Mathematics

Middle School Mathematics

Placement in mathematics courses is dependent on ability and previous work in mathematics, not on age or grade. For returning Shattuck-St. Mary’s students, the current math teacher makes a placement recommendation in early spring for the next academic year. This may confirm or supersede student requests. For newcomers to Shattuck-St. Mary’s, placement is determined by the Mathematics Department Chair, based on careful review of records and recommendations from previous school(s), standardized test results, and placement testing. The overriding concern is to place each student in the mathematics course that will best present an appropriate level of challenge, reinforcement, and advancement. At many levels of the curriculum, several options are available to ensure that all students can progress at an appropriate pace.

Prerequisites are noted for many courses in this guide, and they should be viewed as necessary conditions for enrollment, but not sufficient to guarantee placement.

Students in Pre-Algebra, Algebra Essentials, Algebra I, and Geometry are expected to purchase a calculator and bring it to class each day – at a minimum, an inexpensive scientific calculator that can handle exponents, square roots, and basic trigonometric functions. At various points during the Algebra Essentials and Algebra I courses, students are introduced to certain features of the Texas Instruments TI-84 graphing calculator. To support this instruction, loaners are available for classroom use. This introductory work is intended to foster an emerging understanding of the capabilities and limitations of the graphing calculator and to lay a foundation for broader use in upper level courses. As such, students in Algebra Essentials and Algebra I are permitted, but not expected, to purchase their own TI-83 or TI-84 graphing calculator.

Mathematics (year-long course)
Mathematics is a course designed to strengthen and extend skills and reasoning in arithmetic and number theory, operations with whole numbers, decimals and fractions, as well as ratio, proportion, and percent problems. Measurement skills, geometric concepts, and area and volume formulas also are included. Students explore a variety of problem-solving strategies throughout the year.

Pre-Algebra (year-long course)
Pre-Algebra has a dual emphasis: firmly establishing the quick and accurate computation skills required for the study of Algebra I and beginning to represent quantities and situations with variable expressions. Concepts studied are fractions, decimals, percents, coordinate graphing, formulas, probability, simple statistics, operations with signed numbers, exponents, and factoring. Throughout the year, students work with variables, variable expressions, simple algebraic equations, and a variety of problem-solving strategies.

Algebra Essentials (year-long course; first course of a two-year sequence)
This course is appropriate for students who will benefit from review of Pre-algebra topics in order to prepare the foundation for the more advanced topics of algebra. Students will work extensively with linear expressions and equations — simplifying, solving, graphing, interpreting and applying. Extra instructional time is devoted to such algebraic foundations as working with integers, pattern-recognition, synthesizing multiple skills in a single problem, and representing word problems in mathematical symbols and language. The extended pace of this course allows for review of previously discussed material and frequent reinforcement of new material.

Algebra Essentials is not open to students in 7t h Grade, and should not be viewed as a form of “partial acceleration” for capable 7th Graders.

Intermediate Algebra (year-long course)
Intermediate Algebra begins with a condensed review of solving and graphing linear equations and inequalities. It is expected that students will have had considerable experience with these skills in a previous course. Students then proceed to the study of exponents, radicals, polynomials, rational expressions, and quadratic equations and graphs. More time is devoted to these topics than would be possible in a single-year algebra 1 course. Graphing calculators are used to strengthen students’ understanding of concepts that are first introduced via pencil-and-paper exercises. The completion of Algebra Essentials and Intermediate Algebra, as a two year sequence, will be considered as equivalent to our Algebra 1 course.

Prerequisites: A passing grade in Algebra Essentials (this course is strongly encouraged for students who earned a grade of C- or lower in a previous Algebra I course)

Algebra I (year-long course)
Topics in Algebra I include properties of the real number system, variables, functions, graphing, solving first degree equations and inequalities, basic operations on polynomials and rational expressions, systems of linear equations in two variables, exponents, radicals, quadratic equations, and solving word problems. Graphing calculators are used to strengthen students’ understanding of concepts that are first introduced via pencil-and-paper exercises.

Prerequisite: B- or better in Pre-Algebra or an equivalent course

Geometry (year-long course)
This course examines the topics of Euclidean geometry. Throughout the year the emphasis is on learning to reason logically, accurately, abstractly and creatively. Students learn to develop and present deductive proofs and to solve problems dealing with lines, angles, polygons, circles, and some three-dimensional figures. Hands-on manipulatives, along with the computer application “The Geometer’s Sketchpad,” are used to enrich our study of theorems and postulates.

Prerequisite: A grade of C or better in Algebra I is expected, prior to beginning Geometry. Students who have earned a C- or below in Algebra I are strongly encouraged to enroll in Intermediate Algebra

Advanced Algebra II (year-long course)
Advanced Algebra II is designed for students who enjoy more in-depth discussions of the mathematical concepts presented in the regular course. Additional topics include three-dimensional space, matrices and determinants, and further work with series and sequences. Graphic display calculators are used to promote student exploration and assist in visualizing relationships.

Prerequisites: A- or better in both Geometry and Algebra I and department approval. Supplies: Students enrolled in Advanced Algebra II are required to have a TI-83 or TI-84 graphing calculator.

