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
Other resources
Other resources
Other resources
Other resources
Other resources
Other resources
Other resources
Other resources
Other resources
Other resources
Other resources
Other resources
Other resources
Factorials
Other resources
Other resources
Other resources
Other resources
Other resources
Other resources
Other resources
Binomial theorem
Other resources
Other resources
Other resources
Other resources
Other resources
Other resources
Other resources
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Rounding decimals (unsorted)
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Adding and subtracting with negative numbers
Multiplying and dividing with negative numbers
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Circles
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Remainder and factor theorems
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Solving polynomials
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Permutations
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Direct and inverse variation
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Area of a sector formula
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Solving proportions
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Multiplying and dividing functions
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Integration by partial fractions
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Solving trig equations by factoring
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Using the law of cosines
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Polynomials (algebra 1)
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Congruent triangles
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Calculus
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Evaluating inverse trig functions
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Imaginary numbers
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Angle intro
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Polygon angle sum theorems
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Volume of a pyramid
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Polynomial factorization
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Finding the GCD of polynomials
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Multiplying binomials by polynomials using the abstract method
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Finding the domain and graphing rational functions
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Intro to conic sections
Arc length and sector formulas
Intro to radians
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Telling time to the nearest 5 minutes
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Distance formula
Irrational numbers
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Solving literal rational equations
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Relatively prime
Central angle theorem
Visually determining antiderivative
Solving non-monic quadratics by factoring
Gauss's trick
Dividing mixed numbers
Changing linear dimensions
Volume
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Finding and verifying the inverse of a nonlinear function
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Analyzing categorical data
Displaying and comparing quantitative data
Summarizing quantitative data
Modeling data distributions
Exploring bivariate numerical data
Study design
Random variables
Sampling distributions
Confidence intervals
Significance tests (hypothesis testing)
Two-sample inference for the difference between groups
Inference for categorical data (chi-square tests)
Advanced regression (inference and transforming)
Analysis of variance (ANOVA)
Power set
False position method
Rigid transformations
Permutations and factorials
Combinations
Midpoint formula
Proving properties of even and odd numbers
Sums of squares
Solving proportions by cross multiplying
Evaluating and graphing the floor function
Evaluating piecewise functions
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Basic statistics
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Multiplying complex numbers
Multiplying and dividing complex numbers in polar form
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Proving the divisibility tests
Triangles
Area of a regular polygon
Powers of complex numbers
Find the angle of rotation
Divisibility with sums and differences
Logarithmic scale
Finding exponential functions from tables, graphs, and points
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Age problems
Length of a vector
Adding and subtracting mixed numbers with regrouping
Short division
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Evaluating logarithms
Platonic solids
Logarithms with negative bases and arguments
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Water pouring puzzles
Multiplication principle
Classifying quadrilaterals from four points
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Shifting, scaling, and reflecting
Adding vectors in polar form
Side splitter theorem
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Koch curve
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Set operations
Vector equations of lines
Adjacency and degrees
Complex conjugate root theorem
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Quadratic equations with complex solutions
Evaluating trig functions and solving trig equations using the unit circle
Tournament graphs
Intro to groups
Finding the quadrant of an angle
Center of a group
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Determining derivatives from graphs
Basics of geometry
Golden ratio
Determining quadratics from their roots
Solving quadratic equations by taking square roots
Finding the radius given the area
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Area of a regular polygon
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Evaluating the six basic trig functions
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Evaluate the remaining basic trig functions
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Estimating the line of best fit
Graphing trig functions
Reciprocal identities
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Finding parabolas given three points
Solving linear systems of equations in three variables by elimination
Basic set theory proofs using set identities
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Solving equations with rational exponents
Similar triangles
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SSS congruence
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Graphing harder absolute value equations
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Factoring non-monic quadratics by factoring out the GCD
Equivalent expressions with negative numbers
Comparing and ordering fractions
Finding the equation of a line
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Solving proportions using equivalent fractions
Factoring monic quadratics using algebra tiles
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Counting objects by property
