The Mathematics Department assumes “primary responsibility” for assisting students in achieving proficiency in Academic Expectations 5 (Data Analysis), 6 (Logical Reasoning), and 7 (Technology). We also acknowledge our collaborative efforts in reinforcing and supporting all of the other academic expectations outlined on page vi of this Program of Studies. The goals and objectives of the course offerings listed below reflect the overall goals of Lexington High School's Mathematics program 9-12. In the case where a specific course might concentrate on an additional academic expectation, the number of the expectation addressed is listed below the course title.
Quick Reference
Goals of Mathematics - Teaching and Learning
Graphing Calculators and Computer Technology
Course and Level Selection
Placement Review and Outside Coursework
Course Expectations and Final Examinations
Common Course Sequences
Course Descriptions
The Mathematics Department offers a substantive four-year sequence of college-preparatory courses for students with varied learning styles and academic interests. Our goal is to enable every student to reach his or her potential in a supportive, academically focused environment. In every mathematics course, we want students to learn what it means to explore and discover mathematics; what it means to collect data, observe patterns, make conjectures, and generalize these findings; what it means to produce a coherent logical argument-to think deductively; what it means to create a mathematical model; what it means to represent a solution analytically, geometrically, numerically and verbally; what it means to analyze a problem and persevere until it is solved; in essence, what it means to develop the habits of mind of a mathematician and to think critically. We believe all students can reach high standards of academic achievement and come to appreciate the power and beauty of mathematics.
As the Mathematics Department continues to integrate technology into the mathematics curriculum in educationally sound ways, we are excited about the potential that these tools offer to the teaching and learning of mathematics. Through the use of educational technology, students have greater opportunity to be actively engaged in genuine mathematical exploration, inquiry and analysis, to develop deeper mathematical understanding and insight, and to understand the limitations of technology.
The Mathematics Department strongly recommends that all students purchase a graphing calculator which will be used in their mathematics courses for classwork, homework and assessment throughout their high school education. In order for all of our students to have access to graphing calculators, we are asking for your continued support with our graphing calculator policy. We have arranged with a distributor of graphing calculators for students to be able to purchase the Texas Instruments TI-83/84 Plus® Graphing Calculator at a discounted price as part of a volume purchase plan. Ordering information will be available from the classroom teacher on the first day of school in September.
The prerequisite course listed with each course description is the strongly recommended background necessary for student success at that level, however, teacher recommendations take priority over the prerequisite. Although our courses do have ability levels, the courses are not “tracked.” There is a misconception that once you are in a level, it is impossible to move. This is untrue as students do move up and down levels during their high school education.
We strongly encourage students to maintain a reasonable balance among academic course load, extracurricular activities, and personal time to contribute to their social and emotional well-being. It is extremely important for students and parents to make an informed decision during the scheduling process regarding which course and level is most appropriate for the student. Due to a variety of factors, the selection of a course and level should be considered a year-long commitment. In order to maintain class sizes that are equitable for all students, it has become very difficult to switch levels once the schedule has been completed. As a result there can be no guarantee that a space will be available in another course or level during a preferred block. Only extraordinary circumstances will be considered for a course change request as outlined in the LHS Student/Parent Handbook.
The Mathematics Department offers courses at three instructional levels: Level 2, Level 1 and Honors. It is important to note that all three levels are college preparatory and share an essential common core curriculum which is aligned with both the Massachusetts Mathematics Curriculum Frameworks (2000) and the NCTM Principles and Standards for School Mathematics (2000). The level descriptions which follow are not intended to be exclusive but rather are intended to help students and parents identify a learning profile that comes closest to that of the student and to determine which level will most likely meet the student's specific learning needs.
Level 2 courses progress at a pace that allows for skill development and reinforcement of concepts. The course is designed to support the learning of students who may not have fully retained the skills and concepts covered in prior courses which will be reviewed when needed in the course. Mathematical concepts tend to be introduced at a concrete level and developed with an increasing level of abstraction. New ideas are often developed through student investigation with significant guidance from the teacher. Students will usually learn to solve problems through repetition of routine problems. Students will receive support from the teacher in developing study skills and using the textbook as a resource. Classes typically include substantial review of homework and previously covered content. Students are expected to take responsibility for their own learning with guidance from the teacher and to seek help when needed. The course is designed to meet the needs of a student who thrives in a directed learning environment.
