• Graph theory
  • \(x^y = y^x\)
  • Conic sections
  • Recreational mathematics
  • Intro to radians
  • Algebra 2
  • Group theory
  • Trigonometry
  • Countable and uncountable sets
  • Precalc
  • Permutation of the natural numbers
  • Sphinx
  • Abstract algebra
  • Complex analysis
  • Real analysis
  • Undergrad probability theory
  • Linear algebra
  • Elementary number theory
  • Differential equations
  • Generating functions
  • Discrete mathematics
  • Proof by induction
  • Bridge course
  • Logarithms
  • Zero factorial
  • Statistics and probability
  • Tidbits on Aaron numbers
  • Duodecimal
  • Factoring and solving quadratics
  • Completing the square
  • Euler's formula and identity
  • Infinite series
  • Teaching algebra
  • Chinese remainder theorem
  • Modular arithmetic
  • Intro
  • Inverse functions (algebra 1)
  • Polynomial long division
  • Math education
  • Solving right triangles
  • Rationalizing the denominator
  • Pythagorean theorem
  • Algebra 1
  • Solving linear equations
  • Solving linear systems of equations in two variables by substitution
  • Other resources
  • Intro to irrational numbers
  • Other resources
  • Sum and product of roots of polynomials
  • 3rd grade
  • Subtracting within 1000
  • Knot theory
  • Linear systems of equations in two variables
  • Visual proof
  • Evaluating infinite series
  • Continued fractions
  • \(\displaystyle \dfrac{1}{2} + \dfrac{1}{4} + \dfrac{1}{8} + \dfrac{1}{16} + \ldots\)
  • Proofs involving infinitely many digits
  • Pigeonhole principle
  • Eulerian cycles and paths
  • Hamiltonian cycles and paths
  • High school courses
  • Law of cosines
  • Find a length using the law of cosines
  • Law of sines
  • Harmonic series
  • Counter-intuitive mathematics
  • Magic hexagon (recreational mathematics)
  • Goldbach's conjecture
  • Other resources
  • Other resources
  • Other resources
  • Calculus 1
  • Resources for undergrads
  • Other resources
  • Solving two-step equations
  • Solving multi-step equations
  • Solving and graphing linear inequalities
  • Solving and graphing one-step inequalities in one variable
  • Solving and graphing two-step inequalities
  • Other resources
  • Order of operations (grade 6)
  • Factorials, permutations, and combinations
  • Intro to \(e\)
  • High school geometry
  • History of \(\pi\)
  • History of mathematics
  • History of trigonometry
  • Math in art
  • Learning mathematics
  • Complex numbers
  • Applications of complex numbers
  • Calculus 2
  • Calculus 3
  • Mathematical logic
  • Teaching mathematics
  • Resources for graduates
  • Proving Vandermonde's identity
  • Ring theory
  • History of calculus
  • Applications of linear algebra
  • Where does \(\pi\) appear?
  • Where does \(e\) appear?
  • Applications of statistics and probability
  • Applications to criminal investigation
  • Misleading statistics
  • Euler characteristic
  • Algebraic geometry
  • Biographies
  • Manipulatives
  • Triangle midsegment theorem
  • Cuisenaire rods
  • Applications of mathematics
  • Plotting integer coordinates
  • Multilink Cubes
  • Other resources
  • Other resources
  • Using the formula
  • Squaring the square
  • Combining like terms (abstract method)
  • Active learning
  • Combinatorics
  • Simplifying square root expressions
  • Parallelogram law
  • Euler line
  • Rational exponents and radicals
  • Mayan mathematics
  • Unsolved problems
  • Inscribed square problem
  • Twin prime conjecture
  • Other resources
  • Finding the domain and range of functions from graphs
  • Properties of exponents
  • Difference of cubes
  • Sum of cubes
  • Factoring difference of squares (abstract methods)
  • Derivation
  • Similarity
  • \(\pi\)
  • Napkin ring problem
  • Pascal's rule
  • Other resources
  • End behavior
  • Other resources
  • Wilson's theorem
  • Proof
  • Geometric definitions
  • Transformations of functions
  • Absolute value function under transformations
  • Graphing linear equations
  • Standard form for linear equations
  • Forms of linear equations
  • Slope-intercept form
  • Point-slope form
  • Shifting functions
  • Reflecting functions
  • Even and odd functions
  • Computer-assisted proof
  • Scaling functions
  • Card tricks
  • Other resources
  • Hyperboloid
  • Si Stebbins stack
  • Squaring the torus
  • Mandelbrot set
  • The Leaning Tower of Lire
  • Strictly-convex deltahedron
  • \(\pi\) tape
  • Genaille–Lucas rulers
  • Puzzles
  • Challenging exercises
  • Secretary problem
  • Definite integral of a polynomial function
  • The monkey and the coconuts
  • Riemann sums
  • Midpoint rule
  • Trapezoidal rule
  • Other resources
  • Comparing and ordering integers
  • Absolute value of a number
  • Adding integers
  • Subtracting integers
  • Subtracting decimals
  • Composition of functions
  • Inverse functions (algebra 2)
  • Synthetic division
  • Napier's bones
  • Converse of the Pythagorean theorem
  • 5th grade
  • Adding decimals using the standard algorithm
  • Decimals
  • Other resources
  • Other resources
  • Rounding to the nearest 1000
  • Other resources
  • Interval notation
  • Solving and graphing compound linear inequalities with AND
  • Solving and graphing compound linear inequalities with OR
  • Solving and graphing compound linear inequalities
  • 6th grade
  • Other resources
  • Finding angles and side lengths in similar polygons
  • Double pendulum
  • 4th grade
  • Multiplying one-digit numbers by multiples of \(10,\) \(100,\) and \(1000\)
  • Other resources
  • Other resources
  • Education
  • Other resources
  • Kindergarten
  • K-12 courses
  • Exponential growth and decay
  • Exponential vs. linear growth
  • 1st grade
  • 2nd grade
  • Other resources
  • 7th grade
  • 8th grade
  • Babylonian mathematics
  • Fractions (prealgebra)
  • Types of fractions
  • Other resources
  • Area of a trapezoid
  • Simpson's paradox
  • Difference between correlation and causation
  • Other resources
  • Other resources
  • Cartesian product
  • Finding the tangent or normal line through the given point
  • Infinite sets
  • Stable marriage problem
  • Stereographic projection
  • Bisection method
  • Newton's method
  • Sine rule for area of a triangle
  • Dividing by zero
  • Converting between decimals and fractions
  • Other resources
  • Museum
  • Other resources
  • Multiplying complex numbers algebraically
  • Other resources
  • Dividing complex numbers
  • Plotting complex numbers
  • Linear factorization theorem
  • Solving certain cubic equations
  • Simplifying fractional powers
  • When is a logarithm undefined?
  • Complex number logarithm
  • How many ways can you arrange a deck of cards?
  • Other resources
  • Finding the vertex of a parabola
  • Derivatives: composite, implicit, and inverse functions
  • Simplifying rational expressions
  • Intro to limits
  • Chain rule
  • First derivative using implicit differentiation
  • Quotient rule
  • Solving logarithmic equations
  • Sum, difference, and power rules for derivatives
  • Intersection of two lines in \(\mathbb{R}^3\)
  • Hilbert's paradox of the Grand Hotel
  • Lines in \(\mathbb{R}^3\)
  • Other resources
  • Minimum vertex covers
  • Ternary numeral system
  • \(100\) prisoners problem
  • Fractals
  • Paradoxes
  • Fixed point
  • Brachistochrone curve
  • Proof by cases
  • Other resources
  • Perfect graph
  • Interviews of teachers
  • \(\LaTeX\)
  • Intro to logarithms
  • Futoshiki
  • Biconditional
  • Conditional statements
  • Solving exponential equations
  • Direct proof
  • Proof by contrapositive
  • Proof techniques
  • Flows and cuts
  • Inclusion–exclusion principle
  • Random
  • Using the theorem
  • SAT math
  • History of combinatorics
  • Biographies (combinatorics)
  • Catalan numbers
  • Various topics
  • SageMath
  • History
  • Euclid's Elements
  • Undergrad geometry
  • Addition rule of probability
  • Multiplying two-digit numbers
  • Trick for multiplying by 11
  • Trick for multiplying multi-digit numbers by 11-19
  • Trick for multiplying by numbers one less than a power of ten when number of digits are equal
  • Logic puzzles
  • Srinivasa Aiyangar Ramanujan
  • Biographies
  • Georg Cantor
  • William Rowan Hamilton
  • Évariste Galois
  • Galois theory
  • History
  • Biographies
  • Probability trees
  • History of probability theory
  • Biographies
  • Abraham de Moivre
  • Intro to probability
  • Sprouts
  • Chomp
  • Two-player games
  • Multi-digit multiplication and division
  • Multi-digit multiplication
  • Multi-digit division
  • List all the divisors of a number
  • Multiply fractions, abstract
  • Other resources
  • Converting between improper fractions and mixed numbers
  • \(n\)-th root
  • Solving and graphing absolute value inequalities
  • Other resources
  • Necklace splitting problem
  • Intro to circles and \(\pi\)
  • What is volume?
  • Other resources
  • Intro to integers
  • Integers
  • Multiplying integers
  • Other resources
  • Recognize fractions less than or equal to 1
  • Scientific notation
  • Common denominators
  • Reducing fractions
  • Adding and subtracting fractions with like denominators (abstract method)
  • Introduction to percents
  • Division (grade 4)
  • Points, lines, and planes
  • Other resources
  • Types of quadrilaterals (grade 5)
  • Intro to polynomials
  • Distributive property with variables (abstract method, grade 7)
  • Introduction to functions
  • Metric system
  • Other resources
  • Archimedes's cattle problem
  • Sum and product rules
  • Stars and bars
  • Double counting
  • Kakeya set
  • Ellipse
  • Expected value
  • Factoring trinomials using SageMath
  • Extremal Principle
  • Nontraditional education
  • Videos for kindergarten teachers
  • Teaching preschool mathematics
  • Montessori education
  • Education reform
  • Large numbers
  • Flexagon
  • Ruled surface
  • Sum of three cubes
  • Graphs of sequences
  • Frieze patterns
  • Adding and subtracting polynomials
  • Polygons
  • Line-circle and circle-circle relationships
  • Long division (two-digit divisors)
  • Area of a parallelogram
  • Equivalence of a decagon to a rectangle
  • Equivalence of a trapezoid to a rectangle
  • Equivalence of a parallelogram to a rectangle
  • Equivalence of a triangle to a rectangle
  • Adding within 10
  • History of counting
  • Other resources
  • Add and subtract fractions (word problems)
  • Other resources
  • Subtract within 10
  • Classifying triangles by angles
  • Classifying triangles by side lengths
  • Multiplication of one-digit by two-digit
  • Multiply by 2-digit numbers (grade 4)
  • Dividing fractions by whole numbers
  • Adding fractions with unlike denominators
  • Long division (three-digit divisors)
  • Division using the stamp game
  • Division using the stamp game (grade 4)
  • Multiplying multi-digit numbers by one-digit numbers
  • Multiplication of a multi-digit number by a two-digit number
  • Multiplication of a multi-digit number by a three-digit number
  • Intro to geometric series
  • Partial sum of a geometric progression
  • Reading travel graphs
  • Unitary method
  • Derivatives of exponential functions
  • Counting, permutations, and combinations
  • Two-way tables
  • Probability
  • Other resources
  • Discrete random variables
  • Middle school courses
  • Elementary school courses
  • Median
  • Stem and leaf plots
  • Evaluating square roots of small perfect squares
  • Evaluating cube roots of small perfect cubes
  • Arithmetic series
  • Net of a cube
  • Net of a cuboid
  • Other resources
  • Factoring linear expressions
  • Measurement
  • For teachers: Fraction talks
  • Add and subtract fractions (grade 4)
  • Royal arrangements
  • Estimation
  • Multiplying monomials by binomials
  • Other resources
  • Frequency tables
  • Other resources
  • Factoring a cubic polynomial with a double root
  • Motion graphs
  • Product rule
  • Leibniz's derivative notation
  • Constant rule
  • Biographies for calc
  • Perimeter of composite figures
  • Proof by induction (inequalities)
  • Net of a polyhedron
  • Zero
  • Collatz conjecture
  • Adding and subtracting free vectors
  • Infinitude of the primes
  • Polynomial arithmetic
  • Other resources
  • Small-angle approximation
  • Double angle identities
  • Triple angle formulas
  • Polynomial long division and graphing cubics
  • Other resources
  • Multiplying polynomials
  • Transformations of the square and cube root functions
  • Graphing the square root function under transformations
  • Other resources
  • Equation of a circle and semicircle
  • Adding functions
  • Subtracting functions
  • Solving certain cubic inequalities
  • Graphing parabolas
  • Quadratic equations
  • Graphing with complex numbers
  • Lattice paths
  • Combinations without restrictions
  • Other resources
  • Multi-stage events
  • Greatest binomial coefficient
  • Simple harmonic motion
  • Integration by u-substitution (less difficult)
  • Motion
  • Straight line motion
  • Projectile motion
  • Related rates
  • Graphing inverse trigonometric functions
  • Applications of trigonometric integrals
  • Applications of trigonometric derivatives
  • Derivatives of trigonometric functions under transformations
  • Definite integrals
  • Intermediate value theorem
  • Finding the acute angle between two lines
  • Sum and difference formulas
  • Finance
  • Integrating exponential functions
  • Integrating exponential functions
  • Logarithmic functions
  • Logarithmic functions
  • Solids of revolution
  • Area between two curves
  • Antiderivatives
  • Other resources
  • Extrema
  • Finding absolute extrema
  • Primitive functions
  • Oblique asymptotes
  • Graphing using derivatives
  • Inflection points
  • Solving equations with complex numbers
  • Line of intersection between two planes
  • Vectors
  • Arc length (calculus 2)
  • Surface area of solids of revolution
  • L'Hopital's rule
  • Geometrical interpretation
  • Simultaneous equations
  • Inverse matrices
  • Further integration
  • 3D matrices
  • Determinants
  • Matrices
  • Invariance
  • Classifying stationary points
  • Other resources
  • Special points
  • Deriving the quadratic formula
  • Series and sequences
  • Partial sums
  • Quadratic formula
  • Other resources
  • Parametric equations and polar coordinates
  • Finding the domain of radical functions
  • Finding the domain and range of functions
  • Parabolas
  • Finding the intersection point of two graphs
  • Continuity
  • Linear equations
  • Sketching angles in radians
  • Angle measures and circles
  • Degrees-minutes-seconds
  • Wythoff's game
  • Game of Nine
  • Variance and standard deviation
  • Other resources
  • Multiplying and dividing in scientific notation
  • Finding the inverse of discrete and linear functions
  • Finding the inverse of rational functions
  • Adding and subtracting rational expressions
  • Rational functions
  • Simplifying square roots of nonnegative integers
  • Simplifying square roots of monomials with variables
  • Exterior angles of regular polygons
  • Circle theorems
  • Other resources
  • Significant figures
  • Rounding to \(n\) significant figures
  • Counting significant figures
  • Measures of central tendency from frequency tables
  • Simplifying ratios
  • Dividing a quantity by a ratio
  • Volume of right rectangular prisms
  • Other resources
  • Factoring monic quadratics
  • Area of a circle
  • Circumference of a circle
  • Other resources
  • Solving quadratic equations by factoring
  • Percent change
  • Graphing linear equations in slope-intercept form
  • Other resources
  • GCD and LCM of numbers (word problems)
  • Other resources
  • Other resources
  • Inquiry-based learning
  • Zebra Puzzle
  • Wason selection task
  • Dice puzzle
  • Utilities puzzle
  • Tidbits on Burnside's lemma
  • Bridge and torch problem
  • The Hardest Logic Puzzle Ever
  • Hat puzzle
  • Pirate game
  • Power of a point
  • Converting fractions to percents
  • Converting between fractions and percents
  • Converting percents to fractions
  • Multiply any number by twelve
  • Trick for dividing a number by nine
  • Mental math: Subtract a near multiple of 10 from a two-digit number by adjusting
  • Finger tricks for multiplication
  • Non-transitive games
  • Combination and permutation word problems
  • Arranging in a circle
  • Difference between rational and irrational numbers
  • Dividing decimals
  • Multiplying decimals
  • Adding and subtracting mixed numbers
  • Graphing the absolute value function under transformations from equations
  • Converting between decimals and percents
  • Converting decimals to percents
  • Box plots
  • Bearings
  • Surface area
  • Surface area of a cylinder
  • Adding and subtracting square root expressions
  • Disc and washer methods (circular cross sections)
  • Shell method
  • Geometric series
  • Icosian game
  • Horizontal and vertical lines
  • Converting standard form to slope-intercept form
  • Area of kites and rhombuses
  • Area of a kite
  • Expanding quadratic expressions using algebra tiles
  • Solving linear systems of equations in two variables by graphing
  • Other resources
  • Factoring monic quadratics using algebra tiles
  • Other resources
  • Other resources
  • Is it injective?
  • Injective, surjective, and bijective
  • Partial order
  • Compound interest
  • Simple and compound interest
  • Evaluating definite integrals using geometry
  • Adding mixed numbers
  • Subtracting mixed numbers
  • Simple interest
  • Trees
  • Graphing sin and cos under transformations
  • Graphing the tangent function under transformations
  • Is it surjective?
