Math
The Arroyo High School math department is committed to helping all students build strong problem-solving skills, confidence, and logical thinking. We offer courses that support learners at every level, from foundational math to advanced studies. Math is more than numbers—it is a way to understand the world and think critically.
Graduation Requirements
- District Requirements: 2 years of math (IM1 and IM2 or IM1 and Math with Life Applications)
- UC/CSU A-G Courses: 3 years of college-preparatory courses, with a 4th year strongly recommended for competitiveness
COURSES OFFERED
Integrated Math 1 (P)
Prerequisite: Entry level high school math course
This UC approved college preparatory course is the first of a sequence of three courses, each of which includes number, algebra, geometry, probability and statistics. The fundamental purpose of Integrated Math I is to formalize and extend the mathematics that students learn in middle school. The critical areas, organized into units, deepen and extend understanding of linear relationships in part by contrasting them with exponential phenomena, and in part by applying linear models to data that exhibit a linear trend. Integrated Math I uses properties and theorems involving congruent figures to deepen and extend understanding of geometric knowledge from prior grades. The final unit in the course ties together the algebraic and geometric ideas studied.
Integrated Math 2 (P)
Prerequisite: Successful completion of IM 1. The AHS Math Department highly recommends that students earn a C or better in IM1.
This UC approved college preparatory course is the second of a sequence of three courses, each of which includes number, algebra, geometry, probability and statistics. Topics include: Extending the Number System · Quadratic Functions and Modeling · Expressions and Equations · Applications of Probability · Similarity, Right Triangles, Trigonometry, and Proof · Circles with and without Coordinates · Absolute Values. This course is designed to meet the Common Core State Standards for high schools following the Integrated Math Pathway.
Integrated Math 3 (P)
Prerequisite: Successful completion of IM 2. The AHS Math Department highly recommends that students earn a C or better in IM2.
This UC approved college preparatory course is the second of a sequence of three courses, each of which includes number, algebra, geometry, probability and statistics. Integrated Math 3 students integrate and apply the mathematics they have learned from their earlier courses. This course includes standards from the conceptual categories of Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability. Instructional time should focus on four critical areas:
· Apply methods from probability and statistics to draw inferences and conclusions from data
· Expand understanding of functions to include polynomial, rational, and radical functions
· Expand right triangle trigonometry to include general triangles
· Consolidate functions and geometry to create models and solve contextual problems
Precalculus (P)
Prerequisite: Successful completion of IM 3. The AHS Math Department highly recommends that students earn a C or better in IM3.
Precalculus is a year course which focuses on latter Integrated Math 3 concepts in order to deepen the understanding, right triangle trigonometry, and analytical trigonometry. Technology, including the use of a TI 84 graphing calculator or the online Desmos graphing calculator, is incorporated in the course work. Topics covered are functions such as polynomial, rational, exponential, logarithmic, and trigonometric. Students study conic sections and they verify trigonometric identities.
Mathematical Reasoning with Connections (MRWC) (P)
Prerequisites: Senior level class for students who got a C or better in IM 3
The MRWC curriculum has been developed by a consortium of mathematics professors and math educators from CSU, UC, and CCC higher education systems, together with mathematics specialists from County Offices of Education and local school districts. It has been specifically designed to address the need for stronger mathematics preparation for transitioning from high school to college and career pathways. Based on the Common Core State Standards viewpoint that mathematics is a cohesive and connected body of work, the MRWC is structured to highlight conceptual connections in the more advanced study of topics leading to calculus. Emphasis is given to conceptual understanding and making connections between numerical, symbolic, verbal, and graphical representations, discussion and analysis of alternative representations and multiple perspectives for approaching and understanding. The distinctiveness of MRWC lies in its unique design and topic sequencing, and in the emphasis on instructional delivery that promotes exploratory and collaborative student engagement. MRWC seamlessly interwaves the CCSS Mathematical Practices throughout the curriculum and develops key Habits of Mind and a mathematical disposition required for mastering advanced, challenging college-level content knowledge. MRWC uses a non-traditional instructional approach emphasizing collaboration and exploration ; through mathematical activities, problem posing, and the use of technology that will address diverse learning styles. Instruction is designed to challenge students to approach mathematics as sense-making through a focus on questioning and probing deeper. Teacher-led instruction and student explorations will focus on discovering the conceptual basis for standard procedures. It will facilitate the development of students' ability to choose strategically among multiple solutions options, and to articulate the reasons for those decisions. Students will use informal and formal justifications to define their understanding and critique the reasoning of others. Instruction will emphasize the use of and fluency in the full range of the language of mathematics. Content topics will be approached through six instructional modalities i.e. verbal, numeric, symbolic, graphical, geometric, and technological.