Level 1 courses progress at a fast pace. Students are expected to have developed most of the skills and understood most of the concepts covered in prior courses, but the course will include some review of difficult topics that may not have been fully retained. Mathematical concepts are introduced using a balance of abstract and concrete approaches. New ideas are often developed through student investigation with moderate guidance from the teacher. Students will be expected to solve routine problems independently and solve open-ended and non-routine problems with teacher support. Students will be expected to use the textbook as a resource and occasionally to learn new material independently. Typical classes include some review of homework and previously covered content before new material is introduced. Students are expected to be self-motivated, taking responsibility for their own learning and seeking help when needed. The course is designed to meet the needs of a student who thrives in a guided learning environment.
Honors courses progress at a very fast pace covering the greatest breadth and depth of topics. Students are expected to have mastered the skills and thoroughly understood the concepts covered in prior courses. They are expected to have retained this past knowledge, which will generally not be reviewed in the course. Mathematical concepts are often introduced at an abstract and theoretical level. New ideas are often developed through student investigation with minimal guidance from the teacher. Students will be expected to apply their knowledge to open-ended and non-routine problems. Students will sometimes be expected to learn material by reading the textbook and/or solving problems on their own. Typical classes include minimal review of homework and previously covered material. Students are expected to be highly self-motivated, taking the fullest responsibility for their own learning and seeking help when needed. The course is designed to meet the needs of a student who thrives in a more independent learning environment.
Students and parents are advised to consider teacher recommendations very carefully and to consult with the teacher if there is disagreement about placement. If mutual agreement cannot be reached after consultation with the teacher, then a Placement Review Form should be requested from the teacher and sent to the Department Head. Placement decisions will be made by a committee consisting of the Department Head and at least two teachers (not including the student's current teacher).
Please note that a separate form, Summer School Preapproval, is required if you anticipate any outside course of study might impact the appropriate placement of a student in the mathematics program. No schedule change requests resulting from any outside course of study will be honored without this prior approval which must be submitted by May 1.
Although each teacher writes his or her own course expectations and grading policies for each course, there are certain expectations common to all sections of the same course. For example, the extent to which students are allowed to use notecards or reference sheets during assessments will be consistent across sections. Since reinforcement and extension of classwork are important components of mathematics instruction, all sections of the same course will have similar homework expectations. All agreed-upon common expectations will be included as part of the teacher's course expectations which are distributed at the beginning of each course.
All sections of the same course are administered a departmental final examination with at least 80 percent common questions consisting of multiple choice, short answer and open-response. The intent is to insure that all students have learned the essential common core of curriculum for each course and are adequately prepared for subsequent courses. It also gives flexibility to cover optional topics based on student and teacher interest. Departmental final exams will become public on a rotating basis by course. Course syllabi for each course will be available on the Mathematics Department website: http://lhs.lexingtonma.org/Dept/Math/ .
| 8th Grade | 9th Grade | 10th Grade | 11th Grade | 12th Grade |
Grade 8 Math (formerly Inter- mediate Math) |
#220 Integ. Math I |
#230 Integ Math II |
#231 Lv 2 Geometry |
#241 Lv 2 Algebra 2 |
| #221 Algebra I |
#231 Lv2 Geometry |
#241 Lv2 Algebra 2 |
#251 Adv. Alg. & Trig or #257 Integ. Math & Physics . |
|
| Grade 8 Algebra 1A (formerly Advanced Math) |
#222 Algebra 1B |
#232 Lv1 Geometry |
#242 Lv1 Algebra 2 |
#252 Lv1 Adv. Math or #257 Integ. Math & Physics or #272 Lv1 Statistics |
| Grade 8 Algebra 1 (formerly Extended Math) |
#242 Lv1 Alg. 2 See Note* |
#232 Lv1 Geometry |
#252 Lv1 Adv. Math |
#262 Lv1 Intro to Calculus or #272 Lv1 Statistics |
| #243 Honors Algebra 2 |
#233 Honors Geometry |
#253 Honors Adv. Math |
#263/4 AP Calculus AB/BC or #273 AP Statistics |
|
| Note: Students completing Algebra 1 during the summer after 8th grade with preapproval may be allowed to enroll in #242 Level 1 Algebra 2. | ||||
| IMPORTANT: Starting with the 8th-grade course, each row represents a common course sequence, however, this chart does NOT show all of the possible course sequences. Although our courses do have ability levels, the courses are not “tracked.” There is a misconception that once you are in a level it is impossible to move. This is untrue as students do move up and down levels during their high school education. |
||||
220 Integrated Math I
Prerequisite: Successful completion
grade 8 Mathematics
A non-traditional course in which students learn mathematics in the context
of practical applications organized in five strands: Number sense and Operations;
Patterns, Relations, and Algebra; Geometry; Measurement; and Data Analysis, Statistics and Probability.
