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Mathematics
world examples and case studies. Developing international mindedness and an awareness of multiple perspectives is at the heart of this course and builds on the skills students began in Global Peace & Justice class in 9th grade. It encourages dialogue and debate. All students complete material under a unifying theme of “people, power and politics.” This consists of four core units: 1) Power, sovereignty and international relations; 2) Human rights; 3) Development; and 4) Peace and conflict. All students also undertake an engagement activity through which they study a political issue of interest experientially. In this vein, students are exploring the Quaker values of stewardship and community and bringing service learning to the forefront.
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. 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 1, 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. Upon completing Integrated Math 3, students who enter the International Baccalaureate program are placed in IB Mathematics: Analysis and Approaches Standard Level. For those students completing Advanced Integrated Math 3, an additional two-year sequence is offered, called IB Mathematics: Analysis and Approaches Higher Level,. Those students not opting for an IB experience may select from the following courses: Integrated Math 4, Discrete Mathematics, Integrated Math 5, Calculus, AP Statistics, AP Calculus AB or AP Calculus BC. The last three options listed may be taken for Advanced Placement credit. The graphing calculator is a fundamental tool in all upper school mathematics courses. The TI-84, or TI-84+ is used in all classes.
532 Integrated Math 2 (9,10)
1 credit, full year
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.
532A Advanced Integrated Math 2 (9,10)
1 credit, full year
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.
533 Integrated Math 3 (10,11)
1 credit, full year
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 problemsolving skills. Prerequisite: Integrated Math 2.
533A Advanced Integrated Math 3 (10,11)
1 credit, full year
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 the mathematics and to encourage graphical analysis.
538 Discrete Mathematics (11,12)
1 credit, full year
In today’s ever-changing world, relevance encompasses transferable skills in understanding how math is applied in realworld situations. That is the emphasis of this course: problem solving and relevant application. Through individual (standalone) 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.
534 Integrated Math 4 (11,12, no IB credit)
1 credit, full year
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.
539 Integrated Math 5 (11,12) 761SL1 IB Mathematics: Analysis and Approaches Standard Level (IB Math AA SL), Year 1 (11)
1 credit, full year
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.
761SL2 IB Mathematics: Analysis and Approaches
1 credit, full year
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: Integrated Math 5/IB Math AA SL Year 1.
760HL1 IB Mathematics: Analysis and Approaches
1 credit, full year
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.
760HL2 IB Mathematics: Analysis and Approaches
1 credit, full year
This course is intended as final preparation for the Higher Level IB Examination in mathematics. It is an intensive, high-
