US Curriculum Detail

Math

The mathematics program in upper school continues the integrated approach begun in lower school and expanded in middle school. Algebra, geometry, trigonometry, probability, statistics, graph theory, and logic are all studied but not in isolation. All students continue to learn to read and write mathematics and, in addition, to edit their own work. Mathematics is intended to be a dialogue, and as such, students are required to explain their ideas to others, to interpret their results, and to demonstrate their thinking. Pictorial representations are as important as their written counterparts. Students are responsible for the learning of their classmates as well as their own; in other words, collaboration and individual accomplishment are both valued. There is a balance between theory and application. In some instances, it is theory that precedes the applications while in other cases it is an examination of data that precedes a statement of a theorem. Project-based instruction is incorporated in most courses.
Students are required to take three full years of mathematics in upper school. The graphing calculator is a fundamental tool in all upper school mathematics courses. The TI-84, or TI-84+ is used in all classes.
Based on performance in eighth grade math and the middle school teachers’ assessment of demonstrated ability, rising ninth grade students may be placed in Integrated Math 2 or Advanced Integrated Math 2.  For students new to Friends, results of a challenge test given in the spring or summer are also considered in their placement. 
Students must earn a grade of C or better in Advanced IM2, to move into Advanced IM3. In order to move from IM2 in 9th grade to Advanced IM3 in 10th grade, students must maintain a grade of A in IM2, independently complete additional coursework throughout the spring of the ninth grade year, as well as earn the math department’s recommendation.

In the last two years of our math program, students have a lot more options to choose from.  Each student will be advised by their teacher on the best option for what they want to pursue.  These choices depend on whether they choose to pursue the IB diploma program, their past classes as well as their interests.
Upon completing Integrated Math 3, students who enter the International Baccalaureate program will be placed in IB  Mathematics: Analysis and Approaches Standard Level two year course sequence.
For those students completing Advanced Integrated Math 3, who enter the International Baccalaureate program there are three options. 
  • IB Mathematics: Analysis and Approaches Standard Level (two-year sequence) with 1st year options:
    • IB Mathematics: Analysis and Approaches Standard Level - Precalculus
    • IB Mathematics: Analysis and Approaches Standard Level - Statistics (AP Statistics)
  • IB Mathematics: Analysis and Approaches Higher Level (two-year sequence), 
  • IB Mathematics: Analysis and Approaches Standard Level (one-year sequence). 
For those 11th and 12th students not opting for an IB experience, they may select from the following courses, given that the requirements are met: Integrated Math 4, Discrete Mathematics, Math Analysis, Calculus, AP Statistics, AP Calculus AB or AP Calculus BC. The last three options listed may be taken for Advanced Placement credit.

  • Adv Int Math 2

    This course continues our integrated curriculum with topics from algebra, geometry, and statistics. The curriculum builds upon the theme of mathematical sense making. Investigations of real-life contexts lead to discovery of important mathematics that make sense to students and, in turn, enable them to make sense of new situations and problems. Communication, reasoning, and making connections are integral parts of each lesson of every unit. Students investigate bivariate statistics, matrices, transformations, trigonometry, and quadratic relations to bring theory into concrete terms.
     
     

  • Discrete Mathematics

    In today’s ever-changing world, relevance encompasses transferable skills in understanding how math is applied in real-world situations. That is the emphasis of this course: problem solving and relevant application. Through individual (stand-alone) units, students explore a range of topics selected from graph theory, probability, statistics, logic, matrices, sequences and series, binomial expansion techniques, counting techniques, vectors, and financial math. Working in collaboration, students make observations and pose questions in response to new concepts and thus gain independent learning skills. Students collect data, analyze results, and draw conclusions based on the mathematics studied. Students use technology regularly in class and on exams.  