Calculus (P)
Prerequisite: Successful completion of Precalculus.
The topics will include limits, continuity, derivatives and integrals of polynomials, trigonometric and log exponential functions, curve sketching, and applications.
Calculus AB (P)
Prerequisite: Successful completion of Precalculus. The AHS Math Department highly recommends that students earn a C or better in Precalculus.
AP Calculus AB is an introductory college-level calculus course. Students cultivate their understanding of differential and integral calculus through engaging with real-world problems represented graphically, numerically, analytically, and verbally and using definitions and theorems to build arguments and justify conclusions as they explore concepts like change, limits, and the analysis of functions. Topics covered include functions and graphs, limits and continuity, derivatives and applications, definite integrals and applications, anti-differentiation, differential equations and slope fields, mathematical modeling, L’Hôpital’s Rule. Students should be able to work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal. They should understand the connections among these representations. This course utilizes technology through the use of graphing calculators. Critical thinking skills and problem solving skills are applied to both symbolic manipulation and real world situations.
Calculus BC (P)
Prerequisite: Successful completion of Calculus AB. The AHS Math Department highly recommends that students earn a C or better in Calculus AB.
AP Calculus BC is a full year course in the calculus of functions of a single variable. It includes all topics covered in Calculus AB plus additional topics described in the College Board course description. Topics covered include functions and graphs, limits and continuity, derivatives and applications, definite integrals and applications, anti-differentiation and Euler’s Method, differential equations and slope fields, mathematical modeling, L’Hôpital’s Rule, improper integrals, partial fractions, infinite series including power series and Taylor series, parametric, vector, and polar functions. Students should be able to work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal. They should understand the connections among these representations. This course utilizes technology through the use of graphing calculators. Critical thinking skills and problem solving skills are applied to both symbolic manipulation and real world situations.
Computer Science Principles AP (P)
Prerequisite: Successful completion of IM 1
The course introduces students to the foundational concepts of computer science and challenges them to explore how computing and technology can impact the world. The AP Program designed AP Computer Science Principles with the goal of creating leaders in computer science fields and attracting and engaging those who are traditionally underrepresented with essential computing tools and multidisciplinary opportunities.
Note: Students can take Computer Science Principles AP concurrently with any math class the year after successfully completing IM 1.
Math with Life Applications
Prerequisite: Class for senior students who passed IM 1
The Mathematics with Life Applications course will guide students in building a strong foundation in logical thinking and problem solving that will enable them to make good decisions concerning matters of money and finance in their daily lives. Students will use technology that will allow them to present the skills and knowledge they gain from this course and apply them to real-life situations. Students are introduced to such everyday life skills as calculating retail discounts, budgeting expenses, making cost comparisons, buying and renting a home, calculating the cost of operating a motor vehicle, and may others related to real-world finances. Basic business matters, including borrowing money, investing, and calculating business profits and losses are also included.
Rio Hondo Mathematics Summer Academy
The Rio Hondo Mathematics Summer Academy offers IM1, IM2, IM3 and Precalculus as g0-ahead classes.