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Lower Merion School District

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Mathematics

Course Sequences in Mathematics

While three credits of math at the high school level are required for graduation, students are recommended to enroll in math courses during all four years of high school as part of a well-rounded education in preparation for college and careers. A variety of math courses at the College Prep, Honors, AP, and IB level are offered to students. In addition, a number of support courses are offered to provide students with intervention and/or remediation in mathematics.

Courses labeled H (Honors) require that students be able to operate in an environment where both high degrees of independence and thoughtful collaboration are necessary. A prior demonstration of advanced mathematical reasoning and insight through a variety of measures and a record of high levels of achievement are indicators that a student is sufficiently prepared for the rigors of Honors level work. Appropriate formal mathematical and scientific language are used extensively.

Calculator Philosophy

The mathematics department is committed to using graphing calculators and other forms of technology to enhance and facilitate student learning. Calculator usage is incorporated into the curriculum when such usage is appropriate and supportive of mathematical concept and/or skill development. Graphing calculators are used to compare and contrast the symbolic, numeric, and graphic nature of mathematical concepts and to solve more complex problems. Courses where calculators are used more frequently are clearly indicated in the course descriptions. Students enrolled in these courses will need a graphing calculator. The TI-84 family of calculators are strongly recommended.

Integrated Math 1

  • Length/credit: 1 year - 1.0 credit
  • Grade(s): 9, 10, 11, 12
  • Course Number: 03150102

Course Description: This course is the first in a series of three integrated math courses and is designed to combine some of the basic principles of Algebra, Geometry, and Statistics. Students deepen and extend their understanding of linear relationships and are introduced to exponential functions, modeled through data. Students use properties and theorems involving congruent figures to expand and broaden understanding of geometric knowledge. Students experience mathematics as a coherent, useful, and logical subject that draws on their ability to make sense of problem situations and develop the ability to explore and solve mathematical problems, think critically, work cooperatively with other students, and communicate mathematical ideas clearly.

Integrated Math 2

  • Length/credit: 1 year - 1.0 credit
  • Grade(s): 9, 10, 11, 12
  • Prerequisite: Successful completion of Integrated Math 1.
  • Course Number: 03150202

Course Description: This course is the second in a series of three integrated math courses and is designed to develop an intermediate understanding of the principles of Algebra, Geometry, and Statistics. Students connect and extend topics from Integrated Math 1 and are introduced to Quadratic Functions, Similarity and Congruence, Circles, Basic Trigonometric Functions and Probability. Students experience mathematics as a coherent, useful, and logical subject that draws on their ability to make sense of problem situations, and further develop the ability to explore and solve mathematical problems, think critically, work cooperatively with other students, and communicate mathematical ideas clearly.

**The Keystone Algebra exam will be given annually. Students enrolled in Integrated Math 2 will take the Keystone exam.

Integrated Math 2 H

  • Length/credit: 1 year - 1.0 credit
  • Grade(s): 9, 10, 11, 12
  • Prerequisite: Recommended "A" or "B" on assessments in Integrated Math 1.
  • Course Number: 03150403

Course Description: This course is a faster-paced version of the second in a series of three integrated math courses and is designed to develop an intermediate understanding of the principles of Algebra, Geometry, and Statistics. Students connect and extend topics from Integrated Math 1 and are introduced to Quadratic Functions, Similarity and Congruence, Circles, Basic Trigonometric Functions and Probability. This version of the course will delve significantly deeper into the various topics and includes additional extension topics that are not part of the college preparatory version of Integrated Math 2. Students experience mathematics as a coherent, useful, and logical subject that draws on their ability to make sense of problem situations, and further develop the ability to explore and solve mathematical problems, think critically, work cooperatively with other students, and communicate mathematical ideas clearly.

**The Keystone Algebra exam will be given annually. Students enrolled in Integrated Math 2 will take the Keystone exam.

Integrated Math 3

  • Length/credit: 1 year - 1.0 credit
  • Grade(s): 9, 10, 11, 12
  • Prerequisite: Successful completion of Integrated Math 1 and 2.
  • Course Number: 03150302

Course Description: This course completes the three-course series of integrated mathematics and is designed to extend and apply the principles of Algebra, Geometry, and Statistics learned in the previous two courses to more complex mathematical scenarios. Students expand earlier knowledge of linear, exponential, and quadratic functions to polynomials, rational functions, and trigonometric functions. Students also extend their previous work with circles to other conic sections, their understanding of trigonometry to all triangles, and experiences with data as they solve more sophisticated problems. Students experience mathematics as a coherent, useful, and logical subject that draws on their ability to make sense of problem situations, and further develop the ability to explore and solve mathematical problems, think critically, work cooperatively with other students, and communicate mathematical ideas clearly.