  • Finding polynomials given complex zeros
  • Finding polynomials given irrational zeros
  • Finding polynomials given integer zeros
  • Finding polynomials given zeros
  • Functions (algebra 1)
  • Linear equations and inequalities
  • Intersection of circle and line
  • Absolute value, piecewise, and step functions
  • Evaluating piecewise functions
  • Graphing piecewise functions
  • Find the equation of a piecewise function from its graph
  • Dividing rational expressions
  • Sketching logarithmic functions under transformations
  • Graphing the natural logarithm function under transformations
  • Expanding logarithmic expressions
  • Condensing logarithmic expressions
  • Expanding and condensing logarithmic expressions
  • Solving trig equations
  • Solving harder trig equations by factoring
  • Other resources
  • Finding the inverse of exponential functions
  • Evaluating natural logarithms
  • Solving logarithmic equations with different bases
  • Applications of logarithms
  • Properties of logarithms
  • Multiplying and dividing fractions
  • Converting English to propositional logic
  • Syntax of propositional logic
  • Truth tables
  • Basic propositional logic proofs using natural deduction
  • Rules of inference
  • Modus ponens
  • Modus tollens
  • Disjunctive syllogism
  • Constructive dilemma
  • Destructive dilemma
  • Conjunction introduction and elimination
  • Biconditional introduction and elimination
  • Disjunction introduction
  • Finding the inverse of functions
  • Matrix multiplication
  • Basic transformation matrices
  • Division of multi-digit by one-digit
  • Currency conversion
  • Converting decimals to fractions
  • Adding and subtracting decimals
  • Other resources
  • Converting percents to decimals
  • Percent increase
  • Percent decrease
  • Converting between scientific notation and standard form
  • Converting scientific notation to standard form
  • Converting standard form to scientific notation
  • Standard form to power of ten
  • Intro to slope
  • Finding slope from a graph
  • Finding missing angles in right triangles
  • Zero product property
  • Finding missing side lengths in right triangles
  • Angle bisector theorem
  • Approximating definite integrals
  • Find the orthocenter from coordinates
  • Derivatives of inverse trigonometric functions
  • Proof: Sum identities
  • Limits
  • Finding limits of trigonometric functions
  • Other resources
  • Proofs
  • Triangle angle bisector theorem
  • Converting vertex form to standard form
  • Graphing parabolas in intercept form
  • Simplifying the difference quotient
  • Proving the law of cosines
  • Graphing linear equations in standard form
  • Find a perpendicular or parallel line
  • Find the parallel line
  • Find the perpendicular line
  • Find the parabola from its vertex and a point
  • Solving separable differential equations
  • Proving the law of sines
  • Linear programming
  • Minimization (mathematical problems)
  • Maximization (mathematical problems)
  • Finding a side given an angle and a side
  • Converting repeating decimals to fractions
  • Volume of a cone
  • Solving a quadratic by trial and improvement
  • Other resources
  • Normal distribution
  • Binomial theorem and Pascal's triangle
  • Exponential growth and decay (calculus 1)
  • Functions of displacement
  • Derivatives of trigonometric functions
  • Derivatives of logarithmic functions
  • Mechanics
  • Common knowledge puzzle
  • Locker Problem
  • Other resources
  • Standard form of ellipse equations from graphs
  • Scatter plots
  • Average speed from travel graph
  • Finding the sum of a telescoping series
  • Plotting inequalities on a number line
  • Circles (conic sections)
  • Other resources
  • Finding or estimating the mean from a frequency table
  • Binomial expansion
  • Iterated function systems
  • Other resources
  • Binomial distribution
  • Mean
  • Converting terminating decimals to fractions
  • Solving linear equations and expanding brackets
  • Remainder theorem
  • Intro to the dot product
  • Inner product
  • Cross product
  • Eigenvalues and eigenvectors
  • Diagonalization
  • Area of a triangle using determinant
  • Cramer's rule
  • Applications of the dot product
  • Orthogonal vectors
  • Proof: Vector addition is commutative and associative
  • Adding vectors
  • Multiplying a vector by a scalar
  • Length of a vector
  • Limits that do not exist
  • Finding limits by rationalizing
  • Finding limits by factoring
  • Epsilon-delta definition of limits
  • Finding one-sided limits
  • Knights and Knaves
  • Find the inverse of a trigonometric function
  • Derivative of a function from first principles
  • Rolle's theorem
  • Mean value theorem
  • First derivative test
  • Concavity
  • Linear approximation
  • Reverse power rule for indefinite integrals
  • Properties of antiderivatives
  • Other resources
  • First fundamental theorem of calculus
  • Using the natural log rule
  • Integrating trigonometric functions
  • 3D vectors
  • Definition of \(\mathbb{R}^n\)
  • Other resources
  • Properties of vector addition
  • Properties of vector addition and scalar multiplication
  • Other resources
  • Proof: Derivative of \(\sec(x)\)
  • Proof: Derivative of \(\sin(x)\)
  • Sum formulas
  • Proof: Derivative of \(\tan(x)\)
  • Solving linear systems of equations
  • Solving linear systems of equations using matrix inverses
  • Solving linear systems of equations in three variables using Gaussian elimination
  • Consistency of a system of linear equations
  • Inverse of a \(3{\times}3\) matrix using row operations
  • Inverse of a \(4{\times}4\) matrix using row operations
  • Determinant using row echelon form
  • Inverse of \(3{\times}3\) matrix using determinants and cofactors
  • Solving linear systems in two variables using Cramer's rule
  • Solving linear systems in three variables using Cramer's rule
  • Determinant using cofactors
  • Determinant of a \(4{\times}4\) matrix using cofactors
  • Determinant using row operations
  • Determinant of a \(4{\times}4\) matrix using row operations
  • Linear transformations
  • Linear combinations
  • Linear transformations on \(\mathbb{R}^2\)
  • Basis
  • Basis for a null space
  • Basis for a span
  • Separating rational and irrational components in a binomial expansion
  • Multiplying mixed numbers
  • Volume of a sphere (calculus \(2\))
  • Solving perfect square quadratics by factoring
  • Solving quadratics by factoring (difference of squares)
  • Introduction to sets
  • Set equality and subsets
  • Sets
  • Set operations
  • Binary relations
  • Vertical line test
  • Intro to multivariable functions
  • Two point form
  • Solving linear systems of equations in three variables
  • Solving linear systems of equations in three variables (word problems)
  • Statistics and probability for undergraduates
  • Pólya urn model
  • Half angle identities
  • Converting between radians and degrees
  • Coterminal angles
  • Product-to-sum and sum-to-product formulas
  • Proof: Sum to product identity for sine
  • Proofs: Product to sum identities
  • Algebraic proof the cross product is distributive
  • Geometric proof the cross product is distributive
  • Proof the cross product is distributive
  • Determinant of a \(3{\times}3\) matrix
  • Determinant of a \(2{\times}2\) matrix
  • Competition problems (sum of a geometric progression)
  • Variation of parameters
  • Factoring by grouping (one variable, quadratic)
  • Factor by grouping
  • Identifying and factoring perfect square trinomials
  • Elementary matrices
  • Matrix inverses
  • Power method
  • Shifted inverse power method
  • Gershgorin circle theorem
  • Graphing linear inequalities in point-slope form
  • Finding two-variable inequalities from their graphs
  • Operations with functions
  • Adding and subtracting functions
  • Dividing functions and finding the domain
  • Find \(f \cdot g\) and its domain
  • Recurrence relations
  • Trig substitutions
  • Partial fraction decomposition
  • Solving square root equations
  • Finding and plotting the domain of a function
  • Graphing linear inequalities in two variables
  • Credit and borrowing
  • Simpson's rule
  • Sketching slope fields
  • Matching slope fields with equations
  • Spirograph
  • Harmonograph
  • Overfitting
  • Verifying solutions to differential equations
  • Initial value problems
  • Euler's method
  • Separable first order differential equations
  • Parabolas (conic sections)
  • Graphing the sine and cosine functions under transformations
  • Other topics
  • Proof: Only one magic square of size three
  • Motivation for learning statistics and probability
  • Peano arithmetic
  • Slide rules and log tables
  • \(\sin(z) = 2\)
  • Approximating square roots to hundredths
  • Approximating square roots to tenths
  • False proofs
  • Graphing linear equations in point-slope form
  • Graphing horizontal and vertical equations
  • Complex exponentiation
  • \(i^i\)
  • Naive set theory
  • Negation (bridge course)
  • Relations
  • Equivalence relations
  • Tautologies and contradictions
  • Functions (bridge course)
  • Proving parallelograms with two column proofs
  • Proof
  • Heron's formula
  • Area of a triangle
  • Disjunction
  • Arithmetic properties
  • Additive identity
  • Converting improper fractions to mixed numbers
  • Converting degrees to radians
  • Converting radians to degrees
  • Converting units of measure
  • Converting between minutes and seconds
  • Range
  • Converting mixed numbers to improper fractions
  • Rearrangement proof: Pythagorean theorem
  • Using the Pythagorean theorem (easier mathematical problems)
  • Mode
  • Adjacent angles
  • Integration by parts
  • Other resources
  • Disjoint sets
  • What is symmetric difference?
  • Basic indefinite integrals
  • Perimeter of composite figures
  • Other resources
  • Hyperbola
  • Graphing ellipses
  • Inverse trig functions
  • Tangent half-angle substitution
  • IMO problems
  • Julia set
  • Proving the sum and difference of cubes formulas
  • Visual proof: Area of a circle
  • Squeeze theorem
  • Proof
  • Proof: Derivative of \(\cos(x)\)
  • Proof: Morrie's law
  • Proof: Generalization of Morrie's law
  • Proof
  • Proving Morrie's law and its generalization
  • Proving Mollweide's formula
  • Proofs
  • Proof: Sum of the interior angles of a simple polygon
  • Sum of the interior angles of a simple polygon (algebra problems)
  • Sum of the interior angles for simple polygons
  • General chain rule
  • Other resources
  • Graphing sin and cos
  • Graphing tan and cot
  • Exponents of decimals
  • Finding an angle using the law of cosines
  • Solving triangles using the law of cosines
  • Find a length using the law of sines
  • Find an angle using the law of sines
  • Solving triangles using the law of sines
  • Proving the product rule
  • Pythagorean identities
  • Using the Pythagorean identities
  • Proving the Pythagorean identities
  • Proof
  • Symmetric group
  • Symmetries of an equilateral triangle
  • Is it bijective? (infinite domain)
  • Adding and subtracting matrices
  • Practice
  • Multiplying a matrix by a scalar
  • Practice
  • Area of a triangle using determinants
  • Determinant of a \(3{\times}3\) matrix using expansion by minors
  • Determinant of a \(3{\times}3\) matrix using the diagonal method
  • Intuition: Determinants
  • Intuition: Matrix multiplication
  • Solving matrix equations
  • Solving linear systems of equations in two variables (word problems)
  • Converting circle equations between standard and general form
  • Converting circle equations from standard to general form
  • Converting circle equations from general to standard form
  • Double factorial
  • Other resources
  • Solving unit rate problems
  • Exterior angle theorem
  • Proof
  • Using the theorem
  • Finding the center and radius of a circle by completing the square
  • Binary
  • Multiplying mixed numbers (word problems)
  • Other resources
  • Add within 5
  • Subtract within 5
  • Finger trick for multiplying 6-10 by 6-10
  • Elapsed time
  • Division with small divisor using base ten blocks
  • Division with partial quotients
  • Lattice multiplication
  • Multiplying two-digit numbers using base ten blocks
  • Add within 10 using fingers
  • Subtract within 10 using fingers
  • Multiplying integers using two color counters
  • Adding integers using two color counters
  • Subtracting integers using two color counters
  • Area model for division
  • Finding the area of composite figures by adding
  • Finding the area of composite figures by subtracting
  • Finding the area of composite figures (grade 3)
  • Commutative property of addition (prealgebra)
  • Other resources
  • Other resources
  • Making 10 using a tens frame (concrete)
  • Making 10
  • Add within 20
  • Subtract within 20
  • Lattice division
  • Long division (grade 4)
  • Multiplying two-digit numbers using partial products
  • Subtraction using partial differences
  • Breaking apart to add within 1000
  • Multiplying multi-digit numbers by one-digit numbers using base ten blocks
  • Subtracting within 1000 using base ten blocks
  • Add within 1000
  • Add within 1000 using base ten blocks
  • Adding and subtracting fractions with like denominators using the length model
  • Comparing and ordering fractions with like denominators
  • Equivalent fractions using fraction sectors
  • Equivalent fractions using the length model
  • Adding and subtracting fractions with like denominators (concrete and visual methods)
  • Multiplying fractions using the area and length models
  • Converting improper fractions to mixed numbers using fraction rectangles and two color counters
  • Congruent figures
  • Other resources
  • Ordinal numbers
  • Angle Wars
  • Other resources
  • Other resources
  • Subtracting fractions with unlike denominators
  • Identity element of multiplication and division
  • Adding polynomials
  • Subtracting polynomials
  • Subtracting mixed numbers without regrouping
  • Dividing decimals by whole numbers
  • Divisibility tests
  • Adding within 100 without regrouping (abstract method)
  • Adding within 100 without regrouping using base ten blocks
  • Adding and subtracting within 1000 using place value blocks
  • Special education
  • Adding integers using a number line
  • Dividing integers using Algeblocks
  • Multiplying integers using Algeblocks
  • Subtracting integers using a number line
  • Multiplying linear expressions using Algeblocks
  • Factoring trinomials using the box method
  • Subtracting by counting up
  • Adding and subtracting fractions with like denominators using the set model
  • Dividing fractions using the set model
  • Other resources
  • Comparing and ordering fractions with unlike denominators using the length model
  • Comparing and ordering fractions with like denominators using the set model
  • Subtracting fractions with unlike denominators using the area model
  • Dividing fractions using the area model
  • Shikaku
  • Comparing and ordering fractions with unlike denominators using the area model
  • Converting improper fractions to mixed numbers using fraction rectangles
  • Multiplying whole numbers and fractions using two color counters
  • Converting mixed numbers to improper fractions using fraction rectangles
  • Adding fractions with unlike denominators using the length model
  • Adding fractions with unlike denominators using the area model
  • Adding fractions with unlike denominators using the set model
  • Subtracting fractions with unlike denominators using the set model
  • Subtracting fractions with unlike denominators using the length model
  • Decomposing fractions using fraction rectangles
  • Multiplying whole numbers and fractions using the area model
  • Multiplying fractions using the length model
  • Comparing and ordering fractions with unlike denominators using the set model
  • Multiplying fractions using the set model
  • Dividing fractions using the length model
  • Comparing and ordering fractions with like denominators using the area model
  • Adding and subtracting fractions with like denominators using the area model
  • Comparing fractions with unlike denominators using the set model
  • Comparing and ordering fractions with like denominators using the length model
  • Preschool
  • Representing 1-10
  • Songs about shapes
  • Golden beads addition
  • Division using the bead board
  • Subtracting three-digit numbers using the stamp game
  • Adding within 1000 (concrete and pictorial)
  • Add within 1000 (abstract)
  • Trapezoid midsegment theorem
  • Ordering triangle sides and angles
  • Finding the inverse of square root functions
  • Finding the domain and range of quadratic functions
  • Finding the domain and range of square root functions
  • Finding the rate of change from tables
  • Graphing exponential functions under transformations
  • Add within \(10\) using the strip board
  • Adding multi-digit numbers using the bead frame
  • Adding multi-digit numbers
  • Subtracting multi-digit numbers
  • Subtracting three-digit numbers using the chip model
  • Adding and subtracting within 1000
  • Adding within 1000 using the chip model
  • Adding and subtracting within 100
  • Adding within 100
  • Subtracting within 100
  • Other resources
  • Word problem strategies
  • Adding and subtracting within 1000 using a number line
  • Adding within 100 using base ten blocks
  • Add within 20 using number bonds
  • Add within 10 using counters
  • Subtract within 10 using counters or two color counters
  • Other resources
  • Other resources
  • Number pairs
  • Multiplication using counters and paper plates
  • Making change
  • Division using manipulatives (grade 4)
  • Eureka Math, grade 1
  • Eureka Math, grade 1, module 1
  • Eureka Math, grade 1, module 2
  • Eureka Math, grade 1, module 3
  • Eureka Math, grade 1, module 4
  • Eureka Math, grade 1, module 5
  • Eureka Math, grade 1, module 6
  • Compare within 10 by pairing
  • Eureka Math, grade 2
  • Eureka Math, grade 2, module 1
  • Eureka Math, grade 2, module 2
  • Eureka Math, grade 2, module 3
  • Eureka Math, grade 2, module 4
  • Eureka Math, grade 2, module 5
  • Eureka Math, grade 2, module 6
  • Eureka Math, grade 2, module 7
  • Eureka Math, grade 2, module 8
  • Eureka Math, grade 3
  • Eureka Math, grade 3, module 1
  • Eureka Math, grade 3, module 2
  • Eureka Math, grade 3, module 3
  • Eureka Math, grade 3, module 4
  • Eureka Math, grade 3, module 5
  • Eureka Math, grade 3, module 6
  • Eureka Math, grade 3, module 7
  • Eureka Math, grade 4
  • Eureka Math, grade 4, module 1
  • Eureka Math, grade 4, module 2
  • Eureka Math, grade 4, module 3
  • Eureka Math, grade 4, module 4
  • Eureka Math, grade 4, module 5
  • Eureka Math, grade 4, module 6
  • Eureka Math, grade 4, module 7
  • Eureka Math, grade 5
  • Multiplying whole numbers using the standard algorithm
  • Eureka Math, grade 5, module 1
  • Eureka Math, grade 5, module 2
  • Eureka Math, grade 5, module 3
  • Eureka Math, grade 5, module 4
  • Eureka Math, grade 5, module 5
  • Eureka Math, grade 5, module 6
  • Tabular and graphical estimation of limits
  • Finding limits at infinity
  • Topology teasers
  • Reflecting across axes
  • Reflecting points across axes
  • Reflecting line segments and polygons (grade 8)
  • Estimating limits from tables
  • Add within 1000 using the standard algorithm
  • Counting by 2s starting from any number
  • Other resources
  • Adding and subtracting fractions with unlike denominators
  • Oh Snap!
