Mathematics

This course focuses on solidifying students’ skills learned at the elementary level. In teaching new material, emphasis is placed on collaborative learning, skill automacy, and problem solving. Students are encouraged to support their solutions with work and to explain their reasoning and approach to problems. This course aims to develop strong skills that allow students to take risks and feel confident in their mathematical abilities.

Overview of Topics

• Operations with whole numbers, fractions, and decimals 
• Patterns and algebraic thinking
• Statistics
• Geometry
• Word problems

Signature Activities

• Fenway Park (exposure to statistics through baseball)
• deCordova Sculpture Park (exploring geometric shapes through sculpture)
• Guild Hall (applying logic and math to building robots)

Texts and Other Resource Materials

• Math: Course I, Larson et. al, McDougal Littell 
• Math Department Practice Problems
• IXL skill workbooks

• Operations with whole numbers, fractions, and decimals
• Order of operations
• Algebraic thinking
• Angles and geometry in two dimensions
• Word problems

Signature Activities

• Boston (exploring Mathematics along the Freedom Trail)
• Interdisciplinary project with the Wellness Department involving cooking and fractions

Texts and Other Resource Materials

• Math: Course II, Larson et. al., McDougal Littell
• Math Department practice problems

This course covers a range of essential topics, including operations with integers, fractions, and decimals. Students learn the order of operations and explore the properties of rational numbers. They also study exponent rules, such as product and quotient properties, for both positive and negative exponents. Emphasis is placed on solving multi-step equations and inequalities involving integers, fractions, and decimals. Students work with conversion factors and scale conversions, applying these concepts to ratios and proportions. Additionally, they study percentages and their practical applications. The curriculum focuses on problem-solving, reading comprehension, and mathematical communication. The classroom fosters both independent and collaborative modes of learning.

Overview of Topics

• Operations with whole numbers, fractions, and decimals
• Order of operations
• Algebraic thinking 
• Properties of exponents
• Percentages
• Word problems

Signature Activities

• Boston (exploring Mathematics along the Freedom Trail)
• Interdisciplinary project with the Wellness Department involving cooking and fractions

Texts and Other Resource Materials

• Mathtastic! Volume 1, Steimle and Tavares
• Math Department practice problems 

In this course, students strengthen their foundational math skills while being introduced to pre-algebra concepts. Topics include integers, absolute value, and the order of operations. Students learn to work with simple variable expressions using addition, multiplication, and the distributive property, and begin solving one- and two-step equations involving whole numbers, decimals, and fractions. Students also develop problem-solving strategies by analyzing word problems, defining variables, and setting up equations. The course introduces exponents, polynomial expressions, and an early look at linear relationships through graphing and writing equations. Percentages and inequalities are explored to support real-world applications and mathematical reasoning further. Throughout the course, emphasis is placed on understanding concepts, practicing skills, and developing mathematical confidence. Students are encouraged to ask questions, collaborate with peers, and build habits of persistence and accuracy as they prepare for future algebra coursework.

Overview of Topics 

• Expressions and equations 
• Inequalities
• Properties of exponents
• Percentages 
• Operations with polynomials
• Word problems

Signature Activities

• Math Trails (Boston): Students stop at a variety of sites to explore Mathematics in Boston
• Scale drawing project involving proportions 

Texts and Other Resource Materials

• Pre-Algebra, Larson et. al, McDougal Littell
• Math Department practice problems 

In this course, students build on their foundational math skills while being introduced to key algebraic concepts. Topics covered include integers, absolute value, and the order of operations. Students learn to simplify variable expressions using addition, multiplication, and the distributive properties. They also tackle multi-step equations and inequalities involving decimals and fractions. With these skills, students analyze word problems, define variables, set up equations, and solve them. The curriculum introduces exponent and polynomial operations, as well as graphing
and writing equations for linear functions. Additionally, students work with percentages and inequalities to enhance their problem-solving abilities.

