Arithmetic & Pre-Algebra

This topic covers the foundational arithmetic operations: addition, subtraction, multiplication, and division. Learners will understand how to perform these calculations accurately, apply the order of operations, and solve practical, real-world word problems.

This topic covers the representation and manipulation of fractional numbers using the base-ten system. Learners will understand how to perform arithmetic operations with decimals, convert between decimals and fractions, and solve real-world monetary problems.

Exponents represent repeated multiplication of a number by itself. Learners will understand how to apply the laws of exponents, simplify algebraic expressions involving powers, and work with scientific notation and negative or fractional exponents.

Fractions represent parts of a whole or ratios between numbers. You will understand how to perform basic arithmetic operations—addition, subtraction, multiplication, and division—on fractional values and apply them to solve real-world division problems.

Integers are whole numbers that can be positive, negative, or zero. You will understand how to represent these numbers on a number line and perform basic arithmetic operations, including working with negative values in algebraic contexts.

Introduction to mathematics covers foundational concepts, logical reasoning, and mathematical notation. Learners will understand how to read and write formal proofs, work with basic set theory, and transition to advanced mathematical study.

Number theory is the study of the properties and relationships of integers. You will understand concepts like prime factorization, divisibility, modular arithmetic, and cryptography, enabling you to solve complex mathematical puzzles and secure digital communications.

The order of operations is a standard set of rules used to evaluate mathematical expressions. You will understand how to correctly sequence addition, subtraction, multiplication, division, exponents, and parentheses to solve complex arithmetic and algebraic equations.

Percentages express numbers as fractions of one hundred. You will understand how to calculate percentage increases and decreases, convert between fractions, decimals, and percents, and apply these calculations to financial contexts like interest, taxes, and discounts.

Pre-algebra introduces the fundamental concepts required for higher-level mathematics. You will understand variables, basic equations, inequalities, and coordinate planes, establishing the foundational skills needed to transition from basic arithmetic to formal algebraic problem-solving.

Ratios and proportions compare quantities and establish relationships between different scales. You will understand how to write, simplify, and solve ratios, use proportions to find unknown values, and apply these concepts to scale drawings and rate problems.