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Mathematics

The CATS Academy Math Department is comprised of eight teachers who offer a wide range of exciting and challenging courses. Our teachers pride themselves on reaching all levels of math learners through engaging lessons, projects and hands-on learning.

  • Worcester Polytechnic Institute Math Competition
  • Worcester Polytechnic Institute Math Competition
  • Talk on campus from Mira Bernstein on math and gerrymandering

Mathematics electives

CATS Extra: Integrated Mathematics

Integrated Mathematics advances your math knowledge in the areas of − geometry, algebra, trigonometry, discrete mathematics, probability and statistics. The theme of the course is on mathematical patterns. You will create, model, analyze, and explain the different patterns that occur in each of the math disciplines. Connections will be explored between the different areas of mathematics so that you understand how each can be represented as a data table, equation, picture, and description. You complete projects throughout the year to demonstrate your understanding of the concepts. You will expand your mathematical vocabulary and communication skills while furthering your study of mathematics.

Algebra I

Algebra I class uses the Glencoe Mathematics series to build on your mathematical skills and language. This course explores a range of topics including − expressions and equations, linear functions, quadratic functions, polynomials and nonlinear functions, radical functions, and data analysis. By the end of the course, you should be proficient in problem-solving, using any of the previously mentioned skills and should be able to demonstrate an understanding of the algebraic language. You will have the option of doing Honors-level projects/ assessments in order to receive Honors credit.

Algebra II College Prep

This course builds on what you have learned in Algebra I. During the course you will develop advanced algebra skills such as, solving systems of equations, factoring advanced polynomials, and understanding imaginary and complex numbers. You 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 Glencoe Mathematics Algebra 2, and the course makes use of the TI-84 graphing calculator. Prerequisites: Successful completion of Algebra I and Geometry.

Algebra II Honors

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.

Geometry College Prep

In this course, you will explore shapes and their relationships to the two and three-dimensional world. Topics include triangles, quadrilaterals, polygons, circles, area, volume, congruency, similarity, and trigonometry. You will pay particular attention to measurements and calculations of real-world applications. This course also further develops your algebraic skills as you will apply your Algebra I knowledge to geometric concepts. The course textbook is Glencoe Mathematics Geometry.

Geometry Honors

The Geometry Honors course covers the same material as the Geometry College Prep 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.

Pre-Calculus College Prep

This course provides you with the skills you need to study calculus. It highlights the key methods needed for further study, from − algebra, trigonometry. The central unifying concept is the mathematical function. The course focuses on both conceptual understanding and problem-solving ability and will provide you 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 4th ed. by Connally et. al., and the course makes extensive use of the TI-84 graphing calculator. Prerequisite: Successful completion of Algebra II.

Pre-Calculus Honors

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. As Honors students, you will also receive more challenging assignments and projects, with the goal of further developing your critical thinking and logistical skills while keeping them fully engaged. Prerequisites: New students: ESL Level 3; successful completion of Algebra II; placement test results. 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.

Calculus Honors

Calculus Honors is an introduction to differential and integral calculus with a single variable. You will be 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 Advanced Placement (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.

Multivariable Calculus Honors

This course continues your study of calculus begun in Advanced Placement (AP) Calculus AB and will prepare for the BC level of the AP examination. 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. Partial differentiation and multiple integration are the main areas of study. You 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.

Statistics Honors

You will expand your understanding of data collection and the role of statistics. You will collect and use data from real-life contexts such as business and economics, the social and physical sciences, healthcare, education and engineering then analyse it for class assignments and projects. The course includes material from 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 College Prep 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.

Discrete Mathematics College Prep

Discrete Math provides you with an introduction to a range of mathematical topics − 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 will greatly enhance your understanding of topics included in the broader field of mathematics. Throughout the course you will enhance your ability to make sense of problems, persevere in solving them, reason abstractly and quantitatively, construct viable arguments, critique the reasoning of others, model with mathematics, use appropriate tools strategically, and look for and express regularity in repeated reasoning.

Introduction: Abstract Mathematical Thought Honors

Introduction to Abstract Mathematical Thought provides you with an introduction to a range of topics − including formal logic, set theory, number theory, and graph theory. You will learn a variety of proof writing techniques and approaches, including direct proof, proof by contradiction, proof by contrapositive, proof by induction and disproof by counterexample. By viewing the mathematical world as a series of conjectures that must be proven or disproven, you will gain an insight into and an appreciation for how mathematics was developed. Students use the textbook: Chapter Zero: Fundamental Notions of Abstract Mathematics by Carol Schumacher. Prerequisite: Recommendation of current math teacher.

Game Theory

Game theory utilizes both popular and more contrived games to provide a fun, engaging introduction to strategic decision-making. You will begin to understand the different roles that players can take and the behavior that constitutes the optimal strategy for playing these roles. During the course, you will gain an appreciation of how concepts can be applied, including − business, economics, political science, computer science, logic, biology, and philosophy. This is a one-semester course and a CATS Innovation course. Prerequisites: ESL Level 3 or higher; Algebra I; instructor approval.

Introduction to Statistics

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.

Applications of Game Theory: Traditional Game Desi

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. (also a CATS Innovation course)

Advanced Placement electives

AP Statistics

The purpose of Advanced Placement (AP) Statistics is to demonstrate a range of relevant everyday issues that can be addressed with the help of statistical analysis. 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. Prerequisites: Returning students: ESL Level 4 or higher; A- or higher in previous course; recommendation of previous instructor. New students: ESL Level 4 and placement test results.