  • Rounding to the nearest 10 or 100
  • Multiplying 10s (grade 3)
  • Subtracting three-digit numbers using the standard algorithm
  • Converting between words and numbers
  • Converting between whole numbers and expanded form
  • Graphing linear inequalities in slope-intercept form
  • Multiplying binomials
  • Multiplying fractions (concrete and pictorial methods)
  • Classifying real numbers
  • Subtracting mixed numbers using a visual model
  • Approximating square roots
  • Multiplying two-digit numbers using the stamp game
  • Multiplying two-digit numbers using manipulatives
  • Subtracting multi-digit numbers with regrouping using the bead frame
  • Infinity Street
  • Multiplying multi-digit numbers by one-digit numbers using the stamp game
  • Adding multi-digit numbers with regrouping using the stamp game
  • Adding multi-digit numbers without regrouping using base ten blocks
  • Subtracting multi-digit numbers using base ten blocks
  • Adding multi-digit numbers with regrouping using base ten blocks
  • Estimating multi-digit division
  • Finding cube roots using units, tens, and hundreds place blocks
  • Finding square roots using units, tens, and hundreds place beads
  • Multiplying whole numbers using the flat bead board
  • Adding multi-digit numbers with regrouping using the dot game
  • Adding multi-digit numbers without regrouping using the dot game
  • Multiplying multi-digit numbers by one-digit numbers using the bank game
  • Finding square roots with backtracking, using units, tens, hundreds, and thousands place beads
  • Non-decimal bases
  • Making 10 using the addition strip board (concrete)
  • Subtracting multi-digit numbers without regrouping using the bead frame
  • Subtract within 100 using base ten blocks
  • Money word problems
  • Plotting fractions on the number line
  • Unit fractions on the number line
  • Decomposing fractions
  • Adding three numbers in any order
  • Additive identity
  • Addition is commutative (without variables)
  • Subtract within 20 using counters or pictures
  • Subtract within 20 using bar models
  • Subtract within 10 using number bonds
  • Add within 10 using number bonds
  • Add using place value
  • Adding ones or tens using base ten blocks
  • Add within 20 using ten frames
  • Adding ones with regrouping
  • Naming shapes (grade 2)
  • Breaking apart to add within 100
  • Other resources
  • Counting to 10
  • Other resources
  • Count within 1000 by 10s starting at any number
  • Count forwards or backwards by 100s starting at any number
  • Other resources
  • Making bar graphs
  • Comparison word problems
  • Multiply using counters
  • Intersection of parabola and line
  • Comparing numbers within 100 (concrete and visual methods)
  • Bounding square roots
  • Volume of a cylinder (mathematical problems)
  • Volume of spheres
  • Volume of cones, cylinders, and spheres
  • Find a side using the law of cosines (mathematical problems)
  • Finding an angle using the law of cosines (mathematical problems)
  • Finding a length using the law of sines (mathematical problems)
  • Finding a length using the law of sines (word problems)
  • Slope-intercept equation from a graph
  • Lesson
  • Graphing proportional relationships
  • Solving linear equations (word problems)
  • Expanding and factoring
  • Solving quadratic equations by factoring (word problems)
  • Solving quadratic equations by factoring (mathematical problems)
  • Multiplying and dividing rational expressions
  • Other resources
  • Other resources
  • Ratios, rates, and percentages
  • Buffon's needle
  • Paradox: Birthday problem
  • Converting terminating decimals to fractions with denominators 10 or 100
  • Plotting decimals on a number line
  • Other resources
  • Solving systems of linear equations in two variables by substitution (word problems)
  • Solving multi-step linear equations involving simple interest (word problems)
  • Mixture problems
  • Adding measurements with different units (word problems)
  • Other resources
  • Other resources
  • Factoring monomials completely
  • Multiplying monomials by polynomials
  • Intercepts from a graph
  • Understanding slope with similar triangles
  • Other resources
  • Translation
  • Drawing quarter turn rotations about the origin
  • Subtracting fractions with unlike denominators using graph paper
  • Division (grade 3, concrete and visual)
  • Adding a two-digit number and a multiple of ten
  • Add within 10 using a number line
  • Subtract within 10 using a number line
  • Compare within 10 on the number line
  • Other resources
  • Polynomial factorization, division, and end behavior
  • Graphing parabolas in standard form
  • Graphing quadratics in vertex form
  • Other resources
  • Intercepts of a linear function from a table
  • Number of solutions to a system of equations algebraically
  • Graphing linear equations (word problems)
  • Difference between functions and relations
  • Measures of central tendency from stem and leaf plots
  • Other resources
  • Finding area by counting unit squares (whole number side lengths)
  • Area of a rectangle with fractional side lengths
  • Other resources
  • Exponentiation as repeated multiplication
  • Discrete vs continuous functions
  • Solving linear equations with decimals
  • Estimate sums within 1000
  • Adding and subtracting within 100 on your fingers
  • Count to 120 by ones
  • Order of operations with decimals
  • Equivalent fractions on a number line
  • Solving two-step equations (word problems)
  • Multiplying decimals by whole numbers
  • Verifying inverse functions
  • Other resources
  • Graphing ellipses in general form
  • Breaking apart to subtract within 100
  • Missing number problems with multiplication and division
  • Multiplying one-digit by two-digit numbers using the box method
  • Breaking apart to subtract within 100 without regrouping
  • Breaking apart to subtract within 100 with regrouping
  • Percents (word problems)
  • Multiplying trinomials
  • Multiplying mixed numbers (easier mathematical problems)
  • Long multiplication
  • Multiplying two-digit numbers using the box method
  • Vertical angles theorem
  • Solving two-step equations with decimals
  • Comparing fractions using the butterfly method
  • Comparing fractions using manipulatives
  • Multiplying multi-digit numbers with area models
  • Constructing angle and segment bisectors
  • Cofunction identities
  • Hinge theorem and its converse
  • Finding angles of elevation and depression
  • Definite integration by trigonometric substitution
  • Integrals involving trig functions
  • Improper integrals
  • Other resources
  • Intersections of lines, circles, and parabolas
  • Other resources
  • Evaluating natural logarithms with a calculator
  • Graphing hyperbolas in standard form
  • Graphing tan and cot under transformations
  • Graphing sec and csc under transformations
  • Polar coordinates
  • Solving absolute value equations and inequalities
  • Solving absolute value equations
  • Limit comparison test
  • Ratio test
  • Root test
  • Verifying trigonometric identities involving the sum and difference formulas
  • Verifying trig identities involving the half and double angle formulas
  • Ratios and proportions (word problems)
  • Solving linear systems of equations in three variables by substitution
  • Other resources
  • Scientific notation, word problems
  • Average value over an interval
  • Integrating exponential functions by u-substitution
  • Converting between decimals and mixed numbers
  • Converting mixed numbers to decimals
  • Converting decimals to mixed numbers
  • Microsoft Excel
  • Fraction arithmetic
  • Adding and subtracting rational expressions with like denominators
  • Adding and subtracting rational expressions with unlike denominators
  • Multiplying rational expressions
  • Other resources
  • Constant multiple rule for derivatives
  • Extreme value theorem
  • Gaussian elimination
  • Gauss–Jordan elimination
  • Adding and subtracting radicals
  • Other resources
  • Absolute value function under transformations, inequalities
  • Solving one-step absolute value equations
  • Solving two-step absolute value equations
  • Converting exponential form to logarithmic form
  • Converting logarithmic form to exponential form
  • Converting between logarithmic form and exponential form
  • Other resources
  • Sum of the interior angles for regular polygons
  • Other resources
  • Converting between polar and Cartesian form
  • Converting Cartesian points to polar points
  • Converting polar points to Cartesian points
  • Second derivative test
  • Find a side using the law of cosines (word problems)
  • Solving linear systems in slope-intercept form by graphing
  • Solving linear systems of equations in standard form and two variables by graphing
  • Solving and graphing linear inequalities (word problems)
  • Finding asymptotes of rational functions
  • Solving linear systems of equations in two variables using matrix inverses
  • Law of sines (word problems)
  • Circular permutations
  • Simplifying square roots of rational expressions
  • Simplifying radical expressions
  • Other resources
  • Finding reference angles
  • Evaluating trigonometric functions using reference angles
  • Other resources
  • Solving exponential equations using logarithms
  • Other resources
  • Factor theorem
  • Derivatives of natural logarithmic functions
  • Sign of the discriminant
  • Using your calculator
  • Solving linear equations with fractions
  • Earning and managing money
  • Investing money
  • Taxation
  • Graphing the sum of trig functions from their graphs
  • Subtracting functions (linear-linear)
  • Graphing ellipses at the origin
  • Graphing ellipses not at the origin
  • Graphing circles in general form
  • Graphing circles in standard form
  • Graphing the cotangent function under transformations
  • Graphing csc under transformations
  • Graphing circles
  • Determining the type of conic from its equation
  • Properties of radicals
  • Finding the general form of an ellipse by completing the square
  • Graphing hyperbolas in general form
  • Finding the domain of logarithmic functions under transformations
  • Triple integrals
  • Reducing fractions using prime factorization
  • Adding decimals
  • Finding the domain of the sum of functions
  • Holiday math
  • Using the derivatives of the hyperbolic functions
  • Alternating series test
  • Using the theorems
  • Comparison test
  • Finding the other zeros given complex zeros
  • Finding the inverse of a relation on a finite set
  • Graphing a line given a point and a slope
  • Wilcoxon rank-sum test
  • Survey problems
  • Work problems
  • Testing solutions to equations
  • Testing solutions to one-variable inequalities
  • Testing solutions to linear systems of equations in two variables
  • Solving linear equations involving perimeter
  • Wind and current problems
  • Consecutive integer problems
  • Rate problems
  • Solving coin and stamp problems
  • Converting ellipse equations from standard form to general form
  • Converting ellipse equations from general form to standard form
  • Converting ellipse equations between standard form and general form
  • Finding the LCD of rational expressions
  • Multiplying in scientific notation
  • Dividing in scientific notation
  • Converting units of measurement (grade 5)
  • Other resources
  • Solving right triangles (word problems)
  • Graphing sec under transformations
  • Pythagorean theorem (word problems)
  • Solving trigonometric equations using a calculator
  • Adding and subtracting DMS
  • Evaluating trig functions
  • Evaluating trigonometric functions using a calculator
  • Adding and subtracting mixed numbers with unlike denominators
  • Adding and subtracting mixed numbers with like denominators
  • Intersection of parabola and circle
  • Lattice multiplication with decimals
  • Finding the LCD of fractions
  • Desmos
  • Alternating harmonic series
  • Finding the domain and range of piecewise functions
  • Integrating logarithmic functions
  • Plotting integers on a number line
  • Intro to negative numbers
  • Graph a line given \(x\) and \(y\) intercepts
  • Other resources
  • Applying derivatives to analyze functions
  • Solving nonlinear systems in two variables (word problems)
  • Finding missing side lengths in right triangles (word problems)
  • Solving trigonometric equations using t-results
  • Verifying trigonometric identities using t-formulas
  • Two column proofs
  • Solving trigonometric equations quadratic in form
  • Add by making 10s
  • Simplifying square roots of decimals and fractions
  • Subtracting within 100 with regrouping
  • Number of solutions to linear equations
  • Number of real roots of a quadratic
  • Maclaurin series
  • Taylor series
  • Other resources
  • Practice
  • Solving trigonometric equations using sum and difference formulas
  • Manipulatives
  • Number disks
  • Adding multi-digit numbers from left to right
  • Finding the whole
  • Percents: Finding the percent
  • Solving and graphing logarithmic inequalities
  • Graphing the absolute value function
  • Derivatives of inverse functions
  • Finding the inverse of cube root functions
  • Probability with geometry
  • Subtracto Bingo
  • Cryptography
  • Sieve of Eratosthenes
  • Mills's constant
  • Caesar cipher
  • Dijkstra's algorithm
  • Fleury's algorithm
  • Kruskal's algorithm
  • Collecting data
  • Logistic growth
  • Apportionment
  • Octal
  • Hexadecimal
  • Adding and subtracting in binary
  • Hamilton's method
  • Jefferson's method
  • Webster's method
  • Huntington–Hill method
  • Lowndes's method
  • Voting
  • Weighted voting
  • Scheduling
  • Fair division
  • Using even-odd identities to evaluate trigonometric functions
  • Using the theorem
  • Using the theorem
  • Categorical propositions
  • Propositional logic
  • Predicate logic
  • Informal and inductive logic
  • Challenge
  • Adding and subtracting rational trig expressions
  • Using the theorems
  • Simplifying rational trigonometric expressions
  • Finding the inverse of logarithmic functions
  • Solving linear equations with congruent triangles
  • SAS congruence
  • ASA and AAS congruence
  • Dividing square roots
  • Finding the domain of radical functions (monic linear functions)
  • Finding the domain of radical functions (non-monic linear functions)
  • Finding the domain of radical functions (quadratic functions)
  • Other resources
  • Partial sum of an arithmetic series
  • Other resources
  • Multiplying and dividing decimals by powers of ten
  • Vector projection
  • Proof: Vector projection formula
  • Applications of vectors
  • Proving De Moivre's formula by induction
  • Powers of complex numbers using De Moivre's formula
  • First order differential equations
  • First order homogeneous differential equations
  • Using the theorems
  • Using the power reducing identities to evaluate or simplify expressions
  • Comparing fractions with the same numerators or denominators
  • Multiplying fractions and mixed numbers using a visual model
  • Second order differential equations
  • Exact first order differential equations
  • Reduction of order
  • Factoring quadratic equations by graphing
  • Finding the eigenvalues and eigenvectors of \(2{\times}2\) matrices
  • Finding the eigenvalues and eigenvectors of \(3{\times}3\) matrices
  • Finding the eigenvalues and eigenvectors of \(4{\times}4\) matrices
  • Other resources
  • Largest rectangle in a semicircle
  • Apportionment paradox
  • Finding one-sided limits from graphs
  • Sum and difference formulas for sine
  • Sum and difference formulas for tangent
  • Sum formula for cosine
  • Sum formula for tangent
  • Proof
  • Proof: Sum formula for tangent
  • Using the sum formula for tangent
  • Difference formula for tangent
  • Proof 1
  • Using the difference formula for tangent
  • Parallel vectors
  • Test preparation
  • ACT math
  • Other resources
  • Find the value of \(c\) that completes the square
  • Converting standard form to vertex form without completing the square
  • Finding the domain and range of rational functions
  • Finding the domain of rational functions involving radicals
  • Finding extrema graphically
  • Using the theorem
  • Using the difference formula for cosine
  • Converting between DMS and degrees
  • Converting between radicals and rational exponents
  • Converting radicals to rational exponents
  • Converting rational exponents to radicals
  • Classifying polynomials
  • Finding and classifying discontinuities
  • Is the sequence arithmetic, geometric, or neither?
  • Are the vectors parallel, orthogonal, or neither?
  • Finding the domain of rational functions (linear denominator)
  • Finding the quadrant of an angle in degrees
  • Finding the quadrant of an angle in radians
  • Finding the domain of rational functions (quadratic denominator)
  • Pythagorean inequality theorem
  • Evaluating trigonometric functions using the unit circle (negative angles)
  • Graphing exponential functions (reflection and horizontal shift)
  • Graphing exponential functions (stretch and compress)
  • Graphing basic exponential functions by plotting points
  • Evaluating trigonometric functions of angles in degrees using reference angles
  • Evaluating trigonometric functions of angles in radians using reference angles
  • Characteristics of functions
  • Differentiability of a function
  • Collinear points
  • Coplanar points and lines
  • Find the number of sides for a regular polygon given one interior angle
  • Find the number of sides for a regular polygon given one exterior angle
  • Find the number of sides for a simple polygon given the sum of interior angles
  • Is the equation linear?
  • Domain of linear functions
  • Finding the domain and range of the absolute value function under transformations
  • Finding the domain and range of logarithmic functions under transformations
  • Evaluating the six basic trig functions given a point
  • Finding the domain and range of functions from their graphs
  • Finding the domain and range of functions (finite set of ordered pairs)
  • Find the first \(n\) terms of a geometric progression
  • Perpendicular bisector theorem and its converse
  • Finding critical values using derivatives
  • Unit vectors
  • Finding the unit vector
  • Finding the domain and range of functions from tables
  • Practice
  • Lesson
  • Find the angle given the value of a reciprocal trigonometric function
  • What is a relation?
