# Topics with few videos

Here's a list of topics for which there are between 1 and 9 videos. Please consider making videos for these topics, or those topics having no videos.

- \(x^y = y^x\)
- Permutation of the natural numbers
- Ruth–Aaron pair
- Duodecimal
- Genealogy
- Teaching algebra
- Chinese remainder theorem
- Square root
- Lesson: What is an irrational number?
- Grandi's series
- \(1 + 2 + 3 + 4 + \ldots\)
- \(\displaystyle \dfrac{1}{2} + \dfrac{1}{4} + \dfrac{1}{8} + \dfrac{1}{16} + \ldots\)
- Hamiltonian cycles and paths
- Rationalizing the denominator: Lesson
- Goldbach's conjecture
- What is \(e?\)
- History of \(\pi\)
- History of trigonometry
- Math in art
- Learning mathematics
- Applications of complex numbers
- Proving Vandermonde's identity
- Applications of linear algebra
- Where does \(\pi\) appear?
- Where does \(e\) appear?
- Applications of statistics and probability
- Applications to criminal investigation
- Euler characteristic
- Biographies
- Finding the midpoint on the number line
- Using the formula
- Squaring the square
- Euler line
- Inscribed square problem
- Twin prime conjecture
- Derivation
- Congruent angles
- \(\pi\)
- Napkin ring problem
- Missing square puzzle
- Standard form
- Shifting functions
- Computer-assisted proof
- Scaling functions
- Proving there are exactly five Platonic solids
- Hyperboloid
- Si Stebbins stack
- Squaring the torus
- Mandelbrot set
- The Leaning Tower of Lire
- Strictly-convex deltahedron
- \(\pi\) tape
- Genailleâ€“Lucas rulers
- Challenging exercises
- Secretary problem
- Definite integral of a polynomial function
- The monkey and the coconuts
- Comparing and ordering integers
- Adding decimals using the standard algorithm
- What is a variable?
- Double pendulum
- Estimating products
- Lines of symmetry
- Babylonian mathematics
- Mathematical modeling
- Simpson's paradox
- Challenge
- Difference between correlation and causation
- What is a derivative?
- Infinite sets
- Taxicab geometry
- Stable marriage problem
- Stereographic projection
- Isometry
- Bisection method
- Powers of \(i\)
- Plotting numbers on the complex plane
- Linear factorization theorem
- When is a logarithm undefined?
- Complex number logarithm
- How many ways can you arrange a deck of cards?
- Finding horizontal asymptotes of rational functions
- Intro to limits
- Intersection of two lines in \(\mathbb{R}^3\)
- Hilbert's paradox of the Grand Hotel
- Lines in \(\mathbb{R}^3\)
- Minimum vertex cover
- Ternary numeral system
- \(100\) prisoners problem
- Fixed point
- Brachistochrone curve
- What is a planar graph?
- Perfect graph
- Introduction to logarithms
- Futoshiki
- Biconditional
- Flows and cuts
- Inclusion–exclusion principle
- Random
- Division algorithm
- History of combinatorics
- Addition rule of probability
- 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
- Using Sophie Germain's identity
- Georg Cantor
- William Rowan Hamilton
- Évariste Galois
- History
- History of probability theory
- Intro to probability
- Multi-digit addition
- Inclinometer
- \(n\)-th root
- Necklace splitting problem
- Intro to circles and \(\pi\)
- What is volume?
- Intro to integers
- Introduction to percents
- Introduction to polygons
- Introduction to functions
- Intro to linear functions
- Metric system
- Integration by completing the square and using trig substitution
- Archimedes's cattle problem
- Kakeya set
- St. Petersburg paradox
- Videos for kindergarten teachers
- Teaching preschool mathematics
- Education reform
- Large numbers
- Flexagon
- Ruled surface
- Sum of three cubes
- Graphs of sequences
- Frieze patterns
- Polynomial multiplication
- Inscribed and circumscribed figures
- What is the apothem?
- What is a regular polygon?
- Line-circle and circle-circle relationships
- 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
- Add and subtract fractions (word problems)
- Division using the stamp game
- Division using the stamp game (grade 4)
- Multiplication of a multi-digit number by a three-digit number
- Reading travel graphs
- Unitary method
- Median
- Stem and leaf plots
- Approximating square roots to tenths and hundredths by guessing
- Estimation
- Factoring a cubic polynomial with a double root
- Challenge
- Motion graphs
- Leibniz's derivative notation
- Zero
- Collatz conjecture
- Adding and subtracting free vectors
- Triple angle formulas
- Polynomial long division and graphing
- Equation of a semicircle
- Solving certain cubic inequalities
- Graphing with complex numbers
- Straight line motion
- Graphing inverse trigonometric functions
- Applications of trigonometric integrals
- Applications of trigonometric derivatives
- Finding the acute angle between two lines
- Integrating exponential functions
- Integrating exponential functions
- Logarithmic functions
- Finding absolute extrema
- Oblique asymptotes
- Graphing using derivatives
- Line of intersection between two planes
- Arc length (calculus 2)
- Surface area of revolution
- Review of basic integration rules
- Trigonometry (A-Level Maths)
- Gradients
- Differentiation
- Equivalent forms
- Deriving the quadratic formula
- Finding the intersection point of two graphs
- Wythoff's game
- Game of Nine
- Factorization with complex numbers
- Variation of the Monty Hall problem
- Adding and subtracting in scientific notation
- Volume of extruded figures
- Rounding to \(n\) significant figures
- Measures of central tendency from frequency tables
- Dividing a quantity by a ratio
- Wason selection task
- Affine transformation
- Dice puzzle
- First to get a head
- Utilities puzzle
- Tidbits on Burnside's lemma
- Bridge and torch problem
- Puzzle: Find the nine digit number
- The Hardest Logic Puzzle Ever
- Hat puzzle
- Pirate game
- Power of a point
- Multiply any number by twelve
- Mental math: Subtract a near multiple of 10 from a two-digit number by adjusting
- Penney's game
- Combination and permutation word problems
- Arranging in a circle
- Difference between rational and irrational numbers
- Disc method
- Shell method
- Horizontal and vertical lines
- Expanding quadratic expressions using algebra tiles
- Multiplying monomials by binomials (with algebra tiles)
- Factoring monic quadratics using algebra tiles
- Gauss's trick
- Partial order
- What is a path graph?
- What are cycle graphs?
