• Graph theory
• \(x^y = y^x\)
• Conic sections
• Recreational mathematics
• Other resources
• Algebra 2
• Group theory
• Trigonometry
• Countable and uncountable sets
• Precalculus
• 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 trinomials
• Completing the square
• Euler's formula and identity
• Infinite series
• Teaching algebra
• Chinese remainder theorem
• Modular arithmetic
• Intro
• Other resources
• Inverse functions (algebra 1)
• Binomial theorem
• 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
• Graphing trigonometric functions
• High school courses
• Law of cosines
• Find a length using the law of cosines
• Law of sines
• Harmonic series
• Verifying trigonometric identities
• Counter-intuitive mathematics
• Angle relationships
• Magic hexagon (recreational mathematics)
• Prealgebra
• Goldbach's conjecture
• Other resources
• Comparing and ordering fractions
• Other resources
• Calculus 1
• Undergraduate courses
• 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 in one variable
• 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
• Finding the midpoint on the number line
• 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 (grade 8)
• Factoring difference of cubes
• Factoring sum of cubes
• Factoring difference of squares (abstract methods)
• Derivation
• Congruent angles
• Similarity
• \(\pi\)
• Napkin ring problem
• Pascal's rule
• Pascal's triangle
• End behavior
• Missing square puzzle
• Wilson's theorem
• Proof
• Geometric definitions
• Transformations of functions
• Absolute value function under transformations (equations)
• Graphing linear equations
• Standard form
• 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
• Rounding whole numbers (grade 4)
• Area of a rectangle
• 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
• Percents
• 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
• Intro to variables
• Finding side lengths and angles in similar triangles
• Double pendulum
• 4th grade
• Multiplying one-digit numbers by multiples of \(10,\) \(100,\) and \(1000\)
• Estimating products
• Other resources
• Education
• Classifying triangles
• Geometry (kindergarten)
• Kindergarten
• K-12 courses
• Exponential growth and decay
• Exponential vs. linear growth
• 1st grade
• 2nd grade
• Simplifying square roots of negative integers
• 7th grade
• 8th grade
• Babylonian mathematics
• Fractions (prealgebra)
• Types of fractions
• Other resources
• Geometry (6.G)
• 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
• Powers of the imaginary unit
• Museum
• Intro to complex numbers
• Multiplying complex numbers
• Adding and subtracting complex numbers
• Dividing complex numbers
• Plotting numbers on the complex plane
• 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 \(\mathbb{R}^3\)
• River crossing puzzle
• 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
• Probability of simple events from Venn diagrams
• Biographies
• John Venn
• 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 addition and subtraction
• Multi-digit multiplication and division
• Multi-digit addition
• Multi-digit subtraction
• Multi-digit multiplication
• Multi-digit division
• Finding \(x\) and \(y\) intercepts of linear equations
• List all the divisors of a number
• Multiplying fractions
• Other resources
• Converting between improper fractions and mixed numbers
• \(n\)-th root
• Solving and graphing absolute value inequalities
• Solving and graphing quadratic inequalities
• Necklace splitting problem
• Intro to circles and \(\pi\)
• Circumference and area of a circle
• 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)
• Intro to decimals
• Introduction to functions
• Intro to linear 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
• Polynomial multiplication
• 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
• Geometry (4.G)
• 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
• Geometric series
• Partial sum of a geometric progression
• Reading travel graphs
• Unitary method
• Derivatives of exponential functions
• Combinatorics for high schoolers
• Two-way tables
• High school probability
• Complementary events
• Discrete random variables
• Middle school courses
• Elementary school courses
• Median
• Stem and leaf plots
• Evaluating square roots of small perfect squares (abstract method)
• 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
• Quadratics and higher-order polynomials
• Challenge
• Motion graphs
• Product rule
• Leibniz's derivative notation
• Constant rule
• Biographies for calc
• Circles (geometry for high schoolers)
• Finding the area of composite figures (geometry for high schoolers)
• Proof by induction (inequalities)
• Net of a polyhedron
• Zero
• Collatz conjecture
• Adding and subtracting free vectors
• Infinitude of the primes
• Remainder and factor theorems
• Polynomial arithmetic
• Solving polynomials
• Graphing linear inequalities on the coordinate plane
• Parallel lines and transversal
• Small-angle approximation
• A-Level Maths
• A-Level Further Maths
• Double angle identities
• Triple angle formulas
• Compound angles
• Polynomial long division and graphing
• Inverse variation
• Multiplying polynomials
• Transformations of the square and cube root functions
• Graphing the square root function under transformations
• Graphing reciprocal functions
• Equation of a circle and semicircle
• Adding functions
• Subtracting functions
• Solving certain cubic inequalities
• Graphing parabolas
• Solving 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)
• Mathematics Extension 1
• Motion
• Coordinate geometry
• 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
• Trigonometry (A-Level Maths)
• Gradients
• Differentiation
• 3D matrices
• Determinants
• Matrices
• Invariance
• Equivalent forms
• Classifying stationary points
• Other resources
• Special points
• Deriving the quadratic formula
• Series and sequences
• Partial sums
• Factoring and solving quadratics using the quadratic formula
• Direct variation
• Parametric equations and polar coordinates
• Tangents of circles
• 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
• Standard deviation
• Factorization with complex numbers
• Adding and subtracting in scientific notation
• Multiplying and dividing in scientific notation
• Finding the inverse of linear functions
• Finding the inverse of rational functions
• Graphing trigonometric functions under transformations
• 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
• Volume of extruded figures
• 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
• Factoring non-monic quadratics
• Other resources
• 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
• 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
• 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
• Distributing and combining
• 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
• Arithmetic and 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
• Finding slope given two points
• 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
• Transformations of the sine and cosine functions
• 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
• Square roots
• Functions (algebra 1)
• Variation
• Linear equations and inequalities
• Converting standard form to vertex form
• Intersection of circle and line
• Absolute value, piecewise, and step functions
• Other resources
• 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
• Find the equation of a line given two points
• Solving trigonometric equations
• Solving harder trigonometric equations
• Solving trigonometric equations by quadrants
