Pax Academia High School Math Curriculum Overview
6th Grade Mathematics: Foundations of Numerical Reasoning
Objective
Develop strong numerical fluency and mathematical reasoning while introducing students to mathematics as a logical, coherent system. Emphasis is placed on understanding why procedures work, not merely how to perform them.
Students learn to think carefully, reason step by step, and explain their mathematical thinking clearly.
Key Topics
Core Emphases
Activities
Outcome
Students complete 6th grade with strong numerical confidence, fluency with fractions and ratios, and the ability to explain mathematical reasoning clearly. They are prepared for formal pre-algebra study in 7th grade.
Develop strong numerical fluency and mathematical reasoning while introducing students to mathematics as a logical, coherent system. Emphasis is placed on understanding why procedures work, not merely how to perform them.
Students learn to think carefully, reason step by step, and explain their mathematical thinking clearly.
Key Topics
- Whole number operations and number sense
- Fractions, decimals, and percentages
- Ratios and introductory proportional reasoning
- Integers and the number line
- Order of operations
- Introduction to variables and simple expressions
Core Emphases
- Conceptual understanding over rote memorization
- Clear mathematical language and notation
- Step-by-step reasoning and justification
- Mental math and estimation
Activities
- Daily problem-solving exercises
- Word problems tied to real-world contexts
- Explanation of solutions in writing and discussion
- Mental math practice and numerical reasoning drills
- Regular mastery-based assessments
Outcome
Students complete 6th grade with strong numerical confidence, fluency with fractions and ratios, and the ability to explain mathematical reasoning clearly. They are prepared for formal pre-algebra study in 7th grade.
7th Grade Mathematics: Pre-Algebra and Logical Structure
Objective
Transition students from arithmetic reasoning to formal algebraic thinking. Students learn to generalize numerical patterns, work with variables, and solve multi-step problems using logical structure and precision.
This course serves as the bridge between numerical foundations and algebra.
Key Topics
Core Emphases
Activities
Outcome
By the end of 7th grade, students are comfortable working with variables, equations, and proportional reasoning. They enter 8th grade prepared for formal Algebra I–level thinking with confidence, precision, and mathematical discipline.
Transition students from arithmetic reasoning to formal algebraic thinking. Students learn to generalize numerical patterns, work with variables, and solve multi-step problems using logical structure and precision.
This course serves as the bridge between numerical foundations and algebra.
Key Topics
- Review and refinement of fractions, decimals, and integers
- Ratios, rates, and proportional relationships
- Linear expressions and equations
- Introduction to inequalities
- Coordinate plane and basic graphing
- Word problems requiring algebraic representation
Core Emphases
- Algebra as generalized arithmetic
- Logical consistency and symbolic reasoning
- Translating verbal problems into mathematical expressions
- Checking solutions and identifying errors
Activities
- Structured problem sets emphasizing reasoning
- Multi-step word problems and modeling
- Graphing and interpretation exercises
- Written explanations of algebraic solutions
- Cumulative assessments focused on mastery
Outcome
By the end of 7th grade, students are comfortable working with variables, equations, and proportional reasoning. They enter 8th grade prepared for formal Algebra I–level thinking with confidence, precision, and mathematical discipline.
8th Grade Mathematics
Course Description:This course prepares students for high school algebra by strengthening numerical fluency, introducing algebraic reasoning, and developing logical problem-solving skills. Emphasis is placed on understanding mathematical relationships, translating real-world situations into mathematical expressions, and building confidence with foundational concepts required for Algebra I.
Key Topics:Numerical Foundations:
Operations with integers, fractions, decimals, and percentages; ratios and proportions; order of operations; introductory exponents and roots.
Algebraic Expressions and Equations:
Understanding variables, writing and simplifying algebraic expressions, solving one-step and two-step equations, and interpreting equality and balance.
Linear Relationships:
Introduction to the coordinate plane, graphing points, understanding linear patterns, and exploring the concepts of slope and intercept.
Foundations of Geometry:
Area, perimeter, volume, angle relationships, and properties of basic geometric figures, with emphasis on logical reasoning and precision.
Problem Solving and Logical Reasoning:
Multi-step word problems, pattern recognition, estimation, and strategies for checking the validity of solutions.
Concepts and Applications:
Key Topics:Numerical Foundations:
Operations with integers, fractions, decimals, and percentages; ratios and proportions; order of operations; introductory exponents and roots.
Algebraic Expressions and Equations:
Understanding variables, writing and simplifying algebraic expressions, solving one-step and two-step equations, and interpreting equality and balance.
Linear Relationships:
Introduction to the coordinate plane, graphing points, understanding linear patterns, and exploring the concepts of slope and intercept.
Foundations of Geometry:
Area, perimeter, volume, angle relationships, and properties of basic geometric figures, with emphasis on logical reasoning and precision.
Problem Solving and Logical Reasoning:
Multi-step word problems, pattern recognition, estimation, and strategies for checking the validity of solutions.
Concepts and Applications:
- Developing algebra readiness through structured reasoning and clear mathematical communication.
- Applying mathematical concepts to real-world contexts such as budgeting, measurement, and rate problems.
- Building the discipline and precision required for success in Algebra I and higher-level mathematics.