- Finding polynomials given integer zeros
- Intersection of circle and line
- Find the equation of a piecewise function from its graph
- Solving harder trigonometric equations
- Solving trigonometric equations by quadrants
- Finding the quadrant from trigonometric constraints
- Evaluating natural logarithms without a calculator
- Applications of logarithms
- What is modus ponens?
- Modus tollens
- Disjunctive syllogism
- Constructive dilemma
- Destructive dilemma
- Conjunction introduction and elimination
- Biconditional introduction and elimination
- Disjunction introduction
- Division of multi-digit by one-digit
- Volume of similar shapes
- Currency conversion
- Word problems with two variables
- Standard form to power of ten
- Intro to slope
- Find the orthocenter from coordinates
- Converting vertex form to standard form
- Graphing parabolas in intercept form
- Proving the law of cosines
- Solving separable differential equations
- Minimization (mathematical problems)
- Finding a side given an angle and a side
- Volume of a cone
- Midpoint formula (algebra problems)
- Trial and improvement
- Normal distribution
- Binomial theorem and Pascal's triangle
- Exponential growth and decay (calculus 1)
- Perimeter, circumference, and area
- Functions of displacement
- Grouped data
- Common knowledge puzzle
- Locker Problem
- Adding and subtracting exponents with negative powers
- Standard form of ellipse equations from graphs
- Average speed from travel graph
- Finding the sum of a telescoping series
- Finding or estimating the mean from a frequency table
- Solving quadratic equations using trigonometry
- Iterated function systems
- Finding the modulus and argument of a complex number
- Binomial distribution
- Cumulative frequency
- Using calculations
- Converting terminating decimals to fractions
- Solving linear equations and expanding brackets
- Frequency diagrams
- Inner product
- Diagonalization
- Area of a triangle using determinant
- Orthogonal vectors
- Multiplying a vector by a scalar
- Length of a vector
- Orthogonal functions
- Tabular and graphical estimation of limits
- Limits that do not exist
- Properties of limits
- Finding limits by factoring
- Knights and Knaves
- Find the inverse of a trigonometric function
- Rolle's theorem
- Concavity
- Linear approximation
- Reverse power rule for antiderivatives
- Properties of antiderivatives
- Sum of a series
- Properties of definite integrals
- Introduction to vectors
- Length of a 3D vector
- Definition of \(\mathbb{R}^n\)
- Length of a vector in \(\mathbb{R}^n\)
- Properties of vector addition
- Properties of vector addition and scalar multiplication
- Dot product: Lesson
- Consistency of a system of linear equations
- Inverse of a \(4{\times}4\) matrix using row operations
- Determinant using row echelon form
- Determinant of a \(4{\times}4\) matrix using row operations
- Linear combinations
- Linear transformations on \(\mathbb{R}^2\)
- Basis for a null space
- Basis for a span
- Separating rational and irrational components in a binomial expansion
- Surface area of a sphere
- Volume of a sphere (calculus \(2\))
- Introduction to sets
- Set equality and subsets
- Set operations
- Binary relations
- Multivariable functions
- Two point form
- Pólya urn model
- Geometric proof the cross product is distributive
- Competition problems (sum of a geometric progression)
- Competition problems with differential equations
- Solving differential equations using variation of parameters
- Elementary matrices
- Power method
- Shifted inverse power method
- Gershgorin circle theorem
- Graphing linear inequalities in point-slope form
- Recurrence relations
- Finding and plotting the domain of a function
- Overfitting
- Testing solutions to differential equations
- Euler's method
- Separable first order differential equations
- Motivation for learning statistics and probability
- Peano arithmetic
- \(\sqrt{i}\) using Euler's formula
- \(\sqrt{i}\) without using Euler's formula
- Slide rules and log tables
- \(\sin(z) = 2\)
- Approximating square roots to tenths
- Graphing linear equations in point-slope form
- \(i^i\)
- Negation (bridge course)
- Equivalence relations
- Tautologies and contradictions
- Proving parallelograms with two column proofs
- Converting slope-intercept form to standard form
- Evaluating numeric expressions involving factorials
- Disjunction
- Converting between minutes and seconds
- Range
- Using the Pythagorean theorem (easier mathematical problems)
- Mode
- Adjacent angles
- What is symmetric difference?
- Sum rule (calculus 2)
- Perimeter of composite figures
- Logarithmic differentiation
- Washer method
- Constant multiple rule (calculus 2)
- IMO problems
- Julia set
- Proving the sum and difference of cubes formulas
- Visual proof: Area of a circle
- Heron's formula: Proof
- Proving Mollweide's formula
- General chain rule
- Solving trigonometric equations by factoring trinomials
- Find a length using the law of cosines (word problems)
- Finding an angle using the law of cosines (word problems)
- Exercise: Pythagorean identities
- Symmetric group
- Symmetries of an equilateral triangle
- Is it bijective? (infinite domain)
- 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
- Converting circle equations from general to standard form
- Converting to slope-intercept form
- Diamond problems
- Double factorial
- Comparing properties of functions represented in different forms
- Multiplying mixed numbers (word problems)
- Add within 5
- Division with small divisor using base ten blocks
- Multiplying two-digit numbers using base ten blocks
- Add within 10 using fingers
- Subtract within 10 using fingers
- Multiplying integers using two color counters
- Area model for division
- Finding the area of composite figures by adding
- Commutative property of addition (prealgebra)
- Making 10 using a tens frame (concrete)
- Lattice division
- Subtraction using partial differences
- Breaking apart to add within 1000
- Multiplying multi-digit numbers by one-digit numbers using base ten blocks
- Add within 1000 using base ten blocks
- Adding fractions with like denominators using the length model
- Equivalent fractions using fraction sectors
- Equivalent fractions using the length model
- Ordinal numbers
- Angle Wars
- Telling time to the minute
- Identity element of multiplication and division
- Subtracting mixed numbers without regrouping
- Adding within 100 without regrouping (abstract method)
- Dividing integers using Algeblocks
- Multiplying integers using Algeblocks
- Subtracting integers using a number line
- Multiplying linear expressions using Algeblocks
- Factoring trinomials using algebra tiles (for teachers)
- Subtracting by counting up
- Subtracting fractions with like denominators using the length model
- Adding fractions with like denominators using the set model
- Dividing fractions using the set model
- 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 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 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
- Subtracting fractions with like denominators using the area model
- Subtracting fractions with like denominators using the set model
- Comparing and ordering fractions with like denominators using the length model
- Golden beads addition
- Division using the bead board
- Subtracting three-digit numbers using the stamp game
- Ordering triangle sides and angles
- Finding the domain and range of square root functions
- Finding \(x\) and \(y\) intercepts of linear equations in standard form
- Add within \(10\) using the strip board
- Adding multi-digit numbers using the bead frame
- Subtracting three-digit numbers using the chip model
- Adding within 1000 using the chip model
- Division using repeated subtraction
- Word problem strategies
- 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
- Drawing scaled picture graphs
- Volume of right rectangular prisms with fractional dimensions
- Multiplication using counters and paper plates
- Compare within 10 by pairing
- Multiplying whole numbers using the standard algorithm
- Add within 1000 using the standard algorithm
- Counting by 2s starting from any number
- Oh Snap!
