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Program of Studies - Math

MATHEMATICS DEPARTMENT COURSES

Mathematics courses are offered in four levels that are based upon performance in previous math courses and external assessments:
Level 1 - students who have demonstrated superior mathematical performance (Advanced)
Level 2 - students who have demonstrated high mathematical performance (Honors)
Level 3A- students who have demonstrated average mathematical performance (College Preparatory A)
Level 3B- students who have struggled with math previously (College Preparatory B)
Students enrolled in Advanced Placement Courses are expected to take the Advanced Placement Examination for that course. These courses are: 412 Advanced Placement Statistics with an Introduction to Calculus; 413 Advanced Placement Calculus BC; 414 Advanced Placement Calculus AB
NOTE: All math courses require an approved graphing calculator.
Students seeking to enroll in a course, but who have not met the grade prerequisite, must get the approval of their current math teacher and the approval of the Director of Mathematics.

ADVANCED (Level 1)

ADVANCED GEOMETRY/ALGEBRA 2
Level 1 410 5 credits
This course covers the field of Euclidean Geometry with topics such as points, lines, planes, angles, polygons, circles, direct and indirect proofs, congruence and its applications, area, perimeter, surface area, and volume. During the second semester the first half of Algebra 2 will be taught. This will cover such topics as linear equations and inequalities, polynomials, factoring and special products, rational expressions, radicals and rational number exponents, quadratic equations, and problem solving applications. This course has a required summer assignment covering the first three chapters of the Geometry text. Prerequisite: Students are placed in the course based on Grade 8 performance, teacher grades and external assessments.


ADVANCED PLACEMENT STATISTICS Level 1 411 5 credits
This course includes all topics included in the Advanced Placement course description for Statistics. It also includes a study of the preliminary topics in Calculus. It has a required lab period. Students are expected to take the Advanced Placement Examination in May.
Prerequisite: Students enrolling in this course must have achieved a grade of at least a "B-" in Advanced Geometry/ Algebra 2 (410) OR successful completion of Honors Pre-Calculus (422).

ADVANCED PRE-CALCULUS
Level 1 412 5 credits
Students study algebraic, trigonometric, logarithmic and exponential functions, as well as analytical geometry. Curve sketching and other graphic techniques will be emphasized as a means to achieve visual understanding of abstract ideas. The course also includes a study of limits and the derivative.
Prerequisite: Students enrolling in this course must have achieved a grade of at least a "B-" in Advanced Placement Statistics (411).

ADVANCED PLACEMENT CALCULUS BC
Level 1 413 6 credits
This course includes all of the topics included in the Advanced Placement course description for Calculus BC. It is a study of Intermediate Calculus topics including applications of the integral, infinite sequences and series, and elementary differential equations with applications. It will include a thorough review in preparation for the AP Examination in Calculus, which the students are expected to take in May. . This course has a required lab period and a required summer assignment.
Prerequisite: Students enrolling in this course must have achieved a grade of at least a "B-" in Advanced Placement Statistics (412).

HONORS (Level 2/1)

HONORS ALGEBRA I /ALGEBRA II
Level 2 420 5 credits
This course is open to students in Grade 9 who are capable of learning mathematical concepts at an accelerated rate. It begins with a review of the basic algebra concepts covered in Grade 8 and continues through rational expressions, irrational numbers to quadratic equations. It also includes 3 units of Algebra II topics, including the conics as well as exponential and logarithmic functions.
Prerequisite: Students are placed in the course based on Grade 8 performance, teacher grades and external assessments.

HONORS GEOMETRY/)ALGEBRA 2
Level 2 421 5 credits
This course is open to students who have demonstrated the ability to learn mathematics at an accelerated rate. This course contains the field of Euclidean Geometry with topics such as points, lines, planes, angles, polygons, circles, proofs, congruence and its applications, area, perimeter, surface area and volume. During the fourth term students will begin the study of algebraic, trigonometric, logarithmic and exponential functions. Prerequisite: Students enrolling in this course must have achieved a grade of at least "C" in Honors Algebra I / Algebra II (420).