• Finding the quadrant from trigonometric constraints
• Finding the inverse of exponential functions
• Evaluating natural logarithms without a calculator
• 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
• Other resources
• Division of multi-digit by one-digit
• Currency conversion
• Converting decimals to fractions
• Adding and subtracting decimals
• Converting between words and algebraic expressions
• Converting percents to decimals
• Comparing and ordering 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
• Simplifying trigonometric expressions
• 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
• Triangle centers
• Intersecting chords theorem
• 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
• Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres (8.G.C)
• Volume of a cone
• Trial and improvement
• Finding general solutions to trigonometric equations
• Normal distribution
• Binomial theorem and Pascal's triangle
• Exponential growth and decay (calculus 1)
• Perimeter, circumference, and area
• Functions of displacement
• Grouped data
• Derivatives of trigonometric functions
• Derivatives of logarithmic functions
• Mechanics
• Common knowledge puzzle
• Locker Problem
• Other resources
• Adding and subtracting exponents with negative powers
• 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)
• Volume and surface area of a sphere
• Finding or estimating the mean from a frequency table
• Binomial expansion
• Solving quadratic equations using trigonometry
• Iterated function systems
• Finding the modulus and argument of a complex number
• Binomial distribution
• Solving proportions
• Cumulative frequency
• GCSE maths
• Using calculations
• Mean
• Converting terminating decimals to fractions
• Solving linear equations and expanding brackets
• Solving literal equations
• Frequency diagrams
• 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
• Evaluating inverse trigonometric functions without a calculator
• 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
• Properties of sigma notation
• 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
• Surface area of a sphere
• 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
• 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
• Sum to product and product to sum identities
• 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
• Multiplying and dividing functions
• 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 standard form
• 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
• Converting slope-intercept form to standard form
• 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
• Composite figures (geometry for high schoolers)
• Perimeter of composite figures
• Other resources
• Hyperbola
• Graphing ellipses
• Focus of ellipse from equation in standard form
• 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
• Solving trigonometric equations by factoring trinomials
• Solving trigonometric equations by factoring
• Graphing the sine and cosine functions
• Graphing the tangent and cotangent functions
• 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
• Multiplying square roots
• 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
• Converting quadratic equations between vertex and standard form
• Converting quadratic equations from vertex to standard form
• Converting quadratic equations from standard to vertex form
• Converting to slope-intercept form
• Double factorial
• Proofs using the unit circle
• Solving unit rate problems
• Exterior angle theorem
• Proof
• Using the theorem
• Finding the center and radius of a circle by completing the square
• Binary
• Counting and cardinality (K.CC)
• Multiplying mixed numbers (word problems)
• Operations and algebraic thinking (4.OA)
• 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
• Understand place value. (2.NBT.A)
• 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 and subtract within 20. (1.OA.C)
• 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
• Geometry (8.G)
• Congruent figures
• Other resources
• Ordinal numbers
• Angle Wars
• Other resources
• Relating whole number division to multiplication
• 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
• Factoring trinomials using algebra tiles (for teachers)
• 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
• Operations and algebraic thinking (K.OA)
• Number and operations in base ten (K.NBT)
• Measurement and data (K.MD)
• Geometry (K.G)
• Operations and algebraic thinking (1.OA)
• Number and operations in base ten (1.NBT)
• Measurement and data (1.MD)
• Geometry (1.G)
• Operations and algebraic thinking (2.OA)
• Number and operations in base ten (2.NBT)
• Measurement and data (2.MD)
• Geometry (2.G)
• Operations and algebraic thinking (3.OA)
• Number and operations in base ten (3.NBT)
• Number and operations–fractions¹ (3.NF)
• Measurement and data (3.MD)
• Geometry (3.G)
• Number and operations in base ten¹ (4.NBT)
• Number and operations—fractions¹ (4.NF)
• Measurement and data (4.MD)
• Operations and algebraic thinking (5.OA)
• Number and operations in base ten (5.NBT)
• Number and operations–fractions (5.NF)
• Measurement and data (5.MD)
• Geometry (5.G)
• Ratios and proportional relationships (6.RP)
• The number system (6.NS)
• Expressions and equations (6.EE)
• Statistics and probability (6.SP)
• Ratios and proportional relationships (7.RP)
• The number system (7.NS)
• Expressions and equations (7.EE)
• Geometry (7.G)
• Statistics and probability (7.SP)
• The number system (8.NS)
• Expressions and equations (8.EE)
• Functions (8.F)
• Statistics and probability (8.SP)
• 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
• 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
• 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
• Understand place value (1.NBT.B)
• Extend the counting sequence (1.NBT.A)
• Use place value understanding and properties of operations to add and subtract (1.NBT.C)
• Add within 10 using counters
• Subtract within 10 using counters or two color counters
• Reason with shapes and their attributes (3.G.A)
• Geometric measurement: understand concepts of area and relate area to multiplication and to addition (3.MD.C)
• Represent and interpret data (3.MD.B)
• Other resources
• Volume of right rectangular prisms with fractional dimensions
• Define, evaluate, and compare functions. (8.F.A)
• Number pairs
• Multiplication using counters and paper plates
• Solve problems involving measurement and conversion of measurements. (4.MD.A)
• Making change
• Use place value understanding and properties of operations to perform multi-digit arithmetic. (4.NBT.B)
• Multiply and divide within 100. (3.OA.C)
• Multiplying within 100 (3.OA.C)
• Division using manipulatives (grade 4)
• Rounding and estimation
• Eureka Math, grade 1
• Eureka Math, grade 1, module 1
• Apply and extend previous understandings of arithmetic to algebraic expressions. (6.EE.A)
• 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
• Solve real-life and mathematical problems using numerical and algebraic expressions and equations. (7.EE.B)
• Compare numbers. (K.CC.C)
• 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
• Work with equal groups of objects to gain foundations for multiplication. (2.OA.C)
• 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
• Perform operations with multi-digit whole numbers and with decimals to hundredths. (5.NBT.B)
• 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
• Work with radicals and integer exponents. (8.EE.A)
• Reflection (grade 8)
• Reflecting points
• 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
