01

Addition

Addition combines two or more numbers to find a total value. It’s the foundational operation for everyday tasks — from counting items to tallying scores.

02

Subtraction

Subtraction determines the difference when one quantity is taken away from another, helping students understand comparisons, change, and losses. It’s essential for balancing numbers and checking work.

03

Multiplication

Multiplication quickly calculates the total when equal-sized groups are combined, turning repeated addition into a single step. It builds a strong base for scaling, ratios, and later algebraic concepts.

04

Division

Division splits a total into equal parts or determines how many times one number fits into another, helping with sharing, rates, and proportions. Mastery of division supports fraction work and problem solving.

01

Trigonometric Functions

Students learn trigonometric functions to describe relationships between angles and side lengths in right and non-right triangles. This opens doors to advanced mathematics and real-life applications (waves, periodic motion, angles).

02

Trigonometric Identities

Learning key trig identities allows students to simplify expressions, solve complex equations, and transform functions — essential for integration, wave analysis, and more.

03

The Law of Sines and Cosines

Applying the Laws of Sines and Cosines helps students solve for unknown sides or angles in any triangle, expanding their problem-solving to more general geometric and real-world scenarios.

04

Unit Circle & Angle Measures

Using the unit circle and understanding radians/degrees helps students see how angles correspond to coordinates and function values — building readiness for calculus and advanced trigonometry.

01

Solving Equations and Inequalities

Students learn to set up and solve equations or inequalities, discovering how to find unknown values and understand relationships between variables. This gives them tools to tackle real-world problems with precision.

02

Functions

Students explore different types of functions — how inputs map to outputs, and how changing parameters affects graphs. This builds intuition for mathematical modeling and patterns.

03

Polynomials and Factoring

Working with polynomials and factoring expressions reinforces manipulation of algebraic forms, simplifying complex problems and uncovering roots or factors. It’s a key step toward advanced algebra and solving equations.

04

Exponents and Radicals

Understanding exponents and radicals helps students work with repeated multiplication, growth/shrink rates, and roots — foundational for higher-level math. This topic supports later work in functions, powers, and scientific notation.

01

Foundations of geometry

Students start with the basic building blocks of shapes — points, lines, planes, and angles — learning definitions and relationships that underlie all geometry. This sets the stage for understanding space and structure.

02

Shapes and figures

Exploring the properties of different shapes — triangles, polygons, and circles — lets students understand relationships between sides, angles, and other metrics. This forms the basis for proofs and real-world geometry.

03

Measurement and calculation

Students learn formulas and methods to measure length, area, volume, and surface area — skills useful in planning, construction, and everyday spatial measurements.

04

Transformations and coordinate geometry

By placing shapes on coordinate grids and exploring transformations (translations, rotations, reflections), students blend algebra and geometry — strengthening their understanding of how shapes move and relate in space.

01

Advanced Functions

Students dive deeper into a variety of function types — learning their behaviors, transformations, and applications. This unlocks a broader range of mathematical modeling and real-world problem solving.

02

Polynomials and rational expressions

Manipulating polynomials and rational expressions (fractions of polynomials) helps students simplify complex expressions, perform division, and prepare for calculus. This develops algebraic fluency and flexibility.

03

Systems of equations and matrices

Solving systems — whether by substitution, elimination, or matrix methods — teaches students how multiple relationships interact and how to find precise solutions in multi-variable contexts.

04

Conic sections

Exploring conic sections (circles, ellipses, hyperbolas, parabolas) deepens students’ understanding of geometry and algebra interplay. Graphing these shapes builds spatial reasoning and analytic geometry skills.