Explore Our Curriculum

Mathematics

  • Algebra I

    “Algebra is like a treasure hunt; we’re always trying to find X,” said a young math student. Students discover how non-numerical symbols (variables) can be used as placeholders for unknown numerical quantities. The class builds upon a basic understanding of pre-algebraic concepts, including equations, graphs, and symbolic rules. Students build an understanding of mathematical relationships, including linear and exponential equations, systems of equations, inequalities, factoring, and quadratic equations. These topics establish a foundation of algebraic skills for future mathematics studies, preparing students for Geometry and Algebra II, as well as the SAT and ACT. Students have the opportunity to solve application-based problems and improve their ability to communicate mathematically. This is a High School math class; Middle School students who complete the course successfully earn High School credit.

  • Algebra II

    This course extends and deepens work done in Algebra I and prepares students for future math courses. They will gain proficiency in working with polynomials, complex numbers, radical expressions, rational expressions, exponential and logarithmic expressions; the emphasis is on solving equations and written and verbal expressions. Students will master creating and interpreting graphical representations of linear, quadratic, polynomial, rational, exponential, and logarithmic functions and explore their use in modeling phenomena in a variety of contexts. Students work with graphing calculators to deepen the connections between equations and graphs. Students must have an approved graphical display calculator for daily use (such as a TI-84 Plus).

  • Geometry

    In Ancient Greece, Geometry was used to reveal the rational structure of the universe. Ancient Romans used it to build architectural marvels.  In Austin, Texas, at Headwaters School, students are presented with mathematics from a similar discovery perspective as those ancient civilizations.  The class uses a problem-based learning approach. We examine a series of questions that scaffold to a larger understanding of concepts. We are striving to discover geometry in a similar manner as those first mathematicians.  The course empowers students to examine their own understanding, prove their logic, ask questions, and accept that getting things wrong is a step toward understanding. Through this process, we analyze the properties of lines, triangles, polygons, circles, and other shapes with rigor and precision.  Our end goal for students is for them to have a deeper understanding of geometric concepts. And beyond that, they should emerge as profoundly critical thinkers and problem solvers.

  • IB Mathematics: Analysis HL I

    Prerequisite: Pre-Calculus

    This course recognizes the need for analytical expertise in a world where innovation is increasingly dependent on a deep understanding of mathematics. This course includes topics that are both traditionally part of a pre-university mathematics course (for example, functions, trigonometry, calculus) as well as topics that are amenable to investigation, conjecture, and proof, for instance the study of sequences and series at both SL and HL, and proof by induction at HL. The course allows the use of technology, as fluency in relevant mathematical software and hand-held technology is important regardless of the choice of course. However, Mathematics: Analysis and Approaches has a strong emphasis on the ability to construct, communicate, and justify correct mathematical arguments.

     

  • IB Mathematics: Analysis HL II

    Prerequisite: Pre-Calculus

    This course recognizes the need for analytical expertise in a world where innovation is increasingly dependent on a deep understanding of mathematics. This course includes topics that are both traditionally part of a pre-university mathematics course (for example, functions, trigonometry, calculus) as well as topics that are amenable to investigation, conjecture, and proof, for instance the study of sequences and series at both SL and HL, and proof by induction at HL. The course allows the use of technology, as fluency in relevant mathematical software and hand-held technology is important regardless of the choice of course. However, Mathematics: Analysis and Approaches has a strong emphasis on the ability to construct, communicate, and justify correct mathematical arguments.

  • IB Mathematics: Applications SL I

    Prerequisite: Geometry and Algebra II

    This course recognizes the increasing role that mathematics and technology play in a diverse range of fields in a data-rich world. As such, it emphasizes the meaning of mathematics in context by focusing on topics that are often used as applications or in mathematical modeling, such as statistics. To give this understanding a firm base, this course also includes topics that are traditionally part of a pre-university mathematics course, such as trigonometry and calculus. The course makes extensive use of technology to allow students to explore and construct mathematical models. Mathematics: Applications and Interpretation will develop mathematical thinking, often in the context of a practical problem, and use technology to justify conjectures.

     

  • IB Mathematics: Applications SL II

    Prerequisite: Geometry and Algebra II

    This course recognizes the increasing role that mathematics and technology play in a diverse range of fields in a data-rich world. As such, it emphasizes the meaning of mathematics in context by focusing on topics that are often used as applications or in mathematical modeling, such as statistics. To give this understanding a firm base, this course also includes topics that are traditionally part of a pre-university mathematics course, such as trigonometry and calculus. The course makes extensive use of technology to allow students to explore and construct mathematical models. Mathematics: Applications and Interpretation will develop mathematical thinking, often in the context of a practical problem, and use technology to justify conjectures.

  • Introductory Statistics

    In Introductory Statistics, you'll explore how we collect, analyze, and interpret data to make informed decisions. We'll start by examining different methods for sampling and gathering data, and move on to descriptive statistics to summarize and understand datasets. You'll learn about probability theory, covering both discrete and continuous random variables, and explore the normal distribution and its significance.

    As we progress, we'll delve into the Central Limit Theorem, a cornerstone of statistical inference, and apply this understanding to construct confidence intervals and perform hypothesis testing. We’ll also investigate the chi-squared distribution and its applications in categorical data analysis. Additionally, we'll explore linear regression and correlation to model relationships between variables, and understand the F distribution and one-way ANOVA for comparing means across multiple groups. By the end of the course, you’ll have a robust toolkit for analyzing data and drawing meaningful conclusions from statistical evidence.

  • Photo of Kelly Dickens
    Kelly Dickens
    HS Math Guide
    University of Texas at Austin
    Bio
  • Photo of Raghav Goel
    Raghav Goel
    MS Math Guide
  • Photo of Paul Lambert
    Paul Lambert
    MS/HS Math Guide
    512-480-8142
    Bio
  • Photo of Daniel Ramirez
    Daniel Ramirez
    MS Math Guide
    Bio
  • Photo of Stephanie Roach
    Stephanie Roach
    River Campus & High School Director
    Bio

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As a 501(c)3 non-profit school, Headwaters School does not discriminate because of race, color, creed, national origin, religion, gender, age, disability, veteran status, sexual orientation, or any other classes protected by federal, state, or local law in its admissions, financial aid, hiring, or board membership processes.