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Academics

Junior High Math

The approach to teaching mathematics varies greatly from school to school and from country to country. At St. Ambrose we believe in a classical approach, striving to develop mathematical intuition and problem-solving skills in our students. Successful students approach mathematical problems as they would an investigation or puzzle. They ask questions, try out different approaches, and reflect and revisit their solutions. We do not want to limit ourselves to a cookbook-style approach in which students follow a prescribed set of steps by rote without a feeling for how the method works and why. For St. Ambrose math students, how one reaches a solution is as important as the solution itself.

We believe that problem solving is central to the teaching and learning of mathematics. Problem-solving involves logical reasoning; it is important to explore the reasons why step two follows step one; but successful students also understand the process of modifying, adapting, and combining mathematical tools to find new ways to reach a solution.

Our philosophy is to place students in the proper math sequence – one that provides enough challenge to reach their potential without needlessly pushing them beyond their means. 

Each student who comes to SAA is given our own in-house math placement exam in order to determine the best possible starting point. A student who begins with Math 6 and follows the courses sequentially will proceed through: Pre-Algebra, Algebra, Geometry, Algebra II, Pre-Calculus, and Calculus. 

Students entering in the 6th grade have been placed as high as Algebra, and students who are below grade level are supported through Learning Services. Students are re-evaluated prior to entering the Senior High, with some students starting with 9th grade Algebra in order to gain greater mastery and to be on the best math track for their upper-level courses. In the Senior High, Calculus II is available along with opportunities for independent studies or off-campus college courses for accelerated students. 

Math 6

The Math 6 course is designed to strengthen the student’s ability to perform arithmetical operations. Special emphasis will be placed on mental math for students who have not yet mastered addition and times tables. Students will also be expected to develop the ability to present their work in a clear and legible manner. The course will introduce students to more challenging problems and will begin the process of relating word problems to mathematical expressions and calculations. The idea of algebraic expressions and unknown quantities will be introduced.

Topics to be covered in this course include:

  • Numeric operations and order of operations
  • Summary statistics including mean, median, and mode
  • Prime Factorization, GCF, LCM
  • Operations with fractions
  • Calculations involving ratios and percentages
  • Introduction to geometry: areas, volumes, angles, and symmetries
  • Understanding the coordinate plane.

A more detailed list of topics is provided here.

Pre-Algebra

The Pre-Algebra course builds upon and expands topics introduced in Math 6 and prepares students for the more detailed treatment of Algebraic concepts in Algebra I. Students will learn how to work with factors and multiples. The application of percentage and ratios to financial problems will be covered. Algebraic notation and concepts will be introduced in a formal way.

Topics covered in the course include:

  • Introduction to expressions and variables
  • Solving basic equations with one variable
  • Working with multiple step equations and inequalities
  • Exploring prime factors and the rules of exponents
  • Understanding rational numbers and their application in equations
  • Solving ratio, percentage, and probability problems
  • Introduction to linear equations
  • Square roots
  • Areas and volumes

A more detailed list of topics is provided here.

Algebra

The Algebra course is designed for students who have demonstrated mastery of arithmetic and pre-algebra as outlined in the Math 6 and Pre-Algebra curriculum and shown the ability to engage in abstract mathematical reasoning.

Algebra provides the critical foundation for future math courses. The language and concepts are more formal than offered in Pre-Algebra and offer a more sophisticated understanding of mathematical concepts.

Topics covered in the course include:

  • Properties of numbers and operations
  • Mathematical axioms and definitions
  • Solutions to Algebraic Equations
  • Solving Absolute Value Equations and Deriving Solution Sets
  • Working with Inequalities and Solutions Sets
  • Multiplying Binomials and Higher-Order Polynomials
  • Factoring Quadratic Expressions
  • Solving Quadratic Equations: The Quadratic Formula
  • Using the Determinant to Interpret Quadratic Equations
  • Introducing Irrational Numbers
  • Closure Axioms
  • Graphing Linear Equations
  • Solving Systems of Two Variables
  • Working with Rational Algebraic Expressions and Equations
  • Working with Radical Algebraic Expressions and Equations

A more detailed list of topics is provided here.

For course descriptions of Algebra I and above, please see the Senior High Math Curriculum.