Mathematics

Welcome to the Mathematics Department

MATH 1 (pre-IB)

GRADE: 9 CREDITS: 10

COLLEGE RECOMMENDED? YES

PREREQUISITES: None

This first-year math course is intended to help students learn and develop solid mathematical thinking and to demonstrate mastery of CCSS Integrated Math 1 content and practice standards, which include key concepts from Algebra, Geometry, and Statistics. Some of the topics for this course are:

-Linear Equations

-Solving Equations

-Visual patterns and functions

One and two variable statistics

-Foundations of Geometry

-Geometric Transformations

-Congruence

This course is structured around Capuchino’s adaptation of the six Approaches to Teaching defined by IB.

Educational practice is based on inquiry

Learning is focused on conceptual understanding

Educational practice and personal identity are developed in local and global contexts

Instruction is focused on effective teamwork and collaboration

Curriculum, instruction, intervention, and support are differentiated to meet the needs of all learners

Instruction and educational practice is informed by formative and summative assessment

This course employs standards-based grading (in both Foundation Quizzes and Performance Tasks), so that all students can reach proficiency in key learning targets. Students write IB-style reports for each Performance Task, to begin preparing them for their future IB Internal Assessment. There is a heavy emphasis on developing agency and mathematical identity for all students; this includes a strong emphasis on group work, problem solving, and mathematical discourse.

Note: the three course sequence of Capuchino Pre-IB Math 1, Math 2, and Math 3 cover the same content standards as the traditional Algebra 1, Geometry, Algebra 2 sequence, but in a different order with a greater emphasis on the connections between strands.

MATH 1 EL (pre-IB, for English Language learners)

GRADE: 9 CREDITS: 10

COLLEGE RECOMMENDED? YES

PREREQUISITES: None

This course teaches the same concepts as Capuchino Pre-IB Math 1, but materials and strategies are adapted to meet the needs of English Language Learners. This course is taught as a two hour block with Sheltered Strategic Algebra Support as the second hour.

SHELTERED STRATEGIC ALGEBRA SUPPORT (for English Language Learners)

GRADE: 9-12 CREDITS: 10

This is the second hour of Capuchino Pre-IB EL Math 1 where students have an opportunity to practice what they are learning in EL Math 1. All students are provided with a subscription to the online math tutoring program Mathspace.co as well as individual attention from the teacher, peer tutors and an instructional aide.

MATH 2 (pre-IB)

GRADE: 9-10 CREDITS: 10

COLLEGE RECOMMENDED? YES

PREREQUISITES: Math 1 or equivalent

This second-year math course continues and builds on the practices and structures of Capuchino Pre-IB Math 1. This course is intended to help students deepen their mathematical thinking and to demonstrate mastery of CCSS Integrated Math 2 content standards, as well as the Standards for Mathematical Practice. This includes key concepts, such as working with Quadratic functions in multiple representations (A-SSE 1 - 3, F-LE 3, 6), performing operations on polynomials (A-APR 1), creating equations to model situations (A-CED 1 - 4), solving equations and inequalities in one variable, and systems of equations in two variables (A-REI 4-7), interpreting and analyzing functions in multiple representations (F-IF 4-9), similarity, right triangles, and trigonometry, with congruence as a special case of similarity (G-SRT 1 - 8, G-CO 9 - 11), expressing geometric properties with equations (G-GPE 1, 2, 4, 6), solving problems involving volume and surface area (G-GMD 1, 3, 5, 6), and conditional probability (S-CP 1 - 7). There is a heavy emphasis on developing agency and mathematical identity for all students; this includes a strong emphasis on group work, problem-based curriculum, and frequent mathematical discourse.

This course uses the same six approaches to teaching as discussed in the Capuchino Pre-IB Math 1 course. Students who successfully finish this course will move on to Capuchino Pre-IB Math3 or IB Math Applications and Interpretations SL1 or Integrated Math 2. This course also uses the same types of foundational quizzes, performance tasks, group work and problem solving strategies as Capuchino Pre-IB Math 1.

MATH 3 (pre-IB)

GRADE: 10-11 CREDITS: 10

COLLEGE RECOMMENDED? YES

PREREQUISITES: Math 2 or equivalent

This third-year math course continues and builds on the practices and structures of Capuchino Pre-IB Math 1 & 2.

This course is intended to help students learn and develop solid mathematical thinking and to demonstrate mastery of CCSS Integrated Math 3 content standards, as well as the Standards for Mathematical Practice. This includes key concepts such as: writing and interpreting polynomial and rational expressions (A-SSE), performing operations on polynomials and understanding the relationship between zeros and factors of a polynomial (A-APR), creating and working with equations and inequalities in one and two variables, including absolute value, to represent relationships and solve problems (A-CED, A-REI), analyzing and interpreting function families, including square root, rational, exponential, and logarithmic functions (F-IF), building functions from existing functions through transformations and compositions (F-BF), constructing and comparing linear, quadratic, and exponential models to solve problems, and using logarithms to solve exponential equations (F-LE), understanding the unit circle (F-TF), applying trigonometry to general right triangles (G-SRT), working with 2- and 3-dimensional shapes, and applying geometry to modeling situations (G-GMD and G-MG), using probability to evaluate outcomes of decisions (S-MD), and making inferences from sample surveys, experiments, and observational studies (S-IC). There is a heavy emphasis on developing agency and mathematical identity for all students; this includes a strong emphasis on group work, problem-based curriculum, and frequent mathematical discourse.

