Math in Upper School 3
Upper School students are able to take the appropriately-challenging math class based on their understanding and skills in math. Math placement is based on a number of factors including demonstrated skills and knowledge, prerequisite experience, and past performance on classes and tests. The following math courses may be offered to Upper School 3 students:
Students begin their exploration of the first half of the Algebra I curriculum with a focus on problem-solving, discussion, and developing confidence in math. Students develop advanced problem-solving skills, perseverance, and creativity through explorations of progressively complex mathematical concepts from the Pearson text series.
- Evaluate and simplify expressions
- Master divisibility, factors, exponents, radicals and rational numbers.
- Solve equations and inequalities.
- Work with exponents and scientific notation.
- Graph and find equations of lines and systems on the coordinate plane.
Students delve deeper into foundations of Algebra using Pearson’s Algebra I textbook and The Art of Problem Solving: Introduction to Algebra as core texts. Students develop advanced problem-solving skills, perseverance, and creativity through explorations of progressively complex mathematical concepts.
- Identify arithmetic, geometric, and exponential patterns.
- Graph linear and quadratic equations and inequalities, and absolute value functions.
- Factor polynomials, exponentials, logarithms, and other functions.
- Analyze complex numbers.
- Solve one-variable equations and linear systems with multiple variables.
Students build on foundations of algebra utilizing The Art of Problem Solving: Intermediate Algebra as a core text. In this Algebra course, students delves deeper into the algebraic concepts with progressively greater complexity. While the focus remains on students developing advanced problem-solving skills, perseverance, and creativity skills while learning the mathematical topics, this course allows for students to be challenged with more advanced Algebraic problems as they master each concept.
- Manipulate linear and polynomial functions.
- Graph polynomial, exponential, logarithmic, rational functions, and complex numbers and functions on the polar plane.
- Recognize factoring patterns.
- Model using linear and exponential relationships.
- Understand Conic sections.
- Practice Trigonometric functions and identities.
Students focus on geometry, trigonometry, and advanced topics in Algebra. Using The Art of Problem Solving: Introduction to Geometry as a core text, students continue to utilize advanced problem-solving skills, perseverance, and creativity through projects and explorations of mathematical topics. This integrated “hands-on” course enables students to explore design-thinking and STEM-based projects and ideas into their learning.
- Explore the geometric definitions of and derive equations for the conic sections.
- Explore and use the characteristics and properties of triangles, quadrilaterals and circles to solve problems.
- Find the area of composite shapes.
- Explore different types of formal proof. Use deductive reasoning to construct proofs.
- Build on an understanding of 2-dimensional geometry to expand problem solve to figures in 3 dimensions.
- Explore trigonometry, including right triangle trigonometry and the law of sines and cosines
This course is primarily concerned with developing the student’s understanding of the concepts of Pre-calculus and providing experience with its methods and applications, with strong emphasis on graphical, numerical, analytical and verbal expressions.
- Have the opportunity to work with functions represented both numerically and verbally
- Have the opportunity to apply the knowledge of pre-calculus to real-world examples
- Learn how to explain solutions to problems orally in written expressions
- Determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurements
- Develop an appreciation of pre-calculus as a coherent body of knowledge
- Meaning of trigonometric functions and model a written description of a physical situation with various functions
- Communicate mathematics and explain solutions to problems both verbally and in written sentences
- Have the opportunity to explore different coordinate systems and limits
Topics explored in this course include (subject to change):
- Exponential, logarithmic, polynomial and rational functions
- Conic sections
- Partial fractions
- Polar Coordinates
- Trigonometric functions and their properties
- Introduction to Calculus: Differentiation and their applications