- Subtracting three-digit numbers using the standard algorithm
- Converting between whole numbers and expanded form
- Subtracting mixed numbers using a visual model
- Approximating square roots using tables
- Multiplying two-digit numbers using the stamp game
- Subtracting multi-digit numbers with regrouping using the bead frame
- Squaring two-digit numbers using the stamp game
- 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
- Finding cube roots using units and tens place blocks
- Finding cube roots using units, tens, and hundreds place blocks
- Finding square roots using units, tens, and hundreds place beads
- Finding square roots using units and tens place beads
- Finding square roots using units place beads
- Multiplying whole numbers using the flat bead board
- 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
- Making 10 using the addition strip board (concrete)
- Money word problems
- 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 within 20 using ten frames
- Subtract by counting back
- Comparing numbers within 100 (concrete and visual methods)
- 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)
- Buffon's needle
- Probability of winning the lottery
- Birthday problem
- Solving multi-step linear equations involving simple interest (word problems)
- Adding measurements with different units (word problems)
- Estimating a sum or difference
- Multiplying monomials by polynomials
- Finding \(x\) and \(y\) intercepts of linear equations from graphs
- Understanding slope with similar triangles
- Cross-sections
- Subtracting fractions with unlike denominators using graph paper
- 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
- HSN.CN.C.8
- HSA.REI.D.11
- HSF.BF.A.1.a
- HSG.SRT.A.2
- HSS.ID.A.2
- Difference between functions and relations
- Estimating the line of best fit
- Exponentiation as repeated multiplication
- Discrete functions
- Estimate sums within 1000
- Adding and subtracting within 100 on your fingers
- Count to 120 by ones
- Place value understanding of counting by 10s (10 to 120)
- Count to 99 on your fingers
- Naming numbers up to 120 using base ten blocks
- 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
- Graphing ellipses in standard form
- Multiplying one-digit by two-digit numbers using the box method
- Breaking apart to subtract within 100 without regrouping
- Percents (word problems)
- Squaring three-digit numbers using the peg board
- Multiplying mixed numbers (easier mathematical problems)
- Long multiplication
- Multiplying two-digit numbers using the box method
- Comparing fractions using the butterfly method
- Multiplying multi-digit numbers with area models
- Area of regular polygons using trigonometry
- Definite integration by trigonometric substitution
- Graphing hyperbolas in standard form
- Limit comparison test
- Ratio test
- Verifying trigonometric identities involving the sum and difference formulas
- Verifying trigonometric identities involving the half and double angle formulas
- Ratios and proportions (word problems)
- Solving linear systems of equations in three variables by substitution
- Average value over an interval
- Integrating exponential functions by u-substitution
- Converting mixed numbers to decimals
- Converting decimals to mixed numbers
- Extreme value theorem
- Gaussian elimination
- Solving one-step absolute value equations
- Solving two-step absolute value equations
- Converting logarithmic form to exponential form
- Exterior angles of regular polygons
- Law of cosines (word problems)
- Solving and graphing linear inequalities (word problems)
- Solving linear systems of equations in two variables using matrix inverses
- Solving linear systems of equations in three variables using matrix inverses
- Simplifying square roots of rational expressions
- Horizontal line test
- Sketching logarithmic equations
- Rational root theorem
- Graphing the tangent function
- Derivatives of natural logarithmic functions
- Sketching quadratic inequalities
- Adding functions graphically (trigonometric, quadratic, and absolute value functions)
- Subtracting functions (linear-linear)
- Graphing circles in standard form
- Properties of radicals
- Finding the general form of an ellipse by completing the square
- Reducing fractions using prime factorization
- Finding the domain of the sum of functions
- Holiday math
- Alternating series test
- Evaluating expressions using the double angle formulas
- Finding an exponential function from two points
- Comparison test
- Finding the inverse of a relation on a finite set
- Graphing a line given a point and a slope
- Wilcoxon rank-sum test
- Testing solutions to linear systems of equations in two variables
- Wind and current problems
- Converting ellipse equations from standard form to general form
- Converting ellipse equations from general form to standard form
- Finding the LCD of rational expressions
- Solving right triangles (word problems)
- Pythagorean trigonometric identity
- Adding degrees-minutes-seconds
- Subtracting degrees-minutes-seconds
- Intersection of parabola and circle
- Lattice multiplication with decimals
- Finding the LCD of fractions
- Desmos
- Expressing the sum of two wave functions in auxiliary angle form
- Alternating harmonic series
- Finding the domain and range of piecewise functions
- Integrating logarithmic functions
- Graph a line given \(x\) and \(y\) intercepts
- Solving nonlinear systems in two variables (word problems)
- Finding missing side lengths in right triangles (word problems)
- Verifying trigonometric identities using t-results
- Simplifying square roots of decimals and fractions
- Multi-digit subtraction with regrouping
- Subtracting within 100 with regrouping
- Finding the number of roots of a quadratic in vertex form
- Maclaurin series
- Taylor series
- Finding complementary and supplementary angles in degrees
- Adding multi-digit numbers from left to right
- Percents: Finding the percent
- Solving and graphing logarithmic inequalities
- Graphing the absolute value function
- Graphing the cotangent function
- Finding the inverse of cube root functions
- Subtracto Bingo
- Sieve of Eratosthenes
- Mills's constant
- Solving rational inequalities by graphing
- Caesar cipher
- Dijkstra's algorithm
- Fleury's algorithm
- Kruskal's algorithm
- Hamilton's method
- Jefferson's method
- Webster's method
- Huntington–Hill method
- Lowndes's method
- Using even-odd identities to evaluate trigonometric functions
- Challenge
- Using the cofunction identities
- Simplifying rational trigonometric expressions
- Reciprocal identities: Practice
- Triangle congruence by SSS and SAS
- Triangle congruence by AAS
- Finding the domain of radical functions (monic linear functions)
- Finding the domain of radical functions (quadratic functions)
- Proving De Moivre's formula by induction
- Powers of complex numbers using De Moivre's formula
- Using the half angle formulas
- Multiplying fractions and mixed numbers using a visual model
- Second order differential equations
- Finding the eigenvalues and eigenvectors of \(3{\times}3\) matrices
- Finding the eigenvalues and eigenvectors of \(4{\times}4\) matrices
- Finding trigonometric functions from graphs
- Finding relative extrema
- Largest rectangle in a semicircle
- Apportionment paradox
- Finding one-sided limits from graphs
- Sum and difference formulas for tangent
- Proving the difference formula for tangent
- Parallel vectors
- Applications: Cross product
- Fundamental theorem of algebra
- Converting standard form to vertex form without completing the square
- Evaluating the sine of angles in degrees using the sum formula for sine
- Evaluating the sine of angles in radians using the sum formula for sine
- Converting DMS to degrees
- Finding and classifying discontinuities
- Is the sequence arithmetic?