    Prerequisite: Integrated Math 3
     

  • IB Math HL, Yr 1

    This course is the first year of the two-year IB Higher Level Mathematics sequence. This course is designed for the most successful mathematics students who either have a genuine interest in mathematics and enjoy meeting its challenges and problems, or need such mathematics for related subjects such as physics, engineering, and technology at the university level. The primary emphasis is on an intuitive understanding of limits, continuity, and the concepts of differential and integral calculus with exploration of basic techniques and applications. Successful completion of the course will prepare students to take the Advanced Placement Exam in May.

    Prerequisite: Mathematical Methods or Advanced Integrated Math 3

  • IB Math HL2

    This course is intended as a final preparation for the Higher Level IB Examination in mathematics. It is an intensive, higher-level calculus course that also includes linear algebra, vector geometry, and higher trigonometry. The course is designed for students whose level of mathematical sophistication is high, since it covers a variety of college-level mathematics topics with independent work required outside of class. Because it is primarily an IB course, students taking this class will be expected to complete the IB internal assessment, an independent written work exploring an area of mathematics, and take the IB Higher Level Examination as their final examination. Students may obtain credit toward an International Baccalaureate diploma or certificate if they desire. If a student does not wish to take this course for IB credit and he or she received at least a 4 on the AP Calculus AB exam, then he or she may instead take the AP Calculus BC option and, consequently, the AP BC exam at the end of the year.

    Prerequisite: IB Mathematics HIgher Level, Year 1 or AP Calculus AB
     

  • IB Math Methods SL1

    Mathematical Methods is primarily intended for students who expect to need a sound mathematical background in future studies. It is an advanced course, which prepares students for both of our Advanced Placement math course offerings, AP Calculus AB and AP Statistics. IB students will need to take IB Mathematical Methods Year 2 in their senior year, which is cross listed with Calculus. Advanced mathematical topics including functions, trigonometry, vectors, sequences and series, limits, probability and statistics, and differential and integral calculus will be covered at a fast pace and rigorous level. This is a demanding course and should be taken by students who have an interest in mathematics and a strong background in mathematical techniques.

    Prerequisite: Integrated Math 3 or Advanced Integrated Math 3
     

  • IB Math Methods SL2

    This is a one-year course in calculus that includes a review of elementary functions and covers the topics normally found in one semester of college-level calculus. The primary emphasis is on an intuitive understanding of limits, continuity, and the concepts of differential and integral calculus with exploration of basic techniques and applications. IB students taking this class will be expected to take the IB Standard Level Examination at the end of the year, which covers materials from Year 1 and Year 2 of Mathematical Methods.  An IB internal assessment which is referred to as the math exploration or math paper is a required part of the course for IB students. Students may obtain credit toward an International Baccalaureate diploma or certificate. 

    Prerequisite: Mathematical Methods/IB Mathematical Methods SL Year 1
     

  • IB Math Studies SL2

    This integrated math course is an introductory course in advanced mathematics for students who intend to take college mathematics. This course will prepare a student to sit for the IB Mathematical Studies Standard Level exam. The emphasis is on the decision-making aspect of mathematics, and students are expected to explain the concepts behind the algorithms that they use. This is a fast-paced course with major emphasis on the study of functions (quadratic, trigonometric, polynomial, rational, logarithmic, and exponential). The course also includes units on complex numbers, sequences and series, statistical analysis, probability, and an introduction to limits and the derivative. There is a three-pronged emphasis throughout the course on graphic, numeric, and algebraic solutions. An extensive research project is an important feature of this course.  As the IB program is undergoing a worldwide mathematics curriculum review, these topics are subject to change as new information becomes available.

    Prerequisite: Integrated Math 3
     

  • Int Math 2

    Continuing the integrated approach, students investigate patterns of association between two variables, the properties of plane figures, coordinate geometry, and quadratic functions. This course integrates algebra with geometry and emphasizes applications and problem solving. Students gain experience with both informal and formal proof. Interdisciplinary connections with physics and computer science are an important feature of the course. There is also focus on mathematical language and expression. Lab activities using manipulatives, graphing calculators, and other data analysis software reinforce and clarify concepts.   
     

  • Int Math 3

    As the culmination of the integrated math sequence, this course builds on the algebraic skills needed for advanced study. There is a strong emphasis on the concept of function, data/graph interpretation, and modeling data in lab settings. Linear, rational, quadratic, absolute value, inverse, exponential, logarithmic and trigonometric functions are explored. Students also study sets and Venn diagrams, univariate data analysis, probability and the factor label method for conversions. Students gain experience reading mathematics and acquire additional problem-solving skills.

    Prerequisite: Integrated Math 2
     

  • Int Math 4

    This integrated math course is an introductory course in advanced mathematics for students who intend to take college mathematics. This course will prepare a student to sit for the IB Mathematical Studies Standard Level exam. The emphasis is on the decision-making aspect of mathematics, and students are expected to explain the concepts behind the algorithms that they use. This is a fast-paced course with major emphasis on the study of functions (quadratic, trigonometric, polynomial, rational, logarithmic, and exponential). The course also includes units on complex numbers, sequences and series, statistical analysis, probability, and an introduction to limits and the derivative. There is a three-pronged emphasis throughout the course on graphic, numeric, and algebraic solutions. An extensive research project is an important feature of this course.  

    Prerequisite: Integrated Math 3 

     

  • Math Methods

    Mathematical Methods is primarily intended for students who expect to need a sound mathematical background in future studies. It is an advanced course, which prepares students for both of our Advanced Placement math course offerings, AP Calculus AB and AP Statistics. IB students will need to take IB Mathematical Methods Year 2 in their senior year, which is cross listed with Calculus. Advanced mathematical topics including functions, trigonometry, vectors, sequences and series, limits, probability and statistics, and differential and integral calculus will be covered at a fast pace and rigorous level. This is a demanding course and should be taken by students who have an interest in mathematics and a strong background in mathematical techniques.

    Prerequisite: Integrated Math 3 or Advanced Integrated Math 3

  • AP Calculus AB

    This course is the first year of the two-year IB Higher Level Math AA sequence. This course is designed for the most successful mathematics students who either have a genuine interest in mathematics and enjoy meeting its challenges and problems, or need such mathematics for related subjects such as physics, engineering, and technology at the university level. The primary emphasis is on an intuitive understanding of limits, continuity, and the concepts of differential and integral calculus with exploration of basic techniques and applications. Successful completion of the course will prepare students to take the Advanced Placement Calculus AB Exam in May. 

    Prerequisite: Integrated Math 5 or Advanced Integrated Math 3
     

  • AP Statistics

    The AP Statistics course acquaints students with the major concepts and tools for collecting, organizing, analyzing, and drawing conclusions from data. Students will work on projects involving hands-on gathering and analysis of real-world data. Ideas and computations presented in this course will have immediate connections with actual events. Computers and calculators will allow students to focus deeply on the concepts involved. Successful completion of the course will prepare students to take the Advanced Placement Exam in May. Those enrolled in the IB course will additionally study precalculus topics after the AP exam to prepare for learning calculus in the second year of the IB SL program.

    Prerequisite for Advanced Placement Statistics:  IM4, IB Math AA SL1, IB Math AA HL1, Advanced Integrated Math 3 or Math Analysis. Teacher recommendation is also required.

    Prerequisite for IB Math AA-Stats SL1:  Advanced Integrated Math 3. Teacher recommendation is also required.

  • Calculus

    This is a one-year course in calculus that includes a review of elementary functions and covers the topics normally found in one semester of college-level calculus. The primary emphasis is on an intuitive understanding of limits, continuity, and the concepts of differential and integral calculus with exploration of basic techniques and applications. IB students taking this class will be expected to take the IB Standard Level Examination at the end of the year, which covers materials from Year 1 and Year 2 of Mathematical Analysis and Approaches.  An IB internal assessment which is referred to as the math exploration or math paper is a required part of the course for IB students. Students may obtain credit toward an International Baccalaureate diploma or certificate. 