UPPER SCHOOL MATHEMATICS
Graduation Requirement: All students are required to be enrolled in a mathematics class every year. To graduate, students must earn a minimum of nine credits in mathematics, including a minimum of three credits each in Algebra I, Algebra II, and Geometry or courses advanced beyond these levels.

Placement in mathematics courses is dependent on ability and previous work in mathematics, not on age or grade. For returning Shattuck-St. Mary’s students, the current math teacher makes a placement recommendation in early spring for the next academic year. This may confirm or supersede student requests. For newcomers to Shattuck-St. Mary’s, placement is determined by the Mathematics Department Chair, based on careful review of records and recommendations from previous school(s), standardized test results, and placement testing. The overriding concern is to place each student in the mathematics course that will best present an appropriate level of challenge, reinforcement and advancement. At many levels of the curriculum, several options are available to ensure that all students can progress at an appropriate pace.

Prerequisites are noted for many courses in this guide, and they should be viewed as necessary conditions for enrollment, but not sufficient to guarantee placement. Enrollment in Advanced Placement courses also requires approval of a formal letter of application to the Department Chair.

All students are expected to bring a calculator to class daily. In Algebra Essentials, Algebra I and Geometry, a scientific calculator is sufficient, though a number of classroom demonstrations and activities are done with the Texas Instruments TI-84 graphing calculator. To support this instruction, some loaners are available for classroom use. At the Algebra II level, the TI-83 or TI-84 graphing calculator is recommended; in all course beyond Algebra II, students are expected to purchase their own TI-83 or TI-84 graphing calculator. A word of caution: the Texas Instruments TI-83 is an appropriate substitute for the TI-84, but the TI-86 and TI-89 calculators are not compatible and should be avoided.

Algebra Essentials (year-long course; first course of a two-year sequence)
This course is appropriate for students who will benefit from review of pre-algebra topics in order to prepare the foundation for the more advanced topics of algebra. Students will work extensively with linear expressions and equations — simplifying, solving, graphing, interpreting and applying. Extra instructional time is devoted to such algebraic foundations as working with integers, pattern-recognition, synthesizing multiple skills in a single problem, and representing word problems in mathematical symbols and language. The extended pace of this course allows for review of previously discussed material and frequent reinforcement of new material.

Intermediate Algebra (year-long course)
Intermediate Algebra begins with a condensed review of solving and graphing linear equations and inequalities. It is expected that students will have had considerable experience with these skills in a previous course. Students then proceed to the study of exponents, radicals, polynomials, rational expressions, and quadratic equations and graphs. More time is devoted to these topics than would be possible in a single-year Algebra 1 course. Graphing calculators are used to strengthen students’ understanding of concepts that are first introduced via pencil-and-paper exercises. The completion of Algebra Essentials and Intermediate Algebra, as a two year sequence, will be considered as equivalent to our Algebra 1 course.

Prerequisites: A passing grade in Algebra Essentials (this course is strongly encouraged for students who earned a grade of C- or lower in a previous Algebra I course).

Prerequisite: B- or better in Pre-Algebra or an equivalent course.

Geometry (year-long course)
This course examines the topics of Euclidean geometry. Throughout the year the emphasis is on learning to reason logically, accurately, abstractly, and creatively. Students learn to develop and present deductive proofs and to solve problems dealing with lines, angles, polygons, circles, and some three-dimensional figures. Hands-on manipulatives, along with the computer application “The Geometer’s Sketchpad,” are used to enrich our study of theorems and postulates.

Algebra II (year-long course)
This year-long course reinforces and develops the concepts introduced in Algebra I. Additional topics include complex numbers, conic sections, exponential and logarithmic functions, sequences and series, and the binomial theorem. Graphic display calculators are used to promote student exploration and assist in visualizing relationships.

Prerequisites: A grade of C or better in Algebra I and successful completion of Geometry are required prior to beginning Algebra II. Students who have earned a C- or below in Algebra I are strongly encouraged to enroll in Intermediate Algebra.

Prerequisites: A- or better in both Geometry and Algebra I and department approval. Supplies: Students enrolled in Advanced Algebra II are required to have a TI-83 or TI-84 graphing calculator.

College Prep Algebra and Trigonometry (year-long course)
This course provides students with the opportunity to consolidate their understanding of Algebra II and basic trigonometry before tackling Pre-Calculus. It is designed for students who have found that they benefit from frequent reinforcement in previous mathematics courses. The course begins with a thorough review of essential topics from Algebra II and goes on to examine the behavior of elementary functions (quadratic, polynomial, exponential, and logarithmic). Trigonometric functions are introduced, and students examine their properties, graphs, and applications. Students enrolled in College

Prerequisite: Algebra II

Pre-Calculus (year-long course)
Methods of graphing as well as the solving of equations are reviewed and extended. The course emphasizes applications of trigonometry to the real world using the Law of Sines, the Law of Cosines, and other theorems. Polynomial, rational, exponential, and logarithmic functions introduced in previous algebra courses are re-examined from a more unified, sophisticated point of view. Elementary concepts and applications of differential and integral calculus are also introduced.