Overview of Topics

• Expressions and equations
• Inequalities
• Properties of exponents
• Percents
• Operations with polynomials
• Word problems

Signature Activities

• Math Trails (Boston): Students stop at a variety of sites to explore mathematics in Boston
• Scale Drawing Project involving proportions 

Texts and Other Resource Materials

• Pre-Algebra, Larson et. al., McDougall Littell
• Math department practice problems

This course delves into a broad range of mathematical concepts, including both positive and negative numbers, rational numbers, and various operations involving equations and inequalities. Their studies encompass an exploration of polynomials, fractions, decimals, and percents, along with an introduction to probability. The curriculum integrates key elements from algebra, geometry, number theory, and trigonometry, providing a comprehensive foundation in these disciplines. Emphasis is placed on developing deductive reasoning skills, enabling students to approach mathematical problems with logical precision. Throughout the course, students engage in independent work as well as collaborative projects in small groups. They receive close guidance and supervision to ensure a thorough understanding of the material and to support their problem-solving processes. This approach helps students build confidence and mastery in their mathematical abilities.

Overview of Topics

• Expressions and equations
• Inequalities 
• Properties of exponents
• Percents
• Operations with polynomials
• Word problems 
• 3D Geometry 
• Probability

Signature Activities

• Math Trails (various locations): Students stop at a variety of sites off campus to explore mathematics
• Scale Drawing Project involving proportions

Texts and Other Resource Materials

• Mathtastic! Volume 2, Steimle and Tavares
• Math Department practice problems

The goal of this course is to build upon pre-Algebra topics and skills. The course begins with a review of summer assignments and a diagnostic exam, setting the stage for the first semester focused on linear topics. Students engage in studying expressions, performing operations with negative numbers, distributing, and solving linear and absolute value equations and inequalities. They also tackle systems of equations and various word problems. When needed,
additional scaffolding is offered to support students as they wrestle with multilevel problems. As the course progresses into the second semester, students shift their focus to the properties of exponents and operations with polynomials. The nature of quadratics is explored. Throughout the course, the concept of functions is introduced and integrated into their study of algebraic principles.

Overview of Topics

• Expressions and equations
• Inequalities and absolute value equations/inequalities 
• Linear functions
• Systems of equations
• Properties of exponents 
• Operations with polynomials
• Word problems 
• Quadratic functions and equations
• Factoring
• Function notation

Signature Activities

• Jewelry making project, involving systems of equations
• Interdisciplinary project with the Art Department featuring stained glass window design that utilizes linear and quadratic functions
• Linear graphing with Desmos Project

Texts and Other Resource Materials 

• Algebra I: Structure and Method, Brown et. al, Houghton Mifflin 
• Math Department practice problems

The primary goal of this course is to build students' confidence and refine their skills in solving fundamental algebraic problems. The course begins with a review of summer assignments and a diagnostic exam, setting the stage for the first semester focused on linear topics. Students engage in studying expressions, performing operations with negative numbers, distributing, and solving linear and absolute value equations and inequalities. They also tackle systems of equations and various word problems. As the course progresses into the second semester, students shift their focus to the properties of exponents and operations with polynomials. They learn how to factor and solve quadratic equations and explore operations with radicals and rational algebraic expressions. Additionally, students solve equations involving both rational and radical expressions. Throughout the course, the concept of functions are introduced and integrated into their study of algebraic principles. More complex problems are covered in the
accelerated course.

Overview of Topics

• Expressions and equations
• Inequalities and absolute value equations/inequalities
• Linear functions
• Properties of exponents
• Systems of equations
• Operations with polynomials
• Word problems
• Quadratic functions and equations
• Factoring
• Function notation

Signature Activities

• Jewelry making project, involving systems of equations
• Interdisciplinary project with the Art Department featuring stained glass window design that utilizes linear and quadratic functions
• Linear graphing with Desmos Project

Texts and Other Resource Materials

• Algebra I: Structure and Method, Brown et. al, Houghton Mifflin
• Math Department Practice Problems

This course provides a comprehensive study of first-year Algebra concepts. It is designed to prepare students for subsequent course work in geometry and second-year algebra. Topics include numbers and equations, solving multi-layered linear equations and inequalities, solving absolute value equations and inequalities, graphing and writing linear functions, systems of equations, properties of exponents, polynomial operations, factoring, solving polynomial equations by factoring, completing the square and the quadratic formula, graphing and writing quadratic functions, operations with rational and radical expressions, and solving rational and radical equations. By the end of the year, students are able to apply algebraic skills to a myriad of both linear and quadratic word problems. Emphasis is placed on developing a strong foundation upon which future mathematics can be built. Prerequisite: Pre-Algebra

