Math Concepts
Explore K-12 math concepts with instant definitions, intuitive explanations, and interactive visualizations. Learn at your own pace with a concept-first approach.
Explore by Topic
Number & Quantity
Counting, place value, number types
48 conceptsOperations
Addition, multiplication, properties
64 conceptsFractions & Ratios
Parts of wholes, proportions
27 conceptsAlgebra
Variables, equations, expressions
98 conceptsGeometry
Shapes, space, transformations
99 conceptsFunctions
Mappings, rates, transformations
76 conceptsStatistics
Data, probability, uncertainty
82 conceptsCalculus
Limits, derivatives, integrals
39 conceptsSets & Logic
Sets, proofs, meta-thinking
65 conceptsBrowse by Grade
Concepts organized by grade level, aligned with the North American K-12 curriculum.
Popular Concepts
Fractions
A fraction is a number of the form $\frac{a}{b}$ where $a$ (the numerator) counts how many equal parts you have and $b$ (the denominator, which must not be zero) tells how many equal parts the whole is divided into.
Addition
The arithmetic operation of combining two or more numbers into a single total, representing joining or accumulating quantities.
Multiplication
Finding the total when a quantity is repeated a given number of times; the result of repeated addition of equal groups.
Equations
A mathematical statement that two expressions are equal, connected by an equals sign ($=$). Equations assert a relationship between quantities and can be solved to find the values of unknown variables that make the statement true.
Slope
A measure of the steepness and direction of a line, calculated as the ratio of vertical change (rise) to horizontal change (run) between any two points on the line. Slope is written as $m = \frac{y_2 - y_1}{x_2 - x_1}$ and indicates how much $y$ changes for each unit increase in $x$.
Area
The amount of two-dimensional space inside a flat shape, measured in square units.
Ratios
A ratio compares two or more quantities by showing how many times one contains the other, written as $a:b$ or $\frac{a}{b}$. Unlike fractions, ratios can compare parts to parts, not just parts to wholes.
Percentages
A way of expressing a quantity as a fraction of 100, written with the symbol % to mean 'per hundred.'
Variables
A symbol (usually a letter like $x$) that represents an unknown or changing quantity in a mathematical expression.
Factoring
Rewriting an algebraic expression as a product of two or more simpler expressions that multiply to give the original.
Quadratic Functions
A quadratic function is a polynomial function of degree 2, written as $f(x) = ax^2 + bx + c$ with $a \neq 0$, whose graph is a U-shaped curve called a parabola that opens upward when $a > 0$ or downward when $a < 0$.
Derivative
The instantaneous rate of change of a function at a single point, defined as the limit of the slope of secant lines.
Math Guides
In-depth guides that go beyond concept pages — worked examples, practice problems, common mistakes, and strategies for each major topic.
Functions and Graphs
Domain, range, types, transformations, inverses, and composition.
Quadratic Equations
Factoring, completing the square, and the quadratic formula.
Factoring Polynomials
GCF, grouping, trinomials, difference of squares, and cubes.
Rational Expressions
Simplifying, multiplying, dividing, and understanding restrictions.
Exponents and Logarithms
Laws of exponents, log properties, and growth/decay applications.
Systems of Equations
Substitution, elimination, and matrix methods.
Rational Functions
Asymptotes, holes, graphing behavior, and end behavior.
Polynomial Long Division
Step-by-step algorithm with remainders and synthetic division.
Partial Fractions
Decomposing rational expressions for integration.
Limits
Intuitive foundation of calculus with algebraic techniques.
Derivatives
Power, product, quotient, and chain rules with applications.
Integration of Rational Functions
Long division and partial fractions for integration.
Place Value and Measurement
Number sense foundations: place value, decimals, number lines, and measurement.
Geometry Transformations and Cross-Sections
Translations, rotations, cross-sections, rigid shapes, and central angles.
Roots and Irrational Numbers
Cube roots, square roots, rational and irrational numbers explained.
Patterns and Sequences
Growing patterns, arithmetic and geometric sequences.
Symmetry and Congruence
Line symmetry, rotational symmetry, reflection, and congruence.
Math Properties
Commutative, associative, and distributive properties explained.
Features
Intuitive Explanations
Every concept includes an intuition section that explains the "why" in plain language.
Connected Knowledge
Related concepts are linked together so you can explore connections and build understanding.
Interactive Playground
Manipulate visual diagrams to develop deeper intuition for geometric and algebraic concepts.
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