The course is intended for students
who have difficulty with the abstract nature of the traditional
approach. Preparation for the MCAS exam will be included in the
curriculum. It is expected that this course is part of a two-year
sequence.
221 Algebra 1
Prerequisite: Final grade of B in grade
8 Mathematics
222 Algebra 1B
Prerequisite: Final grade of C in Grade 8
Advanced Mathematics and teacher recommendation
These courses emphasize algebraic language, structure, concepts
and skills. Major topics include algebraic properties and the real number system,
functions and their graphs, linear equations and inequalities, linear regression and
modeling, systems of linear equations and inequalities, polynomials and factoring,
algebraic fractions and real world applications.
230 Integrated Math II
Prerequisite: Successful completion of
Integrated Math I
A non-traditional course which builds on the mathematics learned
in Integrated Math with Applications I with more advanced topics from the
five strands: Number sense and Operations;
Patterns, Relations, and Algebra; Geometry; Measurement; and Data Analysis, Statistics and Probability.
Preparation for the MCAS exam with emphasis on solving open response questions will be
included in the curriculum. It is expected that this course is part of a two-year
sequence.
231 Lv 2 Geometry
Prerequisite: Algebra 1
232 Lv 1 Geometry
Prerequisite: Final grade of B in Algebra 1B or C in Lv 1 Algebra 2 in grade 9
233 Hon Geometry
Prerequisite: Final grade of B in Honors
Algebra 2 or teacher recommendation
These courses will focus on mathematical ways of knowing, basic geometric objects and ideas,
parallelism and perpendicularity, congruence, similarity, transformations, right triangles,
coordinate geometry, circles, area and volume, and concurrency. Exploratory software such as
The Geometer's Sketchpad will be used to develop inductive and deductive reasoning skills.
In addition to Euclidean topics the Honors course may include
topology, and non-Euclidean geometries.
241 Lv 2 Algebra 2
Prerequisite: Lv 2 Geometry
242 Lv 1 Algebra 2
Prerequisite: Final grade of C in Algebra 1 taken in eighth grade and teacher recommendation or final grade of C in Algebra 1B and Lv 1 Geometry
243 Hon Algebra 2
Prerequisite: Final grade of A in Algebra 1 taken in eighth grade and teacher recommendation
These courses will focus on the extension of the number system to a complex field, elementary functions using multiple representations (graphical, numerical, algebraic and verbal) including linear, quadratic, polynomial, rational, exponential, and logarithmic functions, linear systems and matrices, and the study of probability and of sequences and series. Honors classes will have an introduction to statistics.Problem solving will be emphasized throughout the course.
257 Integrated Math and Physics
357 Science
251 Advanced Algebra and Trigonometry
Prerequisite: Lv 2 Algebra 2
An extension of Algebra 2 and a beginning study of more advanced
topics in algebra including probability and statistics, number
theory and some discrete mathematics. The first semester includes
a thorough treatment of trigonometry. This is a course for
students who wish to reinforce their knowledge of algebra and to
gain an appreciation for trigonometry in preparation for further
mathematics study.
252 Lv 1 Advanced Mathematics
Prerequisite: Final grade of C in Lv 1
Algebra 2 and Lv 1 Geometry
This course provides students with an in-depth study of families of functions including
polynomial and rational, exponential and logarithmic, and trigonometric and circular functions.
Emphasis is placed on both conceptual understanding and practical problem solving.
An introduction to probability and statistics is also an integral part of the course.