    Prerequisite: Integrated Math 5/IB Math AA Year 1
     

  • Adv Int Math 3

    Students in this course are challenged to focus on the underlying concepts of each unit, to hypothesize, and to draw conclusions based on their findings. Students investigate linear, rational, quadratic, absolute value, inverse, and logarithmic and exponential functions with a strong emphasis on problem solving, communication of mathematical reasoning, and data/graph interpretation. The course includes units on multiple-variable models, statistics, symbolic reasoning, geometric reasoning, standard deviation and families of functions, as well as on furthering the understanding of matrices, solutions of quadratic equations over complex numbers, sequences and series, and trigonometry. The graphing calculator is used daily to model mathematics and to encourage graphical analysis. 
    Prerequisite: C or better in Advanced Integrated Math 2
     

  • AP Calculus BC

    This course is intended as final preparation for the Higher Level IB Examination in mathematics. It is an intensive, higher-level calculus course that also includes linear algebra, vector geometry, and higher trigonometry. The course is designed for students whose level of mathematical sophistication is high, since it covers a variety of college-level mathematics topics with independent work required outside of class. Because it is primarily an IB course, students taking this class will be expected to complete the IB internal assessment, an independent written work exploring an area of mathematics, and take the IB Higher Level Examination as their final examination. Students may obtain credit toward an International Baccalaureate diploma or certificate if they desire. If a student does not wish to take this course for IB credit and he or she received at least a 4 on the AP Calculus AB exam, then he or she may instead take the AP Calculus BC option and, consequently, the AP BC exam at the end of the year.

    Prerequisite: IB Mathematics HIgher Level, Year 1 or AP Calculus AB
     

  • Calculus

    This is a one-year course in calculus that includes a review of elementary functions and covers the topics normally found in one semester of college-level calculus. The primary emphasis is on an intuitive understanding of limits, continuity, and the concepts of differential and integral calculus with exploration of basic techniques and applications. IB students taking this class will be expected to take the IB Standard Level Examination at the end of the year, which covers materials from Year 1 and Year 2 of Mathematical Analysis and Approaches.  An IB internal assessment which is referred to as the math exploration or math paper is a required part of the course for IB students. Students may obtain credit toward an International Baccalaureate diploma or certificate. 
    Prerequisite: Math Analysis/IB Math AA SL Year 1 or AIM3.

  • IB Math Analysis & Approaches SL2

    This is a one-year course in calculus that includes a review of elementary functions and covers the topics normally found in one semester of college-level calculus. The primary emphasis is on an intuitive understanding of limits, continuity, and the concepts of differential and integral calculus with exploration of basic techniques and applications. IB students taking this class will be expected to take the IB Standard Level Examination at the end of the year, which covers materials from Year 1 and Year 2 of Mathematical Analysis and Approaches.  An IB internal assessment which is referred to as the math exploration or math paper is a required part of the course for IB students. Students may obtain credit toward an International Baccalaureate diploma or certificate. 
    Prerequisite: Math Analysis/IB Math AA SL Year 1 or AIM3.

  • IB Math Analysis and Approaches HL1

    This course is the first year of the two-year IB Higher Level Math AA sequence. This course is designed for the most successful mathematics students who either have a genuine interest in mathematics and enjoy meeting its challenges and problems, or need such mathematics for related subjects such as physics, engineering, and technology at the university level. The primary emphasis is on an intuitive understanding of limits, continuity, and the concepts of differential and integral calculus with exploration of basic techniques and applications. Successful completion of the course will prepare students to take the Advanced Placement Calculus AB Exam in May. 

