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Mathematics
US MATH CALCULATOR/TECHNOLOGY USAGE POLICY
A TI-84 Plus CE graphing calculator is required for all Upper School math courses. Students should not purchase other models. Some other models have a Computer Algebra System (CAS) and IB does not allow CAS calculators to be used. Please do not purchase other TI models (or other brands), as they are not appropriate for our classes and may not have similar capabilities as the models we use. The SAT, ACT, AP, and IB will allow use of the TI-84 Plus CE model on its exams. Calculators are available in the Tiger Shop and may also be purchased through online retail sites.
Understanding that a comprehensive mathematics curriculum should help students learn to use calculators, computers, and other tools of technology as a part of learning mathematics, the US Mathematics Department promotes the use of technology as an integral part of our mathematics program. This position is supported by the National Council of Teachers of Mathematics (NCTM) that states: “…instructional programs should use technology to help all students understand mathematics and should prepare them to use mathematics in an increasingly technological world.” “…Technology is essential in teaching and learning mathematics, it influences the mathematics that is taught and enhances students’ learning.” The NCTM makes it clear that such tools do not replace the need to learn basic math skills, to compute mentally, or to do reasonable paper and pencil computation. In fact, the NCTM Standards suggest that when used appropriately, calculators and computers enable students to explore new areas of mathematics and to tackle challenging mathematical problems that would not be possible without the help of such tools. In line with this philosophy, we offer the following policy on the use of technology.
We require the appropriate use of technology in the classroom. Games are not to be played during class. Students need to consider when use of mental mathematics, paper & pencil, or a calculator is appropriate. Calculator dependency, as evidenced by the use of a calculator for multiplying single or double digit numbers, often should be avoided. (Keep in mind that over one-half of the AP Calculus exam does not allow calculator use. Also note that a portion of the SAT test does not allow calculator use as well.) We recognize that calculators left unattended may be targets for theft. To help combat theft, the US Mathematics Department has purchased an engraver that students may use at any time that classes are not in session for engraving their name on their calculator. We strongly encourage students to engrave their calculators! Engraving can be done in the math office before school, during breaks, and after school. Students will be required to show all work in their solutions and may have to explain how they arrived at their solution as a demonstration of their understanding. This applies to homework, quizzes, and tests, whether a calculator is used or not. The calculator should not replace the understanding of fundamental concepts of mathematics. Therefore, a reasonable emphasis will be placed on teaching with mental computation and paper & pencil calculation.
IB AND AP MATH COURSES
The AP Calculus AB and BC courses are designed to mirror typical undergraduate college Calculus 1 and 2 courses for students heading into math-focused majors and careers. The focus is purely on differential and integral calculus with a mostly analytical approach. AP exams may be taken at any grade level. The IB math curriculum has two branches: Analysis & Approaches and Applications & Interpretation. Both branches include calculus and statistics and are equivalent in difficulty. IB Diploma students should plan on taking the SL external exam in grade 11 or 12. The HL external exam is offered in grade 12 only.
The Analysis & Approaches branch focuses more on calculus than statistics, and on a deep understanding of mathematics. Students will be asked to prove, investigate, etc. An analytical approach is encouraged. This branch is aimed at students who will go on to study subjects with substantial mathematics content such as mathematics itself, engineering, physical sciences, or economics for example. Analysis & Approaches will be offered at the SL and HL level.
The Applications & Interpretation branch focuses more on statistics than calculus, and on the role of mathematics and technology in a diverse array of contexts. Using tech is the norm with an emphasis on interpreting
those results. This branch is aimed at students who will go on to study subjects such as social sciences, natural sciences, statistics, business, some economics, psychology, and design, for example. Applications & Interpretation will be offered at the SL and HL level.
COURSES OFFERED THROUGH GLOBAL ONLINE ACADEMY
Students who complete AP Calculus BC can choose to take a math course online through Global Online Academy. Course selection varies each year and the latest information can be found at https://globalonlineacademy.org/. Please discuss with your math teacher and academic counselor about how to sign up.