INTEGRATED MATH II

GRADE: 10-12 CREDITS: 10

NON-COLLEGE ELECTIVE

PREREQUISITES: Math 2 or equivalent

This course is intended to meet the needs of students who have completed Algebra 1 and Geometry and are not yet ready to continue in the college preparatory path. The course includes substantial work in geometry as well as probability and statistics with review of Algebra throughout. The core Geometry topics include lines, angles, geometric constructions, properties of parallel and perpendicular lines, congruence, similarity, right triangles, trigonometry, polygons, transformations, circles, area and volume. Review and introduction to key Algebra 2 topics include linear, quadratic and exponential equations and functions. The course emphasizes applications and makes extensive use of technology.

IB MATH Applications and Interpretations SL I (Standard Level year 1)

GRADE 10-12 CREDITS: 10

COLLEGE RECOMMENDED? YES

PREREQUISITES: Students must meet the following criteria: C or better in Math 3 or an A in Math 2. A previous teacher’s recommendation is needed to skip Math 3.

This is the 1st year of IB Math Standard Level Students are in the same course. This course is compropable to a pre-Calculus at a traditional high school. This course is intended for highly proficient students engaged in meeting and or exceeding state and district standards in:

Probability

Non-Right Triangle Trigonometry

Voronoi Diagrams

Surface Area and Volume

-Functions, Domain, Range, Composite and Inverse Functions

-Quadratics

-Exponentials and Logarithms

-Arithmetic and Geometric Sequences and Series

It is designed to prepare students for the International Baccalaureate (IB) Mathematics – Standard Level Exam which is given at the 2nd year of the program. Special attention is paid to the internationalism of mathematics and to help students to appreciate the multiplicity of cultural and historical perspectives of mathematics. Students complete investigation and/or modeling portfolios related to the topics taught in this course. A graphing calculator is required. (recommended calculator: TI-83, TI-84)

IB MATH Applications and Interpretations SL II (Standard Level, year 2)

GRADE 11-12 CREDITS: 10

COLLEGE RECOMMENDED? YES

PREREQUISITES: Students must meet the following criteria: C or better in Mathematics Applications and Interpretations SL I.

This college level course is designed for highly proficient students. This course gives students an introduction and exposure to Calculus and Statistics. This course is intended for highly proficient students engaged in meeting and or exceeding state and district standards in:

-Descriptive Statistics

-Bivariate Data, Pearson & Spearman Correlation Coefficients

-Discrete Random Variables and Binomial Distribution

-Continuous Random Variables and Normal Distribution

-Derivative Calculus Introduction

-Integral Calculus Introduction

-Financial Mathematics

It is designed to prepare students for the International Baccalaureate Mathematics – Standard Level Exam which is an intensive comprehensive exam given at the end of 2nd year of the course in May. During this year students complete an internal assessment (IA) which consists of a written paper of a mathematical topic of their choice. A graphing calculator is required. (recommended calculator: TI-83, TI-84)

IB MATH Applications and Interpretations HL II (Higher Level, year 3)

GRADE 12 CREDITS: 10

COLLEGE RECOMMENDED? YES

PREREQUISITES: Students must meet the following criteria: C or better in Mathematics Applications and Interpretations SL II.

This college level course is designed for highly proficient students who finish IB Math Applications and Interpretations SL11 during 11th grade. It consists of advanced calculus, differential equations, linear algebra, and statistics.

-Trigonometric Phase Transformations

-Vectors, Magnitude, Dot-Product, Cross Product, Vector Equations of lines

-Complex Numbers, Argand Diagrams, Cartesian, Polar & Euler Form, Combining periodic functions using complex numbers.

-Matrices: Determinant, Inverse Matrices, Solving systems of equations using matrices, Transformations of Matrices, Transition Matrices and Markov Chains, Eigenvalue and Eigenvector characteristic equations, Diagonalization and Powers of Matrices

-Derivatives, Chain Rule, Product Rule, Derivatives of Trig, exponential and log functions, 2nd derivatives, concavity and points of inflection, properties of curves and Kinematics

-Integration: Area between 2 curves, Antiderivative family of functions, Integration by substitution, Solid of Revolution

-Differential Equations, Slope fields, Euler’s method for solving differential equations

-Vector Motion with Variable velocity

-Coupled Differential Equations & Phase Portraits

-Complex Eigenvalue and phase portraits

-Euler’s method for coupled Linear Equations

-Predator and Prey real life models

-Second Order Differential Equations

-Graph Theory: Paths, walks, trails and transition Matrices.

-Kruskal’s Algorith and Prim’s Algorithm

-Chinese Postman Problem, Hamiltonian cycles and paths, Traveling Salesman Problem (TSP)

-Poisson Distribution

It is designed to prepare students for the International Baccalaureate Mathematics – Higher Level Exam which is an intensive comprehensive exam given at the end of 3rd year of the course in May. During this year students revise their internal assessment (IA) paper from last year. A graphing calculator is required. (recommended calculator: TI-83, TI-84)

INTRO TO DATA SCIENCE

GRADES: 12 CREDITS: 10

COLLEGE RECOMMENDED? YES

PREREQUISITES: None (must be in 12th grade)

Intro to Data Science is a college prep course in UCLA’s curriculum. In this class, students learn to use the coding language R to evaluate real-world data sets covering topics ranging from sports and video games to police fatalities and workplace discrimination. This is a challenging course with a significant workload because students will learn to code while understanding deep and applicable subjects in statistics and data science. The units of study include Where Data Come From, Exploring Variation, The Empty Model, The Complex Model, Evaluating Models, and Model Comparison with the F Distribution. This course is an excellent introductory class that anyone can take and provides a solid foundation for further study in statistics in college. This course is a 4th year math course.

Conceptual Concepts: