Math

Grade: 9
Year: 1.0 Math credit

The fundamental purpose of this course is to formalize and extend the mathematics that students learned in the middle grades. The content of Algebra 1 deepens and extends students’ understanding of linear and exponential relationships by contrasting them with each other and identifying and exploring their underlying mathematical structures. Students explore many examples of functions, including sequences, and analyze them graphically, numerically, symbolically, and verbally, making connections between them and identifying the strengths and weakness of these forms. Extending the statistics studied in Grade 8, students apply linear models to data that exhibit a linear trend, and mathematically analyze how well the model fits the data. Additionally, students engage in methods for analyzing, solving, and applying quadratic functions and become familiar with the usefulness of multiple forms of quadratic functions. The Mathematical Practice Standards are applied to the content of this course, allowing students to experience Algebra 1 as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. Summer work for this course can be found on the school website.

Grades: 10, 11
Year: 1.0 Math credit
Prerequisite: Geometry
Required: Graphing Calculator

Building on their work with linear, quadratic, and exponential functions, students extend their reper- toire of functions to include polynomial and radical functions. Students work closely with the expressions that define the functions and continue to expand their abilities to model situations and to solve equations, including solving quadratic equations over the set of complex numbers and solving exponential equations using the properties of logarithms. Functions are studied in relation to one another by analysis of multiple representations of functions with unrestricted domains, as well as those with restricted domains. Additionally, students extend their understanding of the trigonometric ratios and circles from geometry and use the coordinate plane to model periodic phenomena with trigonometry. Students further develop their statistical knowledge by studying the collection, analysis, and interpretation of data and the connections to probability. The Mathematical Practice Standards are applied to the content of this course, allowing students to experience Algebra 2 as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.

Grades: 9, 10, 11
Year: 1.0 Math credit
Prerequisite: Geometry/Pre-Calculus Honors or teacher recommendation
Required: Graphing Calculator

For students interested in studying Advanced Placement Calculus in high school and/or STEM-related careers post-graduation, condensed courses are offered so that students do not need to take two math classes in one year. In this more rigorous and fast-paced course, students will study all the content of the Algebra 2 course as outlined above. Additionally, the Pre-Calculus topics that connect mathematically to the concepts of the Algebra 2 course will be included. These topics include but are not limited to parametric equations, a deeper study of rational and logarithmic functions, trigonometric functions & identities, and limits. The Mathematical Practice Standards will again be an integral part of the course, supporting students in having conceptual understanding, procedural skill and fluency, and an ability to fully apply their understanding of mathematics.

Grades: 11, 12
Year: 1.0 Math credit
Prerequisite: College Algebra and College Trigonometry, Trig/Pre-Calculus Honors, or Algebra 2/Precalculus Honors
Required: Summer coursework

This course emphasizes a multi-representational approach to calculus, with results and problems being expressed graphically, numerically, analytically, and verbally. Topics include graphs and limits, differentiation, applications of differentiation, integration, and applications of integration. The pace and rigor of instruction will be geared toward preparing students for the AP exam, which they are expected to take in the Spring. Students should expect 1.5 hours of homework per class session and/or teacher led outside-of-class AP study sessions. Summer work for this course can be found on the school website.

Grades: 11, 12
Year: 1.0 Math credit
Prerequisite: Algebra 2/Pre-Calculus Honors, Trig/Pre-Calc Honors, and teacher recommendation

This is the more rigorous of the two AP calculus courses we offer. Students will learn both the theoretical foundations and proper techniques of both differential and integral calculus and apply them extensively in problem-solving contexts. The pace and rigor of instruction will be geared toward preparing students for the AP exam, which they are expected to take in the Spring. Students should expect 1.5 hours of homework per class session and/or teacher led outside-of-class AP study sessions. Summer work for this course can be found on the school website.

Grades: 10, 11, 12
Year: 1.0 Math credit
Prerequisite: Algebra 2
Required: Graphing Calculator

The AP Precalculus course is designed for students to have a capstone experience of their learning through Algebra, Geometry and Algebra 2, while also focusing on preparing them for future courses, specifically AP Calculus AB/BC. This course applies real-world model- ing situations and develops a deeper conceptual understanding of polynomial, rational, exponential, logarithmic, trigonometric, and polar functions. This includes compositions, inverses and transformations using graphical, numerical, verbal, and analytical representations. Research shows that deepening student understanding of functions and their graphs and understanding the relationships between these two best supports the student in preparing for calculus. Units of study also include limits, vectors, and matrices. Before taking this course, students should be proficient in solving equations of all types using a variety of techniques.

Grades: 11, 12
Year: 1.0 Math credit
Prerequisite: Algebra 2

This is an advanced course in statistics. Topics include exploratory analysis of data, planning a study and collection of data, and producing statistical models using probability distributions and statistical inference. The pace and rigor of instruction will be geared toward preparing students for the AP exam, which they are expected to take in the Spring. Exam fees apply. Students should expect 1.5 hours of homework per class session and/or teacher led outside-of-class AP study sessions.

Grades: 11, 12
Semester: 0.5 Math credit
Prerequisite: Algebra 2
Required: Graphing Calculator
*To receive CE credit, student must have grade waiver or qualifying score (Accuplacer, ACT, AP, SAT)

This course aligns with the Colorado Community College course. Students who earn a C or better in the class will receive 4 community college credits. These are guaranteed transfer credits to public colleges and universities in Colorado. This course will cover advanced math topics necessary for college success in math or non-math related majors. Topics studied include graphs and applications of linear, quadratic, polynomial, and exponential functions; conic sections probability and statistics; and elementary trigonometry. Topics such as graphing of conic sections, introductions to sequences and series, permutations and combinations, the binomial theorem, and theory of equations will be included.

Grades: 12
Year: 1.0 Math credit
Prerequisite: Algebra 2
Required: Graphing Calculator
*To receive CE credit, student must have grade waiver or qualifying score (Accuplacer, ACT, AP, SAT)

This course aligns with the Colorado Community College course. Students who earn a C or better in the class will receive 4 community college credits. These are guaranteed transfer credits to public colleges and universities in Colorado. This course will cover advanced math topics necessary for college success in math or non-math related majors. Topics studied include graphs and applications of linear, quadratic, polynomial, and exponential functions; conic sections; probability and statistics; and elementary trigonometry. Topics such as graphing of conic sections, introductions to sequences and series, permutations and combinations, the binomial theorem, and theory of equations will be included.

Grades: 11, 12
Semester: 0.5 Math credit
Prerequisite: CE College Algebra Required: Graphing Calculator
*Must meet minimum scores on Accuplacer, ACT-M, or SAT-M

This course aligns with the Colorado Community College course. Students who earn a C or better in the class will receive 3 community college credits. These are guaranteed transfer credits to public colleges and universities in Colorado. This course includes trigonometric functions (with graphs and inverse functions), identities and equations, solutions of triangles, complex numbers, and other topics as time permits. This is a traditional prerequisite course to the calculus sequence.

Grade: 12
Semester: 0.5 Math credit
Prerequisite: CE College Algebra
*To receive CE credit, student must have grade waiver or qualifying score (Accuplacer, ACT, AP, SAT)

This course aligns with the Colorado Community College course. Students who earn a C or better in this class will receive 3 Community College credits. These are guaranteed transfer credits to public colleges and universities in Colorado. This course explores and applies data presentation and summarization, introduction to probability concepts and distributions, statistical inference-estimation, hypothesis testing, comparisons of populations, correlation, and regression. Students will use statistical software and the World Wide Web to engage in an active, visual approach to the topics covered. Students will work with real world data on problems of a practical nature.

Grade: 9, 10
Year: 1.0 Math credit
Prerequisite: Algebra 1

The high school Geometry course formalizes and extends students’ geometric experiences from the middle grades. Students explore more complex geometric situations and deepen their explanations of geometric relations, moving toward formal mathematical arguments. In this course, rigid and non-rigid transformations (including translations, reflections, rotations, and dilations) are the frame through which students build and prove the concepts of congruence and similarity. Students apply similar reasoning to geometric constructions. Previous experiences with proportional reasoning and the Pythagorean Theorem lead students to understand the trigonometry of right triangles to find unknown measures in general triangles. The geometry of two- and three-dimensional figures is the focus, including work and analysis in the coordinate plane. The Mathematical Practice Standards are applied to the content of this course, allowing students to experience Geometry as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. Summer work for this course can be found on the school website.

Grades: 9, 10
Year: 1.0 Math credit
Prerequisite: Algebra 1
Required: Graphing Calculator

For students interested in studying Advanced Placement Calculus in high school and/or STEM-related careers post-graduation, condensed courses are offered so that students do not need to take two math classes in one year. In this more rigorous and fast-paced course, students will study all the content of the geometry course as outlined above. Additionally, the Pre-Calculus topics that connect mathematically to the concepts of the geometry course will be included. These topics include but are not limited to vectors, trigonometry, parametric equations and graphs, and polar equations and graphs. The Mathematical Practice Standards will again be an integral part of the course, supporting students in having conceptual understanding, procedural skill and fluency, and an ability to fully apply their understanding of mathematics. Summer work for this course can be found on the school website.

Grades: 11, 12
Year: 1.0 Math credit
Prerequisite: Algebra 2
Required: Graphing Calculator

This course is a further exploration of the algebra of the real number system with extension into complex numbers. It will emphasize problem-solving with further study of equations, slopes, inequalities, systems of equations, polynomials, quadratic equa- tions, rational expressions, rational exponents, radical expressions, graphing, and applications. The course is designed to prepare students to successfully take a college algebra course either at the high school level (as concurrent enrollment with CCA) or at the college they choose to attend.

*This class will not count as an additional core year for NCAA Clearinghouse if the student has completed Algebra 2.

Grade: 10, 11
Year: 1.0 Math credit
Prerequisite: Acceptance to IB program
Required: Graphing Calculator

This course is designed for students who enjoy describing the real world and solving practical problems using mathematics; those who are interest- ed in harnessing the power of technology alongside exploring mathematical models and enjoy the more practical side of mathematics. This course is part of a 2-year curriculum that prepares students to take the IB Mathematics Applications Standard level test in the Spring of the 2nd year.

Grades: 11, 12
Year: 1.0 Math credit
Prerequisite: IB Math SL 1 Applications
Required: Graphing Calculator

This course is designed for students who enjoy describing the real world and solving practical problems using mathematics; those who are interest- ed in harnessing the power of technology alongside exploring mathematical models and enjoy the more practical side of mathematics. Students enrolled in this course take the IB Mathematics Applications Standard level test in the Spring.

Grades: 10, 11
Year: 1.0 Math credit
Prerequisite: Acceptance to the IB program
Required: Graphing Calculator

This course is intended for students who wish to pursue studies in mathematics at university or subjects that have a large mathematical content; it is for students who enjoy developing mathematical arguments, problem solving and exploring real and abstract applications, with and without technology. This course is part of a 2-year curriculum that prepares students to take the IB Mathematics Analysis Stan- dard level test in the Spring of the 2nd year.

Grades: 11, 12
Year: 1.0 Math credit
Prerequisite: IB Math SL 1 Analysis
Required: Graphing Calculator

This course is intended for students who wish to pursue studies in mathematics at university or subjects that have a large mathematical content; it is for students who enjoy developing mathematical arguments, problem-solving, and exploring real and abstract applications, with and without technology. Students enrolled in this course take the IB Mathe- matics Analysis Standard level test.

Grade: 11
Year: 1.0 Math credit
Prerequisite: Acceptance to the IB program
Required: Graphing Calculator

This course is intended for students who wish to pursue studies in mathematics at university or subjects that have a large mathematical content; it is for students who enjoy developing mathematical arguments, problem-solving, and exploring real and abstract applications, with and without technology. This course coincides with AP Calculus BC and is part of a 2-year curriculum that prepares students to take the IB Mathematics Analysis Higher level test in the Spring of the 2nd year.

Grade: 12
Year: 1.0 Math credit
Prerequisite: IB Math HL 1 Analysis or AP Calculus BC
Required: Graphing Calculator

This course is intended for students who wish to pursue studies in mathematics at university or subjects that have a large mathematical content; it is for students who enjoy developing mathematical arguments, problem-solving, and exploring real and abstract applications, with and without technology. Students enrolled in this course take IB Mathematics Analysis Higher level test in the Spring.