INTRODUCTION TO ALGEBRA (UMAT01)
Duration: 1 year Credit: 1 Homework: Moderate
This course is for students who need additional work solidifying basic concepts before they can be successful in Algebra I. It is a bridge course that reviews pre-algebra topics while introducing algebraic concepts. Application problems are emphasized throughout the course.
Text: Algebra (McDougal/Littell)
ALGEBRA 1 (UMAT02)
Duration: 1 year Credit: 1 Prerequisite: Successful completion of Pre-Algebra or Introduction to Algebra Homework: Moderate
Included in this course is the real number system, linear equations and their graphs, inequalities, polynomials, rational expressions, quadratic equations, relations and functions.
GEOMETRY (UMAT03)
Duration: 1 year Credit: 1 Prerequisite: Successful completion of Algebra 1 or recommendation of math department Homework: Moderate
While this course does not require proofs as Honors Geometry does, it examines many of the same concepts through constructions, drawings, and explorations. These concepts include points; lines and planes; congruence and similarity of triangles and other polygons; angles; circles; perimeter; area and volume; Pythagorean Theorem; and an introduction to trigonometry.
Text: Geometry 978-0-13-350041-7
HONORS GEOMETRY (UMAT041)
Duration: 1 year Credit: 1 Prerequisite: Successful completion of Algebra 1; recommendation of the department Homework: Heavy
Students study the basic definitions used in deductive reasoning, basic principles of logic, properties of different polygons, perpendicularity, congruence, similarity of triangles, properties of circles, constructions, areas, and volumes. Proofs will be studied, but not emphasized.
Text: Geometry 978-0-13-350041-7
ALGEBRA 2 (UMAT06)
Duration: 1 year Credit: 1 Prerequisite: Successful completion of Algebra 1 and Geometry or Honors Geometry; recommendation of the department Homework: Moderate
This course is a standard college prep class. Algebra 2 provides a thorough review of the topics covered in Algebra 1 and develops concepts in complex numbers, polynomial and rational functions, exponential and logarithmic functions, conic sections, probability, and sequences and series.
Text: Beginning & Intermediate Algebra, 6th edition 978-0-13-419309-0
MODELING, DESIGN, & FINANCE (UMAT065)
Duration: 1 year Credit: 1 Prerequisite: Successful completion of Algebra 2; recommendation of the department Homework: Light
This course is designed to give students access and experience to a wide range of mathematical models and techniques used for solving problems in many contexts of human endeavor. These contexts include business, probability, and research focused from the individual and community perspective. Students will work on developing proficiency with mathematical skills and strategies in problem-solving through topics such as applied geometry, financial literacy, and statistics.
In mathematics, the art of proposing a question must be held of higher value than solving it.
George Cantor (1845-1918)
Algebra 1 Geometry
Intro to Algebra
Honors Geometry
Graduation Requirement:
3 Credits in Mathematics.
Mathematics Flow Chart
Modeling, Design, & Finance
Algebra 2 Precalculus
Honors Algebra 2
Honors Advanced Algebra 2
Honors Precalculus
Hon. Precal & Differential Calc
Dashed arrows are by permission
Algebra 1 (Grade 9)
IB Mathematics Options
SL Applications & Interpretation 1
Geometry Algebra 2
Honors Geometry Honors Algebra 2
Honors Advanced Algebra 2
Dashed arrows are by permission
Honors Precal HL Applications & Interpretation 1
SL Analysis & Approaches 1
HL Analysis & Approaches 1
AP Statstics elective course see description
Calculus
AP Calculus AB
AP Calculus BC
Honors Modern Topics
SL Applications & Interpretation 2
HL Applications & Interpretation 2
SL Analysis & Approaches 2
HL Analysis & Approaches 2
HONORS ALGEBRA 2 (UMAT070)
Duration: 1 year Credit: 1 Prerequisite: Successful completion of Algebra 1 and Geometry, Honors Geometry, or Honors Advanced Geometry, or recommendation of the department Homework: Heavy
This course extends the topics covered in Algebra 1 and develops concepts in complex numbers, polynomial and rational functions, exponential and logarithmic functions, conic sections, probability, and sequences and series.