These courses will enable students to continue their mathematics education in statistics,
calculus or a related field.
253 Hon Advanced Mathematics
Prerequisite: Final grade of B in Honors Algebra 2 and Honors Geometry or teacher recommendation
Students are encouraged to review selected content from the prerequisite courses during the preceding summer.
This intensive course prepares students to take college level courses in calculus and statistics. General ideas about functions are developed and used throughout the course, such as: multiple representations (graphical, numerical, algebraic, and verbal), function operations, composition and inverses, transformations, and modeling and regression. Specific topics include polynomial and rational functions, exponential and logarithmic functions, trigonometric functions, complex numbers and vectors, polar and parametric equations, matrices and linear systems, analytic geometry, combinations and probability, sequences and series, and limits. Students must adopt a theoretical approach to mathematics, reason carefully to solve problems, and communicate their ideas effectively. The course demands a substantial commitment of time and effort, and strong mathematical abilities and interests are essential for success.
262 Lv 1 Introduction to Calculus
Prerequisite: Final grade of C in Lv1
Advanced Mathematics, or successful completion of Honors Advanced Mathematics
The focus of this course is on
understanding the concepts of calculus from a geometric or
intuitive point of view. Units from differential and integral
calculus provide the main themes, but time will be taken to
master topics not adequately studied in pre-calculus. Practical
applications will be emphasized rather than theoretical aspects.
This course is not intended as preparation for the Advanced
Placement Calculus exam. While some students may be eligible for
advanced standing in college calculus, all students will be
thoroughly prepared for a beginning college calculus course.
263 Hon AP Calculus-AB
Prerequisite: Final grade of B in Hon Advanced Mathematics or teacher recommendation
This is a college-level course in differential and integral calculus,
equivalent to one semester of calculus at most universities.
Topics include a review of functions, an introduction
to limits and continuity, derivatives and their applications, integrals
and their applications, anti-derivatives and the Fundamental Theorem of Calculus,
and an introduction to differential equations using slope fields. There is an emphasis on
conceptual understanding and working with functions represented graphically, numerically,
analytically, and verbally.
The TI-83/84 graphing calculator is used extensively. The Advanced Placement Calculus AB exam
is expected of all students in this course. More information can be found at
http://www.collegeboard.com/ap/students/calculus.
264 Hon AP Calculus - BC
Prerequisite: Final grade of B in Honors
Advanced Mathematics
This is a college-level course in differential and integral calculus, equivalent
to the first two semesters of calculus at most
universities. Topics include an introduction to limits and continuity, derivatives and
their applications, integrals and their
applications, anti-derivatives and the Fundamental Theorem of
Calculus, an introduction to differential equations using slope
fields and Euler's Method, Taylor polynomials and series, and
calculus using parametric, vector and polar equations. There is
an emphasis on conceptual understanding and working with
functions represented graphically, numerically, analytically,
and verbally. The TI-83/84 graph ing calculator is used extensively.
The Advanced Placement Calculus BC exam is expected of
all students in this course. More information can be found at
http://www.collegeboard.com/ap/students/calculus.
272 Lv 1 Statistics
Prerequisite: Final grade of C
in Lv1 Algebra 2
An introductory course which provides students with a learner-
centered resource of activities through which students can discover
statistical concepts, explore statistical properties, and apply statistical techniques.
Emphasis is on active learning, conceptual understanding, use of genuine real-world data, and
technology integration with the TI-83/84 graphing calculator. Students will explore the
design of surveys, polls, and experiments to assess the validity of their results,
to identify potential
sources of bias, and to identify the types of conclusions that
can be drawn. Many activities lend themselves to collaborative
learning and emphasis is placed on the importance of students'
communication skills. Other topics include probability through
simulations and experimental design.
273 Hon AP Statistics
Prerequisite: Open to juniors and
seniors who have a superior background in Level 1 Algebra 2 or
Honors Algebra 2 or higher
The purpose of this course is
to introduce students to the major concepts and tools for
exploring data, planning a study, analyzing patterns, and drawing
conclusions from data. The course will rely heavily graphing calculator-based
processes and the analysis of data produced by graphing
calculator and some data produced by computer software packages.
The Advanced Placement Statistics
exam is expected of all students in this course.