• Represent and interpret data (2.MD.D)
• Solve problems involving measurement and estimation (3.MD.A)
• Other resources
• Adding and subtracting fractions with unlike denominators
• Oh Snap!
• Rounding to the nearest 10 or 100
• Use place value understanding and properties of operations to perform multi-digit arithmetic.¹ (3.NBT.A)
• Multiplying 10s (grade 3)
• Subtracting three-digit numbers using the standard algorithm
• Converting between words and numbers
• Generalize place value understanding for multi-digit whole numbers. (4.NBT.A)
• Converting between whole numbers and expanded form
• Apply and extend previous understandings of multiplication and division to divide fractions by fractions. (6.NS.A)
• Graphing linear inequalities in slope-intercept form
• Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. (7.G.B)
• 7.G.B.6
• Multiplying binomials
• Multiplying fractions (concrete and pictorial methods)
• Classifying real numbers
• Know that there are numbers that are not rational, and approximate them by rational numbers. (8.NS.A)
• 8.NS.A.1
• 8.NS.A.2
• Subtracting mixed numbers using a visual model
• Understand ratio concepts and use ratio reasoning to solve problems. (6.RP.A)
• 6.RP.A.1
• 6.RP.A.2
• 6.RP.A.3
• 6.RP.A.3.a
• 6.RP.A.3.b
• 6.RP.A.3.c
• 6.RP.A.3.d
• Apply and extend previous understandings of numbers to the system of rational numbers. (6.NS.C)
• 6.NS.C.5
• 6.NS.C.6
• 6.NS.C.7
• 6.NS.C.8
• 6.NS.C.6.a
• 6.NS.C.6.b
• 6.NS.C.6.c
• Apply and extend previous understandings of operations with fractions. (7.NS.A)
• 7.NS.A.1
• 7.NS.A.2
• 7.NS.A.3
• 7.NS.A.1.a
• 7.NS.A.1.b
• 7.NS.A.1.c
• 7.NS.A.1.d
• Analyze proportional relationships and use them to solve real-world and mathematical problems. (7.RP.A)
• 7.RP.A.1
• 7.RP.A.2
• 7.RP.A.3
• 7.RP.A.2.a
• 7.RP.A.2.b
• 7.RP.A.2.c
• 7.RP.A.2.d
• Draw construct, and describe geometrical figures and describe the relationships between them. (7.G.A)
• Understand congruence and similarity using physical models, transparencies, or geometry software. (8.G.A)
• Understand and apply the Pythagorean Theorem (8.G.B)
• 8.G.A.1
• 8.G.A.2
• 8.G.A.3
• 8.G.A.4
• 8.G.A.5
• 8.G.B.6
• 8.G.B.7
• 8.G.B.8
• Approximating square roots
• 7.G.B.4
• 7.G.B.5
• 6.NS.A.1
• Compute fluently with multi-digit numbers and find common factors and multiples. (6.NS.B)
• 6.NS.B.2
• 6.NS.B.3
• 6.NS.B.4
• 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
• 5.NBT.B.5
• 5.NBT.B.6
• 5.NBT.B.7
• Use random sampling to draw inferences about a population. (7.SP.A)
• Draw informal comparative inferences about two populations. (7.SP.B)
• Investigate chance processes and develop, use, and evaluate probability models. (7.SP.C)
• 7.SP.A.1
• 7.SP.A.2
• 7.SP.B.3
• 7.SP.B.4
• 7.SP.C.5
• 7.SP.C.6
• 7.SP.C.7
• 7.SP.C.8
• 7.SP.C.7.a
• 7.SP.C.7.b
• 7.SP.C.8.a
• 7.SP.C.8.b
• 7.SP.C.8.c
• Solve real-world and mathematical problems involving area, surface area, and volume. (6.G.A)
• 6.G.A.1
• 6.G.A.2
• 6.G.A.3
• 6.G.A.4
• Reason about and solve one-variable equations and inequalities. (6.EE.B)
• Represent and analyze quantitative relationships between dependent and independent variables (6.EE.C)
• 6.EE.A.1
• 6.EE.A.2
• 6.EE.A.3
• 6.EE.A.4
• 6.EE.A.2.a
• 6.EE.A.2.b
• 6.EE.A.2.c
• Know number names and the count sequence. (K.CC.A)
• Count to tell the number of objects. (K.CC.B)
• K.CC.A.1
• K.CC.A.2
• K.CC.A.3
• K.CC.B.4
• K.CC.B.5
• K.CC.B.4.a
• K.CC.B.4.b
• K.CC.B.4.c
• K.CC.C.6
• K.CC.C.7
• Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. (K.OA.A)
• K.OA.A.1
• K.OA.A.2
• K.OA.A.3
• K.OA.A.4
• K.OA.A.5
• Work with numbers 11-19 to gain foundations for place value. (K.NBT.A)
• K.NBT.A.1
• Describe and compare measurable attributes. (K.MD.A)
• Classify objects and count the number of objects in each category. (K.MD.B)
• K.MD.A.1
• K.MD.A.2
• K.MD.B.3
• Identify and describe shapes. (K.G.A)
• Analyze, compare, create, and compose shapes. (K.G.B)
• K.G.A.1
• K.G.A.2
• K.G.A.3
• K.G.B.4
• K.G.B.5
• K.G.B.6
• Represent and solve problems involving addition and subtraction. (1.OA.A)
• Understand and apply properties of operations and the relationship between addition and subtraction. (1.OA.B)
• 1.OA.C.5
• 1.OA.C.6
• Work with addition and subtraction equations. (1.OA.D)
• 1.OA.A.1
• 1.OA.A.2
• 1.OA.B.3
• 1.OA.B.4
• 1.OA.D.7
• 1.OA.D.8
• 1.NBT.A.1
• 1.NBT.B.2
• 1.NBT.B.3
• 1.NBT.B.2.a
• 1.NBT.B.2.b
• 1.NBT.B.2.c
• 1.NBT.C.4
• 1.NBT.C.5
• 1.NBT.C.6
• Measure lengths indirectly and by iterating length units. (1.MD.A)
• Tell and write time. (1.MD.B)
• Represent and interpret data. (1.MD.C)
• 1.MD.A.1
• 1.MD.A.2
• 1.MD.B.3
• 1.MD.C.4
• Reason with shapes and their attributes. (1.G.A)
• 1.G.A.1
• 1.G.A.2
• 1.G.A.3
• Represent and solve problems involving addition and subtraction. (2.OA.A)
• Add and subtract within 20. (2.OA.B)
• 2.OA.A.1
• 2.OA.B.2
• 2.OA.C.3
• 2.OA.C.4
• 2.NBT.A.1
• 2.NBT.A.2
• 2.NBT.A.3
• 2.NBT.A.4
• 2.NBT.A.1.a
• 2.NBT.A.1.b
• Use place value understanding and properties of operations to add and subtract. (2.NBT.B)
• 2.NBT.B.5
• 2.NBT.B.6
• 2.NBT.B.7
• 2.NBT.B.8
• 2.NBT.B.9
• Measure and estimate lengths in standard units. (2.MD.A)
• Relate addition and subtraction to length. (2.MD.B)
• Work with time and money. (2.MD.C)
• 2.MD.A.1
• 2.MD.A.2
• 2.MD.A.3
• 2.MD.A.4
• 2.MD.B.5
• 2.MD.B.6
• 2.MD.C.7
• 2.MD.C.8
• 2.MD.D.9
• 2.MD.D.10
• Reason with shapes and their attributes. (2.G.A)
• 2.G.A.1
• 2.G.A.2
• 2.G.A.3
• Represent and solve problems involving multiplication and division. (3.OA.A)
• Understand properties of multiplication and the relationship between multiplication and division. (3.OA.B)
• Solve problems involving the four operations, and identify and explain patterns in arithmetic. (3.OA.D)
• 3.OA.C.7
• 3.OA.B.5
• 3.OA.B.6
• 3.OA.A.1
• 3.OA.A.2
• 3.OA.A.3
• 3.OA.A.4
• 3.OA.D.8
• 3.OA.D.9
• 3.NBT.A.1
• 3.NBT.A.2
• 3.NBT.A.3
• Develop understanding of fractions as numbers. (3.NF.A)
• 3.NF.A.1
• 3.NF.A.2
• 3.NF.A.3
• 3.NF.A.2.a
• 3.NF.A.2.b
• 3.NF.A.3.a
• 3.NF.A.3.b
• 3.NF.A.3.c
• 3.NF.A.3.d
• 3.G.A.1
• 3.G.A.2
• Geometric measurement: recognize perimeter. (3.MD.D)
• 3.MD.A.1
• 3.MD.A.2
• 3.MD.B.3
• 3.MD.B.4
• 3.MD.C.5
• 3.MD.C.6
• 3.MD.C.7
• 3.MD.C.5.a
• 3.MD.C.5.b
• 3.MD.C.7.a
• 3.MD.C.7.b
• 3.MD.C.7.c
• 3.MD.C.7.d
• 3.MD.D.8
• Use the four operations with whole numbers to solve problems. (4.OA.A)
• Gain familiarity with factors and multiples. (4.OA.B)
• Generate and analyze patterns. (4.OA.C)
• 4.OA.A.1
• 4.OA.A.2
• 4.OA.A.3
• 4.OA.B.4
• 4.OA.C.5
• 4.NBT.A.1
• 4.NBT.A.2
• 4.NBT.A.3
• 4.NBT.B.4
• 4.NBT.B.5
• 4.NBT.B.6
• Extend understanding of fraction equivalence and ordering. (4.NF.A)
• Build fractions from unit fractions. (4.NF.B)
• Understand decimal notation for fractions, and compare decimal fractions. (4.NF.C)
• 4.NF.A.1
• 4.NF.A.2
• 4.NF.B.3
• 4.NF.B.4
• 4.NF.B.3.a
• 4.NF.B.3.b
• 4.NF.B.3.c
• 4.NF.B.3.d
• 4.NF.B.4.a
• 4.NF.B.4.b
• 4.NF.B.4.c
• 4.NF.C.5
• 4.NF.C.6
• 4.NF.C.7
• 4.MD.A.1
• 4.MD.A.2
• 4.MD.A.3
• Represent and interpret data. (4.MD.B)
• Geometric measurement: understand concepts of angle and measure angles. (4.MD.C)
• 4.MD.B.4
• 4.MD.C.5
• 4.MD.C.6
• 4.MD.C.7
• 4.MD.C.5.a
• 4.MD.C.5.b
• Draw and identify lines and angles, and classify shapes by properties of their lines and angles. (4.G.A)
• 4.G.A.1
• 4.G.A.2
• 4.G.A.3
• Finding cube roots using units, tens, and hundreds place blocks
• Write and interpret numerical expressions. (5.OA.A)
• Analyze patterns and relationships. (5.OA.B)
• 5.OA.A.1
• 5.OA.A.2
• 5.OA.B.3
• Understand the place value system. (5.NBT.A)
• 5.NBT.A.1
• 5.NBT.A.2
• 5.NBT.A.3
• 5.NBT.A.4
• 5.NBT.A.3.a
