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Mathematics

US MATH CALCULATOR/TECHNOLOGY USAGE POLICY

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 require that students purchase their own calculator. Since demonstrations will be done using the TI-84 Plus CE calculator, this is the model we require students to have. The TI-84 Plus CE model is acceptable for all TAS math classes. 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.

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.

Course Offerings 2019-2020

INTRODUCTION TO ALGEBRA (UMAT01)

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. Story problems are emphasized throughout the course.

Text: Algebra (McDougal/Littell)

ALGEBRA 1 (UMAT02)

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. Students need a TI-84 Plus CE graphing calculator.

Text: Algebra (ISBN: 978-0-07-663923-6)

GEOMETRY (UMAT03)

 

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: announced Spring 2019

HONORS GEOMETRY (UMAT041)

 

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. Students need a TI-84 Plus CE graphing calculator. Text: announced Spring 2019

HONORS ADVANCED GEOMETRY (UMAT042)

 

HONORS ADVANCED GEOMETRY (UMAT042)

Duration: 1 year

Credit: 1

Prerequisite: Successful completion of Algebra 1; recommendation of the department

Homework: Heavy

This course is a high-powered honors class that is both fast-paced and in-depth. Students study the basic definitions used in inductive and deductive reasoning, principles of logic, properties of different polygons, perpendicularity, congruence, similarity of triangles, properties of circles, constructions, areas, and volumes. Emphasis is placed on proofs and problem solving. Students need a TI-84 Plus CE graphing calculator.

Text: announced Spring 2019

ALGEBRA 2 (UMAT06)

 

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. Students need a TI-84 Plus CE graphing calculator.

Text: Intermediate Algebra (ISBN: 978-0-321-88012-3)

HONORS ALGEBRA 2 (UMAT070)

 

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. Students need a TI-84 Plus CE graphing calculator.

Text: Intermediate Algebra (ISBN: 978-0-321-88012-3)

HONORS ADVANCED ALGEBRA 2 (UMAT071)

HONORS ADVANCED ALGEBRA 2 (UMAT071)

Duration: 1 year

Credit: 1

Prerequisite: Successful completion of Algebra 1, 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. Students need a TI-84 Plus CE graphing calculator.

Text: College Algebra (ISBN: 978-0-321-72964-4)

PRECALCULUS (UMAT08)

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 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. Students need a TI-84 Plus CE graphing calculator.

Text: Precalculus, 9th edition (ISBN: 978-1-133-94903-9

HONORS PRECALCULUS (UMAT12)

HONORS PRECALCULUS (UMAT12)

Duration: 1 year

Credit: 1

Prerequisite: Successful completion of Algebra 2 or Honors 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. Students need a TI-84 Plus CE graphing calculator.

Text: Precalculus 5th edition (ISBN: 978-0-321-83734-9)

HONORS PRECALCULUS & DIFFERENTIAL CALC (UMAT123)

 

HONORS PRECALCULUS & DIFFERENTIAL CALC (UMAT123)

Duration: 1 years

Credit: 1 per year

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. Students need a TI-84 Plus CE graphing calculator.

Text: Precalculus (ISBN: 978-0-321-83734-9); and Calculus: Graphical, Numerical, Algebraic (ISBN: 978-0-13-331161-7)

CALCULUS (UMAT121)

CALCULUS (UMAT121)

Duration: 1 year

Credit: 1

Prerequisite: Successful completion of Precalculus or Honors Precalculus, and recommendation of math department

Homework: Heavy

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. Students need a TI-84 Plus CE graphing calculator.

Text: Calculus: Graphical, Numerical, Algebraic (ISBN: 978-0-13-331161-7)

AP CALCULUS AB (UMAT13)

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, trigonometry, 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. Students need a TI-84 Plus CE graphing calculator.

Text: Calculus: Graphical, Numerical, Algebraic (ISBN: 978-0-13-331161-7)

AP CALCULUS BC (UMAT14)

 

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 good 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. Students need a TI-84 Plus CE graphing calculator.

Text: Calculus (ISBN: 978-0-618-50304-9)

AP STATISTICS (UMAT09)

 

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. Students need a TI-84 Plus CE graphing calculator.

Text: The Practice of Statistics for AP (ISBN: 978-1-4641-0873-0)

HONORS DIFFERENTIAL EQUATIONS (UMAT16)

 

HONORS DIFFERENTIAL EQUATIONS (UMAT16)

Duration: 1 semester, offered in Semester 2 only

Credit: 0.5

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. Differential Equations are mathematical formulations that translate the laws of nature; therefore, in order to understand contemporary science and engineering one must understand differential equations and the properties of their solutions.