- Do the lengths form a triangle? (triangle inequality)
- Evaluating the cosine of angles in degrees-minutes-seconds using the half angle formula for cosine
- Evaluating the tangent of angles in degrees using the half angle formula for tangent
- Evaluating the sine of angles in degrees using the half angle formula for sine
- Conditional probability from tree diagrams
- Finding the quadrant of an angle in degrees-minutes-seconds
- Pythagorean inequality theorem
- Finding the area of composite figures by subtracting
- Evaluating trigonometric functions of angles in degrees using reference angles
- Evaluating trigonometric functions of angles in radians using reference angles
- 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
- Domain of linear functions
- Finding the domain and range of the absolute value function under transformations
- Evaluating the sine of angles using the half angle formula for sine when given a triangle
- What are coterminal angles?
- Finding limits by simplifying complex fractions
- Find one exterior angle given the number of sides for a regular polygon
- 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 rectangles
- Sum of a geometric series
- Intro
- Set intersection
- Using the difference formula for cosine when given two right triangles
- Using the difference formula for tangent when given two right triangles
- Graphing rational functions with holes
- Graphing inequalities in one variable
- Common mistake with exponents
- Multiplying by 5 (Trachtenberg system)
- Evaluating logarithmic expressions using the one-to-one property
- Evaluating logarithmic expressions using properties of logarithms
- Sketching logarithmic functions under transformations (level 3)
- Graphing the secant and cosecant functions
- Finding the \(x\) and \(y\) intercepts of a polynomial in factored form
- Finding the domain and range of trigonometric functions
- Evaluating exponential functions
- Evaluating linear functions
- Finding the domain of composite functions
- Testing ordered pair solutions to linear equations
- Negative bases
- Graphing linear inequalities in two variables
- Distance between two numbers
- Multiplying binomials by polynomials using the box method
- Find the number of sides for a regular polygon given the sum of interior angles
- Corresponding angles postulate
- What is a radicand?
- Evaluating quadratics
- Derivation: Area of a kite
- Using the area of a triangle formula
- Derivation: Area of a right triangle
- Solving absolute value equations: Lesson
- Solving and graphing linear inequalities: Lesson
- Finding one-variable inequalities from graphs
- Graphing the absolute value function under transformations from tables
- Graphing the absolute value function under transformations (inequalities): Lesson
- What is a Saccheri quadrilateral?
- Derivation
- Find the parabola from its focus and directrix
- Relatively prime
- Temperature conversion
- Area of a segment
- Reciprocals of mixed numbers
- Graphing two variable inequalities
- What is a zero matrix?
- Area of an ellipse
- Set complement
- Condensing logarithmic expressions: Lesson
- Expanding logarithmic expressions: Lesson
- Integrating hyperbolic functions
- Simplifying factorial expressions
- Proving the absorption laws for sets
- Competition problems (calculus 2)
- Chord properties
- Lesson: Solving linear systems of equations in two variables by graphing
- Solving exponential equations in quadratic form using u-substitution
- 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
- Lesson: Adding and subtracting rational expressions
- Solving quadratic equations by taking square roots: Lesson
- Derivation
- Power of a product rule for exponents
- What is a Lambert quadrilateral?
- Finding the diagonal length of a cube
- Proving the perpendicular bisector theorem
- Proving the converse of the perpendicular bisector theorem
- Proving lines are parallel
- Finding \(x\) and \(y\) intercepts of quadratic equations
- Finding the diagonal length of a rectangle
- Find the missing side given the perimeter
- Subtract within 1000 (word problems)
- Division (word problems, concrete and visual): Lesson
- Multiplication using the array model
- Using the theorem
- Lesson: Midpoint formula
- Adding multi-digit numbers with regrouping using the standard algorithm
- Multiplying one-digit by three-digits
- Subtracting multi-digit numbers with regrouping using the standard algorithm
- Comparing fractions using a number line
- Experimental compound probability
- Identifying functions from ordered pairs and tables
- Finding the growth or decay factor given a table
- Factoring difference of squares (concrete and visual methods)
- Finding the volume of composite figures
- Finding the growth or decay factor from a graph
- Comparing numbers in scientific notation
- Recursive to explicit formula for arithmetic series
- Finding an exponential function from a table
- Experimental probability
- Finding the scale factor for similar polygons
- 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 \(\sin(x)\)
- What is the Cartesian product?
- Evaluating integers raised to whole number powers
- 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
- 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: Rounding to the nearest 10 or 100 (concrete and pictorial)
- 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
- Trick for subtracting from powers of ten
- Missing numbers for adding and subtracting multi-digit numbers
- Missing number problems for equivalent fractions
- 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
- Elapsed time for analog clocks
- Estimating decimal sums
- Practice: Volume of right rectangular prisms (mathematical problems)
- Challenge problems (probability)
- Constants of proportionality
- Binomial probability
- Commutative
- Closed binary operations
- Additive group of integers
- Is the table a commutative semigroup?
- Klein four-group
- Order of an element in a group
- Is it a subgroup?
