology is an essential tool for effective mathematics education. Mathematics assessment is a multifaceted tool that monitors student performance, improves instruction, enhances learning, and encourages student self-reflection. The National Council of Teachers of Mathematics Curriculum and Evaluation Standards provide educators with goals for school mathematics and guidelines for achieving these goals. The fifty-four standards are presented as a vision for school mathematics based on societal goals, student goals, research, and teaching and learning, and professional guidelines.

Prerequisites: NONE Open to: Enrollment is based on 8th grade placement test and midyear average Pre-Algebra || FULL YEAR || 5 COURSE CREDITS || In this course, students learn algebraic concepts such as number systems, operations, solving equations and inequalities. Students engage in activities which require them to identify, analyze, and solve problems involving the following topics: number sentences in the forms of ax+b= cx+d, and ax+b< cx+d, number properties, and formulas, order of operations, graphs of lines, slopes, and parabolas, exponents, powers, solving proportions, polynomials and factoring, absolute value, quadratic equations, and radical expressions. The concept of a function will be studied. This will allow the student to graph functions such as lines and parabolas. The student will be introduced to writing equations of lines in point slope- form. This course is more comprehensive than the Applied Algebra I course and is designed for students who are interested in attending a four-year college. This course emphasizes the need for students to comprehend the abstract and symbolic nature of algebra.
 * ALGEBRA I **- Level: Standard (CP)
 * COURSE NUMBER: 20133

**APPLIED ALGEBRA 1** - Level: Essentials (CP) Prerequisites: NONE Open to: Students referred by mathematics teacher || FULL YEAR || 5 COURSE CREDITS || In this course, students learn algebraic concepts such as number systems, operations with signed integers and fractions. and language of Algebra. Students engage in activities, which require them to identify, analyze, and solve equations simple word problems involving the following topics: integers, equations involving addition, subtraction, multiplication and division. The student will learn how to solve proportional equations and investigate scale drawings and models. Functions and graphs will be discussed. The student will be introduced to writing of a linear equations in point slope- form and will learn how to graph lines. Powers and roots, polynomials, factoring, and solving quadratic equations will also be discussed. Inequalities and systems of equations and inequalities are also a part of this course. This course emphasizes the need for students to comprehend the abstract and symbolic nature of algebra. This course is not recommended for someone interested in attending a four-year college.  Prerequisites: Algebra 1 in Grade 8 Open to: Enrollment is based on 8th grade placement test and average of first three terms in Algebra 1 || FULL YEAR || 5 COURSE CREDITS || In this course, students learn about patterns and inductive reasoning. Students engage in activities, which require them to use a compass, protractor, and straight edge. Course work includes studying parallel and perpendicular lines and the relationships between corresponding angles, alternate interior angles, same side interior angles, and alternate exterior angles. The students will be introduced to the concept of slope and the writing of equations of lines. The student will learn how to prove triangles congruent and study the implications of these types of triangles. Relationships within triangles such as concurrent lines, medians and altitudes will also be explored. All types of quadrilaterals including formal proofs will be discussed. Areas of parallelograms, triangles, rhombuses and regular polygons will be included. The Pythagorean theorem will be reviewed. This review will include simplifying radicals. Similar polygons will be studied. The student will be exposed to the sine, cosine, and tangent ratios. This trigonometry will be extended to include area. Surface area and volume of all prisms, cylinders, and pyramids are essentials topics for any student interested in pursuing a course in AP Calculus as a senior. The study of circles includes secant and tangent lines; chords and arcs are also an essential part of this course. The course emphasizes abstract mathematical principles. Back to top. Prerequisites: Individualized Educational Plan (IEP) and team recommendation Open to: Students with Individualized Educational Plans (IEPs) || <span style="display: block; font-family: Verdana,Arial,Helvetica,sans-serif; text-align: center;">FULL YEAR || <span style="display: block; font-family: Verdana,Arial,Helvetica,sans-serif; text-align: center;">5 COURSE CREDITS || <span style="display: block; font-family: Verdana,Arial,Helvetica,sans-serif; text-align: left;">This course focuses on providing students with instruction in core concepts of algebra and provides the foundation for a more in-depth understanding to algebraic concepts addressed in Applied Algebra 1B.
 * <span style="color: #006400; font-family: Verdana,Arial,Helvetica,sans-serif;">COURSE NUMBER: 20023
 * HONORS GEOMETRY **(Grade 9) - Level: Honors
 * <span style="color: #006400; font-family: Verdana,Arial,Helvetica,sans-serif;">COURSE NUMBER: 20143
 * APPLIED ALGEBRA 1A**
 * <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">COURSE NUMBER:92823AF