  • Graphing linear equations from tables
  • Finding basic limits
  • Finding limits of rational functions
  • Finding limits by simplifying complex fractions
  • Find one exterior angle given the number of sides for a regular polygon
  • Evaluating trigonometric functions using coterminal angles
  • Evaluating the tangent of angles in degrees using the sum formula for tangent
  • Evaluating the tangent of angles in radians using the sum formula for tangent
  • Evaluating the tangent of angles in degrees using the difference formula for tangent
  • Evaluating the tangent of angles in radians using the difference formula for tangent
  • Area and perimeter of parallelograms
  • Finding the \(n\)th term of a binomial expansion
  • Graphing exponential functions (vertical shift)
  • Using the Pythagorean theorem to find the missing side of a right triangle
  • Finding missing side lengths in special right triangles
  • Sketching the inverse of a function from its graph
  • Finding the inverse of quadratic functions
  • Other resources
  • Graphing the secant function under transformations (phase and vertical shift)
  • Graphing the secant function under transformations (period and amplitude)
  • Higher order derivatives
  • Convergent and divergent geometric series
  • Finding the \(x\) and \(y\) intercepts of rational functions
  • Volume and surface area
  • Derivatives of transcendental functions
  • Volume of prisms and cylinders
  • Proof
  • Intro
  • Evaluating finite sets using Venn diagrams
  • Set union
  • Set intersection
  • Using the difference formula for cosine when given two right triangles
  • Using the difference formula for tangent when given two right triangles
  • Solving quintic polynomials
  • Solving quartic polynomials
  • Other resources
  • Graphing hyperbolas centered at the origin
  • Graphing vertical parabolas not at the origin
  • Graphing the tangent function under transformations (period and amplitude)
  • Graphing the tangent function under transformations (phase and vertical shift)
  • Solving multi-step absolute value equations
  • Solving exponential equations using the one-to-one property
  • Other resources
  • Sketching logarithmic functions under transformations (level 2)
  • Systems of inequalities, horizontal and vertical lines
  • Adding and subtracting vectors
  • Finding the rate of change (word problems)
  • Graphing exponential functions with base \(e\)
  • Graphing horizontal ellipses at the origin
  • Graphing vertical ellipses at the origin
  • Graphing horizontal parabolas at the origin
  • Graphing horizontal parabolas not at the origin
  • Graphing vertical ellipses in general form
  • Graphing vertical parabolas at the origin
  • Graphing the cube root function under transformations
  • Solving exponential equations with fractional powers
  • Other resources
  • Graphing inequalities in one variable
  • Other resources
  • Solving polynomials (difference of two squares)
  • Other resources
  • Other resources
  • Solving logarithmic equations using the quadratic formula
  • Multiplying by 5 (Trachtenberg system)
  • Other resources
  • Other resources
  • Evaluating the six basic trig functions given a triangle
  • Evaluating trigonometric functions using special right triangles
  • Evaluating logarithmic expressions using the one-to-one property
  • Solving linear systems of equations in two variables by elimination (basic)
  • Solving trigonometric equations by factoring out the GCD (no angle constraint)
  • Solving trigonometric equations by factoring out the GCD (angle constraint)
  • Finding the value that makes the function continuous
  • Second fundamental theorem of calculus
  • Fundamental theorem of calculus
  • Geometric mean
  • Graphing horizontal parabolas in general form
  • Graphing horizontal and vertical inequalities
  • Graphing logarithmic functions
  • Sketching logarithmic functions under transformations (level 3)
  • Sketching logarithmic functions under transformations (level 1)
  • Graphing parabolas in general form
  • Graphing vertical parabolas in general form
  • Systems of inequalities, slope-intercept form
  • Systems of inequalities, standard form
  • Graphing horizontal ellipses in general form
  • Other resources
  • Solving monic quadratics by factoring
  • Other resources
  • Other resources
  • Using the zero product property (polynomials)
  • Solving polynomials (non-factorable)
  • Finding the other zeros
  • Finding the other zeros given rational zeros
  • Finding the other zeros given irrational zeros
  • Other resources
  • Graphing sec and csc
  • Congruent polygons (algebra problems)
  • Other resources
  • Finding polynomials given rational zeros
  • Finding parabolas given three points
  • Finding linear equations from tables using first differences
  • Functions and relations
  • Eliminating the parameter
  • Rational functions
  • Other resources
  • Evaluating expressions with multiple variables
  • Other resources
  • Hypotenuse-leg congruence theorem
  • Simplifying radicals of monomials
  • Finding the domain of composite functions
  • Adding and subtracting cube root expressions
  • Testing ordered pair solutions to linear equations
  • Solving and graphing linear inequalities in two variables
  • Finding the GCD and LCM of polynomials
  • Finding the domain and range of relations
  • Negative bases
  • Distance between two numbers
  • Evaluating expressions with a single variable
  • Other resources
  • Multiplying perfect squares
  • Multiplying binomials by polynomials
  • Multiplying binomials by polynomials using the box method
  • Find the number of sides for a regular polygon given the sum of interior angles
  • Alternate interior angles theorem
  • Alternate exterior angles theorem
  • What is a radicand?
  • Multiplying binomials with square roots
  • Derivation: Area of a kite
  • Using the area of a triangle formula
  • Derivation: Area of a right triangle
  • Lesson
  • Intro to solving and graphing linear inequalities
  • Finding one-variable inequalities from graphs
  • Method 1
  • Lesson
  • What is a Saccheri quadrilateral?
  • Product of powers rule for exponents
  • Area of an equilateral triangle
  • Derivation
  • Isosceles triangle theorem and its converse
  • Find the parabola from its focus and directrix
  • Temperature conversion
  • Area of a segment
  • Reciprocals of mixed numbers
  • Zero matrix
  • Other resources
  • Set-builder notation
  • Area of an ellipse
  • Quotient of powers rule for exponents
  • Set complement
  • Lesson
  • Lesson
  • Integrating hyperbolic functions
  • Simplifying factorial expressions
  • Proving the absorption laws for sets
  • Proof: Intersection distributes over union
  • Proof: Composite of surjections is surjection
  • Book reviews
  • Compact sets
  • Competition problems (calculus 2)
  • Evaluating fractions raised to whole number powers
  • Cyclic quadrilaterals
  • Lesson
  • Solving exponential equations in quadratic form using u-substitution
  • Sustainability
  • Negative powers with variables
  • Negative powers without variables
  • Adding rational expressions (word problems)
  • Subtracting rational expressions (word problems)
  • Distance between a point and a line
  • Dividing polynomials with area models
  • Linear inequalities in one variable
  • Proof by induction (divisibility)
  • Proof by induction (matrices)
  • Proof by induction (recurrences)
  • Adding and subtracting rational expressions (word problems)
  • Lesson: Adding and subtracting rational expressions
  • Spherical geometry
  • List of math software
  • Lesson
  • List of math encyclopedias
  • Power of a product rule for exponents
  • What is a Lambert quadrilateral?
  • Non-Euclidean geometry
  • Diagonal length of a right rectangular prism
  • Geometric constructions
  • Proving the perpendicular bisector theorem
  • Proving the converse of the perpendicular bisector theorem
  • Proof: Sum of the exterior angles of a triangle
  • Ceva's theorem
  • Proving lines are parallel
  • Intercepts from a quadratic equation
  • Diagonals of a parallelogram bisect each other
  • Finding the diagonal length of a rectangle
  • Chord properties
  • Find the missing side given the perimeter
  • Subtract within 1000 (word problems)
  • Relate division to multiplication word problems
  • Time word problems
  • Line plots (grade 3)
  • Lesson
  • Multiplication using the array model
  • Breaking apart to subtract within 1000
  • Inquiry-based learning (kindergarten)
  • Inquiry-based learning (grade 1)
  • Inquiry-based learning (grade 2)
  • Inquiry-based learning (grade 3)
  • Inquiry-based learning (grade 4)
  • Inquiry-based learning (grade 5)
  • Inquiry-based learning (grade 6)
  • Inquiry-based learning (grade 7)
  • Inquiry-based learning (grade 8)
  • Inquiry-based learning (grade 9)
  • Inquiry-based learning (grade 10)
  • Inquiry-based learning (grade 11)
  • Inquiry-based learning (grade 12)
  • Using the theorem
  • Other resources
  • Using the theorem
  • Adding multi-digit numbers with regrouping using the standard algorithm
  • Division (grade 4 word problems)
  • Multiplying one-digit by three-digits
  • Multiplying whole numbers and fractions (word problems)
  • Estimating quotients
  • Multiplying 10s (grade 4)
  • Comparing fractions using tape diagrams (visual)
  • Subtracting multi-digit numbers with regrouping using the standard algorithm
  • Comparing decimals using a number line
  • Comparing fractions using a number line
  • Comparing decimals using fraction rectangles
  • Multiplying fractions (word problems)
  • Adding fractions with power of 10 denominators
  • Multi-step problems, properties of exponents
  • Identifying functions from ordered pairs and tables
  • Factoring difference of squares (concrete and visual methods)
  • Using the theorem
  • Geometric transformations
  • Finding the volume and surface area of composite figures
  • Comparing numbers in scientific notation
  • Recursive to explicit formula for arithmetic series
  • Finding the scale factor for similar polygons
  • Explicit to recursive formula for arithmetic series
  • Recursive to explicit formula for geometric sequences
  • Volume of a triangular prism
  • Volume of a trapezoidal prism
  • Surface area of a triangular prism
  • Visual proof: Derivative of \(\sin(x)\)
  • Using the intermediate value theorem
  • Direct proof (divisibility)
  • What is the Cartesian product?
  • Evaluating integers raised to whole number powers
  • Multiplying fractions by cross-simplifying
  • Adding multiples of 10 on a hundreds chart
  • Count forwards or backwards by 1000s starting at any number
  • Counting forwards by 50s starting at any number
  • Mental math: Adding near double decimals by adjusting
  • Adding within 1000 using a number line
  • Adding and subtracting within 100 using a hundreds chart
  • Adding within 100 using a hundreds chart
  • Subtracting within 100 using a hundreds chart
  • Division (grade 4)
  • Counting forward in 100s starting at any number
  • Adding multi-digit numbers using place value disks
  • Counting forward in 1000s starting at any number
  • Missing number problems for adding and subtracting within 1000
  • Lesson
  • Mental math: Add a near multiple of 100 to a three-digit number by adjusting
  • Mental math: Subtract a near multiple of 100 from a three-digit number by adjusting
  • Whole number addition pyramids
  • Partitioning numbers in different ways
  • Other resources
  • Other resources
  • Other resources
  • Trick for subtracting from powers of ten
  • Missing number problems for equivalent fractions
  • Converting whole numbers to fractions
  • Adding fractions with like denominators using the area model without simplifying
  • Adding fractions with like denominators using the area model with simplifying
  • Mental math: Multiplying teen numbers
  • Trick for multiplying two-digit numbers
  • Trick for multiplying whole numbers
  • Trick for multiplying a number by a number ending in five
  • Crisscross method for multiplying numbers
  • Other resources
  • Add and subtract fractions with like denominators (word problems)
  • Estimating volume (cups, pints, quarts, and gallons)
  • Whole number arithmetic (word problems)
  • Other resources
  • Elapsed time for analog clocks
  • Multiplying numbers or binomials by crossing lines
  • Multiplying multi-digit numbers by one-digit numbers with area models
  • Equivalent fractions with denominators of 10 or 100
  • Multiplying whole numbers by powers of 10
  • Adding and subtracting mixed numbers with like denominators (word problems)
  • Identifying hundredths on a number line
  • Other resources
  • Choosing the appropriate unit of measure (inches, feet, yards, miles)
  • Rounding decimals (word problems)
  • Converting US customary units (word problems)
  • Rules for linear equations (graphs)
  • Fraction multiplication as scaling
  • Estimating the sum of fractions with unlike denominators (word problems)
  • Estimating the difference of decimals
  • Dividing whole numbers by decimals
  • Estimating decimal sums
  • Rules for linear equations (tables)
  • Volume of right rectangular prisms (word problems)
  • Multiplying whole numbers by decimals less than 1
  • Adding decimals using a visual model
  • Multiplying by taking out factors of 10
  • Powers of 10
  • Lesson
  • Dividing whole numbers by unit fractions
  • Adding decimals with tenths
  • Adding decimals with hundredths
  • Estimating decimal products
  • Subtracting fractions with unlike denominators (word problems)
  • Converting centimeters to meters
  • Multiplying decimals with tenths
  • Estimating the product of multi-digit numbers
  • Dividing whole numbers to get a decimal
  • Add and subtract fractions with unlike denominators (word problems)
  • Rounding decimals using a number line
  • Finding the volume of composite rectangular prisms
  • Adding and subtracting mixed numbers with unlike denominators (no regrouping)
  • Adding and subtracting mixed numbers with unlike denominators (regrouping)
  • Multiplying fractions using a number line
  • Converting yards to inches
  • Adding decimals with tenths using shaded rectangles
  • Adding fractions with unlike denominators (word problems)
  • Division with two-digit divisors by trial-and-error
  • Comparing decimals in different forms
  • Dividing whole numbers by 0.1 and 0.01
  • Subtracting decimals with hundredths
  • Multiplying whole numbers and fractions using a number line
  • Finding the volume of composite rectangular prisms (word problems)
  • Equivalent fractions with denominators of 10 or 100 using shaded rectangles
  • Comparing decimals using visual models
  • Factoring the GCD out of linear expressions using algebra tiles
  • Practice: Volume of right rectangular prisms (mathematical problems)
  • Theoretical and experimental probability
  • Constants of proportionality
  • Other resources
  • Other resources
  • Probability models
  • Lesson
  • Finding the circumference from the area of a circle
  • Other resources
  • Construction of the integers
  • Construction of the rationals
  • Construction of the reals
  • Binomial probability
  • Solving permutation equations
  • Associative
  • Commutative
  • Proof: Symmetric difference is associative
  • Closed binary operations
  • Binary operations and relations
  • Is the table a commutative semigroup?
  • Klein four-group
  • Proof: Inverse of group inverse
  • Proof: If \(y\) is a left or right inverse for \(x\) in a group, then \(y\) is the inverse of \(x\)
  • Proof: Symmetric difference on power set forms group
  • Order of an element in a group
  • Proof: Order of group element equals order of inverse
  • Cyclic groups
  • Proof: Inverse of generator of cyclic group is generator
  • Subgroups
  • Proof: Centralizer of group element is subgroup
  • Proof: Center of group is subgroup
  • Normal subgroups
  • Proof: The conjugation map is an automorphism
  • Other resources
  • Law of total probability
  • Section formula
  • Simplifying trigonometric expressions by factoring
  • Simplifying trigonometric expressions using the even and odd identities
  • Reciprocal and quotient identities
  • Intersection of parabola and line (word problems)
  • Solving equations with radicals and rational exponents
  • Is it even, odd, or neither? (given an equation)
  • Rationalization
  • Finding one-sided limits of piecewise functions
  • Finding limits of exponential functions
  • Limits
  • Mutually exclusive events
  • Discrete compound interest
  • Continuous compound interest
  • Adding and subtracting square root expressions with variables
  • Rationalizing the numerator
  • Modeling piecewise functions (word problems)
  • Solving rational equations (word problems)
  • 3D vector operations
  • Finding the LCM of polynomials
  • Properties of binary operations
  • Proof: Order of element divides order of finite group
  • Finding the equation of a parabola from its graph
  • Finding the inverse of quadratic functions (word problems)
  • Using the theorem
  • Derivative at a point from first principles
  • Verifying trig identities
  • Direct product of finite cyclic groups
  • Adding and subtracting square root expressions without variables (hard)
  • Adding and subtracting square root expressions without variables (easy)
  • Adding and subtracting square root expressions without variables
  • Comparing numbers within 100 (abstract method)
  • Trick for dividing a number by five
  • Trick for squaring a two-digit number
  • Paradox: Bertrand's box paradox
  • Trick for multiplying three-digit numbers
  • Trick for multiplying four-digit numbers
  • Trick for multiplying by numbers one less than a power of ten when number of digits are not equal
  • Trick for multiplying numbers near the same power of ten when deviations have the same sign
  • Trick for multiplying numbers near the same power of ten when deviations have different signs
  • Trick for squaring a number ending in five
  • Adding and subtracting fractions by cross-multiplying (no common factor in the denominators)
  • Adding and subtracting fractions by cross-multiplying (common factor in the denominators)
  • First trick for finding the square root of perfect squares within \(120^2\)
  • Trick for multiplying 2-4 digit numbers
  • Trick for multiplying numbers near the same multiple of a power of ten
  • Trick for multiplying two numbers equidistant from a third number
  • Trick for multiplying by 5
  • Finger trick for multiplying 1-10 by 9
  • Trick for dividing a number by twenty five
  • Trick for dividing a number by one hundred twenty five
  • Trick for squaring a number near a power of ten
  • Trick for squaring a number near a multiple of a power of ten
  • Trick for squaring a number near fifty
  • Trick for squaring a three-digit number
  • Second trick for finding the square root of perfect squares within \(120^2\)
  • Trick for cubing a two-digit number
  • Trick for cubing a two-digit number near a power of ten
  • Trick for finding the cube root of 4-6 digit perfect cubes
  • Check your addition by casting out nines
  • Check your multiplication by casting out nines
  • Trick for percent of a number when percent is a multiple of ten
  • Trick for percent of a number
  • First trick for percent of a number (percent not always a multiple of ten)
  • Multiplying by 6 (Trachtenberg system)
  • Trick for finding all primes within one hundred
  • Trick for squaring repeating ones, three, or nines
  • Trick for listing the multiples of a two digit number
  • Trick for doubling numbers
  • Trick for multiplying by 2, 4, 8
  • Trick for dividing by two, four, and eight
  • Trick for multiplying by 5, 25, 50, 500
  • Trick for dividing by particular numbers
  • Speedy math
  • Multiplying by 7 (Trachtenberg system)
  • Trachtenberg system
  • Multiplying by 8 (Trachtenberg system)
  • Multiplying by 2 (Trachtenberg system)
  • Multiplying by 3 (Trachtenberg system)
  • Multiplying by 4 (Trachtenberg system)
  • Multiplying by 9 (Trachtenberg system)
  • Multiplying by 11 (Trachtenberg system)
  • Multiplying by 12 (Trachtenberg system)
  • Proving the altitude of an isosceles triangle cuts two congruent right triangles
  • Compare within 10 by counting
  • Lesson
  • Compare length
  • Other resources
  • Vampire numbers
  • Slide method of multiplication
  • Tricks for multiplication
  • Tricks for division
  • Tricks for roots
  • Math of the 15 puzzle
  • Computer assisted math
  • Missing dollar riddle
  • Nim-like games
  • Factoring non-monic quadratics using algebra tiles
  • Coin problem
  • Balance puzzles
  • Weighing 9 balls puzzle
  • Weighing 10 bags puzzle
  • Weighing 12 balls puzzle
  • Magic Caterpillars
  • Plum Tree
  • Instant Insanity
  • Overarch 1
  • Overarch 2
  • Proving properties of even and odd functions (calculus 1)
  • Isosceles Reduction (NRICH activity)
  • Challenge
  • Isosceles (NRICH activity)
  • Parabolic Patterns (NRICH activity)
  • Pent (NRICH activity)
  • Challenge
  • Challenge
  • Pond Runners (NRICH activity)
  • NRICH activities (geometry for undergraduates)
  • Challenge
  • Nine Colours (NRICH activity)
  • Proof
  • Challenge
  • Other resources
  • Partly Circles (NRICH activity)
  • Counting Binary Ops (NRICH activity)
  • Venn diagrams (combinatorics)
  • Challenge
  • Challenge
  • Laps (NRICH activity)
  • Constructing a square inside a triangle
  • British flag theorem
  • Polyominoes
  • Challenge
  • Comparing and ordering exponents
  • Twisting and Turning (NRICH activity)
  • Speeding Boats (NRICH activity)
  • Postage (NRICH activity)
  • Latin squares
  • Euler squares
  • Challenge
  • Menelaus's theorem
  • 18 or 20 trees?