• 5.NBT.A.3.b
• Use equivalent fractions as a strategy to add and subtract fractions. (5.NF.A)
• Apply and extend previous understandings of multiplication and division. (5.NF.B)
• 5.NF.A.1
• 5.NF.A.2
• 5.NF.B.3
• 5.NF.B.4
• 5.NF.B.5
• 5.NF.B.6
• 5.NF.B.7
• 5.NF.B.4.a
• 5.NF.B.4.b
• 5.NF.B.5.a
• 5.NF.B.5.b
• 5.NF.B.7.a
• 5.NF.B.7.b
• 5.NF.B.7.c
• Convert like measurement units within a given measurement system. (5.MD.A)
• Represent and interpret data. (5.MD.B)
• Geometric measurement: understand concepts of volume. (5.MD.C)
• 5.MD.A.1
• 5.MD.B.2
• 5.MD.C.3
• 5.MD.C.4
• 5.MD.C.5
• 5.MD.C.3.a
• 5.MD.C.3.b
• Graph points on the coordinate plane to solve real-world and mathematical problems. (5.G.A)
• Classify two-dimensional figures into categories based on their properties. (5.G.B)
• 5.G.A.1
• 5.G.A.2
• 5.G.B.3
• 5.G.B.4
• 6.NS.C.7.a
• 6.NS.C.7.b
• 6.NS.C.7.c
• 6.NS.C.7.d
• 6.EE.B.5
• 6.EE.B.6
• 6.EE.B.7
• 6.EE.B.8
• 6.EE.C.9
• Develop understanding of statistical variability. (6.SP.A)
• Summarize and describe distributions. (6.SP.B)
• 6.SP.A.1
• 6.SP.A.2
• 6.SP.A.3
• 6.SP.B.4
• 6.SP.B.5
• 6.SP.B.5.a
• 6.SP.B.5.b
• 6.SP.B.5.c
• 6.SP.B.5.d
• 7.NS.A.2.a
• 7.NS.A.2.b
• 7.NS.A.2.c
• 7.NS.A.2.d
• Use properties of operations to generate equivalent expressions. (7.EE.A)
• 7.EE.A.1
• 7.EE.A.2
• 7.EE.B.3
• 7.EE.B.4
• 7.EE.B.4.a
• 7.EE.B.4.b
• 7.G.A.1
• 7.G.A.2
• 7.G.A.3
• 8.EE.A.1
• 8.EE.A.2
• 8.EE.A.3
• 8.EE.A.4
• Understand the connections between proportional relationships, lines, and linear equations. (8.EE.B)
• Analyze and solve linear equations and pairs of simultaneous linear equations. (8.EE.C)
• 8.EE.B.5
• 8.EE.B.6
• 8.EE.C.7
• 8.EE.C.8
• 8.EE.C.8.a
• 8.EE.C.8.b
• 8.EE.C.8.c
• 8.F.A.1
• 8.F.A.2
• 8.F.A.3
• Use functions to model relationships between quantities. (8.F.B)
• 8.F.B.4
• 8.F.B.5
• 8.G.A.1.a
• 8.G.A.1.b
• 8.G.A.1.c
• 8.G.C.9
• Investigate patterns of association in bivariate data. (8.SP.A)
• 8.SP.A.1
• 8.SP.A.2
• 8.SP.A.3
• 8.SP.A.4
• 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)
• Polynomials (algebra 1)
• Expanding and factoring
• Solving quadratic equations by factoring (word problems)
• Solving quadratic equations by factoring (mathematical problems)
• Multiplying and dividing rational expressions
• Simplifying complex fractions with variables
• 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
• Prealgebra word problems
• Dilation
• Exponential growth and decay (word problems)
• 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)
• Estimating a sum or difference
• Other resources
• Factoring monomials completely
• Multiplying monomials by polynomials
• Finding \(x\) and \(y\) intercepts of linear equations from graphs
• Evaluating square roots of decimals
• 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 division
• Dividing quadratics by linear expressions
• Graphing parabolas in standard form
• Graphing parabolas in vertex form
• 8.EE.C.7.a
• 8.EE.C.7.b
• Number and quantity (HSN)
• Algebra (HSA)
• Functions (HSF)
• Geometry (HSG)
• Statistics and probability (HSS)
• The real number system (HSN.RN)
• Quantities* (HSN.Q)
• Reason quantitatively and use units to solve problems. (HSN.Q.A)
• HSN.Q.A.1
• HSN.Q.A.2
• HSN.Q.A.3
• Extend the properties of exponents to rational exponents. (HSN.RN.A)
• Use properties of rational and irrational numbers. (HSN.RN.B)
• HSN.RN.A.1
• HSN.RN.A.2
• HSN.RN.B.3
• The complex number system (HSN.CN)
• Perform arithmetic operations with complex numbers. (HSN.CN.A)
• Represent complex numbers and their operations on the complex plane. (HSN.CN.B)
• Use complex numbers in polynomial identities and equations. (HSN.CN.C)
• HSN.CN.A.1
• HSN.CN.A.2
• HSN.CN.A.3
• HSN.CN.B.4
• HSN.CN.B.5
• HSN.CN.B.6
• HSN.CN.C.7
• HSN.CN.C.8
• HSN.CN.C.9
• Vector and matrix quantities (HSN.VM)
• Represent and model with vector quantities. (HSN.VM.A)
• Perform operations on vectors. (HSN.VM.B)
• Perform operations on matrices and use matrices in applications. (HSN.VM.C)
• HSN.VM.A.1
• HSN.VM.A.2
• HSN.VM.A.3
• HSN.VM.B.4
• HSN.VM.B.5
• HSN.VM.B.4.a
• HSN.VM.B.4.b
• HSN.VM.B.4.c
• HSN.VM.B.5.a
• HSN.VM.B.5.b
• HSN.VM.C.6
• HSN.VM.C.7
• HSN.VM.C.8
• HSN.VM.C.9
• HSN.VM.C.10
• HSN.VM.C.11
• HSN.VM.C.12
• Seeing structure in expressions (HSA.SSE)
• Interpret the structure of expressions. (HSA.SSE.A)
• Write expressions in equivalent forms to solve problems. (HSA.SSE.B)
• HSA.SSE.A.1
• HSA.SSE.A.2
• HSA.SSE.A.1.a
• HSA.SSE.A.1.b
• HSA.SSE.B.3
• HSA.SSE.B.4
• HSA.SSE.B.3.a
• HSA.SSE.B.3.b
• HSA.SSE.B.3.c
• Arithmetic with polynomials and rational expressions (HSA.APR)
• Perform arithmetic operations on polynomials. (HSA.APR.A)
• Understand the relationship between zeros and factors of polynomials. (HSA.APR.B)
• Use polynomial identities to solve problems. (HSA.APR.C)
• Rewrite rational expressions. (HSA.APR.D)
• HSA.APR.A.1
• HSA.APR.B.2
• HSA.APR.B.3
• HSA.APR.C.4
• HSA.APR.C.5
• HSA.APR.D.6
• HSA.APR.D.7
• Creating equations* (HSA.CED)
• Create equations that describe numbers or relationships. (HSA.CED.A)
• HSA.CED.A.1
• HSA.CED.A.2
• HSA.CED.A.3
• HSA.CED.A.4
• Reasoning with equations and inequalities (HSA.REI)
• Understand solving equations as a process of reasoning and explain the reasoning. (HSA.REI.A)
• Solve equations and inequalities in one variable. (HSA.REI.B)
• Solve systems of equations. (HSA.REI.C)
• Represent and solve equations and inequalities graphically. (HSA.REI.D)
• HSA.REI.A.1
• HSA.REI.A.2
• HSA.REI.B.3
• HSA.REI.B.4
• HSA.REI.B.4.a
• HSA.REI.B.4.b
• HSA.REI.C.5
• HSA.REI.C.6
• HSA.REI.C.7
• HSA.REI.C.8
• HSA.REI.C.9
• HSA.REI.D.10
• HSA.REI.D.11
• HSA.REI.D.12
• Interpreting functions (HSF.IF)
• Understand the concept of a function and use function notation. (HSF.IF.A)
• Interpret functions that arise in applications in terms of the context. (HSF.IF.B)
• Analyze functions using different representations. (HSF.IF.C)
• HSF.IF.A.1
• HSF.IF.A.2
• HSF.IF.A.3
• HSF.IF.B.4
• HSF.IF.B.5
• HSF.IF.B.6
• HSF.IF.C.7
• HSF.IF.C.8
• HSF.IF.C.9
• HSF.IF.C.7.a
• HSF.IF.C.7.b
• HSF.IF.C.7.c
• HSF.IF.C.7.d
• HSF.IF.C.7.e
• HSF.IF.C.8.a
• HSF.IF.C.8.b
• Building functions (HSF.BF)
• Build a function that models a relationship between two quantities. (HSF.BF.A)
• Build new functions from existing functions. (HSF.BF.B)
• HSF.BF.A.1
• HSF.BF.A.2
• HSF.BF.A.1.a
• HSF.BF.A.1.b
• HSF.BF.A.1.c
• HSF.BF.B.3
• HSF.BF.B.4
• HSF.BF.B.5
• HSF.BF.B.4.a
• HSF.BF.B.4.b
• HSF.BF.B.4.c
• HSF.BF.B.4.d
• Linear, quadratic, and exponential models* (HSF.LE)
• Construct and compare linear, quadratic, and exponential models and solve problems. (HSF.LE.A)
• Interpret expressions for functions in terms of the situation they model. (HSF.LE.B)
• HSF.LE.A.1
• HSF.LE.A.2
• HSF.LE.A.3
• HSF.LE.A.4
• HSF.LE.A.1.a
• HSF.LE.A.1.b
• HSF.LE.A.1.c
• HSF.LE.B.5
• Trigonometric functions (HSF.TF)
• Extend the domain of trigonometric functions using the unit circle. (HSF.TF.A)
• Model periodic phenomena with trigonometric functions. (HSF.TF.B)
• Prove and apply trigonometric identities. (HSF.TF.C)
• HSF.TF.A.1
• HSF.TF.A.2
• HSF.TF.A.3
• HSF.TF.A.4
• HSF.TF.B.5
• HSF.TF.B.6
• HSF.TF.B.7
• HSF.TF.C.8
• HSF.TF.C.9
• Congruence (HSG.CO)
• Experiment with transformations in the plane (HSG.CO.A)
• Understand congruence in terms of rigid motions (HSG.CO.B)
• Prove geometric theorems (HSG.CO.C)
• Make geometric constructions (HSG.CO.D)
• HSG.CO.A.1
• HSG.CO.A.2
• HSG.CO.A.3
• HSG.CO.A.4
• HSG.CO.A.5
• HSG.CO.B.6
• HSG.CO.B.7
• HSG.CO.B.8
• HSG.CO.C.9
• HSG.CO.C.10
• HSG.CO.C.11
• HSG.CO.D.12
• HSG.CO.D.13
• Similarity, right triangles, and trigonometry (HSG.SRT)