Text: Intermediate Algebra, 4th edition 978-0-13-455580-5
HONORS ADVANCED ALGEBRA 2 (UMAT071)
Duration: 1 year Credit: 1 Prerequisite: Successful completion of Algebra 1 and Honors Geometry or Honors Advanced Geometry; recommendation of math department Homework: Heavy
This course is a high-powered honors class that is both fast-paced and indepth. It considers such topics as linear equations, systems of equations, determinants, polynomials, sequences, series, probability, complex numbers, quadratic relations, logarithms, and trigonometry. This class prepares students for Honors Precalculus & Differential Calc.
Text: College Algebra, 4th edition 978-0-13-447002-3
PRECALCULUS (UMAT08)
Duration: 1 year Credit: 1 Prerequisite: Successful completion of Algebra 2 Homework: Moderate
This course covers essentially the same curriculum as Honors Precalculus, but several topics of study are not covered at the same depth as the Honors course. The course consists of such topics as trigonometry, polynomial
Algebra is nothing more than Geometry, in words. Geometry is nothing more than Algebra, in pictures.
Sophie Germain (1776-1831)
functions, logarithms and exponents, and complex numbers. Successful completion of this course should prepare a student for first term introductory to calculus in a typical U.S. college.
Text: Announced Spring 2022
HONORS PRECALCULUS (UMAT12)
Duration: 1 year Credit: 1 Prerequisite: Successful completion of Algebra 2, Honors Algebra 2, or Honors Advanced Algebra 2 Homework: Heavy
This course includes trigonometry, polynomial functions, logarithms and exponents, and complex numbers. Successful completion of this course should prepare a student for AP Calculus AB or first term calculus in a typical U.S. college.
Text: Announced Spring 2022
HONORS PRECALCULUS & DIFFERENTIAL CALC (UMAT123)
Duration: 1 year Credit: 1 Prerequisite: Successful completion of Honors Advanced Algebra 2; recommendation of math department Homework: Heavy
This fast-paced, comprehensive course covers the Honors Precalculus curriculum including trigonometry, analytic geometry, logarithms, conics, and vectors. In addition, limits and differential calculus is studied in depth.
Text: Precalculus text announced Spring 2022, and Calculus: Graphical, Numerical, Algebraic (ISBN: 978-0-13-331161-7)
CALCULUS (UMAT121)
Duration: 1 year Credit: 1 Prerequisite: Successful completion of Precalculus or Honors Precalculus, and recommendation of math department Homework: Moderate
This course includes a review of polynomials, trigonometric, exponential, and logarithmic functions, followed by discussion of limits, derivatives, and applications of differential calculus to real-world problem areas. An introduction to integration concludes the course.
Text: Calculus: Graphical, Numerical, Algebraic (ISBN: 978-0-13-3311617)
AP CALCULUS AB (UMAT13)
Duration: 1 year Credit: 1 Prerequisite: Successful completion of Honors Precalculus and recommendation of math department Homework: Heavy
This course is similar to first semester calculus as taught in most U.S. colleges and universities. Topics include differentiation of polynomials, trigonometric, exponential, and logarithmic functions as well as integration techniques and theory. Students are required to take the AP exam at the completion of the course.
Text: Calculus: Graphical, Numerical, Algebraic (ISBN: 978-0-13-3311617)
AP CALCULUS BC (UMAT14)
Duration: 1 year Credit: 1 Prerequisites: Successful completion of Honors Precalculus & Differential Calc and recommendation of math department Homework: Heavy
This course is intended for those students who have advanced mathematical ability. The curriculum is similar to the first two semesters of college calculus as taught in most United States colleges and universities. The Calculus topics covered include integration techniques, polar coordinates, vectors, parametric equations, sequences and series, differential equations and slope fields. Projects that extend the course content will be an integral component of the course. Students are required to take the AP Calculus BC exam upon completion of the course.