Prerequisites: Applied Algebra IA, Individualized Educational Plan (IEP) and team recommendation Open to: Grades 9 - 12 students with Individualized Education Plans (IEPs) || <span style="display: block; font-family: Verdana,Arial,Helvetica,sans-serif; text-align: center;">FULL YEAR || <span style="display: block; font-family: Verdana,Arial,Helvetica,sans-serif; text-align: center;">5 COURSE CREDITS || <span style="display: block; font-family: Verdana,Arial,Helvetica,sans-serif; text-align: left;">This course provides students with more detailed instruction of algebraic concepts addressed in Algebra 1A. Concepts include: the language of Algebra, integers, simple equations that involve addition, subtraction, multiplications and division. Other topics involve functions and their graphs, linear equations, powers and square roots, polynomials and some factoring. This course is designed for students who require additional exposure to instruction in order to master math concepts.
 * APPLIED ALGEBRA 1B**
 * <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">COURSE NUMBER:92823BF

<span style="font-family: Verdana,Arial,Helvetica,sans-serif;">**AP/HONORS CALCULUS AB** - Level: Advanced Placement
 * <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">COURSE NUMBER: 20553

Prerequisites: Algebra 1, Algebra 2 (Grade 10), Geometry (Grade 9) and Pre-Calculus

Open to: Grade 12 students who have averaged 87% or better in Pre-Calculus, or with recommendation of Mathematics Department Curriculum and Instructional Leader (CIL).NO WAIVERS WILL BE ALLOWED for students to enter AP/Honors Calculus AB || <span style="display: block; font-family: Verdana,Arial,Helvetica,sans-serif; text-align: center;">FULL YEAR || <span style="display: block; font-family: Verdana,Arial,Helvetica,sans-serif; text-align: center;">5 COURSE CREDITS || <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">This course is offered to the student who plans on taking the Advanced Placement examination, which offers college credits. These students should demonstrate the ability to handle the abstract theories of calculus. Topics covered include: limits and continuity of functions, the derivative, and applications of the derivative, the definite integral and its applications, exponential and logarithmic functions, techniques of integration, areas and volumes of solid figures, indeterminate forms, and improper integrals. Word problems involving related rates and maximum and minimum problems will be emphasized. There will be an extensive review at the conclusion of the course, in preparation for the AP examination given in the spring. It is required that a student has at least a B+ (87 or better) in all of their math courses to be successful in this high-level math course. A graphing calculator is required so that students can engage in classroom activities. The student will not be able to complete many of the homework assignment without the use of a graphing calculator. A Texas instrument 83-plus, TI-84. TI-86, or TI-89 are calculators that AP College Board recommends. Advanced placement credit and weight will be awarded for this course only if the student takes the May advanced placement exam. Honors credit and weight will be awarded for this course if the student does not take the May advanced placement exam.

<span style="font-family: Verdana,Arial,Helvetica,sans-serif;">COURSE NUMBER: 20443
 * PRE-CALCULUS** - Level: Honors

Prerequisites: For Juniors - Honors Algebra 2 For Seniors - Analysis

Open to: Grades 11 or 12 students || <span style="display: block; font-family: Verdana,Arial,Helvetica,sans-serif; text-align: center;">FULL YEAR || <span style="display: block; font-family: Verdana,Arial,Helvetica,sans-serif; text-align: center;">5 COURSE CREDITS || <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">In this course, students learn foundational principles of calculus. Students engage in activities, which require them to study the following concepts: linear and quadratic functions, polynomial functions, inequalities, properties of functions which includes graphing of functions and inverse functions, reflecting these graphs, using symmetry to stretch, shrink, and translate these functions. The student's knowledge of exponents and logarithms will be expanded and will include word problems on growth and decay. Applications will include examine the prices of commonly purchased items, as well of applications to saving money. Analytic geometry will include topics such as coordinate proofs; equations of circles, ellipses, hyperbolas and parabolas Systems of second-degree equations will also be included in their study of analytic geometry. Trigonometric equations and their applications are discussed in great detail. Such topics will include the sine, cosine, and tangent curves. Solving triangles with these trig ratios. The law of Sines and the law of Cosines, which are essential to understand in any Calculus course, will be expanded on. Trigonometric Addition formulas, double angle and half angle formulas are an essential part of this course. Solving linear and quadratic trigometric equations will provide the student with the needed background for AP Calculus. Polar coordinates and complex numbers are also studied. This course emphasizes the abstract connections between these complex mathematics topics. Course work includes preparation for mathematics, science, engineering, and technology as potential college majors. The student must have his or her own graphing calculator. A TI-83 plus or TI-84 is recommended. A graphing calculator is required so that students can engage in classroom activities. The student will not be able to complete many of the homework assignments without the use of a graphing calculator. It is recommended that a student have at least a B+ (87-89) in all of their math courses to be successful in this high-level math course. If a student does not want to take AP Calculus in their senior year then the student should take Analysis.