HONORS PRE-CALCULUS
Level 2 422 5 credits
This is a full-year Pre-Calculus course. Topics to be discussed include algebraic, trigonometric, logarithmic and exponential functions, analytic geometry, limits and the use of derivatives. An analytical and theoretical approach is emphasized using graphic techniques to achieve visual understanding of abstract ideas. Prerequisite: Students enrolling in this course must have achieved a grade of at least "C-" in Honors Geometry/Algebra 2 (421).

(Name Change) HONORS CALCULUS
Level 2 423(number change) 5 credits
This Level 2 course is an introduction to the study of integration and differentiation of rational algebraic, trigonometric, exponential, and logarithmic functions. It also introduces their application to related rates, areas of surfaces of revolution, and other topics. This course does not lead to an Advanced Placement Examination. Prerequisite: Students enrolling in this course must have completed (name Change) Honors Pre-Calculus (422)

ADVANCED PLACEMENT CALCULUS AB
Level 1 414 5 credits
This course includes all of the topics included in the Advanced Placement course description for Calculus AB. This course is a study of differentiation and integration of rational algebraic, trigonometric, exponential and logarithmic functions, and includes an in-depth study of the above and their application to related rates, areas of surfaces of revolution and volumes of solids of revolution. Students enrolled in this course are expected to take the AP Calculus AB exam in May. This course has a required summer assignment.
Prerequisite: Students enrolling in this course must have achieved a grade of at least a "B-" in (name Change) Honors Pre-Calculus (422) or Advanced Pre-Calculus (412).


COLLEGE PREPARATORY A (Level 3/2)

COLLEGE ALGEBRA IA
Level 3 430 5 credits
This is a first course in Algebra beginning with an introduction to variables and phrases and a study of rational and real numbers. Open sentences including both equalities and inequalities are covered, as well as related word problems. Other topics include factoring polynomials, relations and function, rational expression and quadratic functions.
Prerequisite: Students are placed in this course based on Grade 8 performance, teacher grades and external assessments. All grade 10, 11, or 12 students taking this course who have not yet passed MCAS must also take (Change) College Geometry (433)

CONTINUATION OF ALGEBRA 1 WITH INTEG. MATH TOPICS
Level 3 439 5 credits
This course contains the second part of a two-year course in Algebra 1, statistics, geometry, and probability. Topics include linear functions, matrices, transformations, exponents, area, volume, coordinate geometry, and theoretical probability. Students enrolled in this course are required to have an approved graphing calculator.
Prerequisite: This course is primarily designed for grade 10 students who struggled in their grade 9 Algebra course. Students who received a C-or lower in 431 must also take this course. Also students who received a D+ or lower in 430 must take this course. All grade 10, 11 or 12 students taking this course who have not yet passed MCAS must also take College Geometry (432) or Geometry (433).

COLLEGE GEOMETRY
Level 3 432 5 credits
This course is the study of traditional Euclidean geometry integrated with a computer-assisted approach where applicable and subject to lab availability. It includes the study of such topics as points, lines, planes, triangles, congruence, parallel lines, quadrilaterals, polygons, similarity and its applications, circles, areas, perimeters and volume.
Prerequisite: Students enrolling in this course must have successfully completed College Algebra 1 A (430).


COLLEGE ALGEBRA 2
Level 3 434 5 credits
This is a review of Algebra 1 and continues through quadratics, functions and graphs, right-triangle trigonometry, (Add) and the conics. Word problems are included in the study of this course. Formulas will be used in developing algebraic skills and in establishing applications of the algebraic method. Prerequisite: Students enrolling in this course must have (change) successfully completed College Geometry (432).


(New Course) COLLEGE PRE-CALCULUS
Level 3 436 5 credits
This full year pre-Calculus course begins by reviewing algebraic curve sketching from Algebra 2. It then examines algebraic, trigonometric, logarithmic and exponential functions. This is accomplished along with studying analytic geometry, and limits. Graphic techniques will be emphasized as a means to achieve visual understanding of abstract ideas.
Prerequisite: Students enrolling in this course must have achieved at least a grade of "C-" in College Algebra 2 (434).

