Mathematics

Building on the math knowledge that CATS Extra students already have, Integrated Mathematics advances students’ math knowledge in the areas of geometry, algebra, trigonometry, discrete mathematics, and probability and statistics.  The theme of the course is patterns. Students create, model, analyze, and explain the different patterns that occur in each of the math disciplines.  Connections are explored between the different areas of mathematics so that students understand how each can be represented as a data table, equation, picture, and description.  Students complete projects throughout the year to demonstrate their understanding of the concepts. In this way, students expand their mathematical vocabulary and communication skills while furthering their study of mathematics.

In this course, students study the foundations of Algebra and Geometry. Students build an understanding of variables, expressions, and equations. They learn to write and solve linear equations and then apply equations to angles, triangles, and polygons in Geometry. Students learn to work with equations of lines and segments on the coordinate plane, as well as solve systems of equations using various methods. Students also explore basic statistics.

In this course, students continue their study of Algebra and Geometry, completing the second semester of each subject. Students study similarity, right triangles, trigonometry, area, and volume. They also study exponents, quadratic functions, and polynomials. Students continue their study of statistics, including probability, and explore patterns and sequences as well. Prerequisites: Integrated Math I or Placement Test

In this course, students explore shapes and their relationships to the two and three-dimensional world. Topics include triangles, quadrilaterals, polygons, circles, area, volume, congruency, similarity, and trigonometry.  Students pay particular attention to measurements and calculations of real world applications. This course also further develops students’ algebraic skills as students apply their Algebra I knowledge to geometric concepts.

The Geometry Honors course covers the same material as the Geometry CP course but moves at a faster pace and introduces additional topics. There is an increased emphasis on formal geometric proofs and logic. Theorems, postulates, and axioms are discovered and applied to proving why other concepts are true.  Prerequisites: B+ or better in Algebra I and recommendation of teacher. ESL Level 3 or higher.

This course builds on what students have learned in Algebra I. Students in the course develop advanced algebra skills such as solving systems of equations, factoring advanced polynomials, and understanding imaginary and complex numbers. Students also study matrices, rational functions, and conic sections. The focus for all of the topics is on problem-solving and developing formal mathematical language in English. The mathematical training in this course is important as preparation for the ACT and SAT, as well as future courses in Pre-calculus and Calculus. The text for the course is Big Ideas Math: Algebra II, and the course makes use of the TI-84 graphing calculator. Prerequisites: Successful completion of Algebra I and Geometry

The Honors Algebra II course covers the same material as the Algebra II College Prep class, but moves at a faster pace and covers additional topics. As Honors students, you will receive more challenging assignments and projects, with the goal of developing your critical thinking skills and formal mathematical thought processes. Prerequisite: Returning students: Recommendation of current math teacher; New students: Placement test results.

This course provides students with the skills they need to study calculus. It highlights the key methods from algebra, trigonometry, and geometry that are needed for further study. The central unifying concept is the mathematical function. The course focuses on both conceptual understanding and problem solving ability and provides students with a deep understanding of exponential, logarithmic, polynomial, rational, and inverse functions.  It also offers an introduction to sequences and series. The textbook for the course is Functions Modeling Change: A Preparation for Calculus 5th ed. by Connally et. al., and the course makes extensive use of the TI-84 graphing calculator. Prerequisite: Successful completion of Algebra II

The Honors Pre-Calculus class covers the same material as the College Prep class but moves at a faster pace and covers additional material as a preview of calculus. Some additional topics include polar functions, sequences and series, and an introduction to limits and derivatives. Honors students also receive more challenging assignments and projects with the goal of further developing their critical thinking and logic skills and keeping them fully engaged. Prerequisites: Returning students: A- or higher in Algebra II College Prep; B or higher in Algebra II Honors; ESL Level 3 or higher; recommendation of previous instructor. New students: ESL Level 3; successful completion of Algebra II; placement test results.

Discrete Math utilizes a first year college textbook and provides an introduction to a survey of topics in mathematics, including problem solving, set theory, logic, number theory, probability, statistics, and graph theory. Students have not previously had the opportunity to study this content in the Algebra, Geometry, and Algebra II sequence. This greatly enhances students’ understanding of topics included in the broader field of mathematics. Students taking this course enhance their ability to make sense of problems and persevere in solving them, reason abstractly and quantitatively, construct viable arguments and critique the reasoning of others, model with mathematics, use appropriate tools strategically, and look for and express regularity in repeated reasoning. Prerequisites: Successful completion of Algebra II or instructor approval

Through this course students gain a greater appreciation of mathematics as a human endeavor created by a diverse group of individuals whose life experiences and environments are integrally tied to the discoveries they made.  An historical perspective is applied to analyze the conventions and norms of communication adopted by mathematicians, the messages these norms convey, and their implications for the role of mathematics in society. Students focus on the development of the number systems, the development of algebra, and math in modern society. Pre-requisites: ESL 4 or higher; completed Algebra II with a B or higher

Introduction to Abstract Mathematical Thought provides an introduction to a survey of topics not previously covered in the traditional high school algebra to calculus sequence, including formal logic, set theory, number theory, and graph theory. This greatly enhances students’ understanding of topics included in the broader field of mathematics. While the topics in this course have some overlap with those covered in Discrete Mathematics, there is a much greater focus on constructing formal mathematical proofs. Students will learn a variety of proof-writing techniques and approaches, including direct proof, proof by contradiction, proof by contrapositive, and proof by induction and disproof by counterexample. By viewing the mathematical world as a series of conjectures that must be proven or disproven, as opposed to theorems that are simply applied, students gain an insight into and appreciation for how the mathematics was developed. By the end of the course, students will have developed both the skills and mindset necessary for discovering new mathematics. Students use the textbook: Chapter Zero: Fundamental Notions of Abstract Mathematics by Carol Schumacher. Prerequisite: Recommendation of current math teacher.