 

HONORS LINEAR ALGEBRA (UMAT17)

HONORS LINEAR ALGEBRA (UMAT17)

Duration: 1 semester, offered in Semester I only

Credit: 0.5

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. Linear Algebra will include topics that are useful in other disciplines; these might include vector spaces, systems of equations, positive definite matrices, determinants, eigenvalues, and similarity.

Text: Linear Algebra (ISBN: 0-321-28713-4)

HONORS ADVANCED TOPICS IN MATHEMATICS (UMAT18)

HONORS ADVANCED TOPICS IN MATHEMATICS (UMAT18)

Duration: 1 semester, offered in Semester II only

Credit: 0.5

Prerequisite: Successful completion of AP Calculus BC or IBHL Year 2 Math and recommendation of math department

Homework: Heavy

This course is for advanced math students to explore further topics in math such as non-linear dynamics, partial differential equations, abstract algebra, Fourier series, and complex calculus. The specific course content will be directed by student interest.

HONORS MULTIVARIABLE CALCULUS (UMAT19)

HONORS MULTIVARIABLE CALCULUS (UMAT19)

Duration: 1 semester, offered in Semester I only

Credit: 0.5

Prerequisite: Successful completion of AP Calculus BC or IBHL Year 2 Math and recommendation of math department

Homework: Heavy

This course extends the ideas learned in a single variable calculus course to multiple variables. The course first begins by investigating geometric objects and vectors in three dimensional spaces. It then moves onto extending calculus of a single variable to multiple using the formal definition of limits, derivatives, and integrals. Finally vector calculus and its associated theorems are explored - Gauss’, Stokes’, and Greens’ theorems are used and investigated. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

IBSL MATH STUDIES (UMAT10)

 

IBSL MATH STUDIES (UMAT10) 

Offered 2019-20 only

Duration: 1 year

Credit: 1

Prerequisite: Successful completion of Algebra 2 and recommendation of math department

Homework: Moderate

This course is a continuation of Algebra 2 and is designed primarily for IB students who are taking mathematical studies at the subsidiary level. The following topics are covered: functions, computation, sets, logic, data analysis, business techniques, geometry of the earth’s surface and trigonometry. A written project (2000 words in length) is a major part of the course. Students are required to take the IB exam at the completion of the course. Students need a TI-84 Plus CE graphing calculator.

Text: Mathematical Studies Standard Level (ISBN: 978-0-19-839013-8)

IBSL MATHEMATICS 2 (UMAT112)

 

Offered 2019-20 only
IBSL MATHEMATICS YEAR 2 (UMAT112)

Duration: 1 year

Credit: 1 per year

Grade: 11-12

Prerequisite: IBSL Mathematics 1 and recommendation of the math department

Homework: Heavy

The IB Standard Level Mathematics Syllabus is followed in this two year course. Year 1 mathematics topics are introduced, studied in depth, and woven into the remainder of the course: Algebra, Functions, and Circular Functions and Trigonometry. Year 2 Topics include Vectors, Probability and Statistics, and Differential and Integral Calculus. The two year course culminates in the taking of the externally scored IBSL Math Exam at the conclusion of year 2. Taking the IB exam is required of all Year 2 enrolled students. A Mathematics Exploration is also required of all students, which is an independent exploration into a mathematics topic that each student prepares during Year 2, and which is internally assessed as part of the IB score. Students need a TI-84 Plus CE graphing calculator.

Text: Mathematics for the International Student, Mathematics SL, 3rd Edition (ISBN: 978-1-921972-08-9)

IBSL MATH: APPLICATIONS & INTERPRETATION 1 (UMAT31)
IBSL MATH: APPLICATIONS & INTERPRETATION 2 (UMAT32)

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. Students need a TI-84 Plus CE graphing calculator.

Text: announced Spring 2019

IBHL MATH: APPLICATIONS & INTERPRETATION 1 (UMAT33)
IBHL MATH: APPLICATIONS & INTERPRETATION 2 (UMAT34)

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: announced Spring 2019

IBSL MATH: ANALYSIS & APPROACHES 1 (UMAT41)
IBSL MATH: ANALYSIS & APPROACHES 2 (UMAT42)

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. Students need a TI-84 Plus CE graphing calculator.

Text: announced Spring 2019

IBHL MATH: ANALYSIS & APPROACHES 1 (UMAT43)
IBHL MATH: ANALYSIS & APPROACHES 2 (UMAT44)

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: announced Spring 2019

Department Chair

US Math Paths