GLOBAL KNOWLEDGE INDEX

Master Curriculum

Explore our complete library of concepts, organized systematically. Use the index to navigate through logical blocks and sub-domains.

Early Math, Arithmetic, and Logic

Number Sense and Basic Intuition

A. Nature of Numbers and Sets

Natural numbers and the decimal system
The concept of zero and introduction to negative numbers
The number line and coordinate axis
Absolute value

B. Basic Arithmetic

Addition and subtraction of integers
Multiplication and division of integers
Order of operations (PEMDAS/BODMAS)
Laws of arithmetic (commutative, associative, distributive)

C. Fundamentals of Number Theory

Even and odd numbers
Divisibility rules (for 2, 3, 5, 9, 10)
Prime and composite numbers (Sieve of Eratosthenes)
Greatest Common Divisor (GCD) and Least Common Multiple (LCM)

D. Number Intuition and Estimation

Orders of magnitude
Scientific notation: aimes10na imes 10^n
Approximation and estimation
Rounding errors and their accumulation

Fractions, Proportions, and Percentages

A. Common Fractions

Meaning of a fraction: numerator, denominator, parts
Proper, improper fractions, and mixed numbers
Fundamental property of fractions and simplifying
Addition, subtraction, multiplication, and division of fractions

B. Decimal Fractions

Positional notation of decimals
Rounding and comparing decimals
Arithmetic with decimals
Conversion between decimals and common fractions

C. Ratios, Proportions, and Percentages

Concept of ratio and scale
Fundamental property of proportions and solving proportion equations
What is a percent (1% as one-hundredth)
Finding the percent of a number and a number by its percent
Applied problems: discounts, taxes, simple interest

Logic, Dimensions, and Modeling

A. Basic Logic

Basic operations: AND, OR, NOT
Truth tables
Basic structure of statements (If A, then B; necessity and sufficiency)

B. Units of Measurement and Dimensional Analysis

Concept of dimensionality (length, mass, time, speed)
Conversion of units
Verifying formulas using dimensional analysis

C. Mathematical Modeling (Basics)

Translating text into mathematical expressions
Variables as models of the real world
Checking the answer for physical/logical adequacy