• Understand similarity in terms of similarity transformations (HSG.SRT.A)
• Prove theorems involving similarity (HSG.SRT.B)
• Define trigonometric ratios and solve problems involving right triangles (HSG.SRT.C)
• Apply trigonometry to general triangles (HSG.SRT.D)
• HSG.SRT.A.1
• HSG.SRT.A.2
• HSG.SRT.A.3
• HSG.SRT.A.1.a
• HSG.SRT.A.1.b
• HSG.SRT.B.4
• HSG.SRT.B.5
• HSG.SRT.C.6
• HSG.SRT.C.7
• HSG.SRT.C.8
• HSG.SRT.D.9
• HSG.SRT.D.10
• HSG.SRT.D.11
• Circles (HSG.C)
• Understand and apply theorems about circles (HSG.C.A)
• Find arc lengths and areas of sectors of circles (HSG.C.B)
• HSG.C.A.1
• HSG.C.A.2
• HSG.C.A.3
• HSG.C.A.4
• Expressing geometric properties with equations (HSG.GPE)
• Translate between the geometric description and the equation for a conic section (HSG.GPE.A)
• Use coordinates to prove simple geometric theorems algebraically (HSG.GPE.B)
• HSG.GPE.A.1
• HSG.GPE.A.2
• HSG.GPE.A.3
• HSG.GPE.B.4
• HSG.GPE.B.5
• HSG.GPE.B.6
• HSG.GPE.B.7
• Geometric measurement and dimension (HSG.GMD)
• Explain volume formulas and use them to solve problems (HSG.GMD.A)
• Visualize relationships between two-dimensional and three-dimensional objects (HSG.GMD.B)
• HSG.GMD.A.1
• HSG.GMD.A.2
• HSG.GMD.A.3
• HSG.GMD.B.4
• Modeling with geometry (HSG.MG)
• Apply geometric concepts in modeling situations (HSG.MG.A)
• HSG.MG.A.1
• HSG.MG.A.2
• HSG.MG.A.3
• Interpreting categorical and quantitative data (HSS.ID)
• Summarize, represent, and interpret data on a single count or measurement variable (HSS.ID.A)
• Summarize, represent, and interpret data on two categorical and quantitative variables (HSS.ID.B)
• Interpret linear models (HSS.ID.C)
• HSS.ID.A.1
• HSS.ID.A.2
• HSS.ID.A.3
• HSS.ID.A.4
• HSS.ID.B.5
• HSS.ID.B.6
• HSS.ID.B.6.a
• HSS.ID.B.6.b
• HSS.ID.B.6.c
• HSS.ID.C.7
• HSS.ID.C.8
• HSS.ID.C.9
• Making inferences and justifying conclusions (HSS.IC)
• Understand and evaluate random processes underlying statistical experiments (HSS.IC.A)
• Make inferences and justify conclusions from sample surveys, experiments, and observational studies (HSS.IC.B)
• HSS.IC.A.1
• HSS.IC.A.2
• HSS.IC.B.3
• HSS.IC.B.4
• HSS.IC.B.5
• HSS.IC.B.6
• Conditional probability and the rules of probability (HSS.CP)
• Understand independence and conditional probability and use them to interpret data (HSS.CP.A)
• HSS.CP.A.1
• HSS.CP.A.2
• HSS.CP.A.3
• HSS.CP.A.4
• HSS.CP.A.5
• Use the rules of probability to compute probabilities of compound events. (HSS.CP.B)
• HSS.CP.B.6
• HSS.CP.B.7
• HSS.CP.B.8
• HSS.CP.B.9
• Using probability to make decisions (HSS.MD)
• Calculate expected values and use them to solve problems (HSS.MD.A)
• Use probability to evaluate outcomes of decisions (HSS.MD.B)
• HSS.MD.A.1
• HSS.MD.A.2
• HSS.MD.A.3
• HSS.MD.A.4
• HSS.MD.B.5
• HSS.MD.B.6
• HSS.MD.B.7
• HSS.MD.B.5.a
• HSS.MD.B.5.b
• Making and describing scatter plots
• Finding \(y\) intercept 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
• Surface area of a rectangular prism
• Sum and difference of cubes
• 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)
• Squaring trinomials
• 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
• Congruent triangles
• Cofunction identities
• Hinge theorem and its converse
• Finding angles of elevation and depression
• Definite integration by trigonometric substitution
• Integrals involving trig functions
• Improper integrals
• Graphing rational functions
• Solving nonlinear systems in two variables
• Evaluating natural logarithms
• Evaluating natural logarithms with a calculator
• Graphing hyperbolas in standard form
• Graphing the tangent and cotangent functions under transformations
• Graphing the secant and cosecant functions 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 trigonometric 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)
• Converting between standard form and vertex form
• Converting linear equations between standard form and slope-intercept form
• Average value over an interval
• Integrating exponential functions by u-substitution
• Calculus
• 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
• Solving equations in quadratic form using u-substitution
• Constant multiple rule for derivatives
• Extreme value theorem
• Rational zeros theorem
• Gaussian elimination
• Gauss–Jordan elimination
• Adding and subtracting radicals
• Other resources
• Graphing the 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
• Plotting polar points
• 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
• Evaluating inverse trig functions
• Evaluating inverse trigonometric functions with a calculator
• Finding reference angles
• Evaluating trigonometric functions using reference angles
• Other resources
• Solving exponential equations using logarithms
• Rational root theorem
• Factor theorem
• Derivatives of natural logarithmic functions
• Sketching quadratic inequalities
• Sign of the discriminant
• Using your calculator
• Solving linear equations with fractions
• Earning and managing money
• Investing money
• Taxation
• Graphing the sum of two functions
• 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 the cosecant function 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
• Decimal arithmetic
• 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)
• Rate conversion
• Solving right triangles (word problems)
• Graphing the secant function 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
• Solving nonlinear systems in two variables by graphing
• Intersection of parabola and circle
• Lattice multiplication with decimals
• Finding the LCD of fractions
• Proportion word problems
• Finding quadratic equations from their solutions
• 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
• Plotting integers on a number line
• Intro to negative numbers
• Graph a line given \(x\) and \(y\) intercepts
• Double and half angle formulas
• 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
• Multi-digit subtraction with regrouping
• Subtracting within 100 with regrouping
• Number of solutions to linear equations
• Finding the number of roots of a quadratic in vertex form
• 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
• Percents: 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 exponential and logarithmic functions
• Finding the inverse of logarithmic functions
• Solving linear equations with congruent triangles
• SAS congruence
• ASA and AAS congruence
• Finding vertical asymptotes of rational trigonometric functions
• 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)
• Find the first \(n\) terms of an arithmetic series
• Partial sum of an arithmetic series
• Find the explicit formula for an arithmetic series given terms
• 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
• Graphing polar equations
• 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 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
• Fundamental theorem of algebra
• Imaginary numbers
• Test preparation
• ACT math
• Verifying logarithmic identities
• Find the value of \(c\) that completes the square
• Converting standard form to vertex form without completing the square
• Finding the domain of rational functions
• Finding the domain of rational functions involving radicals
• Finding extrema graphically
• Using the theorem
• Using the difference formula for cosine
• Finding the quadrant of an angle
• 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
• Finding the area of composite figures by adding
• 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
• 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
• Inscribed angles
• What is a relation?
