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The goal of the Mathematics Department is to develop the mathematical talents of each student. Our curriculum encourages academic excellence and fosters a love of learning, critical thinking, analytical reasoning, precise expression and a healthy spirit of achievement. It challenges each student according to her ability by offering courses that provide a well-rounded background in fundamentals as well as honors and advanced placement opportunities. Emphasis is placed on applications at all levels of instruction. As a college preparatory school, we strongly recommend that all students take four years of mathematics, and we require each student to own a TI-84 graphing calculator.
The Mathematics department at Villa Maria seeks to graduate young women who understand that:
mathematics is a language through which we can communicate graphically, analytically, numerically, and verbally.
mathematical fluency is the ability to quickly and accurately recall mathematical facts and concepts. It consists of five key components – accuracy, flexibility and appropriate response, efficiency, automaticity, and number sense.
functions can be used to summarize different mathematical relationships and model real-world situations.
mathematics requires us to think critically, reason abstractly, and “identify common underlying structures in problems involving different contextual situations” (The College Board, 2020, p. 14).
mathematics is to be approached with a growth mindset of persistence, resourcefulness, and confidence.
Three years of Mathematics are required of our students for graduation. Curricular options will be considered for those students who enter Villa Maria Academy High School at a level not listed. If a student who has completed a year of honors-level mathematics wishes to accelerate in Villa Maria’s Math sequence and is approved by the Mathematics Department for such consideration, Geometry may be taken concurrently with Honors Algebra 2. Geometry (at the Honors level at Villa Maria) is the only course permitted to be taken for credit in the summer months. Students must have completed a year of Honors level mathematics to gain this approval. Formal paperwork for this approved option is required and can be obtained from the current math teacher. Other advanced elective courses may be taken as outlined below.
Algebra 1 (512)
Grade 9
Credit 1.0
This is a first-year course in the fundamentals of algebra. Its purpose is to provide a comprehensive study of the basic algebraic concepts. The course meets the needs of a wide range of students with a review of operations with real numbers and progressing through solving linear equations and inequalities, systems of equations, quadratic equations, polynomials, factoring, radical expressions, and the properties of exponents. Graphing is emphasized with linear and quadratic functions, scatterplots, and inequalities. Basic statistical concepts are covered. Problem solving and use of the graphing calculator are interjected throughout the course.
Honors Algebra 1 (511)
Grade 9
Credit 1.0
This is a first-year course in the fundamentals of algebra that moves along at an accelerated pace and offers an in-depth study of the basic algebraic concepts. The course reviews operations with real numbers and progresses through solving linear equations and inequalities, absolute value equations, systems of equations and inequalities, quadratic equations, polynomials, factoring, radical expressions, and the properties of exponents. Graphing is emphasized with linear, quadratic, and exponential functions, scatter plots, and inequalities. Basic statistical concepts are covered. Problem solving and use of the graphing calculator are integral parts of the course.
Algebra 2 (532)
Grade 10
Credit 1.0
This course extends the concepts and skills of Algebra 1. Emphasis is placed on finding solutions to linear and quadratic equations, inequalities and systems of equations and inequalities. Various types of functions are presented including linear, quadratic, polynomial, absolute value, exponential and logarithmic. Algebraic properties of the real and complex number systems are incorporated throughout the course. A study of matrix operations, determinants, and conic sections is included along with an overview of series and sequences. Graphing and problem solving techniques are an integral part of the course. The graphing calculator is used extensively.
Honors Algebra 2 (531)
Grade 9, 10
Credit 1.0
Prerequisite: A student in Algebra 1 wishing to register for Honors Algebra 2 must have, at the time of course selection, a 95% or higher average and receive the recommendation of her current teacher. A student in Honors Algebra 1 wishing to register for Honors Algebra 2 must have, at the time of course selection, an 86% or higher average and receive the recommendation of her current teacher. Final year averages must also meet the prerequisite grade requirement.