9th Grade: Algebra I
Course Description:
This course introduces students to the fundamental concepts of algebra, focusing on the development of problem-solving skills and logical thinking. Students will explore variables, expressions, equations, functions, and their real-world applications.
Key Topics:
This course introduces students to the fundamental concepts of algebra, focusing on the development of problem-solving skills and logical thinking. Students will explore variables, expressions, equations, functions, and their real-world applications.
Key Topics:
- Foundations of Algebra: Understanding variables, constants, coefficients, arithmetic operations, and order of operations.
- Linear Equations and Inequalities: Solving single-variable equations, graphing linear equations, understanding slope and intercepts, and solving systems of linear equations.
- Polynomials: Operations on polynomials, factoring, and solving quadratic equations.
- Functions and Relations: Introduction to functions, domain and range, evaluating and graphing functions.
- Rational Expressions and Equations: Simplifying and solving rational expressions and equations.
- Radicals and Exponents: Simplifying expressions involving exponents and radicals, and solving related equations.
- Developing algebraic thinking and problem-solving strategies.
- Applying algebraic concepts to solve real-world problems, such as financial calculations, rate problems, and data analysis.
- Understanding the importance of variables and functions in modeling real-world situations.
10th Grade: Algebra II
Course Description:
Building upon the foundations of Algebra I, Algebra II dives deeper into complex functions, advanced equations, and introduces students to logarithms, sequences, and series. This course is designed to further enhance students’ analytical and logical reasoning skills.
Key Topics:
Building upon the foundations of Algebra I, Algebra II dives deeper into complex functions, advanced equations, and introduces students to logarithms, sequences, and series. This course is designed to further enhance students’ analytical and logical reasoning skills.
Key Topics:
- Advanced Functions: Exploring quadratic, polynomial, rational, exponential, and logarithmic functions.
- Complex Numbers: Understanding and performing operations with complex numbers, solving quadratic equations with complex solutions.
- Systems of Equations and Inequalities: Solving systems using various methods, including matrices, and applying these concepts to real-world scenarios.
- Sequences and Series: Understanding arithmetic and geometric sequences, summation notation, and applications of series.
- Probability and Statistics: Introduction to probability theory and descriptive statistics.
- Advanced Polynomial Functions: Polynomial division, synthetic division, and theorems related to polynomial roots.
- Extending algebraic methods to more complex situations.
- Applying advanced functions and equations to real-world problems, such as population growth models, investment returns, and statistical analysis.
- Enhancing logical reasoning and abstract thinking skills.
11th Grade: Geometry
Course Description:
This course introduces students to the study of shapes, sizes, relative positions of figures, and properties of space. It emphasizes logical reasoning and the use of deductive proof to explore the relationships among geometric figures.
Key Topics:
This course introduces students to the study of shapes, sizes, relative positions of figures, and properties of space. It emphasizes logical reasoning and the use of deductive proof to explore the relationships among geometric figures.
Key Topics:
- Foundations of Geometry: Exploring points, lines, planes, angles, and theorems.
- Triangles: Classifying triangles, congruence and similarity, Pythagorean Theorem, and special triangles.
- Polygons and Quadrilaterals: Properties of polygons, types of quadrilaterals, and area/perimeter calculations.
- Circles: Understanding properties of circles, including arcs, angles, chords, and calculations involving sectors.
- Coordinate Geometry: Utilizing distance and midpoint formulas, slope calculations, and equations of lines and circles.
- Transformations: Studying translations, rotations, reflections, and dilations, with an emphasis on symmetry.
- Volume and Surface Area: Calculating volumes and surface areas of prisms, cylinders, pyramids, cones, and spheres.
- Developing spatial reasoning and visualization skills.
- Applying geometric principles to real-world problems, such as architecture, engineering, and design.
- Enhancing logical reasoning through proof-based learning.
12th Grade: Calculus
Course Description:
This course introduces students to the fundamental concepts of calculus, focusing on limits, derivatives, integrals, and their applications. Students will develop a deep understanding of change and motion, preparing them for further study in mathematics, engineering, and the sciences.
Key Topics:
This curriculum focuses on developing a deep understanding of mathematical concepts while emphasizing their practical applications in various fields.
This course introduces students to the fundamental concepts of calculus, focusing on limits, derivatives, integrals, and their applications. Students will develop a deep understanding of change and motion, preparing them for further study in mathematics, engineering, and the sciences.
Key Topics:
- Limits and Continuity: Understanding the concept of limits, calculating limits, and exploring continuity.
- Derivatives: Learning the definition and interpretation of derivatives, rules of differentiation, and applications in real-world scenarios like optimization and motion.
- Integrals: Understanding antiderivatives, definite and indefinite integrals, and their applications to area, volume, and physical concepts.
- Differential Equations: Introduction to differential equations and their applications in modeling real-world phenomena.
- Sequences and Series: Exploring infinite series, convergence tests, and applications in approximation.
- Multivariable Calculus (Introduction): Introduction to partial derivatives, double and triple integrals, with applications in physics and engineering.
- Developing an understanding of the mathematics of change and motion.
- Applying calculus concepts to real-world problems in physics, engineering, economics, and biology.
- Enhancing analytical thinking and problem-solving skills through the study of advanced mathematical concepts.
This curriculum focuses on developing a deep understanding of mathematical concepts while emphasizing their practical applications in various fields.