- Law of total probability
- Section formula
- Simplifying trigonometric expressions by factoring
- Simplifying trigonometric expressions using the even and odd identities
- Intersection of parabola and line (word problems)
- Challenge problems (precalculus)
- Factoring radical expressions
- Discrete compound interest
- Continuous compound interest
- Rationalizing the numerator
- Modeling piecewise functions (word problems)
- Intersection of two parabolas
- Finding the composition of two functions
- Finding the equation of a parabola from its graph
- Finding the inverse of quadratic functions (word problems)
- Direct product of finite cyclic groups
- Adding and subtracting square root expressions without variables (easy)
- Comparing numbers within 100 (abstract method)
- Trick for dividing a number by five
- Trick for squaring a two-digit number
- 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 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
- 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
- Formula for Pythagorean triplets
- Trick for listing the multiples of a two digit number
- 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
- Decimal arithmetic using algebra
- Multiplying by 7 (Trachtenberg system)
- Proving the altitude of an isosceles triangle cuts two congruent right triangles
- Compare within 10 by counting
- Counting by 10s within 100: Lesson
- Compare length
- Sorting and counting
- Vampire numbers
- Slide method of multiplication
- Math of the 15 puzzle
- Lewis Carroll's Pillow Problem #5
- Computer assisted math
- Missing dollar riddle
- Nim-like games
- Factoring non-monic quadratics using algebra tiles
- Weighing 9 balls puzzle
- Proving Euler's identity without Taylor series
- Remainders of large powers
- Venn diagrams (combinatorics)
- Constructing a square inside a triangle
- Comparing and ordering exponents
- Solving systems of equations in two variables (challenge problems)
- 18 or 20 trees?
- Conway's Soldiers
- One Golden Equation (Flammable Maths)
- Surviving The Deadliest Game (Vsauce2)
- Combinations with restrictions
- Problem: Nontransitive dice
- Challenge
- What Is The Square's Area? (MindYourDecisions)
- Puzzle ~ Packing Eight Numerals Into Eight Squares (Crystal Clear Maths)
- Using the Pythagorean theorem to find a leg of a right triangle
- Menseki Meiro
- What is sigma notation?
- Converting closed form to expanded form
- Proving equations involving sigma notation
- Challenge problem involving sigma notation
- Infinite nested fractions
- Careful counting 5
- Careful counting 6
- Proving that opposite angles of a parallelogram are congruent
- A number theory proof (blackpenredpen)
- Intro to similarity
- Centroid
- Putnam exam
- Newton–Pepys problem
- Potato paradox
- Counting divisors of a number
- 36 factors, again! (blackpenredpen)
- Two envelopes problem
- Challenge
- Careful counting 1
- Solving floor and ceiling equations
- Direct proof (floor and ceiling)
- Surface area of a pyramid
- Challenge
- Linear system of inequalities from a graph
- Fifth root trick
- Multiplying decimals using base ten blocks
- Power of a quotient rule for exponents
- Multiplying monomials by binomials (without algebra tiles)
- Zero exponents
- Graphing the cube root function under transformations (level 2)
- Factoring by grouping (one variable, not quadratic)
- Solving trigonometric equations linear in form
- Solving trigonometric equations quadratic in form by taking square roots
- Derivation: Formula for polygonal numbers
- Characteristic equation and characteristic roots of linear homogeneous recurrence relations
- Tiling the strip with dominos and monominos
- Arithmagons
- Derivation: Formula for pentagonal 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
- Olympic rings puzzle
- Careful counting 2
- Challenge 32: Dots and Boxes (Science Mom)
- Untraceable (Science Mom)
- What portion is shaded? 6
- Challenge 19: A Chicken and a Half (Science Mom)
- Challenge 20: Timing 9 Minutes (Science Mom)
- Challenge 21: Self-Counting Sequence (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
- Strimko
- Handshaking couples
- Frogs 1
- Area mazes
- How To Solve Amazon's Pair Of Socks Interview Puzzle (MindYourDecisions)
- Picking socks in the dark
- Challenge
- 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)
- Can you make this billiards trick shot? (Brilliant.org)
- Factoring monic quadratics with difference of squares using algebra tiles (all resources)
- Factoring non-monic quadratics with difference of squares using algebra tiles
- Quinary multiplication
- Prove or disprove
- Number of ways to triangulate a regular polygon
- Determinant of a \(3 \times 3\) matrix using cofactors
- Solving linear systems of equations in two variables using Gauss–Jordan elimination
- Using Fermat's little theorem
- Converting interval notation to set builder notation
- Vacuous truth
- Converting polar equations to Cartesian equations
- Converting Cartesian equations to polar equations
- Proving the binomial theorem by induction
- Making rectangles with a given area from unit squares
- Combinatorial proof: Binomial theorem
- \(\sec^2\left(\tan^{-1} x\right)\)
- Solving trigonometric equations by graphing
- Lambert W function
- Gabriel's Horn
- Add using number disks
- Direct product of groups
- Sum of exterior angles (algebra problems)
- Proving the inverse Pythagorean theorem
- Similarity proof: Pythagorean theorem
- Epsilon-delta proofs for limits with two variables
- Jack Oliver's proof: Pythagorean theorem
- Survivorship bias
- Derivation: Area of a non-obtuse triangle
- Derivation: Area of an obtuse triangle
- James Garfield's proof: Pythagorean theorem
- Bhaskara's proof: Pythagorean theorem
- Epsilon-delta proof: Sum of limits
- Finding delta given epsilon
- Subsets
- Interior point of a set
- Disproof by counterexample
- Intro to subgroups
- Simple groups
- Solvable groups
- Quotient groups
- Symmetries of a square
- Trivial group
- Alternating groups
- Group automorphisms
- Proving group homomorphisms
- Group isomorphisms
- Multiplying permutations in array notation
- Evaluating square roots of small perfect squares (abstract)
- Challenge
- Cosets of a subgroup
- Proving equivalence relations
- Equivalence classes
- Number of edges in a complete graph
- Properties of cyclic groups
- Derivative using u-substitution
- Size of tree is one less than order
- Properties of relations
- WFFs in propositional logic
- Representing relations using digraphs
- What are De Morgan's laws?
- Composition of relations
- Converting English to predicate logic
- Representing relations using matrices
- Intro to continuity
- Proving a sequence converges
- Proving divergence using proof by contradiction
- Proving divergence using subsequences
- Every convergent sequence is a Cauchy sequence
- Using the Archimedean principle
- Intersection of open sets
- Open if and only if complement is closed
- Bernoulli's inequality
- Rationals are dense in the reals
- Intro to supremum and infimum
- Properties of supremum
- What is the least upper bound property?
- Identifying the sides of a right triangle
- Epsilon-delta proof: Product of limits
- 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?
- Properties of the power set
- Combinatorial proof: Cardinality of power set of finite set
- What are upper and lower bounds?
- What is a field?
- Euclid's lemma
- Sufficient conditions for a group to be abelian
- Necessary and sufficient
- Using the triangle inequality
- Construct a rhombus with given side
- Copy an angle
- What is a complete graph?
- What is a graph?
- What is the size of a graph?
- What is a spanning subgraph?