• Graphing linear equations from tables
• Finding basic limits
• Finding limits of rational functions
• Finding limits by simplifying complex fractions
• Polygon angle sum theorems
• Find one exterior angle given the number of sides for a regular polygon
• Evaluating trigonometric functions of negative angles
• 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
• Area and perimeter of rectangles
• 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
• Finding the point on the unit circle
• Evaluating inverse trigonometric functions using the unit circle
• Evaluating sine inverse using the unit circle
• 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
• Volume and surface area of a pyramid
• Volume and surface area of cylinders
• Derivatives of transcendental functions
• Volume and surface area of a prism
• Proof
• Finding angle relationships in figures
• 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
• Graphing hyperbolas not centered at the origin
• 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
• Descartes's rule of signs
• Sketching logarithmic functions under transformations (level 2)
• Solving and graphing linear systems of inequalities in two variables (vertical and horizontal)
• 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
• Finding angles on parallel lines (harder)
• Graphing inequalities in one variable
• Graphically finding the increasing, decreasing, and constant intervals
• Common mistake with exponents
• Solving polynomials (difference of two squares)
• Simplifying cube roots of integers
• Solving logarithmic equations using the one-to-one property
• 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
• Evaluating logarithmic expressions using properties of logarithms
• Evaluating logarithmic expressions
• Solving linear systems of equations in two variables (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
• Graphing linear systems of inequalities in two variables
• Graphing linear systems of inequalities in two variables (slope-intercept form)
• Graphing linear systems of inequalities in two variables (standard form)
• Graphing horizontal ellipses in general form
• Solving logarithmic equations using the properties of logarithms
• Solving monic quadratics by factoring
• Other resources
• Solving quadratics lacking a constant term
• Using the zero product property (polynomials)
• Similar figures (algebra problems)
• Solving polynomials (non-factorable)
• Finding the other zeros
• Finding the other zeros given rational zeros
• Finding the other zeros given irrational zeros
• Dividing a polynomial by a monomial
• Graphing the secant and cosecant functions
• Congruent polygons (algebra problems)
• Using the zero product property (trigonometric equations)
• Solving trigonometric equations (angle constraint)
• 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
• Finding the \(x\) and \(y\) intercepts of a polynomial in factored form
• Other resources
• Evaluating expressions with multiple variables
• Other resources
• Hypotenuse-leg congruence theorem
• Simplifying radicals of monomials
• Polynomial factorization
• 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
• Solving and graphing polynomial inequalities
• Finding the GCD and LCM of polynomials
• Finding the domain and range of relations
• Negative bases
• Graphing linear inequalities in two variables
• 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
• Corresponding angles postulate
• Other resources
• 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
• Find the parabola from its focus and directrix
• Relatively prime
• Temperature conversion
• Area of a segment
• Reciprocals of mixed numbers
• Graphing two variable inequalities
• Zero matrix
• Power of a power rule for exponents
• 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
• Simplifying rational expressions by quotient property of powers and cancelling
• 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
• Derivation
• Power of a product rule for exponents
• Proof: Congruent supplementary angles are right angles
• What is a Lambert quadrilateral?
• Non-Euclidean geometry
• Diagonal length of a rectangular prism
• Height formula for equilateral triangles
• 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
• Finding \(x\) and \(y\) intercepts of quadratic equations
• Proving the medians cut a triangle into six equal area triangles
• Diagonals of a parallelogram bisect each other
• Proof: Intersecting secants theorem
• Finding the diagonal length of a rectangle
• Radius is perpendicular to a chord it bisects
• 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
• Using the properties of exponents
• Experimental compound probability
• Identifying functions from ordered pairs and tables
• Factoring difference of squares (concrete and visual methods)
• Using the theorem
• Geometric transformations (grade 8)
• Finding the volume of composite figures
• Comparing numbers in scientific notation
• Recursive to explicit formula for arithmetic series
• Experimental probability
• 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 and subtracting multiples of 10 within 100
• 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
• Distributive property (grade 5)
• Other resources
• Adding and subtracting multi-digit numbers
• Trick for subtracting from powers of ten
• Missing numbers for adding and subtracting multi-digit numbers
• 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
• Long division
• Add and subtract fractions with like denominators (word problems)
• Estimating volume (cups, pints, quarts, and gallons)
• Whole number arithmetic (word problems)
• Numbers in standard, word, and expanded form (grade 4)
• 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
• Dividing by taking out factors of 10
• 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
• Finding the constant of proportionality given a graph
• Lesson: Intro to theoretical probability
• Finding the constant of proportionality given a table
• Practice: Volume of right rectangular prisms (mathematical problems)
• Finding the constant of proportionality given an equation
• Theoretical and experimental probability
• Relating circumference and area of a circle by formulas
• Constants of proportionality
• Other resources
• Other resources
• Probability models
• Lesson
• Finding the circumference from the area of a circle
• Identifying proportional relationships
• Identifying proportional relationships from graphs
• Identifying proportional relationships from tables and word problems
• Finding volume by displacement (word problems)
• 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
• Quotient identities
• Intersection of parabola and line (word problems)
• Solving radical equations
• Is it even, odd, or neither? (given an equation)
• Rationalization
• Finding one-sided limits of piecewise functions
• Finding the domain and graphing rational 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)
• Intersection of two parabolas
• 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
• Practice: Verifying trigonometric 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
• Compose shapes (kindergarten)
• 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)
• Viviani's theorem
• Out of the Window (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)
• Pythagoras' Dream (NRICH activity)
• Square and Triangle (NRICH activity)
• Challenge
• 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
• Measures of central tendency
• Challenge
• Proof: 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
• Converting sums between sigma notation and expanded form
• Sigma notation
• Proving equations involving sigma notation
• Properties of sigma notation
• Challenge
• 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
• Proof: Opposite sides of a parallelogram are congruent
• A number theory proof (blackpenredpen)
• Proof: Area of a rhombus from diagonals
• Intro to similarity
• GMAT math
• Centroid
• Putnam exam
• Practice: Area of a sector
• Newton–Pepys problem
• Potato paradox
• Simplifying rational expressions by factoring and cancelling
• Two envelopes problem
• Challenge
• Careful counting 1
• Challenge
• Rachel's Problem (NRICH activity)
• Solving floor and ceiling equations
• Direct proof (floor and ceiling)
• Surface area of a pyramid
• Other resources
• Linear system 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 factoring
• Solving trigonometric equations quadratic in form by taking square roots
• One and Three (NRICH activity)
• Challenge
• Challenge
• Centered hexagonal number
• One Basket or Group Photo (NRICH activity)
• Ratios of length, area, and volume for similar shapes
• 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
• Area mazes
• 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)
• Can you make this billiards trick shot? (Brilliant.org)
• Proof: Law of cosines using the dot product
• Geometric proofs using vectors
• Totality (NRICH activity)
• Subtracting decimals with tenths
• Subtracting decimals with thousandths
• Factoring monic quadratics with difference of squares (all resources)
• Factoring non-monic quadratics with difference of squares (all resources)
• Factoring monic quadratics with difference of squares using algebra tiles (all 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
• Solving trigonometric equations by graphing
• 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
• Challenge
• 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
• Using the triangle inequality
• Properties of complex modulus
• 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?