275 Accounting I
Prerequisite: None
Open to all students.
Accounting is the language of business! This is a beginning
course for those students preparing for college work in business
management or business administration or for those students
interested in a business career in the field of accounting. It is
also a useful course for those who are considering
operating their own businesses. Emphasis is placed upon the
reasons and the purpose of accounting rather than on mechanical
procedure alone. Students are expected to be able to journalize,
post, prepare a trial balance and financial statements and
manage customer and/or vendor accounts. In
addition, the computer lab will be available so that students
will be able to apply their accounting skills using a computer.
276 Lv 1 Accounting II
Prerequisite: Successful completion of Accounting I
This is an advanced course for those students interested in an
in-depth study of the specialized accounting procedures used
today and how management decisions can be based on accounting
data. Students will be given an opportunity to use their
accounting skills to solve problems similar to those encountered
in the business world and in collegiate work. Included are
special units on corporation records, partnerships, depreciation
methods, computer services, “analysis of trends,”
break-even computation and analysis, and cost accounting. The
computer lab is available to accounting students for the solution
of some of their accounting problems and will enhance their
hands-on experience with the computer.
281 Lv 1 Introduction Programming I
Prerequisite: None
This is an introductory course in computer science using C++ as the
programming language. The course will emphasize the analysis of
problems, the careful selection of an appropriate algorithm, and the
implementation of the algorithm in C++. Topics covered include
input and output streams, variables, operators, conditional statements,
functions, looping, strings, recursion, arrays, and computer number
systems. Course grades will be based primarily on success in completing
programming projects.
282 Lv 1 Introduction to Programming II
Prerequisite: Lv I Introduction to Programming I or permission of
the Department Head for students having past programming experience
This is a continuation of the introductory course in computer
programming which will explore some of the more intricate
aspects of computer programming. Using C++ students will
study string manipulation, matrices, sorting, and be introduced
to object oriented programming. As preparation for continued studies in
computer science, Java will be introduced in the second half of the course.
Course grades will be based
primarily on success in completing programming projects.
283 Hon AP Computer Science
Prerequisite: Lv 1 Introduction to Programming II or
permission of the Department Head
The goals of this course are comparable to a first-year college
course in computer science. The course is intended to serve both
as an introductory course for computer science majors and as a
substantial course for those who will major in other disciplines
that require significant involvement with computing. The topics
covered will be those set by the Advanced Placement Course
Description for Computer Science. Students who successfully
complete this course are expected to take the Advanced Placement
examination in Computer Science at the A or AB level.
284 Advanced Computer Programming
Prerequisite: Teacher recommendation
This course is designed to allow students to experience how a
real world computer application comes to life. This course
builds on their previous programning skills and includes more
advanced GUI techniques. In addition to smaller projects, students
will work together to complete a large programming project of their
choosing by the end of the semester. After many
weeks of coding, they will complete an online help file,
present their work to the class. Course may be repeated for credit.
285 Computer Applications
Prerequisite: None
This is an introductory course in the computer applications that are
used daily in such activities as presentation, desktop publishing,
information processing and decision-making. The course will prepare
students to create documents, presentations, and spreadsheets using
Microsoft Office, edit images and video using iPhoto, Photoshop Elements,
and iMovie, create a basic web page that incorporates many
of the projects completed in the class, and finally introduce computer
programming using KarelJ Robot. Classes will be project-based. Students
from all grades and all academic levels are encouraged to enroll.
Previous computer experience is not a prerequisite.
289 Web Design
See Interdisciplinary Studies202 Math Teaching Assistant Program
Prerequisite: Teacher recommendation and department head approval
Gading: Pass/Fail
Open to seniors only. This program formalizes a two-year field test
of teaching assistants in the mathematics department. Under the close
supervision and guidance of mentor teachers, students serve as teaching
assistants to provide additional support for students who struggle
mathematically in our ninth grade courses. Teaching assistants experience
first-hand the teaching and learning process from an educator's
perspective, come to understand and value what it takes to make mathematics
accessible to all students, and make connections with younger
students that foster academic achievement and meaningful relationships.
If you are interested in becoming a teaching assistant, please see
your current mathematics teacher or the mathematics department head
for more detailed information.
Posted January 28, 2008 by Steve Ellis
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