Calculus Honors is an introduction to differential and integral calculus with a single variable. Students are introduced to limits, derivatives, integrals, the fundamental theorem of calculus, the mean value theorem, differential equations, optimization problems, and a variety of other topics and their applications to real-world problems. The course includes most of the material in AP Calculus but at a more relaxed pace, and the AP exam is not a component of this course. Prerequisites: Returning students: Recommendation of previous instructor. New students: ESL Level 3; placement test results

Students in this course continue their study of calculus begun in AP Calculus AB and complete their preparation for the BC level of the Advanced Placement examination in calculus to be taken in the spring. Coverage includes integration by parts and by partial fractions, improper integrals, first order separable differential equations, infinite series and power series, and parametric and polar coordinates. Students continue their study of mathematics by extending their knowledge to the calculus of three-dimensional space. Partial differentiation and multiple integration are the main areas of study. Students must have a TI-84 Plus graphing calculator and must take the College Board BC Calculus exam at the end of the year. Prerequisite:  Successful Completion of AP Calculus AB and recommendation of Calculus Instructor

This course provides a basic introduction to statistics. It is recommended for students who are interested in business, social science, human resources, and criminal justice, and it provides an excellent preparation for any career. Topics include descriptive statistics, probability, probability distribution, normal distribution, hypothesis testing, estimates and sample sizes, the chi square distribution, correlation, and regression. The course is a critical thinking course as well as an analytical one, where students do many short-term projects and a long-term project. This course also provides an overview on how to collect, analyze, interpret, and display data from various real life sources and topics, emphasizing pop culture, politics, and the sporting world. Prerequisites: successful completion of Algebra II

Students expand their understanding of data collection and the role of statistics in making inferences from data. Applications from many realistic contexts such as business and economics, the social and physical sciences, healthcare, education, engineering, and leisure activities are examined throughout the course. Students use realistic data that they collect and analyze for class assignments and projects. The course includes most of the material in AP Statistics but at a more relaxed pace, and the AP exam is not a component of this course. Prerequisites: Returning students: A- or higher in CP Math course; B or higher in previous Honors Math course; ESL Level 3 or higher; recommendation of previous instructor. New students: ESL Level 3; placement test results

Game theory utilizes both popular and more contrived games as well as an accessible text to provide a fun and engaging introduction to the fundamentals of strategic decision-making. Through the analysis of games, students begin to understand the different roles that players can take, the behavior that constitutes the optimal strategy for playing these roles, and the behavior that constitutes the optimal strategy for assisting or countering these roles.  Using this knowledge, students interpret the current behavior of teammates and/or opponents in an attempt to determine their roles, recall the optimal strategy associated with these roles, predict the future behavior of other players based on their optimal strategy, formulate their own optimal strategy to best assist teammates and/or counter opponents, recall the role associated with this strategy, and implement the strategy by behaving in accordance with the calculated role. Furthermore, students gain an appreciation for how these concepts can be applied to fields including but not limited to business, economics, political science, computer science, logic, biology, and philosophy. Prerequisites: ESL Level 3 or higher; Algebra I; instructor approval

Using concepts learned in Game Theory, students research popular board games with the aim to design, refine, and construct an original board game. Additionally, students learn how to sell a refined and marketable game to a publisher. This process is ultimately split into four major phases: research, development, refinement, and sale. Prerequisites: Game Theory or permission from instructor

The purpose of AP Statistics is to demonstrate a range of relevant everyday issues that can be addressed with the help of statistical analysis. This course is meant to expand the understanding of data collection and the role of statistics in making inferences from data. Applications from many realistic contexts such as business and economics, the social and physical sciences, healthcare, education, engineering, and leisure activities are examined throughout the course. Students use realistic data that they collect and analyze for class assignments and projects. Preparation towards the AP Examination highlights the four major disciplines within the Statistics class: Exploring Data, Sampling, Probability, and Inference. The primary textbook used is The Practice of Statistics for AP, 4th Ed. by WH Freeman. Students also use the following resources: www.collegeboard.com and www.apstatsmonkey.com and use TI-84 Plus C Silver Edition Calculators. Prerequisites: Returning students: ESL Level 4 or higher; A- or higher in previous math course; recommendation of previous instructor. New students: ESL Level 4 and placement test results

Students prepare for the Advanced Placement Test in order to gain college credit while learning topics in Single Variable Calculus. Students are introduced to limits, differential equations, the derivative, points of tangency, slope fields, optimization problems, the fundamental theorem of calculus, mean value theorem, integration, application of calculus, and a variety of other topics that will provide real world examples as to the importance of calculus. The textbook for the course is Rogawski’s Calculus for AP. Taking the Advanced Placement test is a mandatory component of this course. Upon completing this course, students are eligible to take Multivariable Calculus or an independent study in mathematics. Prerequisites: Returning students: ESL Level 4 or higher; A- or higher in previous course; recommendation of previous instructor. New students: ESL Level 4; placement test results