FUNDAMENTAL COLLEGE PREPARATORY B (Level 3)

COLLEGE ALGEBRA 1B
Level 3 431 5 credits
This course is designed for students who struggled with algebraic concepts in early courses. It contains patterns with data, variable manipulation, linear equations and functions. Freshmen taking this course must also take NUMBER SENSE & ALGEBRA STANDARDS (401). Sophomores, juniors and seniors who have not yet passed the MCAS Math Exam and are taking this course must also take Geometry (433).
Prerequisite: Students are placed in this course based on Grade 8 performance, teacher grades and external assessments.


GEOMETRY
Level 3 433 5 credits
This is a study of plane and solid figures such as triangles, circles, parallelograms, prisms, cylinders, cones and spheres, and the various formulas for their areas, volumes, angles and sides. Emphasis is placed on the development of a logical reasoning process. Algebra will be applied to the geometric problems and a unit in numerical trigonometry will be included. Insert: Freshmen taking this course must also take ALGEBRA & GEOMETRY STANDARDS (402).
Prerequisite: Students enrolling in this course must have successfully completed College Algebra 1B 431)

ALGEBRA 2
Level 3 435 5 credits
This course begins as a review of Algebra 1 and continues through quadratics. Functions and graphs, right-triangle trigonometry, and word problems are included in the study of this course. Formulas will be used in developing algebraic skills and in establishing applications of the algebraic method.
Prerequisite: Students enrolling in this course must have successfully completed Geometry (433).

NUMBER SENSE & ALGEBRA STANDARDS
Unleveled 401 2 ½ credits
This year-long course meets 3 days in every 7-day cycle. It covers all of the Number Sense Standards in the Massachusetts Mathematics Framework and uses them to bridge into the Algebra Standards.
ALGEBRA & GEOMETRY STANDARDS
Unleveled 402 2 ½ credits
This year-long course meets 3 days in every 7-day cycle. It covers all of the Algebraic Standards and uses the Geometry and Measurement Standards in the Algebraic problems.

ELECTIVES-YEAR LONG

MATH STRATEGIES (MCAS Preparation)
Unleveled 405 2 ½ credits
This year-long course meets 3 days in every 7-day cycle. The course includes 22 problem-solving strategies needed to solve problems as well as the mathematics covered in the Massachusetts Mathematics Frameworks (Statistics, Probability, Algebra, Geometry, Ratios, and Discrete Math). Students concerned about MCAS are encouraged to elect this course.
This course is required for several groups of students unless they are taking two full year math courses or are taking course 401 or 402:

1. All tenth grade students who received a grade of 220 or below on their eighth grade MCAS examination. Other students may enroll as an elective.
2. All math level 3 and 4 sophomores who have no grade 8 MCAS Math scores in their school records.
3. All math level 3 and 4 juniors who transfer into Braintree High School. These students may transfer out of the course if their sophomore MCAS score in math is passing.
4. All juniors and seniors who have not yet passed the MCAS Math Exam.


PROBABILITY/STATISTICS/DISCRETE MATH
Level 3 438 5 credits
This course will cover the basic concepts of probability, including probability spaces, events, compound probability, random variables, expectation and frequency distributions. In addition it includes statistical concepts such as measures of central tendency and dispersion, surveying and hypothesis testing. Computer programs using statistical analysis will be used. Pertinent topics in discrete mathematics will also be covered. Prerequisite: Students enrolling in this course must have achieved a grade of at "C" in the previous year of mathematics. This course is open to juniors and seniors.


ELECTIVES-SEMESTER LONG

MATH TUTOR
464 3 credits
To be considered for this course, students must have completed Algebra I and II as well as Geometry. They also must have the recommendation of their current math teacher. Prospective students will be interviewed by the Director of Mathematics. Those candidates who are qualified will be assigned to (change) tutor students in math during the school day in classes and studies.