This course moves at an accelerated pace and extends concepts and skills of Algebra 1. Functions are treated at length in a wide variety of topics, including linear, quadratic, polynomial, absolute value, exponential, and logarithmic. Algebraic properties of both real and complex number systems are studied and used throughout the course. A study of conic sections, quadratic relations, matrix operations, and series and sequences is included. Graphing, problem solving techniques and modeling are an integral part of the course. The graphing calculator is used extensively. Teacher approval required.
Geometry (522)
Grade 10, 11
Credit 1.0
In this course, students explore a broad range of topics in plane and solid geometry. Topics studied include points, lines, planes, triangles, transformations, circles, polygons, areas, and volumes. Students develop deductive and inductive reasoning skills primarily through two-column proofs. Appreciation of the need for precise language is encouraged, and applications to real life situations are made whenever possible.
Honors Geometry (521)
Grade 9, 10, 11
Credit 1.0
Prerequisite: A student in Algebra 2 wishing to register for Honors Geometry must have, at the time of course selection, a 95% or higher average and receive the recommendation of her current teacher. A student in Honors Algebra 2 wishing to register for Honors Geometry must have, at the time of course selection, an 86% or higher average and receive the recommendation of her current teacher. Final year averages must also meet the prerequisite grade requirement.
This accelerated, in-depth course is designed for those students who have excelled in Algebra 1 and Algebra 2 (or concurrently with Honors Algebra 2). Students prove and apply theorems about points, lines, planes, triangles, transformations, circles, polygons, areas and volumes. They develop deductive and inductive reasoning skills that allow them to formulate rigorous two column proofs. Honors Geometry students are exposed to additional methods of proof, including paragraph, flow, and indirect proofs. The use of precise mathematical language is required. Students apply geometric concepts to problem solving. This course emphasizes the cumulative nature of geometry. One section of this course is offered in the summer. See the Summer Study page for further details. Teacher approval required.
Pre-Calculus (548)
Grade 11, 12
Credit 1.0
This is a traditional Pre-Calculus course. In the first semester, emphasis is placed on the trigonometric functions and their graphs. In the second semester, emphasis is placed on linear, quadratic, polynomial, rational, exponential and logarithmic functions and their graphs. The course strives to bring students to an understanding of the connections among the representations of functions graphically, numerically, analytically and verbally. Emphasis is placed more on applications and less on theory. The graphing calculator is used extensively.
Honors Pre-Calculus (541)
Grade 10, 11, 12
Credit 1.0
Prerequisite: A student wishing to register for Honors Pre-Calculus must have the recommendation of her Algebra 2 teacher and her Geometry teacher and
• an 86% or higher in Honors Geometry and an 86% or higher in Honors Algebra 2 OR
• a 95% or higher in Geometry and a 95% or higher in Algebra 2.
These grade requirements apply to both the average at the time of course selection and the final year average.
This course is offered to students who have demonstrated excellent mathematical ability in Algebra 1, Algebra 2, and Geometry and are capable of moving at an accelerated pace. In the first semester, emphasis is placed on the trigonometric functions and their graphs. In the second semester, emphasis is placed on linear, quadratic, polynomial, rational, exponential and logarithmic functions and their graphs. Students will be introduced to both the intuitive and computational approach to determining the limit. The course strives to bring students to an understanding of the connections among the representations of functions graphically, numerically, analytically and verbally. The use of the graphing calculator is an integral part of the course. Teacher approval required.
Honors Calculus (552)
Grade 11, 12
Credit 1.0
Prerequisite: A student wishing to register for Honors Calculus must have the recommendation of her current teacher.
This course is designed for those students who show aptitude in mathematics, have successfully completed Pre- Calculus and are capable of moving at an accelerated pace. Students study limits and continuity, derivatives, the definite and indefinite integral, area, volume, and a variety of applications. Emphasis is placed on the ways that concepts, problems and results can be expressed geometrically, numerically, analytically and verbally. Interpreting results, explaining solutions and justifying conclusions are desired goals. The use of the graphing calculator is an integral part of the course. Teacher approval required.