    Prerequisite: Math Analysis or Advanced Integrated Math 3
     

  • IB Math Analysis and Approaches HL2

    This course is intended as final preparation for the Higher Level IB Examination in mathematics. It is an intensive, higher-level calculus course that also includes linear algebra, vector geometry, and higher trigonometry. The course is designed for students whose level of mathematical sophistication is high, since it covers a variety of college-level mathematics topics with independent work required outside of class. Because it is primarily an IB course, students taking this class will be expected to complete the IB internal assessment, an independent written work exploring an area of mathematics, and take the IB Higher Level Examination as their final examination. Students may obtain credit toward an International Baccalaureate diploma or certificate if they desire. If a student does not wish to take this course for IB credit and he or she received at least a 4 on the AP Calculus AB exam, then he or she may instead take the AP Calculus BC option and, consequently, the AP BC exam at the end of the year.
     
    Prerequisite: IB Mathematics Higher Level, Year 1 or AP Calculus AB

  • IB Math Analysis and Approaches SL

    This is a one-year course in calculus that includes a review of elementary functions and covers the topics normally found in one semester of college-level calculus. The primary emphasis is on an intuitive understanding of limits, continuity, and the concepts of differential and integral calculus with exploration of basic techniques and applications. IB students taking this class will be expected to take the IB Standard Level Examination at the end of the year, which covers materials from Year 1 and Year 2 of Mathematical Analysis and Approaches.  An IB internal assessment which is referred to as the math exploration or math paper is a required part of the course for IB students. Students may obtain credit toward an International Baccalaureate diploma or certificate. 
    Prerequisite: Math Analysis/IB Math AA SL Year 1 or AIM3.

  • IB Math Analysis and Approaches SL1

    This course is primarily intended for students who expect to need a sound mathematical background in future studies. It is an advanced course, which prepares students for both of our Advanced Placement math course offerings, AP Calculus AB and AP Statistics. IB students will need to take IB Math AA Standard Level Year 2 in their senior year, which is cross-listed with Calculus. Advanced mathematical topics including polynomial, exponential and logarithmic functions, transformations, trigonometry, sequences, series, probability and statistics will be covered at a fast pace and rigorous level. This is a demanding course and should be taken by students who have an interest in mathematics and a strong background in mathematical techniques. 

    Prerequisite: Integrated Math 3 or Advanced Integrated Math 3
     

  • IB Math Analysis and Approaches SL2

    This is a one-year course in calculus that includes a review of elementary functions and covers the topics normally found in one semester of college-level calculus. The primary emphasis is on an intuitive understanding of limits, continuity, and the concepts of differential and integral calculus with exploration of basic techniques and applications. IB students taking this class will be expected to take the IB Standard Level Examination at the end of the year, which covers materials from Year 1 and Year 2 of Mathematical Analysis and Approaches.  An IB internal assessment which is referred to as the math exploration or math paper is a required part of the course for IB students. Students may obtain credit toward an International Baccalaureate diploma or certificate. 

    Prerequisite: Math Analysis/IB Math AA SL Year 1/AIM3
     

  • IB Math Applications SL, Yr 1

    In today’s ever-changing world, relevance encompasses transferable skills in understanding how math is applied in real-world situations. 
    This integrated math course is an introductory course in advanced mathematics for students who intend to take college mathematics. This course will prepare a student to sit for the IB Mathematical Studies Standard Level exam. The emphasis is on the decision-making aspect of mathematics, and students are expected to explain the concepts behind the algorithms that they use. This is a fast-paced course with major emphasis on the study of functions (quadratic, trigonometric, polynomial, rational, logarithmic, and exponential). The course also includes units on complex numbers, sequences and series, statistical analysis, probability, and an introduction to limits and the derivative. There is a three-pronged emphasis throughout the course on graphic, numeric, and algebraic solutions. An extensive research project is an important feature of this course.  As the IB program is undergoing a worldwide mathematics curriculum review, these topics are subject to change as new information becomes available.

    Prerequisite: Integrated Math 3
     

  • IB Math Studies SL1

    In today’s ever-changing world, relevance encompasses transferable skills in understanding how math is applied in real-world situations. That is the emphasis of this course: problem solving and relevant application. Through individual (stand-alone) units, students explore a range of topics selected from graph theory, probability, statistics, logic, matrices, sequences and series, binomial expansion techniques, counting techniques, vectors and financial math. Working in collaboration, students make observations and pose questions in response to new concepts and thus gain independent learning skills. Students collect data, analyze results, and draw conclusions based on the mathematics studied. Students use technology regularly in class and on exams.