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Converse of the corresponding angle theorems
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Intro to similarity
Finding cube roots of small perfect cubes
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Negative Fibonacci numbers
Proof by induction (Fibonacci numbers)
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Volume of extruded figures
Using the theorems
Corresponding angle theorems
Method 1
Method 2
Three squares puzzle
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Combining means
Simple hypothesis testing
Hypothesis testing and p-values
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Finding the midpoint on the number line
Missing square puzzle
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Evaluating trig functions using coterminal and reference angles
Measuring and drawing angles
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Adding and subtracting in scientific notation
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Solving proportions using inverse operations and by cross multiplying
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Making and describing scatter plots
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Power of a power rule for exponents
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Slope-intercept equation from two points or a table
Classifying angles
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Reflecting a point over any non-horizontal line
Cavalieri's principle
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More on binary
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Degree of a polynomial
Powers of 10
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Measurement with an unknown unit of length
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Intercepts from a linear equation
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Congruent polygons
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Working with powers of 10
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Theorem 1
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Polynomial identities
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Volume and surface area of a sphere
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Scaling along an axis
Graphing reciprocal functions
Solving hyperbolic equations
Proving hyperbolic identities
Intro to hyperbolic functions
Integral recurrence relations
Integration by long division
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Intro to variables
Rate conversion
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Intro to the triangular numbers
Classifying triangles
Classifying polygons
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Graphing linear inequalities in standard form
Graphing systems of linear inequalities in two variables
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Evaluating expressions with multiple variables
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Find the formula of an arithmetic sequence from two terms
Find the explicit formula for an arithmetic series given terms
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Arithmetic series
Univariate expressions representing consecutive terms
Explicit formula from the first few terms
Explicit formula from two terms
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Graphs of piecewise functions
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Solving floor and ceiling equations
Product property for square roots
The Cambridge Puzzle
Intro to Pascal's triangle
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Simplifying cube roots of integers
Simplifying nested square roots
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Exponential growth and decay
Converting quadratics between standard form and vertex form
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Factoring non-monic quadratics using algebra tiles
Factoring non-monic quadratics
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Ratios of area, surface area, and volume, for similar shapes
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Reducing to a linear equation
Intro to vertex form for quadratics
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Determining quadratics from their roots
First and second differences
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Sums and products of rational and irrational numbers
Intro to the six basic trig functions
Graphing sin and cos
Graphing tan and cot
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Graphing sec and csc
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Finding a sin or cos equation from a graph
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Centroid and orthocenter
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Descartes's rule of signs
Difficult factoring problems
Center and radii of an ellipse
Foci of an ellipse
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Solving equations in quadratic form using u-substitution
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Intro to hyperbolas
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Foci of a hyperbola
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Hyperbolas not centered at the origin
Infinite consecutive independent events
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Graphically finding the increasing, decreasing, and constant intervals
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Complementary events
Solving logarithmic equations using the one-to-one property
Sum and difference of cubes
Proofs using the unit circle
Signs of trig functions
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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Proving inverse hyperbolic identities
Mentally raising small numbers to small powers
Rational root theorem
Higher-order polynomials
Adding and subtracting multi-digit numbers
Distance and midpoint in 3D
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Distributive property without variables
Congruent tangents theorem
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Radii inside right triangles
Circumradii of equilateral and isosceles triangles
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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Solving trigonometric equations by factoring out the GCD
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Plotting polar points
Graphing polar equations
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Even-odd trig identities
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Asymptotes and intercepts of rational functions
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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
Partition rectangles into rows and columns
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Rotational symmetry
Number of diagonals in a convex polygon
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Sequences
Every convergent sequence is a Cauchy sequence
Every convergent sequence is a Cauchy sequence.
46926
Every Convergent Sequence is Cauchy Proof
The Math Sorcerer
70245
9.1 Cauchy Sequences
RGB mathematics