This course continues students’ comprehensive study of algebraic concepts. Students engage in problem solving, small group work, and lectures to solidify their comprehension of Algebra I concepts including linear equations and inequalities, solving and graphing systems of equations, and quadratics. Students explore functions extensively, namely piecewise, polynomial, rational, exponential, polynomial, radical, and logarithmic functions. Inverse functions are introduced along with complex numbers. When time allows, students may also explore probability and statistics. All concepts are applied to a variety of real-life situations through word problems and the use of interactive technology tools. Students emerge from this course with proficiency in graphing functions and solving a host of equations. Prerequisite: Algebra I

This course continues students’ comprehensive study of algebraic concepts. Students engage in problem solving, small group work, and lectures to solidify their comprehension of Algebra I concepts including linear equations and inequalities, solving and graphing systems of equations, and quadratics. Students explore functions extensively, namely piecewise, polynomial, rational, exponential, polynomial, radical, and logarithmic functions. Inverse functions are introduced along with complex numbers. When time allows, students may also explore probability and statistics. All concepts are applied to a variety of real-life situations through word problems and the use of interactive technology tools. Students emerge from this course with proficiency in graphing functions and solving a host of equations. Conic sections are explored. At the honors level, students are expected to engage in a deeper level of abstraction at a significantly faster pace. Assessments include multiple unfamiliar problems to which students must apply innovative thinking in order to solve.
Prerequisite: Successful completion of placement test or attain an A test average in Algebra I or B test average in Accelerated Algebra I 

This course in Euclidean Geometry provides students with the ability to explore the mathematical concepts of two and three dimensional space and shapes through reasoning, analyzing, classifying, and synthesizing. Students first become familiar with geometric building blocks and geometric constructions. They continue with the study of triangle congruence, quadrilaterals, similarity, transformation, Pythagorean Theorem, trigonometry, area, volume, and circles. Students apply algebraic skills in problem solving and employ the principles of logic by writing formal deductive geometric proofs. Students experience a variety of learning styles including direct instruction, independent learning, and group work. To develop logic and critical thinking skills, students are exposed to technological tools and manipulatives as they discern geometric relationships. This course places less emphasis on proofs than other geometry courses and takes more time to review algebraic skills as they are applied to geometric problems. Student-centered learning is emphasized. 
Departmental approval required

This course in Euclidean Geometry provides students with the ability to explore the mathematical concepts of two and three dimensional space and shapes through reasoning, analyzing, classifying, and synthesizing. Students first become familiar with geometric building blocks and geometric constructions. They continue with the study of triangle congruence, quadrilaterals, similarity, transformation, Pythagorean Theorem, trigonometry, area, volume, and circles. Students apply algebraic skills in problem solving and employ the principles of logic by writing formal deductive geometric proofs. Students experience a variety of learning styles including direct instruction, flipped instruction, independent learning, and group work. To develop logic and critical thinking skills, students are exposed to technological tools and manipulatives as they discern geometric relationships. 
Prerequisite: Algebra I 

This course in Euclidean Geometry provides students with the ability to explore the mathematical concepts of two and three dimensional space and shapes through reasoning, analyzing, classifying, and synthesizing. Students first become familiar with geometric building blocks and geometric constructions. They continue with the study of triangle congruence, quadrilaterals, similarity, transformation, Pythagorean Theorem, trigonometry, area, volume, and circles. Students apply algebraic skills in problem solving and employ the principles of logic by writing formal deductive geometric proofs. Students experience a variety of learning styles including direct instruction, independent learning, and group work. To develop logic and critical thinking skills, students are exposed to technological tools and manipulatives as they discern geometric relationships. At the honors level, proofs are studied more extensively than they are at other levels. Students are expected to engage in a deeper level of abstraction at a significantly faster pace. Assessments include multiple unfamiliar problems to which students must apply innovative thinking to reach solutions.
Prerequisite: Attain an A test average in Algebra II or a B test average in Honors Algebra II

In this course, students continue to study polynomial, exponential, and logarithmic functions in greater depth. Additionally, a full semester of trigonometry is examined. Students explore the laws of sine and cosine, solve a full complement of trigonometric equations, graph trigonometric functions, prove trigonometric identities, and apply these skills to modeling problems. Following this, limits are introduced. Graphing calculators are used throughout the course to reinforce comprehension and to solve real-world problems. More traditional analytic and algebraic problem solving methods are emphasized so that students understand multiple approaches to problems from different vantage points. The course equips students with the necessary skills and knowledge to pursue advanced mathematics.  
Prerequisites: Algebra II and Geometry or Principles of Geometry