- What is an edge-induced subgraph?
- What are adjacent vertices?
- What is the order of a graph?
- What are isomorphic graphs?
- What is a star graph?
- What is a vertex-induced subgraph?
- What is a cubic graph?
- What is a regular graph?
- What is an irregular graph?
- What is an empty graph?
- What is the trivial graph?
- What is the null graph?
- Logarithm of a negative number
- 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
- Proving the intersection of subgroups is a subgroup
- Properties of scalar multiplication
- Number patterns (grade 4)
- Multiplying one-digit by two-digit numbers using partial products
- Multiplying three one-digit numbers
- Biography of Sophie Germain
- Basic set theory proofs using membership tables
- What is hypothetical syllogism?
- Converting a Venn diagram to a set expression
- What is intersection?
- Intro to integral ideals
- Basic set theory proofs using set identities
- Square of opposition
- Shading Venn diagrams with two sets
- Shading Venn diagrams with three sets
- More ring theory proofs
- What is the squeeze theorem?
- Solving trigonometric equations using the quadratic formula
- Derivation: Area of regular polygon given apothem or perimeter
- Finding area of regular polygon given apothem or perimeter
- Find the quadratic from its \(x\) intercepts
- Find the quadratic from its \(x\) intercepts and a point
- Dividing whole numbers by fractions
- Is it a ring?
- What is a subring?
- Properties of injections, surjections, and bijections
- Converting improper algebraic fractions to mixed algebraic fractions
- Intro to even and odd functions
- Connection between Pascal's identity and Pascal's triangle
- Explanation for powers of two in Pascal's triangle
- Explanation for powers of eleven in Pascal's triangle
- Using the power reducing identities to graph
- 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
- What is a bipartite graph?
- Minimization (word problems)
- Write a system of linear inequalities given a graph
- Finding square root transformations from graphs
- Graphing the cosecant function
- Derivation: Sine rule for area of a triangle
- Finding equations of sine and cosine functions from graphs
- What are period and amplitude?
- Converting propositional logic to English
- Making truth tables for expressions
- Simplifying expressions in propositional logic
- Converting set-builder notation to set-roster notation
- Converting set-roster notation to set-builder notation
- What are disjoint sets?
- Are they disjoint?
- Operations with set-builder notation
- Testing validity of simple statements in predicate logic
- Basic predicate logic proofs
- Union and intersection of a family of sets
- Heron's formula: Intro
- Adding functions (linear-linear)
- Adding functions (piecewise linear)
- Adding functions (other)
- Square root of a complex number
- Multiplying and dividing complex numbers in polar form
- Roots of complex numbers using De Moivre's theorem
- Measuring angles using a protractor
- What is the underlying graph?
- Difficult factoring problems
- False proofs for calculus 2
- Proving the derivatives of the inverse hyperbolic functions
- Even and odd hyperbolic functions
- Practice: Simpson's rule
- What is a coloring?
- Deriving point-slope form
- What is point-slope form?
- Converting point-slope form to slope-intercept form
- Convert to vertex form by completing the square (using algebra tiles)
- Factoring by completing the square
- Find the missing side of the rectangle given the area
- Proving properties of the subset relation
- Add within 20 using fingers
- Subtract within 5 using counters (concrete and pictorial)
- Subtract within 20 using fingers
- Lesson: Integration by parts
- Practice: Integration by parts
- Area between two curves: Lesson
- Area between two curves: Practice
- Solving exponential equations using the one-to-one property: Lesson
- Distributing and combining: Lesson
- Probability vs odds
- Even and odd whole numbers
- Finding volume using unit cubes: Lesson
- Intro to functions
- Practice: Using the circle theorems
- What is a maximal clique?
- Intro to paths and cycles
- What is a subgraph?
- Lesson: Alternate segment theorem
- Adding or subtracting by adjusting
- Multiplying and dividing decimals by powers of ten: Practice
- What is a vertex coloring?
- What is an orthogonal set?
- Count forwards or backwards by 100s starting at any number: Lesson
- Lesson: Simplifying the difference quotient
- Rewriting before integrating
- Counting by 1s (1 to 50 and 50 to 1)
- Counting by 1s (1 to 100)
- Counting to 5
- Counting by 5s (5 to 100)
- Counting by 2s (2 to 100)
- Subtract within 1000 using a number line
- Multiplication as repeated addition: Lesson
- Lesson: Multiply using counters
- Plotting integer coordinates: Lesson
- Lesson: Proof by induction
- Lesson: What is the image of a set under a function?
- Lesson: What is the preimage of a set under a function?
- Practice: Converting decimals to percents
- Area and perimeter of polygons on the coordinate plane: Lesson
- Dividing fractions (word problems)
- Intro to rates
- Is it even, odd, or neither? (given a graph)
- Derivation: t-results
- Disproving trigonometric identities by counterexample
- Lesson: Evaluating trigonometric functions using the unit circle
- Graphing linear equations in slope-intercept form: Lesson
- Practice: Solving and graphing absolute value inequalities (word problems)
- Simplifying square roots of nonnegative integers: Lesson
- Solving linear systems of equations in two variables by elimination (word problems)
- Solving linear systems of equations in two variables by elimination (harder mathematical problems): Lesson
- Finding the vertex of a parabola: Practice
- Cardinality from Venn diagrams
- Example of a nonconstructive proof
- Lesson: Find the equation of a line given two points
- Lesson: Basic trigonometric functions (mathematical problems)
- Lesson: Basic trigonometric functions (word problems)
- Lesson: Evaluating composite functions
- Practice: Evaluating composite functions
- Evaluating composite trigonometric functions
- Order of operations (grade 6): Lesson
- Derivation: Area of a parallelogram
- Multiplying 10s (grade 3): Lesson
- Angle basics: Lesson
- Naming angles: Lesson
- Lesson: Multiplying 10s
- Unit fractions (grade 3)
- Counting vertices, edges, and faces
- Area of a rectangle with whole number side lengths: Lesson
- Area of a rectangle with whole number side lengths: Practice
- Finding area by counting unit squares (whole number side lengths): Lesson
- Lesson: Dividing fractions by whole numbers
- Dividing whole numbers by unit fractions (abstract methods): Lesson
- Dividing unit fractions by whole numbers (abstract methods): Lesson
- Rounding mixed numbers
- Rounding improper fractions
- Lesson: Multiplying whole numbers by powers of 10
- Practice: Multiplying whole numbers by powers of 10
- Subtracting fractions (word problems)
- Converting between words and decimals
- Subtracting mixed numbers with regrouping