  • Proof: Conway's soldiers cannot reach row five
  • Conway's Soldiers
  • Other resources
  • Isosceles Meld (NRICH activity)
  • One Golden Equation (Flammable Maths)
  • Challenge: Surviving The Deadliest Game
  • Combinations with restrictions
  • Solving factorial equations
  • Basic combinatorics proofs
  • Challenge
  • Proof
  • STEP
  • Puzzle ~ Packing Eight Numerals Into Eight Squares (Crystal Clear Maths)
  • Using the Pythagorean theorem to find the hypotenuse of a right triangle
  • Using the Pythagorean theorem to find a leg of a right triangle
  • Solving 30-60-90 triangles
  • Solving 45-45-90 triangles
  • Menseki Meiro puzzles
  • Other resources
  • Sigma notation and the binomial theorem
  • Properties of sigma notation
  • Challenge
  • Coffin problems
  • Other resources
  • Careful counting 5
  • Careful counting 6
  • Solving linear congruence equations
  • Solving quadratic congruence equations
  • Finding the line of reflection (grade 8)
  • Tangent theorem
  • Diagonals of a rhombus are perpendicular bisectors
  • Proof: Rhombus diagonals are perpendicular bisectors (linear algebra)
  • Proving that opposite angles of a parallelogram are congruent
  • Diagonals of a kite are perpendicular
  • Opposite sides of a parallelogram are congruent
  • A number theory proof (blackpenredpen)
  • Area of a rhombus from diagonals
  • Other resources
  • GMAT math
  • Centroid
  • Putnam exam
  • Newton–Pepys problem
  • Potato paradox
  • Simplifying rational expressions by factoring and cancelling
  • Two envelopes problem
  • Careful counting 1
  • Challenge
  • Other resources
  • Direct proof (floor and ceiling)
  • Other resources
  • Systems of inequalities from a graph
  • Fifth root trick
  • Multiplying decimals using base ten blocks
  • Power of a quotient rule for exponents
  • Zero exponents
  • Simplifying rational expressions by cancelling
  • Find the equation of a square root function under transformations from a graph
  • Graphing the cube root function under transformations (level 2)
  • Factoring by grouping (multiple variables)
  • Factoring by grouping (one variable, not quadratic)
  • Solving trigonometric equations linear in form
  • Solving trigonometric equations quadratic in form by taking square roots
  • One and Three (NRICH activity)
  • Challenge
  • Centered hexagonal number
  • One Basket or Group Photo (NRICH activity)
  • Other resources
  • Challenge
  • Solving linear homogeneous recurrence relations
  • Characteristic equation and characteristic roots of linear homogeneous recurrence relations
  • Tiling the strip with dominos and monominos
  • Arithmagons
  • Deriving formulas for figurate numbers
  • Visual proof for the sum of the first \(n\) odd natural numbers
  • Geometric vanishing puzzles
  • What portion is shaded? 2
  • Cut into identical pieces 1
  • Cut into identical pieces 2
  • What portion is shaded? 1
  • What portion is shaded? 3
  • What portion is shaded? 4
  • What portion is shaded? 5
  • Four fours
  • Ten coins in five rows of four
  • Careful counting 2
  • Challenge 32: Dots and Boxes (Science Mom)
  • What portion is shaded? 6
  • Challenge 19: A Chicken and a Half (Science Mom)
  • Challenge 20: Timing 9 Minutes (Science Mom)
  • What portion is shaded? 7
  • Challenge 23: Sum to 100 (Science Mom)
  • Careful counting 3
  • What portion is shaded? 8
  • River crossing puzzle 1
  • River crossing puzzle 2
  • River crossing puzzle 3
  • What portion is shaded? 9
  • Careful counting 4
  • Careful counting
  • What portion is shaded?
  • Strimko
  • Handshaking couples
  • Frogs 1
  • How To Solve Amazon's Pair Of Socks Interview Puzzle (MindYourDecisions)
  • Picking socks in the dark
  • Multiplayer games
  • Seven coins in six rows of three
  • Challenge 40: Lazy Reflection (Science Mom)
  • Careful counting 7
  • Challenge 44: Mystery Boxes (Science Mom)
  • Challenge 45: Grid Shading Puzzle (Science Mom)
  • Challenge 43: Path Counter (Science Mom)
  • Proof: Varignon's theorem (linear algebra)
  • Billiard Ball Problem (Math for Love)
  • Proof: Law of cosines using the dot product
  • Geometric proofs using vectors
  • Totality (NRICH activity)
  • Subtracting decimals with tenths
  • Subtracting decimals with thousandths
  • Factoring quadratics with difference of squares
  • Factoring non-monic quadratics with difference of squares (all resources)
  • Other resources
  • Factoring non-monic quadratics with difference of squares using algebra tiles
  • Other resources
  • Adding decimals with thousandths
  • Practice: Find a length using the law of sines (mathematical problems)
  • Evaluate a function from its graph
  • Proof: Thales's theorem using the dot product
  • Quinary
  • Quinary multiplication
  • Proof: Cauchy–Schwarz inequality
  • Number of ways to triangulate a regular polygon
  • Young tableau
  • Determinant of a \(3 \times 3\) matrix using cofactors
  • Solving linear systems of equations in two variables using Gauss–Jordan elimination
  • Using the theorem
  • Other resources
  • Basic modular arithmetic proofs
  • Set builder notation
  • Vacuous truth
  • Proof using binomial theorem: Cardinality of power set of finite set
  • Proof by induction: Cardinality of power set of finite set
  • Cardinality of power set of finite set
  • Converting polar equations to Cartesian equations
  • Converting Cartesian equations to polar equations
  • NRICH activities (grade 7)
  • NRICH activities (grade 8)
  • Using the binomial theorem
  • Proving the binomial theorem by induction
  • Making rectangles with a given area from unit squares
  • Combinatorial proof: Binomial theorem
  • Challenge
  • Other resources
  • NRICH activities (grade 6)
  • Challenge problems (geometry for high schoolers)
  • NRICH activities (geometry for high schoolers)
  • Lambert W function
  • Gabriel's Horn
  • Add using number disks
  • Direct product of groups
  • NRICH activities (combinatorics for high schoolers)
  • Group homomorphisms
  • Sum of exterior angles (algebra problems)
  • Epsilon-delta proofs for limits with one variable
  • Proof: Pythagorean theorem
  • Proving the inverse Pythagorean theorem
  • Similarity proof: Pythagorean theorem
  • Epsilon-delta proofs for limits with two variables
  • Jack Oliver's proof: Pythagorean theorem
  • Proofs: Pythagorean theorem
  • Survivorship bias
  • Derivation: Area of a non-obtuse triangle
  • James Garfield's proof: Pythagorean theorem
  • Bhaskara's proof: Pythagorean theorem
  • Epsilon-delta proof: Sum of limits
  • Number tricks
  • Bayes's theorem and false positives
  • Proving properties of absolute value
  • Proving the triangle inequality
  • Proving the reverse triangle inequality
  • Finding delta given epsilon
  • Proof: 1089 trick
  • Subsets
  • Supremum and infimum
  • Interior point of a set
  • Proof: Cantor set is uncountable
  • Disproof by counterexample
  • Dihedral group
  • Proof: One-step subgroup test
  • Simple groups
  • Solvable groups
  • Quotient groups
  • Proof: Union of countably many countable sets is countable
  • Proof: Cardinality of Cartesian product
  • Proof: Group abelian iff cross cancellation property
  • Alternating groups
  • Proof: First isomorphism theorem for groups
  • Proof: Second isomorphism theorem for groups
  • Proof: Fundamental homomorphism theorem
  • Proof: Special linear group is subgroup of general linear group
  • Proof: Two-step subgroup test
  • Proof: Finite subgroup test
  • Group automorphisms
  • Kernel of a group homomorphism
  • Proving group homomorphisms
  • Group isomorphisms
  • Compositions of group morphisms
  • Other resources
  • Basic group theory proofs
  • Multiplying permutations in cycle notation
  • Multiplying permutations in array notation
  • Add within 10 (concrete or pictorial)
  • Subtraction word problems within 10
  • Addition word problems within 10
  • Other resources
  • Cosets of a subgroup
  • Cosets and Lagrange's theorem
  • Proving equivalence relations
  • Equivalence classes
  • Number of edges in a complete graph
  • Other resources
  • Derivative using u-substitution
  • Size of tree is one less than order
  • Properties of relations
  • Representing relations using digraphs
  • Basic set theory proofs using Venn diagrams
  • Basic set theory proofs using predicate logic
  • What are De Morgan's laws?
  • Inverse of composite relation
  • Composition of relations
  • Converting English to predicate logic
  • Combining relations
  • Representing relations using matrices
  • Intersection of equivalence relations
  • Set is subset of intersection of supersets
  • Intersection is largest subset
  • Union is smallest superset
  • Supersets
  • Image and preimage of a set under a function
  • Intro to continuity
  • Proving Cauchy sequences
  • Proving divergence using proof by contradiction
  • Proving divergence using subsequences
  • Every convergent sequence is a Cauchy sequence
  • Sum rule for Cauchy sequences
  • Archimedean principle
  • Using the Archimedean principle
  • Rationals are dense in the reals
  • Proving properties of supremum
  • What is the least upper bound property?
  • Rates and proportional relationships
  • Epsilon-delta proof: Product of limits
  • Proof
  • What is the cardinality of a set?
  • Proving properties of the empty set
  • Multiplying perfect squares using algebra tiles
  • Finding the smallest multiplier to produce a perfect square
  • Sum of squares of binomial coefficients
  • What is a vector space?
  • Proving properties of Cartesian product
  • Properties of the power set
  • Combinatorial proof: Cardinality of power set of finite set
  • Proof: Least upper bound property
  • What are upper and lower bounds?
  • Proving limits of sequences are unique
  • Euclid's lemma
  • Sufficient conditions for a group to be abelian
  • Other resources
  • Proof: Cantor's theorem
  • Construct a rhombus with given side
  • Construct a rhombus with given side and angle
  • Copy an angle
  • What is a complete graph?
  • What is a spanning subgraph?
  • What is an edge-induced subgraph?
  • Proof: Derivative of \(\cot(x)\)
  • Other resources
  • Isomorphic graphs
  • What is a vertex-induced subgraph?
  • What is a cubic graph?
  • What is an irregular graph?
  • Proving isosceles trapezoids
  • Converting between array notation and cycle notation
  • Converting cycle notation to array notation
  • Converting array notation to cycle notation
  • What is cycle notation?
  • What is an equivalence relation?
  • What is a relation? (for undergraduates)
  • Verifying equivalence relations on groups
  • Using the sum identities
  • Epsilon-delta proofs of uniform continuity
  • Properties of scalar multiplication
  • Proof: Scalar multiplication is associative
  • Proof: Dot product formula
  • Proof: Cross product distributes over addition
  • Number patterns (grade 4)
  • What are decimal numbers?
  • Multiplying one-digit by two-digit numbers using partial products
  • Multiplying three one-digit numbers
  • Proof
  • Sophie Germain's identity
  • Fermat's little theorem
  • Proving irrationality
  • Basic set theory proofs using membership tables
  • Basic propositional logic proofs using truth tables
  • What is hypothetical syllogism?
  • Converse, inverse, and contrapositive statements
  • Converting a Venn diagram to a set expression
  • Converting a set expression to a Venn diagram
  • Converting between set expressions and Venn diagrams
  • Intro to integral ideals
  • Other resources
  • Testing validity of syllogisms by drawing Venn diagrams
  • Square of opposition
  • Proof by induction (simplifying sums)
  • Shading Venn diagrams with two sets
  • Shading Venn diagrams with three sets
  • Difference of squares
  • Basic ring theory proofs
  • More ring theory proofs
  • Proving limits using the squeeze theorem
  • What is the squeeze theorem?
  • Solving trigonometric equations using the quadratic formula
  • Adding within 1000 (word problems)
  • Add within 20 (word problems)
  • Missing number for subtraction within 1000
  • Derivation
  • Finding area of regular polygon given apothem or perimeter
  • Percents: Finding the whole (word problems)
  • Other resources
  • Graphing linear equations by plotting points
  • Is it a ring?
  • What is a subring?
  • Proving properties of injective, surjective, and bijective functions
  • Finding absolute extrema on a closed interval
  • Using the theorem
  • NRICH activities (probability theory for high schoolers)
  • NRICH activities (algebra 2)
  • Method of differences
  • Other resources
  • Intro to even and odd functions
  • Proof: Power reducing identities
  • Power reducing trig identities
  • Proofs
  • Pascal's identity
  • Connection between Pascal's identity and Pascal's triangle
  • Properties of Pascal's triangle
  • Explanation for powers of eleven in Pascal's triangle
  • Using the power reducing identities to graph
  • Partial fraction decomposition (linear factors)
  • Partial fraction decomposition (repeated linear factors)
  • Partial fraction decomposition (quadratic factors)
  • Partial fraction decomposition (repeated quadratic factors)
  • Partial fraction decomposition (improper fractions)
  • The cover-up method and why it works
  • False proofs by induction
  • Finding absolute value transformations from graphs
  • Intro to bipartite graphs
  • Maximization (word problems)
  • Minimization (word problems)
  • Write a system of linear inequalities given a graph
  • Finding square root transformations from graphs
  • Using the sine rule for area of a triangle
  • Using the theorem
  • Finding equations of sine and cosine functions from graphs
  • Finding transformations of sine and cosine functions from equations
  • Intro to graphing sine and cosine under transformations
  • Converting between English and propositional logic
  • Converting propositional logic to English
  • Making truth tables for expressions
  • Simplifying expressions in propositional logic
  • Converting between set-builder and set-roster notation
  • Converting set-builder notation to set-roster notation
  • Converting set-roster notation to set-builder notation
  • Operations with set-builder notation
  • Testing validity of simple statements in predicate logic
  • Converting set theory expressions to predicate logic expressions
  • Basic predicate logic proofs
  • Union and intersection of a family of sets
  • Direct proof (inequalities)
  • Intro
  • Adding and subtracting linear and quadratic functions
  • Adding functions (linear-quadratic)
  • Adding functions (piecewise linear)
  • Adding functions (other)
  • Subtracting functions (quadratic-linear)
  • Square root of a complex number
  • Other resources
  • Other resources
  • Roots of complex numbers using De Moivre's theorem
  • Interactive: Sine and cosine functions under transformations
  • Measuring angles using a protractor
  • Graphically finding points of inflection
  • Using the second derivative to find points of inflection
  • Intro to digraphs
  • Other resources
  • False proofs for calculus 2
  • Derivatives of hyperbolic and inverse hyperbolic functions
  • Proving the derivatives of the hyperbolic functions
  • Other resources
  • Other resources
  • Hyperbolic and inverse hyperbolic functions
  • Proving the derivatives of the inverse hyperbolic functions
  • Arc length formula
  • Lesson
  • Practice
  • Practice: Simpson's rule
  • NRICH activities (algebra 1)
  • Multiplying fractions (mathematical problems)
  • What is a quadrilateral?