AP Calculus AB (550)
Grade 11, 12
Credit 1.0
Advanced Placement Prerequisite: A student wishing to register for Advanced Placement Calculus AB must have a 90% or higher average in each semester of Honors Pre-Calculus and receive the recommendation of her current teacher.
Advanced Placement Calculus follows the College Board guidelines and is designed for those students who wish to earn college credit while still in secondary school. The course emphasizes the variety of ways that concepts, problems and results can be expressed: geometrically, numerically, analytically and verbally. The interconnectedness of these representations is very important. Students study the themes of limits, derivatives, integrals, approximation, applications and modeling. Interpreting results, explaining solutions and justifying conclusions are desired goals. The use of the graphing calculator is an integral part of the course. A summer assignment must be completed. Students are required to take the Advanced Placement Examination in AP Calculus AB in May. Teacher approval required.
AP Calculus BC (560)
Grade 11, 12
Credit 1.0
Prerequisite: A student wishing to register for Advanced Placement Calculus BC must have completed AP Calculus AB and have the recommendation of the AP Calculus AB teacher.
This course is designed for the student who has successfully completed AP Calculus AB and wishes to continue her study of Calculus. The topic outline for Calculus BC includes all Calculus AB topics. Students independently review all topics in differential calculus. AP Calculus BC focuses heavily on integral calculus, building on basic skills in order to extend to more advanced techniques and applications. Additional topics are: parametric, polar and vector functions and their derivatives and integrals, analysis of planar curves, numerical solution of differential equations using Euler’s Method, logistic differential equations, and sequences and series and their applications to polynomial approximation, convergence, divergence, and error analysis. A summer assignment must be completed. Students are required to take the Advanced Placement Examination in AP Calculus BC in May. Teacher approval required.
Statistics (547)
Grade 11, 12
Credit 1.0
This course provides a foundation for college statistics courses and develops the student’s ability to understand data in the world at large. The four major themes of statistics are presented more through activities than theory. Students will develop their ability to gather, organize, interpret, and present data, as well as learn how to use the basic tools of probability to draw inferences about populations. The graphing calculator, applets and MINITAB statistical software are used as computational/analytical tools. Projects, laboratories, and group problem solving are incorporated to assist the students to master the concepts.
Honors Statistics (545)
Grade 11, 12
Credit 1.0
Prerequisite: A student wishing to register for Honors Statistics must have the recommendation of her current teacher.
This year-long course is divided into four major themes. Part 1 covers exploratory data analysis, that is, using graphical and numerical techniques to study patterns and departures from patterns; Part 2 emphasizes the importance of data collection according to a well-developed plan of design; Part 3 focuses on the study of probability as a tool for anticipating what a distribution should look like under a given model; Part 4 covers the methods of statistical inference as a guide in the selection of an appropriate model. The graphing calculator, applets and MINITAB statistical software are used as computational/analytical tools. Projects, laboratories, group problem solving, and writing tasks are integral to the concept oriented instruction and assessment. Teacher approval required.
AP Statistics (540)
Grade 11, 12
Credit 1.0
Prerequisite: A student wishing to register for Advanced Placement Statistics must have the recommendation of her current teacher.
Advanced Placement Statistics follows the College Board guidelines and is designed for those students who wish to earn college credit while still in secondary school. The topics in this accelerated course are divided into four major themes. Part 1 covers exploratory data analysis, that is, using graphical and numerical techniques to study patterns and departures from patterns; Part 2 emphasizes the importance of data collection according to a well-developed plan or design so that valid data are obtained; Part 3 focuses on the study of probability as a tool for anticipating what a distribution should look like under a given model; Part 4 covers the methods of statistical inference as a guide in the selection of an appropriate model. Important components of the course include: the use of technology (graphing calculator, applets, and statistical software), projects and laboratories, cooperative group problem solving, and writing as part of concept-oriented instruction and assessment. This approach allows students to build interdisciplinary connections with other subjects and with the outside world. A summer assignment should be expected. Students are required to take the Advanced Placement Examination in May. Teacher approval required.
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