In this course, students continue to study polynomial, exponential, and logarithmic functions in greater depth. Additionally, a full semester of trigonometry is examined. Students explore the laws of sine and cosine, solve a full complement of trigonometric equations, graph trigonometric functions, prove trigonometric identities, and apply these skills to modeling problems. Following this, limits are introduced. Graphing calculators are used throughout the course to reinforce comprehension and to solve real-world problems. More traditional analytic and algebraic problem-solving methods are emphasized so that students understand multiple approaches to problems from different vantage points. The course equips students with the necessary skills and knowledge to pursue advanced mathematics. The honors level covers additional trigonometric topics as well as sequences and series. Students are expected to engage in a deeper level of abstraction at a significantly faster pace. Assessments include multiple unfamiliar problems to which students must apply innovative thinking to reach solutions. 
Prerequisite: Attain an A test average in Geometry or a B test average in Honors Geometry

This is a foundational course, playing an important role in the understanding of science, engineering, economics, and computer science, among other disciplines. Students in Calculus begin by studying limits, and then couple that learning with their understanding of slope and area to develop the concepts of derivatives and integrals. Study of these concepts includes learning to differentiate and integrate functions introduced in previous courses. Topics covered include continuity, tangent lines, the limit definition of derivative and derivative rules, implicit differentiation, related rate applications, curve sketching and graph analysis, anti-derivative and integration techniques, and area and volume of solids of revolution. Students emerge from the course prepared to pursue a more in-depth study of calculus in college. 
Prerequisite: PreCalculus

This 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 include limits and continuity, differentiation rules, application to graphing, related rates, approximations, extremum problems, definite and indefinite integration, the Fundamental Theorem of Calculus, area, volume, techniques of integration, and L’Hôspital’s Rule. Throughout the course, graphing calculators are used as a tool to enhance understanding of concepts and to facilitate problem solving. Students are expected to take the AP exam in May. 
Prerequisite: Attain an A test average in PreCalculus or a B test average in Honors PreCalculus

This course continues the study of AP Calculus AB. Additional topics in the AP curriculum encompass integration by parts, integration using partial fractions, Euler's method and logistic models with differential equations, arc length, distance traveled along a smooth curve, parametric equations, polar coordinates, vector-valued functions, and infinite sequences and series. Moreover, the course explores concepts taught in traditional college courses that do not appear in the AP curriculum. These include, but are not limited to: integration by trigonometric substitution, powers of sine, cosine, tangent, and secant, the epsilon-delta definition of a limit, proofs of numerous theorems including the product and quotient rules, volume using shells, Simpson’s rule, Newton’s method, and logarithmic differentiation. Students are expected to take the AP exam in May.
Prerequisite: Departmental recommendation

This is an introductory college-level statistics course that introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students cultivate their understanding of statistics using technology, investigations, problem solving, and writing as they explore four main areas of study: quantitative and categorical data analysis, designing studies, probability, and statistical inference. Students are asked to both analyze and infer about applicable data sets from many sources. Topics include graphing, density curves, linear regression, analyzing and comparing distributions, observational studies, experiments, probability, random variables, binomial and geometric distributions, sampling distributions, confidence intervals, significance tests, and linearizing nonlinear data. Students are expected to take the AP exam in May.
Prerequisite: Attain a B+ test average in PreCalculus or a B- test average in Honors PreCalculus

This course offers students the opportunity to apply statistics and previously mastered algebraic concepts to solve real-world problems with a financial focus. Students explore algebraic patterns and functions in financial contexts and apply these skills to research topics of personal interest. Core concepts include function analysis, systems of equations, graphing, statistics, linear regression, variables, and mathematical modeling. While emphasizing applied mathematics, the course also engages students in discussions about the economic and societal factors that shape financial systems. Students reflect on how these realities intersect with the goals of a Sacred Heart education and the principles of Catholic Social Teaching. This project-based course places financial applications at its center. Project topics include loans, investments, credit, insurance, taxes, employment, and budgeting. By the end of the year, students gain a strong foundation in financial literacy, equipping them to enter college as informed and responsible individuals. 
Open to students in Grade 12