- For teachers: Add within 20 using number bonds
- For teachers: Add within 10 by making 5-groups
- Subitizing up to 5
- Subitizing up to 10
- Counting with tally marks
- Lesson: Rounding to the nearest 10 or 100 (abstract)
- Line plots (grade 5)
- Classifying angles: Lesson
- Add by making 10s: Lesson
- Subtract by compensating
- Measure lengths (cm, m): Lesson
- Measuring with nonstandard units: Lesson
- Measuring lengths in different units: Lesson
- Measuring to the nearest quarter inch: Lesson
- Telling time to the nearest 15 minutes
- Telling time to the nearest 5 minutes
- Adding within 100 (mental)
- Breaking apart to add within 100: Lesson
- Hard factoring problems
- Finding the LCM of monomials
- Finding the GCD of monomials
- Solving linear equations by clearing fractions and decimals: Lesson
- 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: Evaluating cube roots of small perfect cubes
- Intro
- Changing linear dimensions
- Find the missing lengths and angles for similar polygons
- Finding side lengths and angles in similar triangles: Lesson
- Finding side lengths and angles in similar triangles: Practice
- Finding slope from a graph: Lesson
- Practice: Finding slope from a graph
- Solving quadratic equations (word problems)
- Solving and graphing two-step inequalities in one variable (word problems)
- Find the explicit formula for a geometric series given terms
- Double negatives
- Intro to algebra 1
- Intro to parallel and perpendicular lines
- Lesson: Lines, line segments, and rays
- Lesson: Ratio tables
- Lesson: Adding integers using a number line
- Dependent and independent variables: Lesson
- Plotting integers on a number line: Lesson
- Plotting rational coordinates
- Fraction multiplication as scaling: Lesson
- Relating whole number division to multiplication (mathematical problems)
- Find the center and scale factor: Lesson
- Find the center and scale factor: Practice
- Lesson: Comparing distributions
- Comparing and ordering absolute values: Lesson
- Modeling with linear functions
- Practice: Reflecting points
- Lesson: Reflecting line segments and polygons (grade 8)
- Reflecting figures (geometry for high schoolers)
- 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
- Measuring and comparing lengths (grade 2)
- Interpreting graphs of proportional relationships: Lesson
- Lesson: Probability models
- Lesson: Relative position
- Compare shapes
- Subtracting multiples of 10 within 100
- Missing numbers for addition and subtraction within 20
- Choose the operation for adding and subtracting within 100 (word problems)
- Missing digit problems for adding and subtracting within 1000
- Describing measurable attributes of objects
- Equal sign
- Adding three numbers in any order (mathematical problems)
- Identifying shapes as two or three-dimensional
- Relating addition and subtraction
- Reading bar graphs (grade 1)
- Reading picture graphs: Lesson
- Two-step word problems (grade 2): Lesson
- Mentally add and subtract within 20
- Lesson: Negative signs in fractions
- Fractions of shapes: Lesson
- Counting regardless of arrangement
- Last number said is the number of objects
- Representing decimals using shaded rectangles
- Naming shapes (kindergarten)
- Naming shapes (grade 2): Lesson
- Mentally adding and subtracting 10
- Using different strategies to add and subtract (grade 2)
- Mentally add or subtract 10 or 100
- Partitioning rectangles into rows and columns
- Drawing angles in degrees
- Add multiple two-digit numbers
- Patterns with even and odd: Lesson
- Numbers in standard, word, and expanded form (grade 2)
- Using the distributive property to multiply (grade 3)
- Building and drawing shapes
- Equal parts of shapes: Lesson
- Two-step word problems (grade 3): Lesson
- Area and the distributive property: Lesson
- Adding and subtracting mixed numbers with like denominators (mathematical problems)
- Lesson: Multiplying unit fractions and whole numbers
- Multiplying fractions using the area model
- Multiplying whole numbers and fractions using the area model: Lesson
- Equivalent fraction and whole number multiplication expressions: Lesson
- Order of operations (grade 5): Lesson
- Fractions as division
- Number of solutions to linear equations: Lesson
- Testing solutions to two-variable inequalities
- Plotting inequalities on a number line: Lesson
- Statistical and non-statistical questions: Lesson
- Line plots (grade 2)
- Addition snake game (part 1)
- Addition snake game (part 2)
- Making dot plots and frequency tables
- Graphing the absolute value function under transformations (inequalities): Practice
- Compose shapes (grade 1)
- Naming shapes (grade 1): Lesson
- Lesson: Additive inverses in the real world
- Making histograms: Lesson
- Counting by 1s starting at any number
- Number of observations from line plots and histograms
- Subtracting vectors
- Solving quadratics by u-substitution: Lesson
- Equivalent vectors
- Equivalent exponential expressions
- Coordinate rules for reflection and rotation
- Dilating lines
- Sum of interior angles of a simple polygon (rearranging the formula)
- Determine parallel, skew, or intersecting
- Adding within 100 (abstract method)
- Compare within 5 by pairing
- Book reviews (discrete math)
- Book reviews (bridge course)
- Minigolf
- Book reviews (linear algebra)
- Book reviews (complex analysis)
- Book reviews (field theory)
- Book reviews (number theory)
- Book reviews (abstract algebra for graduates)
- Book reviews (topology)
- Book reviews (differential equations)
- Compare within 5 by counting
- Long division using the box method
- Uniform motion word problems
- Double negation introduction and elimination
- Surface area using nets (mathematical problems)
- Roots of complex numbers using Euler's formula
- 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
- Counting money: Lesson
- Challenge problems (grade 6)
- Simplifying square roots of monomials with real variables
- Simplifying square roots of monomials with nonnegative real variables
- Higher order roots: Lesson
- Higher order roots: Practice
- Simplifying radicals of monomials: Practice
- Adding and subtracting radical expressions
- Prime factorization: Lesson
- Transpose and its properties
- Solving linear systems of equations in two variables by any method
- Using the theorem
- Solving 30-60-90 triangles: Practice
- Proving the linear pair theorem
- Intro
- Using the formula: Area of a parallelogram
- Are the vectors parallel, orthogonal, or neither?: Practice
- Are the vectors parallel, orthogonal, or neither?: Lesson
- Solving a linear system from an arithmetic sequence: Practice
- Solving a linear system from a geometric sequence: Practice
- Solve by completing the square: 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
- Factoring and solving cubics using synthetic division: Practice
- Solving permutation equations: Practice
- Solving equations with complex numbers: Practice
- Squaring large numbers: Practice