Integrated Math 3 H

  • Length/credit: 1 year - 1.0 credit
  • Grade(s): 9, 10, 11, 12
  • Prerequisite: Recommended "A" on assessments in Integrated Math 2 or "B" on assessments in Integrated Math 2 H.
  • Course Number: 03150503

Course Description: This course is a faster-paced version of the final course in the three-course series of integrated mathematics and is designed to extend and apply the principles of Algebra, Geometry, and Statistics learned in the previous two courses to more complex mathematical scenarios. Students expand earlier knowledge of linear, exponential, and quadratic functions to polynomials, rational functions, and trigonometric functions. Students also extend their previous work with circles to other conic sections, their understanding of trigonometry to all triangles, and experiences with data as they solve more sophisticated problems. This version of the course will delve significantly deeper into the various topics and includes additional extension topics that are not part of the college preparatory version of Integrated Math 3. Students experience mathematics as a coherent, useful, and logical subject that draws on their ability to make sense of problem situations, and further develop the ability to explore and solve mathematical problems, think critically, work cooperatively with other students, and communicate mathematical ideas clearly.

Math Support Courses

Algebra Lab

  • Length/credit: 1 year (1 time per cycle) 0.33 elective credit
  • Grade(s): 9, 10, 11, 12
  • Pass/Fail
  • Course Number: 03010000

Course Description: The purpose of this course is to provide once a cycle support to students in their study of mathematics as an intervention and preventative measure. It is a supplement to their regular Integrated Math class. Students are enrolled in Algebra Lab based on a variety of measures, including their most recent math PSSA results, benchmark assessment results, Keystone Algebra Exam results, overall grades in recent math courses, and teacher input/recommendation.

Advanced Mathematics Courses

Pre-Calculus

  • Length/credit: 1 year - 1.0 credit
  • Grade(s): 10, 11, 12
  • Prerequisite: Students should have an assessment grade of C or better in a completed Integrated Math 3 or Integrated Math 3 H course.
  • Course Number: 03030102

Course Description: This course includes extensive work with polynomial, rational, exponential, inverse, and logarithmic functions. Fundamental ideas of trigonometric functions (triangular and circular), trigonometric identities and formulas are developed. The processes involved in interpreting and evaluating functions are explored algebraically, graphically and with technology. Connections are made between functions and their practical applications throughout the course. A TI-84 graphing calculator is required.

Pre-Calculus H

  • Length/credit: 1 year - 1.0 credit
  • Grade(s): 10, 11, 12
  • Prerequisite: It is recommended that students have a grade of "A" or "B" on assessments in Integrated Math 3 H.
  • Course Number: 03030203

Course Description: This course includes extensive work in mathematical induction, trigonometry, circular, exponential, logarithmic and inverse functions, series, combinatorics, limits and derivatives. Calculus concepts are developed theoretically and include applications. Modeling is used extensively throughout the course. The algebraic, numeric, and graphic nature of topics are compared and contrasted to enhance and broaden comprehension. Group collaboration outside of the class is an essential part of the course. Successful completion of this course prepares students for Advanced Placement Calculus (BC or AB). A TI-84 graphing calculator is required.

Financial Algebra

  • Length/credit: 1 year - 1.0 credit
  • Prerequisite: Students must have successfully completed Integrated Math 2.
  • Grade(s): 11, 12
  • Course Number: 03140102

Course Description: In Financial Algebra, students refine mathematical skills developed in previous courses in the context of financial topics. Mathematical skills include linear and quadratic equations, systems of equations, exponential and logarithmic functions, piecewise functions, descriptive statistics, probability, regression, and correlation. These mathematical skills are modeled through such topics as stock market, business applications, banking services, retirement planning, preparing a budget, and consumer credit. A TI-84 graphing calculator is required.