  • Factoring quadratics by trial and error
  • Deriving point-slope form
  • What is point-slope form?
  • Converting point-slope form to slope-intercept form
  • Basic integration problems
  • Definite integrals by u-substitution
  • Reverse power rule for definite integrals
  • Convert to vertex form by completing the square (using algebra tiles)
  • Solve by completing the square
  • Factoring by completing the square
  • Find the missing side of the rectangle given the area
  • Integration by u-substitution (more difficult)
  • Integration by u-substitution
  • Proving properties of the subset relation
  • Counting (kindergarten)
  • Making 10 with written numerals
  • Add within 20 using fingers
  • Subtract within 5 using counters (concrete and pictorial)
  • Subtract within 5 (abstract)
  • Subtract within 20 (concrete and pictorial methods)
  • Subtract within 20 using fingers
  • Counting by 1s (1 to 20)
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Practice
  • Practice
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Probability vs odds
  • Other resources
  • Other resources
  • Lesson
  • Lesson
  • Practice
  • Practice
  • Intro to functions
  • Radius and tangent theorem
  • What is a maximal clique?
  • Subgraphs
  • Alternate segments theorem
  • Subtraction and place value
  • Lesson: Adding and subtracting within 1000 using a number line
  • Practice: Adding and subtracting within 1000 using a number line
  • Adding or subtracting by adjusting
  • Lesson
  • Practice
  • Paths and cycles
  • Planar graphs
  • Coloring
  • Basics of graph theory
  • Intro to vertex colorings
  • What is an orthogonal set?
  • Other resources
  • Other resources
  • Other resources
  • Subtracting (grade 1)
  • Other resources
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Measurement (grade 2)
  • Geometry (grade 2)
  • Rewriting before integrating
  • Practice
  • Other resources
  • Counting by 1s (1 to 50 and 50 to 1)
  • Counting by 1s (1 to 100)
  • Other resources
  • Counting to 5
  • Counting by 5s (5 to 100)
  • Counting by 2s (2 to 100)
  • Subtract within 1000 using a number line
  • Understand fractions
  • Adding and subtracting (grade 3)
  • Area (grade 3)
  • Intro to division
  • Lesson
  • Practice
  • Plane figures (grade 4)
  • Units of measure (grade 4)
  • Understand decimals (grade 4)
  • Factors, multiples, and patterns (grade 4)
  • Place value (grade 4)
  • Properties of shapes (grade 5)
  • Lesson
  • Practice
  • Lesson: Dividing decimals by whole numbers
  • Practice: Dividing decimals by whole numbers
  • Find the mistake in one-step equations
  • Lesson: Find the mistake in one-step equations
  • Practice: Find the mistake in one-step equations
  • Lesson
  • Practice
  • Intro to equations and inequalities (grade 6)
  • Solving multi-step equations (word problems)
  • Lesson
  • Practice
  • Geometry (grade 6)
  • Geometry
  • Geometry (grade 7)
  • Intro to proof by induction
  • Proof: Integers are countable
  • Lesson: What is the image of a set under a function?
  • Proofs: Image and preimage of a set under a function
  • Lesson: What is the preimage of a set under a function?
  • Line integrals
  • Partial derivatives
  • Conservative vector fields
  • Curl and divergence of vector fields
  • Vector magnitude
  • Double integrals over rectangular regions
  • Directional derivatives
  • Total derivatives
  • Lesson: Converting decimals to percents
  • Practice: Converting decimals to percents
  • Polygons on the coordinate plane
  • Practice
  • Lesson
  • Area and perimeter of polygons on the coordinate plane
  • Drawing polygons on the coordinate plane
  • Lesson: Drawing polygons on the coordinate plane
  • Practice: Drawing polygons on the coordinate plane
  • Dividing fractions (word problems)
  • Other resources
  • Lesson: Volume of right rectangular prisms (word problems)
  • Practice: Volume of right rectangular prisms (word problems)
  • Lesson: Volume of right rectangular prisms (mathematical problems)
  • Volume of right rectangular prisms (mathematical problems)
  • Adding and subtracting decimals (word problems)
  • Other resources
  • Area of a triangle on the coordinate plane
  • Find the missing vertex of the parallelogram
  • Lesson: Find the missing vertex of the parallelogram
  • Practice: Find the missing vertex of the parallelogram
  • Is it even, odd, or neither? (given a graph)
  • Practice
  • Practice
  • Finding the inverse of quadratic functions (mathematical problems)
  • Determining whether two functions are inverses of each other
  • Deriving the t-formulas
  • Disproving trigonometric identities by counterexample
  • Lesson: Evaluating trigonometric functions using the unit circle
  • Practice: Evaluating trigonometric functions using the unit circle
  • Lesson
  • Practice
  • Practice
  • Comparing rates
  • Lesson: Comparing rates
  • Practice: Comparing rates
  • Lesson
  • Practice
  • Lesson: Solving and graphing absolute value inequalities (word problems)
  • Practice: Solving and graphing absolute value inequalities (word problems)
  • Solving and graphing absolute value inequalities (mathematical problems)
  • Solving and graphing absolute value inequalities (word problems)
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Solving systems of linear equations in two variables by substitution (mathematical problems)
  • Lesson
  • Practice
  • Solving linear systems of equations in two variables by elimination (harder mathematical problems)
  • Solving linear systems of equations in two variables by elimination (word problems)
  • Lesson
  • Practice
  • Practice
  • Graphing quadratic equations from tables
  • Lesson
  • Practice
  • Cardinality from Venn diagrams
  • Example of a nonconstructive proof
  • Lesson
  • Other resources
  • Lesson
  • Practice
  • Order of operations (grade 3)
  • Lesson
  • Practice
  • Comparing and ordering exponent expressions
  • Derivation: Area of a parallelogram
  • Recognizing common 3D shapes
  • Lesson: Recognizing common 3D shapes
  • Practice: Recognizing common 3D shapes
  • Long division (one-digit divisors)
  • Lesson
  • Practice
  • Naming angles
  • Other resources
  • Lesson: Multiplying 10s
  • Practice: Multiplying 10s
  • Unit fractions (grade 3)
  • Lesson: Plotting fractions on the number line
  • Practice: Plotting fractions on the number line
  • Number patterns (grade 5)
  • Other resources
  • Area of a rectangle with whole number side lengths
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Lesson: Dividing fractions by whole numbers
  • Practice: Dividing fractions by whole numbers
  • Lesson
  • Practice
  • Dividing unit fractions by whole numbers
  • Lesson
  • Practice
  • Rounding mixed numbers
  • Rounding improper fractions
  • Lesson
  • Practice
  • Lesson: Multiplying whole numbers by powers of 10
  • Practice: Multiplying whole numbers by powers of 10
  • Place value (grade 5)
  • Lines, line segments, and rays
  • Order of operations (grade 5)
  • Adding and subtracting fractions with unlike denominators (word problems)
  • Converting between words and decimals
  • Subtracting mixed numbers by converting to improper fractions
  • Subtracting mixed numbers with regrouping
  • Subtracting mixed numbers (word problems)
  • Adding mixed numbers with regrouping
  • For teachers: Add within 20 using number bonds
  • Counting with tally marks
  • Practice
  • Lesson
  • Practice
  • Rounding to the nearest 10 or 100 (abstract)
  • Rounding to the nearest 10 or 100 (concrete and pictorial)
  • Line plots (grade 5)
  • Lesson
  • Practice
  • Decomposing angles
  • Lesson
  • Practice
  • Other resources
  • Lesson
  • Practice
  • Adding and subtracting (grade 2, concrete and pictorial)
  • Adding and subtracting (grade 2, abstract)
  • Lesson
  • Practice
  • Subtract by compensating
  • Lesson: Comparing fractions with the same numerators or denominators
  • Practice: Comparing fractions with the same numerators or denominators
  • Measuring to the nearest quarter inch
  • Measure lengths (cm, m)
  • Measurement (grade 3)
  • Lesson
  • Practice
  • Measuring lengths in different units
  • Other resources
  • Lesson
  • Practice
  • Other resources
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Telling time to the nearest 15 minutes
  • Lesson
  • Practice
  • Adding within 100 (mental)
  • Lesson
  • Practice
  • Adding within 100 (concrete and pictorial methods)
  • Estimating mass (grams and kilograms)
  • Lesson
  • Practice
  • Solving two-step equations (concrete and pictorial)
  • Solving two-step equations (abstract)
  • Find the mistake in two-step equations
  • Solving one-step equations (concrete and pictorial)
  • Solving one-step equations (abstract)
  • Hard factoring problems
  • Other resources
  • Lesson
  • Practice
  • Practice
  • Solving and graphing linear inequalities by clearing fractions
  • Solving linear equations using reciprocals
  • Subtract within 20 using ten frames
  • Culmination: Multiplying and dividing fractions
  • Lesson
  • Practice
  • Intro
  • Other resources
  • Recognize fractions greater than 1
  • Recognize fractions
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Solving quadratic equations (word problems)
  • Adding integers (concrete and pictorial)
  • Adding integers (abstract)
  • Other resources
  • Solving and graphing two-step inequalities in one variable (word problems)
  • Solving and graphing two-step inequalities in one variable (mathematical problems)
  • Find the explicit formula for a geometric series given terms
  • Intro to parallel and perpendicular lines
  • Lesson
  • Practice
  • Recognize ratios
  • Ratio tables
  • Equivalent ratios (mathematical problems)
  • Equivalent ratios (word problems)
  • Ratios with tape diagrams
  • Lesson: Ratios with tape diagrams
  • Practice: Ratios with tape diagrams
  • Lesson: Ratio tables
  • Practice: Ratio tables
  • Ratios and units of measurement
  • Lesson
  • Practice
  • Part-to-whole ratios
  • Lesson: Adding integers using a number line
  • Practice: Adding integers using a number line
  • Lesson: Inverse property of addition
  • Dependent and independent variables
  • Lesson
  • Practice
  • Lesson: Common denominators
  • Practice: Common denominators
  • Representative samples
  • Graphing parabolas by plotting points
  • Number opposites
  • Lesson: Number opposites
  • Practice: Number opposites
  • Lesson
  • Practice: Plotting integers on a number line
  • Plotting rational coordinates
  • Lesson
  • Practice
  • Plotting whole number coordinates
  • Lesson
  • Practice
  • Other resources
  • Lesson
  • Practice
  • Writing numerical inequalities
  • Lesson
  • Practice
  • Rates with fractions
  • Relating whole number division to multiplication (mathematical problems)
  • Relating whole number division to multiplication (word problems)
  • Relating fraction division to multiplication
  • Lesson
  • Practice
  • Subtraction as adding the opposite
  • Lesson
  • Practice
  • Writing proportional equations
  • Writing proportional equations from tables
  • Writing proportional equations (word problems)
  • Lesson: Writing proportional equations (word problems)
  • Practice: Writing proportional equations (word problems)
  • Lesson: Writing proportional equations from tables
  • Practice: Writing proportional equations from tables
  • Find the center and scale factor
  • Lesson
  • Practice
  • Comparing distributions
  • Statistics and probability (grade 7)
  • Comparing areas and perimeters of rectangles
  • Lesson
  • Practice
  • Other resources
  • Sampling methods
  • Lesson
  • Practice
  • Comparing and ordering absolute values
  • Lesson
  • Practice
  • Modeling with linear functions
  • Lesson
  • Practice
  • Reflecting figures
  • Lesson: Reflecting line segments and polygons (grade 8)
  • Practice: Reflecting line segments and polygons (grade 8)
  • Finding the line of reflection (geometry for high schoolers)
  • Lesson
  • Practice
  • Trends in categorical data
  • Lesson
  • Practice
  • Perimeter (grade 3)
  • Perimeter (grade 3, mathematical problems)
  • Perimeter (grade 3, word problems)
  • Uniform and non-uniform probability models
  • Finding the volume of composite rectangular prisms (mathematical problems)
  • Lesson
  • Practice
  • Factor with the distributive property (no variables)
  • Lesson
  • Practice
  • Measuring and comparing lengths (grade 2)
  • Other resources
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Other resources
  • Lesson
  • Practice
  • Other resources
  • Subtracting multiples of 10 within 100
  • Other resources
  • Other resources
  • Missing digit problems for adding and subtracting within 1000
  • Describing measurable attributes of objects
  • Converting decimals between standard form, expanded form, and number names
  • Equal sign
  • Other resources
  • Lesson: Representing numbers using base ten blocks (grade 4)
  • Practice: Representing numbers using base ten blocks (grade 4)
  • Adding three numbers in any order (mathematical problems)
  • Adding three numbers in any order (word problems)
  • Other resources
  • Count in order
  • Other resources
  • Other resources
  • Making and reading bar and picture graphs (grade 2)
  • Reading bar graphs (grade 2)
  • Making picture graphs
  • Reading picture graphs
  • Lesson: Reading bar graphs (grade 2)
  • Practice: Reading bar graphs (grade 2)
  • Lesson: Making bar graphs
  • Practice: Making bar graphs
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Two-step word problems (grade 2)
  • Lesson
  • Practice
  • Other resources
  • Negative signs in fractions
  • Fractions of shapes
  • Lesson
  • Practice
  • Other resources
  • Other resources
  • Representing decimals using shaded rectangles
  • Lesson
  • Practice
  • Other resources
  • Comparing numbers within 100
  • Estimate lengths
  • Lesson
  • Practice
  • Using different strategies to add and subtract (grade 2)
  • Other resources
  • Length word problems
  • Other resources
  • Lesson
  • Practice
  • Drawing angles in degrees
  • Other resources
  • Lesson
  • Practice
  • Subtracting within 100 (concrete and pictorial methods)
  • Add and subtract within 100 on the number line
  • Adding and subtracting within 100 (abstract methods)
  • Patterns in arithmetic
  • Patterns in sequences
  • Patterns with even and odd
  • Patterns in hundreds chart
  • Patterns in multiplication tables
  • Lesson: Patterns in hundreds chart
  • Practice: Patterns in hundreds chart
  • Lesson: Patterns in multiplication tables
  • Practice: Patterns in multiplication tables
  • Lesson: Patterns in sequences
  • Practice: Patterns in sequences
  • Lesson
  • Practice
  • Other resources
  • Commutative property of multiplication (grade 3)
  • Lesson
  • Practice
  • Using the distributive property to multiply (grade 3)
  • Using the associative property of multiplication (grade 3)
  • Lesson
  • Practice
  • Other resources
  • Lesson
  • Two-step word problems (grade 3)
  • Lesson
  • Practice
  • Other resources
  • Lesson
  • Practice
  • Area and the distributive property
  • Lesson
  • Practice
  • Translating to multiplication (mathematical problems)
  • Lesson
  • Practice
  • Adding and subtracting mixed numbers with like denominators (mathematical problems)
  • Multiplying unit fractions and whole numbers
  • Lesson: Multiplying unit fractions and whole numbers
  • Practice: Multiplying unit fractions and whole numbers
  • Area and perimeter of a rectangle (grade 4)
  • Lesson
  • Practice
  • Representing 1 as a fraction
  • Lesson: Representing 1 as a fraction
  • Practice: Representing 1 as a fraction
  • Representing any whole number as a fraction
  • Lesson
  • Practice
  • Music videos: Multiplication (grade 4)
  • Multiplying whole numbers and fractions (concrete and pictorial methods)
  • Multiplying fractions using the area model
  • Lesson
  • Practice
  • Other resources
  • Classifying shapes by line and angle types
  • Equivalent fraction and whole number multiplication expressions
  • Lesson
  • Practice
  • Other resources
  • Lesson
  • Practice
  • Other resources
  • Change in median and mean after shifting, adding, or removing a data point
  • Lesson
  • Practice
  • Fractions as division
  • Dividing with unit fractions
  • Identify coordinates
  • Lesson
  • Practice
  • Testing solutions to two-variable inequalities
  • Lesson
  • Practice
  • Modeling one-variable inequalities
  • Lesson
  • Practice
  • Challenge problems (statistics for high schoolers)
  • Statistical and non-statistical questions
  • Lesson
  • Practice
  • Line plots (grade 2)
  • Find the sequence of rigid transformations
  • Other resources
  • Find measures using rigid transformations
  • Preserved properties of rigid transformations
  • Reading box plots
  • Interpreting quartiles
  • Identifying outliers from box plots
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Analyzing graphs of step functions