Prerequisite: B or better in Algebra II
Supplies: Students enrolled in Pre-Calculus are required to have a TI-83 or TI-84 graphing calculator.

Advanced Pre-Calculus (year-long course)
This course prepares students for Advanced Placement Calculus in the following year. At the outset, the function concept is introduced, and polynomial and rational functions are quickly reviewed. The exponential and logarithmic functions are introduced next, followed by a comprehensive study of trigonometry. Other topics include mathematical induction, complex numbers, parametric equations, and an introduction to series.

Prerequisite: A- or better in Algebra II, B+ or better in Advanced Algebra II, or the equivalent, and departmental approval.
Supplies: Students enrolled in Advanced Pre-Calculus are required to have a TI-83 or TI-84 graphing calculator.

Calculus (year-long course)
Although time will be taken as needed to review topics in algebra, trigonometry, and functions, this class presents the foundation of differential and integral calculus. This Calculus course does not prepare the student for the Advanced Placement examination in May, but rather provides the bridge from advanced algebra and elementary functions to the level of calculus taught in college. Throughout the year students explore functions, limits, derivatives, and integrals using traditional algebraic methods, while the understanding of these topics is enhanced by numerical and graphical explorations with a graphic display calculator.

Prerequisite: C or better in Pre-Calculus. Supplies: Students enrolled in Calculus are required to have a TI-83 or TI-84 graphing calculator.

Statistics (year-long course, not offered every year)
This Statistics course is designed as an alternative for students not taking advanced courses such as Calculus or AP Statistics and who are interested in an introduction to the important topics of statistical analysis. Students will study sampling, surveys, designing of experiments, normal distributions, chance, probability, simulation, and inference. This course will include hands on experiments as well as several projects designed to reinforce the concepts being discussed.

Prerequisites: College Prep Algebra or Pre-Calculus (or Geometry and Algebra II with department approval).
Supplies: Students enrolled in Statistics are required to have a TI-83 or TI-84 graphing calculator.

Advanced Placement Statistics (year-long course)
This course follows the curriculum established by the CEEB (College Entrance Examination Board) Advanced Placement Committee in statistics. AP Statistics introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes, with appropriate emphasis given to each:
 Exploring Data: Describing patterns and departures from patterns
 Sampling and Experimentation: Planning and conducting a study
 Anticipating Patterns: Exploring random phenomena using probability and simulation
 Statistical Inference: Estimating population parameters and testing hypotheses
Students who are successful on the AP Examination may be eligible to earn college credits for an introductory statistics course.

Prerequisites: B or better in Pre-Calculus and departmental approval.
Supplies: Students enrolled in AP Statistics are required to have a TI-83 or TI-84 graphing calculator.

Advanced Placement Calculus AB (year-long course)
This course follows the curriculum established by the CEEB (College Entrance Examination Board) Advanced Placement Committee in mathematics and is designed to parallel a first semester university-level calculus course. The emphasis is on the concepts, techniques, and applications of differential calculus and basic integral calculus. Students explore functions, limits, derivatives, and integrals using traditional algebraic methods, and the understanding of these topics is enhanced by numerical and graphical explorations with a graphic display calculator. Throughout the year, students engage in AP Exam-type problem solving and practice tests in preparation for the AP Examinations in May. Students who are successful on the AP Examination may be eligible to earn college credits for a first semester calculus course.

Prerequisites: A- or better in Pre-Calculus or B- or better in Advanced Pre-Calculus, and departmental approval.
Supplies: Students enrolled in Advanced Placement Calculus AB are required to have a TI-83 or TI-84 graphing calculator.

Advanced Placement Calculus BC (year-long course)
This course follows the curriculum established by the CEEB (College Entrance Examination Board) Advanced Placement Committee in mathematics and is designed to parallel a second semester university-level calculus course. A significant part of the first term is used to review and enhance concepts covered in AP Calculus AB. Topics specific to the Calculus BC curriculum include a variety of integration techniques and applications, first order differential equations, infinite series, parametric functions, and polar coordinates and functions. Throughout the year, students will be practicing AP Exam-type problem solving and practice tests in preparation for the AP Examination in May. Students who are successful on the AP Examination may be eligible to earn college credits for a second semester calculus course.

Prerequisites: B or better in AP Calculus AB and 3 or better on AP Calculus AB Exam.
Supplies: Students enrolled in Advanced Placement Calculus BC are required to have a TI-83 or TI-84 graphing calculator.

Topics in Advanced Mathematics (term course, not offered every year)
In this advanced level course, highly motivated students of mathematics will have the opportunity to explore problems and topics that are not covered in our other advanced level courses. Students will work on challenging problems from the Minnesota Math League, The American Mathematics Examination, and the American Invitational Mathematics Examination. Other topics may include polar graphing and polar representations of complex numbers, proof by induction, recursion, modular arithmetic, matrices and linear algebra. The focus and topics will vary from term to term so that a student could take this course for a single term, two terms, or a full year. This course is in addition to, not a replacement of, other advanced level math courses.
Prerequisites: Completion of Advanced Algebra 2 and departmental approval