Text: Calculus (ISBN: 978-0-618-50304-9)
AP STATISTICS (UMAT09)
Duration: 1 year Credit: 1 Prerequisite: Successful completion of Precalculus or concurrent with Honors Precalculus / Honors Precalculus & Differential Calc; recommendation of math department Homework: Heavy
This course is similar to a first semester statistics course as taught in most U.S. colleges. Students are introduced to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. An external exam at the end of the year can provide students with college credit. Students are required to take the AP exam.
Text: The Practice of Statistics for AP (ISBN: 978-1-4641-0873-0)
HONORS MODERN TOPICS IN MATHEMATICS (UMAT22)
Duration: 1 year Credit: 1 Prerequisite: Successful completion of AP Calculus BC or IBHL Year 2 Math and recommendation of math department Homework: Heavy
This is a university-level course for advanced students who have a passion for mathematics. Topics studied will include Differential Equations, Linear Algebra, Multi-Variable Calculus, and other advanced math topics.
Duration: 2 years Credit: 1 per year Prerequisite: Successful completion of Algebra 2 and recommendation of the department Homework: Heavy
The IB Application & Interpretation Syllabus is followed in this two-year course. Five main topics are studied: Algebra, Functions, Geometry & Trigonometry, Statistics & Probability, and Calculus. The course culminates in an external IBSL Math Exam at the end of Year 2. Taking the IB exam is required of all Year 2 students. A Mathematics Exploration is also required of all students, which is an independent written paper into a mathematics topic that each student prepares, typically during Year 2. This paper is
internally assessed as part of the IB score. This course focuses more on statistics than calculus, and on the role of mathematics and technology in a diverse array of contexts. Using tech is the norm with an emphasis on interpreting those results. This course is aimed at students who will go on to study subjects such as social sciences, natural sciences, statistics, business, some economics, psychology, and design, for example.
Text: Haese Mathematics Core Topics SL Book 1 (ISBN: 978-1-92548955-2) and Book 2 (ISBN: 978-1-925489-57-6)
Duration: 2 years Credit: 1 per year Prerequisite: Successful completion of Honors Advanced Algebra 2 or Honors Precalculus and recommendation of the department Homework: Heavy
This course includes the curriculum of UMAT31 and UMAT32, with an additional 90 hours of study in the five topic areas listed in the SL course description. Year 2 students also complete a written paper assessed internally and sit for the external exam during grade 12.
Text: Haese Mathematics Core Topics HL Book 1 (ISBN: 978-1-92548958-3) and Book 2 (ISBN: 978-1-925489-60-6)
Duration: 2 years Credit: 1 per year Prerequisite: Successful completion of Algebra 2 and recommendation of the department Homework: Heavy
The IB Analysis & Approaches Syllabus is followed in this two-year course. Five main topics are studied: Algebra, Functions, Geometry & Trigonometry, Statistics & Probability, and Calculus. The course culminates in an external IBSL Math Exam at the end of Year 2. Taking the IB exam is required of all Year 2 students. A Mathematics Exploration is also required of all students, which is an independent written paper into a mathematics topic that each student prepares, typically during Year 2. This paper is internally assessed as part of the IB score. This course focuses more on calculus than statistics, and on a deep understanding of mathematics. Students will be asked to prove, investigate, etc. An analytical approach is encouraged. This branch is aimed at students who will go on to study subjects with substantial mathematics content such as mathematics itself, engineering, physical sciences, or economics for example.
Text: Haese Mathematics Core Topics SL Book 1 (ISBN: 978-1-92548955-2) and Book 2 (ISBN: 978-1-925489-56-9)
Duration: 2 years Credit: 1 per year Prerequisite: Successful completion of Honors Advanced Algebra 2 or Honors Precalculus and recommendation of the department Homework: Heavy
This course includes the curriculum of UMAT41 and UMAT42, with an additional 90 hours of study in the five topic areas listed in the SL course description. Year 2 students also complete a written paper assessed internally and sit for the external exam during grade 12.
Text: Haese Mathematics Core Topics HL Book 1 (ISBN: 978-1-92548958-3) and Book 2 (ISBN: 978-1-925489-59-0)
Some things will drop out of the public eye and will go away, but there will always be science, engineering, and technology. And there will always, always be mathematics.
Katherine Johnson