Statistics

  • Length/credit: 1 year - 1.0 credit
  • Grade(s): 11, 12
  • Prerequisite: Students must have successfully completed Integrated Math 2 or Integrated Math 2 H.
  • Course Number: 03050102

Course Description: This is a first course in statistics with an emphasis on both descriptive and inferential statistics, counting techniques, and probability. Experimental design along with correlation/regression techniques are also studied. Please note that this course may be taken concurrently with other advanced math courses following the successful completion of Integrated Math 2 or Integrated Math 2 H. A TI-84 graphing calculator is required.

AP Statistics

  • Length/credit: 1 year - 1.0 credit
  • Grade(s): 10, 11, 12
  • Prerequisite: It is recommended that students have a grade of "A" or "B" on assessments in Integrated Math 3H or a grade of "A" on assessments in Integrated Math 3.
  • Course Number: 03050204

Course Description: This course is designed to prepare the student for the College Board's AP Statistics exam. Major themes include exploratory data analysis, planning a study, probability, and statistical inference. Students should have an independent approach to learning with minimal need for guidance and assistance. Please note that this course may be taken concurrently with other advanced math courses, following the successful completion of Integrated Math 3 or Integrated Math 3H with the recommended grade. A TI-84 graphing calculator is required.

Calculus

  • Length/credit: 1 year – 1.0 credit
  • Grade(s): 10, 11, 12
  • Prerequisite: Successful completion of Pre-Calculus or Pre-Calculus H.
  • Course Number: 03060102

Course Description: This course is designed as a college preparatory course in the calculus of one variable. It begins with a review of functions and their graphs and continues with the study of limits, derivatives and their applications, Riemann sums, integration, and applications of the definite integral. A TI-84 graphing calculator is required.

AP Calculus AB

  • Length/credit: 1 year – 1.0 credit
  • Grade(s): 11, 12
  • Prerequisite: It is recommended that students have a grade of "A" or "B" on assessments in Pre-Calculus CP or a "C" or better on assessment in Pre-Calculus H.
  • Course Number: 03060204

Course Description: This course is the equivalent of a first semester college calculus course and prepares students to take the AP Calculus AB exam. Students who enroll in this class should be prepared for high levels of independent work and group collaboration outside of class. This course includes theory of limits, derivatives, the Fundamental Theorem of Calculus, definite and indefinite integrals and their applications. A TI-84 or higher graphing calculator is required.

AP Calculus BC

  • Length/credit: 1 year - 1.0 credit
  • Grade(s): 11, 12
  • Prerequisite: It is recommended that students have a grade of "A" on assessments only in Pre-Calculus H or have successfully completed AP Calculus AB.
  • Course Number: 03060304

Course Description: This course is planned for students who wish to complete a rigorous calculus course equivalent to that of the most competitive university level courses. Students who enroll in AP Calculus BC should have mastery of skills developed in Pre-Calculus H; an independent approach to learning, and a healthy appetite and intellectual curiosity for exploring rigorous college level math in high school. Topics include theory and applications of differential and integral calculus, infinite series, and differential equations as related to science, history, the arts, and the natural world. A TI-84 or higher graphing calculator is required.

Mathematics Seminar H – Post AP Calculus BC

  • Length/credit: 1 year - 1.0 credit
  • Grade: 11, 12
  • Prerequisite: It is recommended that students have a grade of "A" or "B" in AP Calculus BC.
  • Course Number: 03080103

Course Description: This course is designed for exceptionally capable students of mathematics who have completed the AP Calculus BC course. Some of the great theorems and ideas of mathematics will be studied. Additional topics will be selected from among the following: formal logic, math history, statistics theory, differential equations, linear algebra, complex numbers, as well as others. While some time will be spent in formal instruction, a significant portion of time will include student independent study and research. Students will explore topics and report their findings.

Advanced Topics in Linear Algebra & Discrete Mathematics H

  • Length/credit: 1 year - 1.0 credit
  • Grade(s): 11, 12
  • Prerequisite: Students must have successfully completed Calculus or AP Calculus.
  • Course Number: 03130103

Course Description: Topics include linear algebra, combinatorics, probability and expected value, logic and critical argument. Students complete a mathematical exploration fusing current and past mathematical content resulting in an opportunity for independent research.