• Isosceles trapezoid theorems
• 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
• Other resources
• 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
• Converting improper algebraic fractions to mixed algebraic fractions
• Intro to even and odd functions
• Proof: Power reducing identities
• Power reducing identities
• Proofs
• Pascal's identity
• Connection between Pascal's identity and Pascal's triangle
• Properties of 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 (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
• Graphing the cosecant function
• 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)
• Arithmetic with complex numbers
• Square root of a complex number
• Finding volume using unit cubes
• 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
• Difficult factoring problems
• False proofs for calculus 2
• Derivatives of hyperbolic and inverse hyperbolic functions
• Proving the derivatives of the hyperbolic functions
• Proving the inverse hyperbolic identities
• Using the hyperbolic identities
• Hyperbolic and inverse hyperbolic identities
• Proving the derivatives of the inverse hyperbolic functions
• Even and odd hyperbolic functions
• Other resources
• 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
• Practice
• Lesson
• Practice
• Practice
• Intro to functions
• Practice: Using the circle theorems
• Proof: Radius and chord
• Radius and tangent
• What is a maximal clique?
• Subgraphs
• Proof: Alternate segment theorem
• Lesson: Alternate segment 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 (grade 8)
• Radicals (grade 8)
• 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)
• Intro to rates
• Equivalent ratios
• 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: Find the equation of a line given two points
• Practice: Find the equation of a line given two points
• Composition of trig functions
• 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
• Other resources
• 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
• Lesson
• Practice
• Other resources
• Recognize fractions greater than 1
• Recognize fractions
• Find the missing lengths and angles for similar polygons
• Lesson
• Practice
• Lesson
• Practice: Finding slope from a graph
• Solving quadratic equations (word problems)
• Adding integers (concrete and pictorial)
• Adding integers (abstract)
• Rational number word problems
• 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 algebra
• Intro to parallel and perpendicular lines
• Lesson: Lines, line segments, and rays
• Practice: Lines, line segments, and rays
• Recognize ratios
• HSG.C.B.5
• 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: Ratios and units of measurement
• Practice: Ratios and units of measurement
• 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
• Reflecting points in the coordinate plane
• Lesson
• Practice
• 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)
• Lesson
• Practice
• Comparing areas and perimeters of rectangles
• Lesson
• Practice
• Sums and products of rational and irrational numbers
• Sampling methods
• Lesson
• Practice
• Comparing and ordering absolute values
• Lesson
• Practice
• Modeling with linear functions
• Lesson: Reflecting points
• Practice: Reflecting points
• Reflections (geometry for high schoolers)
• Lesson: Reflecting line segments and polygons (grade 8)
• Practice: Reflecting line segments and polygons (grade 8)
• Reflecting figures (geometry for high schoolers)
• Finding the line of reflection (geometry for high schoolers)
• Lesson: Finding the line of reflection (geometry for high schoolers)
• Practice: Finding the line of reflection (geometry for high schoolers)
• 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
• Equivalent expressions with negative numbers (multiplication and division)
• Lesson: Equivalent expressions with negative numbers (multiplication and division)
• Practice: Equivalent expressions with negative numbers (multiplication and division)
• 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
• Making predictions with probability
• Lesson: Making predictions with probability
• Practice: Making predictions with probability
• Lesson: Probability models
• Practice: Probability models
• Lesson: Identifying proportional relationships from tables and word problems
• Practice: Identifying proportional relationships from tables and word problems
• Other resources
• Lesson
• Practice
• Compare shapes
• Compare size
• Subtracting multiples of 10 within 100
• Other resources
• 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
• Converting decimals between standard form, expanded form, and number names
• Equal sign
• Representing numbers using base ten blocks (grade 4)
• 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)
• Identifying shapes as two or three-dimensional
• Count in order
• Other resources
• Reading bar graphs (grade 1)
• 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
• Mentally add and subtract within 20
• Negative signs in fractions
• Lesson: Negative signs in fractions
• Practice: Negative signs in fractions
• Fractions of shapes
• Lesson
• Practice
• Counting regardless of arrangement
• Last number said is the number of objects
• Representing decimals using shaded rectangles
• Naming shapes (kindergarten)
• Lesson
• Practice
• Other resources
• Comparing numbers within 100
• Estimate lengths
• Lesson
• Practice
• Using different strategies to add and subtract (grade 2)
• Mentally add or subtract 10 or 100
• Length word problems
• Partitioning rectangles into rows and columns
• Other resources
• Lesson
• Practice
• Drawing angles in degrees
• Other resources
• Lesson
• Practice
• Add multiple two-digit numbers
• 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
• Building and drawing shapes
• 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)
• Translating to multiplication (word problems)
• Practice: Translating to multiplication (word problems)
• Lesson: Translating to multiplication (mathematical problems)
• Practice: Translating to multiplication (mathematical problems)
• 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
• Converting between words and arithmetic expressions
• Lesson
• Practice
• Reading line plots to add and subtract fractions
• 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
• Lesson
• Practice
• Other resources
• Find measures using rigid transformations
• Preserved properties of rigid transformations
• Lesson
• Practice
• Reading box plots
• Interpreting quartiles
• Identifying outliers from box plots
• Lesson
• Practice
• Lesson
• Practice
• Lesson
• Practice
• Interpreting graphs of functions
• Lesson
• Practice
• Interpreting linear expressions
• Lesson
• Practice
• Lesson
• Practice
• Constructing triangles
• 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
• Compose shapes (grade 1)
• 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
• Place value (grade 2)
• Using an abacus to represent whole numbers
• 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
• Lesson
• Practice
• Complex number conjugates
• Practice
• Formulas and units
• Word problems with multiple units
• Lesson
• Practice
• 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
• Lesson
• Practice
• Equivalent vectors
• Properties of exponents (algebra 2)
• Rewrite exponential expressions
• Equivalent exponential expressions
• Coordinate rules for reflection and rotation
• 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)
• Statistics and probability for high schoolers
• 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
• Addition, subtraction, and estimation (grade 4)
• Multiply fractions
• Measuring angles
• Decimal place value
• Add and subtract fractions (grade 5)
• Coordinate plane
• Coordinate plane word problems
• Lesson
• Practice
• Algebraic thinking
• Volume (grade 5)
• Dividing fractions
• Multiplying fractions
• Negative numbers
• Factors and multiples (grade 6)
• Arithmetic operations
• Data and statistics (grade 6)
• Variables and expressions
• Expressions, equations, and inequalities
• Fractions, decimals, and percentages
• Travel graphs
• Numbers and operations
• Solving equations with one unknown
• Linear equations and functions
• Data and modeling (grade 8)
• 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
• Solving linear systems of equations in two variables by any method
• Practice
• Practice
• Practice
• Linear pair theorem
• Using the formula: Area of a parallelogram
• Practice
• Lesson
• Solid geometry
• Congruence
• Solving a linear system from an arithmetic sequence
• Solving a linear system from a geometric sequence
• Practice
• Practice
• Practice
• 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)
• Simplifying nested square roots
• Intro
• Intro: Tangents of circles
• Tangent theorem 1
• Distance and midpoint of complex numbers
• Angles standing on the same arc are congruent
• Distance from center of circle to chord
• Find the radius given a chord
• Thales's theorem
• Congruent chords are equidistant from the center