  • Interpreting linear expressions
  • Lesson
  • Practice
  • Approximating with powers of 10
  • Lesson
  • Practice
  • Expression value intuition
  • Lesson
  • Practice
  • Addition snake game (part 1)
  • Addition snake game (part 2)
  • Negative snake game
  • Estimating volume (milliliters and liters)
  • One-step word problems with volume
  • Lesson
  • Practice
  • One-step word problems with masses
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Reading dot plots and frequency tables
  • Making dot plots and frequency tables
  • Dot plots and frequency tables
  • Shape of distributions
  • Identifying symmetric and skewed distributions
  • Clusters, gaps, peaks, and outliers
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Practice
  • Comparing linear functions
  • Comparing linear functions (mathematical problems)
  • Comparing linear functions (word problems)
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Other resources
  • Dividing unit fractions by whole numbers (concrete and pictorial methods)
  • Dividing unit fractions by whole numbers (abstract methods)
  • Lesson
  • Practice
  • Dividing whole numbers by unit fractions (concrete and pictorial methods)
  • Dividing whole numbers by unit fractions (abstract methods)
  • Lesson
  • Practice
  • Other resources
  • Lesson
  • Practice
  • Other resources
  • Place value blocks within 1,000
  • Lesson
  • Practice
  • Place value tables within 1,000
  • Histograms
  • Making histograms
  • Reading histograms
  • Lesson
  • Practice
  • Other resources
  • Counting by 1s starting at any number
  • Number of observations from line plots and histograms
  • Converting complex numbers between polar and rectangular form
  • Complex number conjugates
  • Practice
  • Word problems with multiple units
  • Components of vectors
  • Lesson
  • Practice
  • Area of a parallelogram using determinant
  • Subtracting vectors
  • Other resources
  • Lesson
  • Practice
  • Simple hypothesis testing
  • Lesson
  • Practice
  • Magnitude and direction form of vectors
  • Lesson
  • Practice
  • Properties of matrix multiplication
  • Solving quadratics by u-substitution
  • Other resources
  • Equivalent vectors
  • Other resources
  • Make a dilation given the center and scale factor
  • Dilating lines
  • Sum of interior angles of a simple polygon (using the formula)
  • Sum of interior angles of a simple polygon (rearranging the formula)
  • Adding within 100 (abstract method)
  • Multiplying integers (concrete and pictorial methods)
  • Multiplying integers (abstract methods)
  • Compare within 5 by pairing
  • Book reviews (discrete math)
  • Bridge course books
  • Abstract algebra books for undergrads
  • Book reviews (linear algebra)
  • Book reviews (calculus)
  • Book reviews (complex analysis)
  • Book reviews (field theory)
  • Book reviews (number theory)
  • Abstract algebra books for graduates
  • Topology books
  • Book reviews (differential equations)
  • Compare within 5 by counting
  • Compare within 5
  • Compare within 10
  • Long division using the box method
  • Advice from Eddie Woo
  • Making residual plots
  • Lesson
  • Practice
  • Hypothesis testing in experiments
  • Lesson
  • Practice
  • Double negation introduction and elimination
  • Advice
  • Advice from The Math Sorcerer
  • Surface area using nets (word problems)
  • Surface area using nets (mathematical problems)
  • Missing value given the mean
  • Lesson
  • Practice
  • Age problems (challenge problem)
  • Lesson
  • Book reviews (naive set theory)
  • Book reviews (graph theory)
  • Book reviews (probability theory)
  • Add within 20 using a number line
  • Subtract within 20 by counting forward on the number line
  • Subtract within 20 by counting backward on the number line
  • Subtract within 20 (abstract methods)
  • Add by making 100s
  • Lesson
  • Practice
  • Data (grade 2)
  • Addition, subtraction, and estimation
  • More with multiplication and division
  • Data (grade 3)
  • Arithmetic patterns and problem solving
  • Lesson
  • Practice
  • Multiply fractions
  • Measuring angles
  • Add and subtract fractions (grade 5)
  • Coordinate plane
  • Coordinate plane word problems
  • Lesson
  • Practice
  • Algebraic thinking
  • Dividing fractions
  • Multiplying fractions
  • Negative numbers
  • Arithmetic operations
  • Data and statistics (grade 6)
  • Expressions, equations, and inequalities
  • Fractions, decimals, and percentages
  • Travel graphs
  • Numbers and operations
  • Linear functions and equations
  • Data and modeling
  • Algebra word problems
  • Simplifying square roots of monomials with real variables
  • Simplifying square roots of monomials with nonnegative real variables
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Adding and subtracting radical expressions
  • Lesson
  • Practice
  • Practice
  • Transpose and its properties
  • Other resources
  • Practice
  • Practice
  • Practice
  • Linear pair theorem
  • Using the formula: Area of a parallelogram
  • Practice
  • Lesson
  • Congruence
  • Other resources
  • Expressions representing consecutive terms
  • Other resources
  • Practice
  • Practice
  • Normal distributions and the empirical rule
  • Probability density functions
  • Median of a discrete random variable
  • Practice
  • Mode of a continuous random variable from a probability density function
  • Practice
  • Practice
  • Practice
  • Practice
  • Squaring large numbers
  • Practice
  • Practice
  • Practice
  • Practice
  • Book reviews (real analysis)
  • Other resources
  • Intro
  • Distance and midpoint of complex numbers
  • Angles standing on the same arc are congruent
  • Thales's theorem and its converse
  • Theorem 2
  • Using the theorems
  • Using the theorem
  • Using the theorem
  • Proof
  • Intro
  • Using the theorem
  • Intro
  • Proof
  • Even and odd integers
  • Proofs
  • Intro
  • Proof
  • Using the formula
  • Find an absolute value equation from its solutions
  • Solving absolute value equations by graphing
  • Lesson
  • Practice
  • Solving first-order linear differential equations
  • Working with units
  • Intro
  • Solving multi-step equations (geometry)
  • Determining if a discrete function is invertible
  • Restrict the domain then find the inverse
  • Slope-intercept form from word problems
  • Solving systems of differential equations
  • Proof
  • Intro
  • Lesson
  • Practice
  • Other resources
  • Parity proofs using modular arithmetic
  • Intro to modular arithmetic
  • Congruence in modular arithmetic
  • Solving and graphing rational inequalities using a sign chart
  • Division in modular arithmetic
  • Bezout's identity
  • Addition and subtraction in modular arithmetic
  • Intro
  • Proof
  • Euclid's GCD algorithm
  • Finding Bezout coefficients
  • Equations and inequalities
  • Graceful labeling
  • Proving the difference of squares formula
  • Lesson
  • Practice
  • Proof
  • Using the theorem
  • Intro to naive set theory
  • Intro
  • Proofs
  • Using the theorems
  • Solving literal equations using properties of logarithms
  • Practice
  • Intro
  • Proof
  • Using the theorem
  • Intro
  • Using the theorem
  • Definite integral of an exponential function
  • Definite integral of a piecewise polynomial function
  • Definite integral of a piecewise trigonometric function
  • Definite integral of a trigonometric function
  • Functions
  • Other resources
  • Identify the value of the digit (grade 4)
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Practice
  • Intro
  • Using the theorem
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Other resources
  • Intro to double integrals
  • Changing the order of integration
  • Solving equations by factoring
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Lesson
  • Using the theorem
  • Proof
  • Using the theorem
  • Intro to metric spaces
  • Finding the tangent or normal line through the given point using implicit differentiation
  • Implicit differentiation
  • Second derivative using implicit differentiation
  • Find the absolute value equation from its intercepts
  • Find the absolute value equation from a description
  • Finding \(x\) and \(y\) intercepts of absolute value equations algebraically
  • Functional equations
  • Cauchy's functional equation
  • Proving a function satisfies a functional equation
  • Lesson
  • Practice
  • Transforming a point
  • Composition of transformations
  • Identifying functions algebraically
  • Challenge problems
  • Volume of a cone (calculus 2)
  • Other resources
  • Proving the volume of a sphere formula by integrating
  • False proof that all triangles are equilateral
  • Interviews of mathematicians
  • Challenge
  • Other resources
  • Other resources
  • Art featuring mathematicians or mathematical objects
  • Challenge
  • Challenge
  • Challenge
  • Division (mathematical problems, concrete and visual)
  • Division (word problems, concrete and visual)
  • Checkerboard proofs
  • Challenge
  • Challenge
  • Alternative quadratic formula
  • Solving linear Diophantine equations in two variables
  • Challenge
  • Intro
  • Midsegment and proportionality theorems
  • Intro
  • Proof
  • Using the theorem
  • Converse of the triangle proportionality theorem
  • Proof
  • Using the theorem
  • Proof 1
  • Proof 2
  • Using the theorem
  • Intro to scientific notation
  • Intro to triangle congruence
  • Converse of the corresponding angles postulate
  • Converse of the alternate interior angles theorem
  • Converse of the alternate exterior angles theorem
  • Triangle proportionality theorem
  • Proof
  • Finding relative extrema from the derivative
  • Maximizing profit (optimization problems)
  • Challenge
  • Challenge
  • Challenge
  • Challenge
  • Challenge
  • Pythagorean triples
  • Challenge
  • Challenge
  • Challenge
  • Combining ratios (word problems)
  • Combining ratios (mathematical problems)
  • Combining ratios
  • Lesson
  • Lesson
  • Practice
  • Square It
  • First to 22
  • Stop the Clock
  • Dilating polygons
  • Lesson
  • Intro to dilating polygons
  • Lesson
  • Practice
  • Intro to calc 2
  • Intro to trigonometry
  • Solving linear systems of equations in two variables by elimination (easier mathematical problems)
  • GCD and LCM by listing factors and multiples
  • GCD and LCM from prime factorizations
  • Practice
  • Distance-speed-time problems
  • Multiplying mixed numbers (harder mathematical problems)
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Fourth proof of the sum and difference identities
  • First proof of the sum and difference identities
  • Second proof of the sum and difference identities
  • A pattern in Pascal's triangle
  • Third proof of the sum and difference identities
  • Rationalizing the denominator (type 1)
  • Intro
  • Inverse function theorem
  • Complex numbers in polar form
  • Powers of complex numbers using De Moivre's theorem
  • Trigonometric identities
  • Solving trigonometric equations using the auxiliary angle method
  • Auxiliary angle method
  • Simplifying the sum of two wave functions using the auxiliary angle method
  • Challenge
  • Challenge
  • Odds and Threes
  • Challenge
  • Dicey Operations in Line
  • Lesson
  • Practice
  • Challenge
  • Determine whether linear, quadratic, or neither, using second differences
  • Challenge
  • Challenge
  • Lesson
  • Practice
  • Other resources
  • Solving proportions using inverse operations
  • Lesson
  • Practice
  • Solving rational equations (mathematical problems)
  • Lesson
  • Practice
  • Challenge
  • Using the Pythagorean theorem (harder mathematical problems)
  • Lesson
  • Practice
  • Finding quadratic equations from tables using second differences
  • Other resources
  • Lesson
  • Practice
  • Challenge
  • One-player games
  • Quadrilaterals
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Method 2
  • Challenge
  • Other resources
  • Combining like terms (concrete and visual method)
  • Lesson
  • Practice
  • Challenge
  • Trick for percents
  • Second trick for percent of a number (percent not always a multiple of ten)
  • Challenge
  • Challenge
  • Challenge
  • Challenge
  • Challenge
  • Challenge
  • Challenge: Divisible by 13
  • Lesson
  • Practice
  • American Billions
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Sum and product of roots of quadratics
  • Proving the sum formula for sine and cosine using Euler's formula
  • Intro
  • Proof
  • Angles around a point
  • Lesson
  • Intro to tessellations
  • Proving properties of trees
  • Intro to trees
  • Challenge
  • Challenge
  • Proof
  • Using the theorem
  • Proof
  • Diagonals of a rectangle are congruent
  • Proof 2
  • Using the theorem
  • Consecutive interior angles theorem
  • Proof 1
  • Proof
  • Converse of the consecutive interior angles theorem
  • Intro
  • Using the theorem
  • Challenge
  • Using the theorem
  • Proof
  • Challenge
  • Challenge
  • Challenge
  • Tidbits
  • Tidbits on knot theory
  • Intro
  • Lesson
  • Practice
  • Lesson
  • Challenge
  • Challenge
  • Integral ideals
  • Proving multiples form an integral ideal
  • Additive property of angles
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Intro
  • Proving the product rule from first principles
  • Intro
  • Intro
  • Intro
  • Proof
  • Proving properties of even and odd functions (algebra 2)
  • Lesson
  • Practice
  • Other resources
  • Kernel of a group homomorphism
  • Intro to group homomorphisms
  • Abelian groups
  • Lesson
  • Practice
  • Challenge
  • Lesson
  • Practice
  • Spiralling Decimals
  • Lesson
  • Practice
  • Finding critical values from graphs
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Proof 1
  • Group actions
  • Lesson
  • Practice
  • Tidbits on integer sequences
  • Principle of explosion
  • Deductive, inductive, and abductive reasoning
  • Lesson
  • Practice
  • Proof
  • Intro
  • Using the theorem
  • Lesson
  • Practice
  • Intro to solving separable differential equations
  • Solving separable differential equations with growth and decay
  • Solving more complicated separable differential equations
  • Volumes of solids with known cross sections
  • Work done by a variable force
  • Center of mass (calculus 2)
  • Center of mass for one and two-dimensional systems
  • Center of mass for planar lamina
  • Pappus's theorem
  • Hydrostatic force
  • Intro to vectors
  • Proving equivalence of the dot product definitions
  • Proving a property of the cross product
  • Relating the cross product to the area of a parallelogram
  • Vector functions
  • Multiple integrals
  • Iterated integrals
  • Midpoint rule for double integrals
  • Riemann sums for double integrals
  • Average value of a double integral
  • Orbit stabilizer theorem
  • Double integrals over general regions
  • Finding equations of lines and planes
  • Green's theorem
  • Surface integrals
  • Higher order partial derivatives
  • First order partial derivatives
  • Intro to partial derivatives
  • Curl and divergence
  • Finding limits using u-substitution
  • Proving the derivative of the natural logarithm
  • Lesson
  • Tidbits on the Riemann hypothesis
  • Tidbits on Goldbach's conjecture
  • Proofs
  • Integration techniques
  • Lesson
  • Practice
  • Integrating quadratics by completing the square
  • Lesson
  • Practice
  • Sum, difference, and reverse power rules for indefinite integrals
  • Practice
  • Applications of integrals
  • Using the formula
  • Undetermined coefficients
  • Other resources
  • Intro to differential equations
  • Sketching solution curves in slope fields
  • Intervals of validity
  • Intro to initial value problems
  • Solving initial value problems
  • Real eigenvalues
  • Equilibrium solutions
  • Intro to equilibrium solutions
  • Basic concepts of differential equations
  • Laplace transforms
  • Partial differential equations
  • Systems of differential equations
  • Bernoulli differential equations
  • Po-Shen Loh method
  • Logistic growth
  • 3-dimensional space
  • Cylindrical coordinates
  • Monotonic intervals and functions
  • Expressions vs equations
  • Practice
  • Lesson
  • Exponents and radicals
  • Inequalities and systems of inequalities
  • Triangular numbers
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Lesson
  • Lesson
  • Constants
  • Predicates
  • Intro to calc 1
  • Critical thinking
  • Informal fallacies
  • Applications of partial derivatives
  • Lagrange multipliers
  • Lesson
  • Lesson
  • Triangle and reverse triangle inequalities
  • Lesson
  • Practice
  • Intro
  • Other resources
  • Quadrants
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Memorizing the Pythagorean identities
  • Right triangles and trig
  • Using the theorem
  • Unit circle
  • Non-right triangles and trig
  • Memorizing how the six basic trig functions relate
  • Lesson
  • Intro to the six basic trig functions
  • Practice
  • Lesson
  • Practice
  • Why rationalize the denominator?