 * ANALYSIS** - Level: Standard
 * <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">COURSE NUMBER: 20633

Prerequisites: Algebra 1, Algebra 2, and Geometry Open to: Grades 11 - 12 students || <span style="display: block; font-family: Verdana,Arial,Helvetica,sans-serif; text-align: center;">FULL YEAR || <span style="display: block; font-family: Verdana,Arial,Helvetica,sans-serif; text-align: center;">5 COURSE CREDITS || <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">In this course, students learn applications of complex number systems. Students engage in activities, which require them to explore linear, polynomial, rational, exponential, logarithmic, trigonometric, and circular functions. The course emphasizes abstract mathematical principles. This course is recommended for students who have a solid background in mathematics. An overall average of a B (83-86) is recommended. Students who have taken applied math courses may not have the background to be successful in this course. The student must have his or her own graphing calculator. A TI-83 plus or TI-84 is recommended. A graphing calculator is required so that students can engage in classroom activities. The student will not be able to complete many of the homework assignments without the use of a graphing calculator.

Prerequisites: Algebra 1, Geometry Open to: Grades 11 - 12 students || <span style="display: block; font-family: Verdana,Arial,Helvetica,sans-serif; text-align: center;">FULL YEAR || <span style="display: block; font-family: Verdana,Arial,Helvetica,sans-serif; text-align: center;">5 COURSE CREDITS || <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">In this course, students learn advanced algebraic number systems, operations, and forms. Students engage in activities, which require them to communicate by using the language of algebra, and exploring variations, graphs, linear relations, matrices, systems, parabolas (and quadratic equations), quadratic relations, polynomials, functions, powers, roots, exponents, logarithms, trigonometry, statistics, and dimensions in space.
 * ALGEBRA 2** Level: Standard (CP)
 * <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">COURSE NUMBER: 20333


 * HONORS ALGEBRA 2** - Level: Honors


 * <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">COURSE NUMBER: 20243

Prerequisites: Geometry (Grade 9) Open to: Grade 10 students || <span style="display: block; font-family: Verdana,Arial,Helvetica,sans-serif; text-align: center;">FULL YEAR || <span style="display: block; font-family: Verdana,Arial,Helvetica,sans-serif; text-align: center;">5 COURSE CREDITS || <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">In this course, students will explore advanced algebraic number systems, operations, and equations in more detail than a standard Algebra 2 course. Students engage in activities, which require them to write and solve algebraic equations and inequalities, and explore linear equations, system of linear functions and inequalities, matrices and determinants, quadratic functions and polynomials are discussed in great detail. Polynomials and polynomial functions exponents, roots and radicals including radical equations are all key topic of this course. Exponential and logarithmic functions and their properties will be explored. Rational equations and quadratic relationships, which include the conic sections, are also presented. Trigonometric ratios and functions will allow students who are successful in this course to skip Analysis and take Pre-Calculus next year. The student must have his or her own graphing calculator. A TI-83 plus or TI-84 is recommended. A graphing calculator is required so that students can engage in classroom activities. The student will not be able to complete many of the homework assignments without the use of a graphing calculator.


 * APPLIED ALGEBRA 2**
 * <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">COURSE NUMBER: 96623

Prerequisites: Individualized Education Plan (IEP) and team recommendation

Open to: Grades 11 and 12 students with Individualized Education Plans (IEPs) || <span style="display: block; font-family: Verdana,Arial,Helvetica,sans-serif; text-align: center;">FULL YEAR || <span style="display: block; font-family: Verdana,Arial,Helvetica,sans-serif; text-align: center;">5 COURSE CREDITS || <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">This course stresses the fundamentals of Algebra 2 including solving first degree linear equations and inequalities, slopes, graphing lines, systems of equations and inequalities, matrices, polynomials, factoring, and radical expressions. Solving quadratic functions by factoring, completing the square and the quadratic formula will be emphasized. Some trigonometry will be covered. The trigonometry in this course is limited to right triangles. This course emphasizes the need for students to comprehend the abstract and symbolic nature of algebra and apply these principles to basic geometric concepts. Some 4-year colleges may not accept Applied Algebra 2 as a college preparatory math. Students should consult with their guidance counselor regarding college's admissions requirements for math.