• 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 function is invertible given ordered pairs
• Lesson
• Practice
• Restrict the domain then find the inverse
• Slope-intercept form word problem
• Solving systems of differential equations
• Proof
• Intro
• Lesson
• Practice
• Fractal dimension
• 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
• Solving polynomial and rational inequalities
• Solving and graphing higher-order polynomials
• Proofs
• Using the theorems
• Lesson
• Identify the value of the digit (grade 4)
• Lesson
• Practice
• Lesson
• Practice
• Lesson
• Practice
• Practice
• Intro
• Using the theorem
• Lesson
• Practice
• Lesson
• Practice
• Find the value of the decimal digit
• Intro to double integrals
• Changing the order of integration
• Solving equations by factoring
• Negative Fibonacci numbers
• Dividing square roots without variables
• Lesson
• Practice
• Lesson
• Practice
• Lesson
• Using the theorem
• Inequalities (geometry)
• 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
• Challenge
• Degree of a polynomial
• Factoring and solving polynomials by graphing
• 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
• Finding angles on parallel lines (easier)
• Converse of the corresponding angles postulate
• Converse of the alternate interior angles theorem
• Converse of the alternate exterior angles theorem
• Triangle proportionality theorem
• Proof
• Intro to extrema
• Maximizing profit (optimization problems)
• Challenge
• Challenge
• Challenge
• Challenge
• Challenge
• Challenge
• Pythagorean triples
• Intro
• Challenge
• Challenge
• Challenge
• Challenge
• Combining ratios (word problems)
• Lesson
• Practice
• Combining ratios (mathematical problems)
• Combining ratios
• Lesson
• Practice
• 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
• Lesson
• Practice
• 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
• The auxiliary angle method
• Explanation of the auxiliary angle method
• Challenge
• Challenge
• Odds and Threes
• Challenge
• Challenge
• Dicey Operations in Line
• Lesson
• Practice
• Challenge
• Determine whether linear, quadratic, or neither, using second differences
• Challenge
• Challenge
• Challenge
• Evaluating trigonometric functions by solving equations
• Lesson
• Practice
• Solving proportions using equivalent fractions
• Lesson
• Solving proportions using inverse operations
• Lesson
• Practice
• Solving rational equations (mathematical problems)
• Lesson
• Practice
• Proof
• Using the theorem
• Lesson
• Practice
• Challenge
• Egyptian Rope
• Using the Pythagorean theorem (harder mathematical problems)
• Lesson
• Practice
• Finding quadratic equations from tables using second differences
• Reducing to a linear equation
• Lesson
• Practice
• Challenge
• One-player games
• Properties of quadrilaterals
• Lesson
• Practice
• Lesson
• Lesson
• Practice
• Method 2
• Challenge
• Graphing harder absolute value equations
• Lesson
• Practice
• Combining like terms (concrete and visual method)
• Lesson
• Practice
• Proving the centers and point of contact are collinear
• 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
• 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
• Proving there are exactly three regular tessellations
• Proving properties of trees
• Intro to trees
• Challenge
• Challenge
• Proof
• Using the theorem
• Proof
• Using the theorem
• Proof
• Using the theorem
• Using the theorem
• Diagonals of a rectangle are congruent
• Proof 2
• Using the theorem
• Consecutive interior angles theorem
• Using the theorem
• Proof 1
• Proof
• Converse of the consecutive interior angles theorem
• Solving square root equations involving the distance formula
• Intro
• Using the theorem
• Challenge
• Using the theorem
• Proof
• Challenge
• Challenge
• Challenge
• Challenge
• Challenge
• Challenge
• Tidbits
• Tidbits on knot theory
• Intro
• Lesson
• Practice
• Lesson
• Challenge
• Challenge
• Integral ideals
• Proving multiples form an integral ideal
• Angle addition postulate
• Lesson
• Practice
• Lesson
• Practice
• Intro
• Proving the product rule from first principles
• Intro
• Intro
• Intro
• Proof
• Using the theorem
• Proving properties of even and odd functions (algebra 2)
• Lesson
• Practice
• Lesson
• Practice
• 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
• Parallel lines and transversal (culmination)
• Tidbits on integer sequences
• Principle of explosion
• Deductive, inductive, and abductive reasoning
• Lesson
• Practice
• Proof
• Intro
• Using the theorem
• Evaluating square roots of large perfect squares by trial and improvement
• 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
• Integrals involving quadratics
• Lesson
• Practice
• Sum, difference, and reverse power rules for indefinite integrals
• Practice
• Applications of integrals
• Using the formula
• Undetermined coefficients
• Proving inverse trig identities
• 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
• Linear inequalities (systems and graphs)
• 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
• Evaluating inverse trig functions using the unit circle
• Quadrants
• Lesson
• Practice
• Lesson
• Practice
• Memorizing the Pythagorean identities
• Right triangles and trigonometry
• Using the theorem
• Unit circle
• Non-right triangles and trigonometry
• 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
• Powers of the imaginary unit (precalc)
• Distributive property with variables (visual method, grade 7)
• Intro
• Proof
• Intro
• Proof
• Using the theorem
• Proof
• Using the theorem
• Proof
• Intro
• Proof
• Proof involving the incenter
• 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
• Deriving the equation of a hyperbola
• Reciprocal polynomials
• Adjacency lists, adjacency matrices, and incidence matrices
• Visualizing complex addition, subtraction, and scalar multiplication
• Multiplying complex numbers by scalars
• 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
• Lesson
• Practice
• 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
• Classifying triangles (culmination)
• 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
• Three categories of data
• Definitions of shapes
• Compose 2D and 3D shapes
• Halves and quarters
• One- and 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
• Equivalent fractions, concrete and visual
• 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
• 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
• Additive property of angles
• Geometric definitions
• Lines of symmetry
• Order of operations
• Convert between math and phrases
• 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
• Division involving whole numbers and 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
• Multiplication and division
• Factors, multiples, and patterns
• Equivalent fractions and comparing fractions
• Fraction arithmetic
• Understand decimals
• Geometry
• Units of measurement
• 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
• Classify shapes
• Unit conversion
• Volume by counting unit cubes
• Volume 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
• Ratio basics
• Unit rates
• Equivalent ratios
• Volume of cuboids, fractional lengths
• Coordinate plane
• Nets and surface area
• Divide fractions
• One-step equations
• Divide decimals
• Arithmetic with decimals
• Congruent supplements and complements theorems
• GCD and LCM
• Negative numbers in the real-world
• Negative numbers on the number line
• Absolute value word problems
• Plotting points in all four quadrants
• Identifying statistical questions
• Wishful thinking strategy
• Circumference and area of a circle
• Compound events and sample spaces
• Proving de Moivre's theorem
• Vertical and horizontal line tests
• Challenge: Different Darts
• 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
• GCD and LCM
• 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
• Combinations
• Cross sections
• Graphs of functions
• 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 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
• Quadratics: Multiplying and factoring
• Irrational numbers
• Solving literal linear equations
• Solving and graphing multi-step inequalities in one-variable
• Solving linear equations in standard form
• Other resources
• Transformations
• Solving one-step equations (geometry)
• Complementary and supplementary angles
• Using the circle theorems
• Classifying polygons
• Sum of interior angles for simple polygons
• Sum of exterior angles
• Polynomial graphs
• Other resources
• Additional topics
• Other resources
• Polynomials
• 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
• Other resources
• Other resources
• Other resources
• Other resources
• Other resources
• Other resources
• Other resources
• Other resources
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• Solving quadratic equations by taking square roots
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• Graphing trig functions
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