- Using the zero product property (polynomials): Practice
- Book reviews (real analysis)
- Intro to the perpendicular bisector theorem
- Intro
- Intro: Tangents of circles
- Tangent theorem 1
- Distance from center of circle to chord
- Find the radius given a chord
- Proving the conjecture
- Using the theorems
- Using the theorem
- Using the theorem
- Intro
- Intro
- Problem 2
- Even and odd integers
- Intro
- Using the formula
- Find an absolute value equation from its solutions
- Classifying triangles from coordinates: Practice
- Solving absolute value equations by graphing: Lesson
- Restrict the domain then find the inverse
- Slope-intercept form word problem
- Solving systems of differential equations
- Intro
- Solving one-step equations (abstract): Lesson
- Parity proofs using modular arithmetic
- Intro to modular arithmetic
- Congruence in modular arithmetic
- Bezout's identity
- Addition and subtraction in modular arithmetic
- Intro
- Proving the Euclidean algorithm
- Finding Bezout coefficients
- Graceful labeling
- Proving the difference of squares formula
- Dividing complex numbers: Lesson
- Intro to naive set theory
- Using the theorems
- Solving literal equations using properties of logarithms
- Intro
- Using the theorem
- Intro
- 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
- Using the theorem
- Using the theorems
- Classifying polygons: Lesson
- Reciprocal identities: Lesson
- Identify the value of the digit (grade 4): Lesson
- Reflecting functions: Lesson
- Intro
- Using the theorem
- Intro
- Explicit to recursive formula for arithmetic series: Practice
- Derivatives of inverse trigonometric functions: Lesson
- Find the value of the decimal digit
- Changing the order of integration
- Negative Fibonacci numbers
- Dividing square roots: Lesson
- Scale drawings: Lesson
- Using the theorem
- Percents: Finding the part (mental math)
- Intro to metric spaces
- Finding the tangent or normal line through the given point 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
- Cauchy's functional equation
- Proving a function satisfies a functional equation: Lesson
- Proving a function satisfies a functional equation: Practice
- Transforming a point
- Composition of transformations
- Proving the area of a circle formula by integrating
- Volume of a cone (calculus 2)
- Proving derivative of circle area is circumference
- Proving the volume of a sphere formula by integrating
- False proof that all triangles are equilateral
- Challenge
- Factoring and solving polynomials by graphing
- Challenge
- Challenge
- Challenge
- Challenge
- Challenge
- Challenge
- Challenge
- Challenge
- Challenge
- Solving linear Diophantine equations in two variables
- Intro
- Intro
- Using the theorem
- Using the theorem
- Using the theorem
- Intro to scientific notation
- Intro to triangle congruence
- Finding angles on parallel lines (easier)
- Intro to extrema
- Maximizing profit (optimization problems)
- Challenge
- Challenge
- Challenge
- Challenge
- Challenge
- Pythagorean triples
- Intro
- Challenge
- Challenge
- Challenge
- Combining ratios (word problems): Lesson
- Combining ratios (mathematical problems): Lesson
- Mutually exclusive events: Lesson
- Non-mutually exclusive events: Practice
- Make a dilation given the center and scale factor: Lesson
- Intro to dilating polygons
- Identifying transformations
- Drawing quarter turn rotations about the origin: Practice
- Intro
- Intro
- 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
- Circumference of a circle: Practice
- Distance-speed-time problems
- Multiplying mixed numbers (harder mathematical problems)
- Quotient of powers rule for exponents: Lesson
- Multiplying in scientific notation: Lesson
- 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
- Challenge
- Challenge problems
- Inverse function theorem
- Powers of complex numbers using De Moivre's theorem
- Solving trigonometric equations using the auxiliary angle method
- Challenge
- Finding linear equations from tables using first differences: Lesson
- Challenge
- Intro to polynomials: Lesson
- Solving proportions using equivalent fractions: Lesson
- Solving proportions using inverse operations
- Graphing hyperbolas centered at the origin: Lesson
- Solving rational equations (mathematical problems): Lesson
- Using the theorem
- Solving and graphing rational inequalities using a sign chart: Lesson
- Challenge
- Using the Pythagorean theorem (harder mathematical problems)
- Determine whether linear, quadratic, or neither, using second differences: Lesson
- Determine whether linear, quadratic, or neither, using second differences: Practice
- Finding quadratic equations from tables using second differences: Lesson
- Finding quadratic equations from tables using second differences: Practice
- Using the theorem
- Finding the domain and range of functions from graphs: Lesson
- Finding the domain and range of functions from graphs: Practice
- Interval notation: Lesson
- Challenge
- Product of powers rule for exponents: Lesson
- Product of powers rule for exponents: Practice
- Challenge
- Graphing harder absolute value equations: Lesson
- Graphing harder absolute value equations: Practice
- Combining like terms (concrete and visual method)
- End behavior: Lesson
- End behavior: Practice
- Proving the centers and point of contact are collinear
- Challenge
- Second trick for percent of a number (percent not always a multiple of ten)
- Challenge
- Challenge
- Challenge
- Challenge
- Challenge
- Division property of equality
- Challenge
- Divisibility tests for 6, 12
- Sign of the discriminant: Lesson
- Finding quadratic equations from their solutions: Lesson
- Finding quadratic equations from their solutions: Practice
- Proving the sum formula for sine and cosine using Euler's formula
- Intro
- Angles around a point: Lesson
- Proving properties of trees
- Intro to trees
- Challenge
- Challenge
- Challenge
- Using the theorem
- Using the theorem
- Using the theorem
- Using the theorem
- Using the theorem
- Using the theorem
- Solving square root equations involving the distance formula
- Challenge
- Challenge
- Using the theorem
- Challenge
- Using the theorem
- Challenge
- Tidbits on knot theory
- Intro
- Converse, inverse, and contrapositive statements: Lesson
- Converse, inverse, and contrapositive statements: Practice
- Proof by cases: Lesson
- Proof by strong induction: Lesson
- Challenge
- Proving multiples form an integral ideal
- Angle addition postulate: Lesson
- Angle addition postulate: Practice
- Derivative of a function from first principles: Lesson
- Derivative of a function from first principles: Practice
- Intro
- Intro
- Intro
- Simplifying fractional powers: Lesson
- Intro to group homomorphisms
- Intro to cyclic groups
- Intro to abelian groups
- Finding limits of trigonometric functions: Lesson
- Finding critical values from graphs: Lesson
- Finding critical values from graphs: Practice
- Finding extrema graphically: Lesson
- Finding extrema graphically: Practice