 * APPLIED ALGEBRA 2** - Level: Essentials (CP)


 * <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">COURSE NUMBER: 20323

Prerequisites: Algebra 1, Applied Geometry or approval of Mathematics Department Curriculum and Instructional Leader (CIL)

Open to: Grade 12 students with a recommendation of their Grade 11 teacher or Grade 11 students with Mathematics Department Curriculum and Instructional Leader (CIL) approval || <span style="display: block; font-family: Verdana,Arial,Helvetica,sans-serif; text-align: center;">FULL YEAR || <span style="display: block; font-family: Verdana,Arial,Helvetica,sans-serif; text-align: center;">5 COURSE CREDITS || <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">This course stresses the fundamentals of algebra including solving linear, exponential, logarithmic, and polynomial equations. Students will engage in activities requiring them to graph and find equations for most functions and variations. Some trigonometry will be covered. It will be limited to right triangles, the law of sines and the law of cosines. The student must have his or her own graphing calculator. A TI-83 plus or TI-84 is recommended. A graphing calculator is required so that students can engage in classroom activities. The student will not be able to complete many of the homework assignments without the use of a graphing calculator. Some 4-year colleges may not accept Applied Algebra 2 as a college preparatory math. Students should consult with their guidance counselor regarding colleges that will accept Applied Algebra 2 in their admissions consideration.


 * GEOMETRY **- Level: Standard (CP)
 * <span style="color: #006400; font-family: Verdana,Arial,Helvetica,sans-serif;">COURSE NUMBER: 20233

Prerequisites: Algebra 1

Open to: Grades 9 - 12 students || <span style="color: #006400; font-family: Verdana,Arial,Helvetica,sans-serif;">FULL YEAR || <span style="color: #006400; font-family: Verdana,Arial,Helvetica,sans-serif;">5 COURSE CREDITS || <span style="font-family: Verdana,Arial,Helvetica,sans-serif;"> In this course, students learn foundational geometry concepts using inductive reasoning and algebraic and industry perspectives. Students engage in activities that require them to identify, analyze, and solve problems involving the following topics: segments, parallel and perpendicular lines, angles, triangles, quadrilaterals, surface area and volume, similarity, right triangle trigonometry, circles, sphere, and proofs. Course work includes studying how geometry relates to algebra.


 * APPLIED GEOMETRY** - Level: Essentials (CP)
 * <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">COURSE NUMBER: 20223

Prerequisites: Algebra 1 or approval of the Mathematics Department Curriculum and Instructional Leader (CIL) Open to: Grade 11, 12 students with a recommendation of their Algebra 1 teacher or Grade 10 students with Mathematics Department Curriculum and Instructional Leader (CIL) approval || <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">FULL YEAR || <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">5 COURSE CREDITS || <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">In this course students learn the fundamental concepts of geometry without rigorous proofs. Students will engage in more hands-on and group work used to discover Euclidean concepts. How to label line segments, distance formula, midpoints, slope, parallel and perpendicular lines, congruent triangles, and relationships within triangles, quadrilaterals, right triangle trigonometry, surface area and volume will be explored. Some 4-year colleges may not accept Applied Geometry as a college preparatory math. Students should consult with their guidance counselors to discuss college admissions requirements relating to math.


 * APPLIED GEOMETRY**
 * <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">COURSE NUMBER: 92723

Prerequisites: Individualized Educational Plan (IEP) and team recommendation

Open to: Grades 11 - 12 students with Individualized Educational Plans (IEPs) || <span style="display: block; font-family: Verdana,Arial,Helvetica,sans-serif; text-align: center;">FULL YEAR || <span style="display: block; font-family: Verdana,Arial,Helvetica,sans-serif; text-align: center;">5 COURSE CREDITS || <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">In this course students will learn the fundamental concepts of geometry without rigorous proofs. Lines and line segments, distance formula, midpoints, slope, parallel and perpendicular lines, congruent triangles, relationships within triangles, quadrilaterals, some right triangle trigonometry, area and volume will be discussed. The students will be expected to master key concepts in the curriculum. Some 4-year colleges may not accept Applied Geometry as a college preparatory math. Students should consult with their guidance counselors to discuss college admissions requirements relating to math.


 * STATISTICS** - Level: Essentials (CP)
 * <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">COURSE NUMBER: 20423

Prerequisites: Student must have completed Algebra 2 or Applied Algebra 2. Seniors who have a MCAS Math EPP (Educational Proficiency Plan) are the students who have priority for enrollment in this course. || <span style="display: block; font-family: Verdana,Arial,Helvetica,sans-serif; text-align: center;">FULL YEAR || <span style="display: block; font-family: Verdana,Arial,Helvetica,sans-serif; text-align: center;">5 COURSE CREDITS || <span style="font-family: Verdana,Arial,Helvetica,sans-serif;">Content: Topics include probability, frequency distribution, data analysis, normal distribution, hypothesis testing, correlation and regression and sample simulation.