    Prerequisite: Integrated Math 3

  • IB Math: Analysis and Approaches SL

    This is a one-year course in calculus that includes a review of elementary functions and covers the topics normally found in one semester of college-level calculus. The primary emphasis is on an intuitive understanding of limits, continuity, and the concepts of differential and integral calculus with exploration of basic techniques and applications. IB students taking this class will be expected to take the IB Standard Level Examination at the end of the year, which covers materials from Year 1 and Year 2 of Mathematical Analysis and Approaches.  An IB internal assessment which is referred to as the math exploration or math paper is a required part of the course for IB students. Students may obtain credit toward an International Baccalaureate diploma or certificate. 
    Prerequisite: Analysis/IB Math AA SL Year 1 or AIM3.

  • IB Math: Analysis and Approaches SL1 - Precalculus

    This course is primarily intended for students who expect to need a sound mathematical background in future studies. It is an advanced course, which prepares students for both of our Advanced Placement math course offerings, AP Calculus AB and AP Statistics. IB students will need to take IB Math AA Standard Level Year 2 in their senior year, which is cross-listed with Calculus. Advanced mathematical topics including polynomial, exponential and logarithmic functions, transformations, trigonometry, sequences, series, probability and statistics will be covered at a fast pace and rigorous level. This is a demanding course and should be taken by students who have an interest in mathematics and a strong background in mathematical techniques. 
    Prerequisite: Integrated Math 3 or Advanced Integrated Math 3.

  • IB Math: Analysis and Approaches SL1 - Statistics

    The AP Statistics course acquaints students with the major concepts and tools for collecting, organizing, analyzing, and drawing conclusions from data. Students will work on projects involving hands-on gathering and analysis of real-world data. Ideas and computations presented in this course will have immediate connections with actual events. Computers and calculators will allow students to focus deeply on the concepts involved. Successful completion of the course will prepare students to take the Advanced Placement Exam in May. Those enrolled in the IB course will additionally study precalculus topics after the AP exam to prepare for learning calculus in the second year of the IB SL program.

    Prerequisite for Advanced Placement Statistics:  IM4, IB Math AA SL1, IB Math AA HL1, Advanced Integrated Math 3 or Math Analysis. Teacher recommendation is also required.

    Prerequisite for IB Math AA-Stats SL1:  Advanced Integrated Math 3. Teacher recommendation is also required.

  • Int Math 5

    This course is primarily intended for students who expect to need a sound mathematical background in future studies. It is an advanced course, which prepares students for both of our Advanced Placement math course offerings, AP Calculus AB and AP Statistics. IB students will need to take IB Math AA Standard Level Year 2 in their senior year, which is cross-listed with Calculus. Advanced mathematical topics including polynomial, exponential and logarithmic functions, transformations, trigonometry, sequences, series, probability and statistics will be covered at a fast pace and rigorous level. This is a demanding course and should be taken by students who have an interest in mathematics and a strong background in mathematical techniques. 

    Prerequisite: Integrated Math 3 or Advanced Integrated Math 3 
     

  • Math Analysis

    This course is primarily intended for students who expect to need a sound mathematical background in future studies. It is an advanced course, which prepares students for both of our Advanced Placement math course offerings, AP Calculus AB and AP Statistics. IB students will need to take IB Math AA Standard Level Year 2 in their senior year, which is cross-listed with Calculus. Advanced mathematical topics including polynomial, exponential and logarithmic functions, transformations, trigonometry, sequences, series, probability and statistics will be covered at a fast pace and rigorous level. This is a demanding course and should be taken by students who have an interest in mathematics and a strong background in mathematical techniques. 
    Prerequisite: Integrated Math 3 or Advanced Integrated Math 3. 
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