  • Rationalizing the denominator (type 2)
  • Rationalizing the denominator (type 3)
  • Lesson
  • Practice
  • Distributive property with variables (visual method, grade 7)
  • Intro
  • Proof
  • Intro
  • Proof
  • Using the theorem
  • Proof
  • Using the theorem
  • Intro
  • Proof
  • Incenter theorem
  • Proving differentiable implies continuous
  • Subtracting integers (abstract method)
  • Subtracting integers (concrete and visual methods)
  • Lesson
  • Practice
  • Subtracting integers (word problems)
  • Converting units of time
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Combinatorics and graph theory
  • Intro to graphs
  • Connected graphs
  • Graph components
  • Walks, paths, and cycles
  • Lesson
  • Reciprocal polynomials
  • Adjacency lists, adjacency matrices, and incidence matrices
  • Ordered field
  • Maximum and minimum of a set
  • Cardinality
  • Intro to real analysis
  • Intro to categorical statements
  • Regular graphs
  • Proof
  • Monotone convergence theorem
  • Intro
  • Using the theorem
  • Monotonic sequences
  • Squeeze theorem for sequences
  • Lesson
  • Practice
  • Variations of proof by induction
  • Intro
  • Proofs
  • Proving inequalities
  • Proof 2
  • Double quantifiers
  • Lesson
  • Practice
  • Bolzano-Weirstrass theorem
  • Proving limit laws
  • Lesson
  • Practice
  • Finite calculus
  • Bell numbers
  • Lesson
  • Practice
  • Stirling numbers
  • Intro to the Ackermann function
  • Using the theorem
  • Proof
  • Generating functions from recurrence relations
  • Generating functions (differencing)
  • Boolean SAT
  • Comparison tests for convergence
  • Absolute convergence, conditional convergence, and divergence
  • Lesson
  • Practice
  • Intro to generating functions
  • Equating coefficients
  • Riemann's rearrangement theorem
  • Lesson
  • Practice
  • Other simple planar graphs
  • Minimum spanning tree
  • Other resources
  • Fermat's infinite descent
  • Riemann integrability
  • The real numbers
  • Sequences
  • Topology of the real numbers
  • epsilon-N definition of convergence
  • Lesson
  • Practice
  • Pointwise and uniform convergence
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Lesson
  • Practice
  • Fermat's two squares theorem
  • Follow-up to Euler's formula
  • Using the theorem
  • Automorphisms of a graph
  • Challenge
  • Reference
  • Recursive function theory
  • Female mathematicians
  • Inverse function theorem (calc 3)
  • Intro to calc 3
  • Presburger arithmetic
  • Automated theorem provers
  • Quantifiers
  • Book reviews (popular math)
  • Book reviews (recursive function theory)
  • Tiling
  • Root-finding algorithms
  • Algorithms for evaluating polynomials
  • Perfect numbers
  • Ramanujan's infinite nested roots
  • Graph isomorphism problem
  • Division algorithm
  • Counting from pictures, oral response
  • Write numbers
  • Representing numbers with drawings
  • Understanding zero
  • Compare written numerals
  • Counting to 100 by ones
  • Counting to 100 by tens
  • Counting objects arranged in different ways
  • Counting on by ones or tens
  • Compare by matching or counting
  • Relative positions
  • Naming shapes in the real-world
  • Addition and subtraction, concrete and visual
  • Add and subtract within 10
  • Decompose in multiple ways
  • Addition, missing number word problems
  • Add and subtract within 5
  • Count, represent and write teen numbers
  • Compare measurements without tools
  • More, most, fewer, fewest
  • Name shapes regardless of size
  • Identify shapes and solids
  • Compare attributes of shapes and solids
  • Build solids
  • Compose 2D shapes
  • Add and subtract within 20, word problems
  • Add within 20, word problems involving three addends
  • Use one addition problem to solve another
  • Add by making tens
  • Subtract by adding
  • Add and subtract by counting
  • Add and subtract within 20, abstract
  • Understand the equals sign
  • Add and subtract within 20, missing number problems
  • Count and write numbers within 120
  • Place value with tens
  • Compare two-digit numbers
  • Add within 100
  • 10 more or 10 less
  • Subtract multiples of ten from multiples of ten
  • Order without tools
  • Measure given a unit
  • Tell and write time, hour and half-hours
  • Bar and picture graphs having three categories of data
  • Definitions of shapes
  • Compose 2D and 3D shapes
  • Halves and quarters
  • Two-step word problems, add and subtract within 100
  • Mentally add and subtract within 20
  • Intro to even and odd
  • Add to count rectangular arrays
  • Place value with hundreds
  • Counting and skip-counting within 1000
  • Convert between various representations, numbers within 1000
  • Compare three-digit numbers
  • Add multiple two-digit numbers
  • Add and subtract within 1,000
  • Mentally add or subtract powers of ten
  • Add and subtract within 100, abstract
  • Compare lengths by measuring
  • Estimate lengths
  • Add and subtract within 100 to solve word problems involving lengths
  • Add and subtract within 100 on the number line
  • Tell and write time, five minute increments
  • Money word problems, including dollars
  • Plot measurements on a line plot
  • Draw picture and bar graphs
  • Draw shapes with certain attributes
  • Area of a rectangle by counting unit squares
  • Partition circles and rectangles into equal shares
  • Multiplication using rectangular arrays and equal groups, concrete and visual
  • Divide using equal groups
  • Relating multiplication to division
  • Missing number problems, multiplication and division
  • Use properties to multiply and divide
  • Multiply, abstract
  • Two-step word problems
  • Patterns in addition and multiplication
  • Round to the nearest 10 or 100
  • Add and subtract within 1000, abstract
  • Multiply one-digit numbers by multiples of 10
  • Equal shares of shapes and unit fractions
  • Plot fractions on the number line
  • Comparing fractions with like numerators, denominators, or both
  • Tell and write time, minute increments
  • Measure and estimate volumes and masses
  • Scaled bar and picture graphs
  • Line plots with fractions
  • Area and units of measure
  • Area of composite rectangles by counting unit squares
  • Area as multiplication
  • Area, perimeter, and how they're related
  • Shape heirarchy
  • Solve multiplication and division word problems
  • Multi-step word problems
  • Prime and composite numbers
  • Number patterns
  • Represent numbers within 1000 using place value blocks
  • Multiply and divide by 10
  • Convert between written forms of numbers
  • Round whole numbers
  • Multiplication
  • Quotients and remainders
  • Equivalent fractions
  • Compare fractions with unlike numerators, denominators, or both
  • Add and subtract fractions with like denominators
  • Multiply fractions by whole numbers
  • Add fractions with power of ten denominators
  • Convert fractions to decimals, power of ten denominators
  • Compare decimals to hundredths
  • Convert larger units to smaller ones
  • Word problems involving measures
  • Represent and reason with line plots
  • Intro to angles
  • Adjacent angles and the additive property of angles
  • Geometric definitions
  • Lines of symmetry
  • Intro to parentheses
  • Convert between words and arithmetic expressions
  • Linear equations, tables
  • Add and subtract fractions, abstract
  • Add and subtract fractions, word problems
  • Fraction quotients, word problems
  • Areas and perimeters, fractional side lengths
  • Multiplication as scaling
  • Dividing whole numbers by unit fractions
  • Squaring the circle, visual proof
  • Geometric mean theorem
  • Sum of an infinite geometric series
  • Hashi puzzles
  • Counting and place value
  • Addition and subtraction
  • Measurement and geometry
  • Exploration: Bicycle math
  • Place value
  • Addition and subtraction
  • Measurement, data, and geometry
  • Third angle theorem
  • Add and subtract within 20
  • Place value
  • Add and subtract within 100
  • Add and subtract within 1,000
  • Money and time
  • Measurement
  • Data
  • Geometry
  • Divide, abstract
  • Multiplication
  • Addition, subtraction, estimation
  • Division
  • Fractions
  • Relating multiplication and division
  • Arithmetic patterns and problem solving
  • Geometry
  • Time, measurement, and data
  • Place value of whole numbers
  • Multiplication and division
  • Factors, multiples, and patterns
  • Equivalent fractions and comparing fractions
  • Fraction arithmetic
  • Understand decimals
  • Geometry
  • Units of measurement
  • Decimal place value
  • Multiplying whole numbers by powers of 10
  • Decimals to thousandths
  • Rounding decimals
  • Multiplication, partial products method
  • Long division
  • Decimal arithmetic
  • Plot coordinates
  • Plot coordinates from word problems
  • Classifying shapes
  • Unit conversion
  • Volume by counting unit cubes
  • Volume of right rectangular prisms by multiplying
  • Multiply fractions, word problems
  • Decimal place value
  • Multi-digit multiplication and division
  • Decimal arithmetic
  • Add and subtract fractions
  • Multiply fractions
  • Divide fractions
  • Volume
  • Coordinate plane
  • Algebraic thinking
  • Measurement and data
  • Properties of shapes
  • Raising numbers to whole number powers
  • Tower of Hanoi
  • Convert phrases to algebraic expressions
  • Identify parts of expressions
  • Distributive property with variables
  • Determining equivalence of algebraic expressions
  • Understanding solutions to equations and inequalities
  • Area
  • Intro to ratios
  • Unit rates
  • Equivalent ratios
  • Volume of right rectangular prisms with fractional lengths
  • Coordinate plane
  • Nets and surface area
  • Divide fractions
  • One-step equations
  • Long division
  • Decimal arithmetic
  • Congruent supplements and complements theorems
  • GCD and LCM
  • Negative numbers in the real-world
  • Negative numbers on the number line
  • Absolute value of rational numbers
  • Plotting points in all four quadrants
  • Identifying statistical questions
  • Wishful thinking strategy
  • Circumference and area of a circle
  • Proving de Moivre's theorem
  • Vertical and horizontal line tests
  • Addition rule
  • Expected value
  • Difference of squares
  • Dependent and independent variables
  • Solving one-step equations
  • Modeling one-variable inequalities
  • Analyzing distributions
  • Plotting data
  • Ratios, rates, and percentages
  • Arithmetic operations
  • Negative numbers
  • Factors and multiples
  • Variables and expressions
  • Equations and inequalities introduction
  • Geometry
  • Data and statistics
  • Interpreting graphs of proportional relationships
  • Percents
  • Simplifying complex fractions without variables
  • Scale drawings
  • Basic probability proofs
  • Intro to the triangle inequality
  • Cross sections
  • Distributing, factoring, and combining like terms
  • Convert word problems to linear expressions
  • Multi-step problems
  • Testing polar equations for symmetry
  • Intro to arithmetic sequences
  • Area, volume, and surface area
  • Surface area of rectangular prisms
  • Proving the divisibility rules for 7 and 13
  • Remainders of large powers
  • Percentages
  • Round fractions
  • Negative exponents
  • Challenge: Skipped Counts
  • Solving linear systems of equations in two variables by any method
  • Special right triangles
  • Higher order roots
  • Multiplication as repeated addition
  • Division using repeated subtraction
  • Intro to the Fibonacci sequence
  • Pythagorean theorem
  • Other resources
  • Lesson
  • Symmetry
  • Other resources
  • Other resources
  • Factor pairs
  • Factoring and solving monic quadratics
  • Prime factorization
  • Intro to polyominoes
  • Sketching polynomials using stationary points
  • Simple events
  • Conditional probability
  • Compound probability of independent events
  • Converting fractions to decimals
  • Other resources
  • Comparing and ordering fractions with unlike denominators
  • Dividing whole numbers by fractions
  • Multiplying whole numbers and fractions
  • Finding the part
  • Solving linear equations by clearing decimals and fractions
  • Solving linear systems of equations in two variables by elimination
  • Algebraic expansion with area
  • Solving rational equations
  • Remainders of Fibonacci numbers
  • Counting vertices, edges, and faces
  • Dividing integers
  • Rep-tiles and irrep-tiles
  • River crossing puzzles
  • Sum of the interior angles of a triangle
  • Other resources
  • Other resources
  • Other resources
  • Other resources
  • Other resources
  • Other resources
  • Other resources
  • Solving equations and inequalities
  • Linear equations and graphs
  • Polynomials
  • Irrational numbers
  • Solving literal linear equations
  • Solving and graphing multi-step inequalities in one-variable
  • Solving for a variable given a linear equation in standard form
  • Other resources
  • Transformations
  • Solving one-step equations (geometry)
  • Complementary and supplementary angles
  • Using the circle theorems
  • Sum of interior angles for simple polygons
  • Sum of exterior angles
  • Additional topics
  • Other resources
  • Derivatives: definition and basic derivative rules
  • Epsilon-delta proofs
  • Other resources
  • Integrals
  • Applications of integrals
  • Other resources
  • Comparison test for series
  • Proving the formula for the area of a circle
  • Vectors
  • Other resources
  • Tangent planes and linear approximations
  • Special points of multivariable functions
  • Other resources
  • Proof by strong induction
  • Proof by contradiction
  • Other resources
  • Counting in bases 5 and 2
  • Other resources
  • Other resources
  • Other resources
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  • Other resources
  • Factorials
  • Other resources
  • Other resources
  • Other resources
  • Other resources
  • Other resources
  • Other resources
  • Other resources
  • Binomial theorem
  • Other resources
  • Other resources
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  • Rounding decimals (unsorted)
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  • Intro to conic sections
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  • Telling time to the nearest 5 minutes
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  • Distance formula
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  • Solving literal rational equations
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  • Relatively prime
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  • Finding and verifying the inverse of a nonlinear function
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  • Analyzing categorical data
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  • Modeling data distributions
  • Exploring bivariate numerical data
  • Study design
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  • Sampling distributions
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  • Significance tests (hypothesis testing)
  • Two-sample inference for the difference between groups
  • Inference for categorical data (chi-square tests)
  • Advanced regression (inference and transforming)
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  • Power set
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  • Midpoint formula
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  • Multiplying complex numbers
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  • Age problems
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  • Evaluating logarithms
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  • Determining derivatives from graphs
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  • Solving quadratic equations by taking square roots
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  • Estimating the line of best fit
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  • Intro to hyperbolic functions
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  • Graphing systems of linear inequalities in two variables
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  • Exponential growth and decay
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  • Intro to the six basic trig functions
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  • Solving logarithmic equations using the one-to-one property
  • Sum and difference of cubes
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  • Finding the point on the unit circle
  • Composition of trig functions
  • Evaluating inverse trig functions using the unit circle
  • Evaluating trig functions using a calculator
  • Evaluating inverse trig functions using a calculator
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  • Mentally raising small numbers to small powers
  • Rational root theorem
  • Higher-order polynomials
  • Adding and subtracting multi-digit numbers
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  • Circumcircles and incircles
  • Double and half angle formulas
  • Mentally solving multi-step equations
  • Converting improper algebraic fractions to mixed algebraic fractions
  • t-results
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  • Graphing polar equations
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  • Linear factorization
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  • Multiplying a complex number by a real number
  • Adding and subtracting complex numbers
  • Powers of the imaginary unit
  • Simplifying square roots of negative integers
  • Solving and graphing polynomial inequalities using a sign chart
  • Factoring and solving polynomials by graphing
  • Intro to complex numbers
  • Proving properties of the complex modulus
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  • Inverses of exponential and logarithmic functions
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  • Inverse variation
  • Direct variation
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  • Modulus and argument of a complex number
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  • Dividing a polynomial by a monomial
  • Dividing quadratics by linear expressions
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  • Solving trigonometric equations by graphing
  • Finding general solutions to trig equations
  • Graphing rational functions
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  • Solving logarithmic equations using the properties of logarithms
  • Verifying logarithmic identities
  • Simplifying complex fractions with variables
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  • Intro to Pascal's triangle
  • Converting sums between sigma notation and expanded form
  • Proving inverse trig identities
  • Solving equations with radicals and rational exponents
  • Simplifying expressions with radicals and rational exponents
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  • Solving literal equations
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  • Simplifying trig expressions
  • Rewrite exponential expressions
  • Solving trig equations by factoring trinomials
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  • Fractal dimension
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  • Estimating sums and differences by rounding
  • Estimating products by rounding
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  • Mentally add within 1000
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  • Incenter and circumcenter of a triangle
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  • Intro to the incenter and circumcenter of a triangle
  • Circumcenter theorem
  • Area of composite figures with semicircles
  • Crossed ladders theorem
  • Standard equation of a circle
  • Dividing unit fractions by whole numbers
  • The four fundamental spaces
  • Column space
  • Orthogonal complements
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  • Visualizing a projection onto a plane
  • Linear subspace
  • Characteristics of functions
  • Sketching a polynomial given characteristics
  • Orthogonal projection
  • Nullspace, left nullspace, and row space
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  • Adding multiple two-digit numbers
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  • One-step word problems, add and subtract within 100
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  • z-scores
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  • Lesson
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Proof Index
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    • ▾Abstract algebra
      • ▸Binary operations and relations
        • •Properties of binary operations
        • •What is a relation? (for undergraduates)
        • •What is an equivalence relation?
      • ▾Group theory
        • •Intro to groups
        • •Subgroups
        • •Group isomorphisms
        • ▸Group homomorphisms
          • •Kernel of a group homomorphism
          • •Intro to group homomorphisms
        • •Equivalence classes
        • •Cosets of a subgroup
        • •Cosets and Lagrange's theorem
        • •Basic group theory proofs
        • ▸Abelian groups
          • •Lesson
          • •Practice
        • •Alternating groups
        • •Tidbits on Burnside's lemma
        • ▸Converting between array notation and cycle notation
          • •Converting cycle notation to array notation
          • •Converting array notation to cycle notation
        • •Cyclic groups
        • •Dihedral group
        • •Direct product of finite cyclic groups
        • •Direct product of groups
        • •Group automorphisms
        • •Is the table a commutative semigroup?
        • •Kernel of a group homomorphism
        • •Klein four-group
        • •Multiplying permutations in array notation
        • •Multiplying permutations in cycle notation
        • •Order of an element in a group
        • •Proof: Centralizer of group element is subgroup
        • •Compositions of group morphisms
        • •Normal subgroups
        • •Proof: Finite subgroup test
        • •Proof: First isomorphism theorem for groups
        • •Proof: Fundamental homomorphism theorem
        • •Proof: Group abelian iff cross cancellation property
        • •Proof: If \(y\) is a left or right inverse for \(x\) in a group, then \(y\) is the inverse of \(x\)
        • •Proof: Inverse of generator of cyclic group is generator
        • •Proof: Inverse of group inverse
        • •Proof: One-step subgroup test
        • •Proof: Order of element divides order of finite group
        • •Proof: Order of group element equals order of inverse
        • •Proof: Second isomorphism theorem for groups
        • •Proof: Special linear group is subgroup of general linear group
        • •Proof: Symmetric difference on power set forms group
        • •Proof: The conjugation map is an automorphism
        • •Proof: Two-step subgroup test
        • •Proving group homomorphisms
        • •Quotient groups
        • •Simple groups
        • •Solvable groups
        • •Sufficient conditions for a group to be abelian
        • •Symmetric group
        • •Symmetries of an equilateral triangle
        • •Verifying equivalence relations on groups
        • •What is cycle notation?
        • •Group actions
        • •Orbit stabilizer theorem
        • •Center of a group
      • ▸Ring theory
        • •Is it a ring?
        • •Basic ring theory proofs
        • ▸Integral ideals
          • •Intro to integral ideals
          • •Proving multiples form an integral ideal
        • •More ring theory proofs
        • •What is a subring?
     › Abstract algebra › Group theory

    Intro to groups

    Students will learn the formal definition of a group, and see examples and non-examples. Here's an easy exercise: Prove \((\mathbb{Z}, +)\) is a group (video).

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