AP Calculus AB

You will be 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. The textbook for the course is Rogawski’s Calculus for Advanced Placement (AP). Taking the AP test is a mandatory component of this course. 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.

AP Computer Science A

Advanced Placement (AP) Computer Science A is taught using the Java programming language. The course objectives are to understand object-oriented software design, to gain fluency in Java, to improve proficiency in selecting appropriate algorithms and data structures, to understand algorithm efficiency especially with regard to sorting, and to prepare for the AP Computer Science A exam. There are a variety of exercises, labs and case studies in this course. The course textbook is Java Methods. Prerequisites: ESL Level 4.

AP Computer Science – Principles

This course introduces the main ideas of computer science across several disciplines and you will explore these ideas by building socially useful mobile apps. In addition to programming and computer science principles, you will focus on project-based assignments, which emphasize writing, communication, collaboration, and creativity. The course is designed to be equivalent to a first-semester introductory college course. Pre-requisites: Completion of Algebra I and ESL 3 or above. Students are expected to take the AP exam in May.

Faculty

Mary Carroll
Math Department Chair &
Math Teacher
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Mary Carroll

Math Department Chair &
Math Teacher

BA, Mathematics, Carleton College, Minnesota. MA, Liberal Studies, Reed College, Oregon

Mary Carroll is the Chair of the mathematics department. She works with teachers to provide a challenging math curriculum to suit the needs of all students. She also teaches Multivariable Calculus Honors, AP Statistics and Honors Statistics. Prior to joining CATS Academy, Mary taught high school mathematics in Costa Rica, Turkey, Spain and the Dominican Republic, as well as the US. She has a Master’s degree in Liberal Studies from Reed College in Oregon and an undergraduate degree in mathematics from Carleton College in Minnesota.

Jeff Napior
Director of CATS Innovation,
Chair of Technology Department &
Math Teacher
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Jeff Napior

Director of CATS Innovation,
Chair of Technology Department &
Math Teacher

BS, Aerospace Engineering, Cal Poly, San Luis Obispo
MS, Aeronautical Science, Embry Riddle Aeronautical University

Jeff Napior runs the CATS Innovation Lab where students benefit from a 'design-make-use' philosophy. This approach leverages open-ended exploration and tacit learning, therefore helping students complete projects typically related to the STEAM disciplines. Jeff worked for fifteen years as an aerospace engineer. He has hands-on experience with the electrical integration of flight vehicles ranging from fighter jets to orbital-class rockets. He has professionally trained US Navy aircraft technicians, tutored high school students and provided post-GED math lessons to incarcerated persons. Jeff is a huge sci-fi fan and an avid reader.

Mike Cerbarano
Math Teacher
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Mike Cerbarano

Math Teacher

BS, Mathematics, Bridgewater State University

Michael Cerbarano is a member of the mathematics faculty at CATS Academy. He is currently teaching Geometry and Algebra II. Prior to joining CATS, Michael served and is still serving as an adjunct mathematics professor at Massasoit Community College. Michael brings over eight years of higher education experience in both lower and upper-level mathematics courses. Michael received his BS in Mathematics at Bridgewater State University in 2009.

Justin De Santis
Math Teacher
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Justin De Santis

Math Teacher

Justin De Santis is a Math teacher, specializing in discrete mathematics, proof writing and game theory. He is also the coach of the CATS Boston Ultimate Frisbee team. Originally from New York, Justin is entering his fourth year at CATS Academy. Prior to joining CATS Justin spent five years living in Maine working as a high school math teacher, math team advisor, and tennis coach at Lee Academy. When not delivering inspiring math classes Justin can be found on campus enjoying a meal in the dining hall, or tossing an Ultimate disc next to the soccer field. “As a math enthusiast, I feel so fortunate to be a part of the incredibly passionate and dedicated faculty here at CATS. I could not be more grateful to be given this opportunity to impart the wisdom of a subject I love to those who will sculpt the future of our world."

Kadijah Figarsky
Math Teacher
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Kadijah Figarsky

Math Teacher

BS, Mathematics, Keene State College
MS, Mathematics, University of Connecticut Storrs

Khadija Figarsky joined CATS Academy in the fall of 2017. She teaches both Algebra II CP and Integrated Mathematics. Before joining the CATS faculty she worked in the field of neuroscience research at an NYU School of Medicine affiliated institute. Khadija started teaching math in graduate school, where she was a teaching assistant and adjunct faculty member, teaching numerous college-level courses. Khadija has lived on three continents, and she is fluent in three languages — English, French, and Arabic. And having studied and lived abroad, she is familiar with the unique needs of international students. Khadija holds an MS in Mathematics from the University of Connecticut Storrs and a BS in Mathematics from Keene State College. She is excited to be working with such a dynamic and diverse international student population at CATS.

Dominique Lomax
Math Teacher
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Dominique Lomax

Math Teacher

BA, Mathematics Willamette University
MAT, Mathematics, Willamette University

Prior to joining CATS Academy, Dominique taught at a school in China for three years. Here she taught AP Calculus and Pre-calculus. Once returning to America she worked at various schools that had an international student body or an international focus. Dominique comes to CATS Academy with four years’ of teaching international students both in China and America. She understands how to support international students as they learn, not only mathematics, but the English used in mathematics. Dominique received her BA in Mathematics with a minor in Chinese Studies from Willamette University and her MAT from Willamette University's School of Education.

Muhammad Najib
Math Teacher
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Muhammad Najib

Math Teacher

available soon

Annie Schneider
Math Teacher
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Annie Schneider

Math Teacher

available soon