Math Theory Lessons
Browse lessons by school level, or search for a topic. Click any section to expand or collapse it.
Arithmetic
Addition Basics
Learn the fundamentals of adding numbers together.
Doubling and Halving
Learn to double numbers (multiply by 2) and halve numbers (divide by 2) quickly.
Estimating Products
Learn to estimate multiplication answers by rounding before multiplying.
Fact Families
Understand how addition and subtraction are related using fact families.
Mental Math Strategies
Learn tricks and strategies to solve math problems quickly in your head.
Missing Addends
Learn to find the missing number in addition problems using different strategies.
Mixed Addition and Subtraction
Practice solving problems that mix adding and subtracting in one expression.
Number Bonds
Learn pairs of numbers that add up to 10, 20, and 100 โ a mental math superpower.
Order of Operations
Learn the correct sequence for evaluating mathematical expressions.
Skip Counting
Learn to count by 2s, 5s, and 10s โ a helpful shortcut for quick counting.
Subtraction Basics
Learn how to subtract numbers and understand the concept of taking away.
Subtraction Strategies
Learn different ways to subtract numbers using mental math strategies like counting up and thinking addition.
Division
Division Basics
Learn what division is and how to split numbers into equal groups.
Long Division
Learn the step-by-step process for dividing larger numbers.
Understanding Remainders
Learn what remainders mean in division and how to interpret them in real-world problems.
Measurement
AM and PM
Understand the difference between AM and PM and how to tell time throughout the day.
Calendar Skills
Learn to read calendars, understand days and months, and calculate elapsed days.
Converting Measurement Units
Learn to convert between different units like inches to feet, centimeters to meters, and more.
Metric Units
Learn the metric system and how to convert between units of length, mass, and volume.
Measuring with Non-Standard Units
Learn to measure length, weight, and capacity using everyday objects like paperclips, hands, and cups.
Perimeter and Area Word Problems
Apply perimeter and area formulas to solve real-world problems.
Reading a Ruler
Learn to measure length using a ruler with inches and centimeters.
Reading Analog Clocks
Learn to tell time by reading the hour hand and minute hand on a clock face.
Time and Elapsed Time
Learn to read time, convert time units, and calculate how much time has passed.
Money
Budgeting and Unit Price
Compare costs, find best values, and make smart purchasing decisions.
Coin Values and Combinations
Learn the value of each coin and different ways to make amounts using pennies, nickels, dimes, and quarters.
Comparing Prices
Learn to compare prices and find the best deal using unit price, sales, and value comparison.
Counting Money
Practice counting coins and bills to find the total amount.
Dollar Bills and Paper Money
Learn to identify and count dollar bills, and combine bills and coins.
Making Change
Learn how to calculate change when buying items.
Sales Tax and Tips
Learn to calculate sales tax and tips using percentages in real-world shopping and dining situations.
Multiplication
Arrays and Groups
See multiplication visually using arrays, rows, and equal groups.
Multiplication Basics
Understand what multiplication is and how it relates to repeated addition.
Times Tables: 1 Through 5
Master the multiplication tables from 1 to 5 with tips and practice.
Times Tables: 6 Through 10
Master the multiplication tables from 6 to 10 with patterns and tricks.
Number Sense
Absolute Value
Understand absolute value as distance from zero on a number line.
Comparing Numbers
Learn how to compare whole numbers and understand place value.
Divisibility Rules
Learn quick tricks to tell if a number is divisible by 2, 3, 5, 10, and other numbers.
Estimating Sums and Differences
Learn to estimate answers by rounding before you add or subtract.
Even and Odd Numbers
Learn to tell if a number is even or odd by looking at the ones place.
Factors and Multiples
Learn the difference between factors and multiples, and find GCD and LCM.
GCF and LCM
Learn to find the Greatest Common Factor and Least Common Multiple of numbers.
Greater Than, Less Than, and Equal
Practice using >, <, and = to compare numbers and simple expressions.
Number Line Basics
Learn to read and use a number line to understand numbers, order, and distance.
Ordinal Numbers
Learn to use 1st, 2nd, 3rd and other ordinal numbers to show position and order.
Place Value
Understand how the position of a digit determines its value.
Prime Numbers
Learn what prime and composite numbers are and how to find them.
Rounding Numbers
Learn how to round whole numbers and decimals to a given place value.
Decimals
Adding and Subtracting Decimals
Master adding and subtracting decimal numbers by lining up the decimal point.
Comparing Decimals
Learn how to determine which decimal is larger or smaller.
Converting Between Decimals and Fractions
Master the skill of converting decimals to fractions and fractions to decimals.
Dividing Decimals
Learn how to divide decimal numbers step by step.
Multiplying Decimals
Learn how to multiply decimal numbers step by step.
Rounding Decimals
Learn to round decimal numbers to the nearest tenth, hundredth, or whole number.
Tenths and Hundredths
Understand decimal place value for tenths and hundredths using grids and real-world examples.
What Are Decimals?
Understand decimal numbers, place value, and how decimals relate to fractions.
Fractions
Adding and Subtracting Fractions
Learn how to add and subtract fractions with like and unlike denominators.
Finding Common Denominators
Learn to find common denominators to add and subtract fractions with different denominators.
Dividing Fractions
Learn how to divide fractions using the 'keep, change, flip' method.
Equivalent Fractions
Learn how different fractions can represent the same value.
Fraction Basics
Understand what fractions are, how to read them, and how to simplify.
Fractions as Parts of Shapes
See fractions visually by dividing shapes into equal parts.
Fractions on a Number Line
Learn to place fractions on a number line and understand their size and position.
Mixed Numbers and Improper Fractions
Convert between mixed numbers and improper fractions with confidence.
Multiplying Fractions
Learn how to multiply fractions and whole numbers by fractions.
Simplifying Fractions
Reduce fractions to their simplest form using the greatest common divisor.
What is a Fraction?
A gentle introduction to fractions โ what they mean and how to read them.
Negative Numbers
Adding and Subtracting Negative Numbers
Learn the rules for adding and subtracting when negative numbers are involved.
Integer Operations
Master adding, subtracting, multiplying, and dividing positive and negative numbers.
Introduction to Negative Numbers
Learn what negative numbers are and where they appear in real life.
Multiplying and Dividing Negative Numbers
Learn the sign rules for multiplication and division with negatives.
Patterns
AB and ABC Patterns
Learn to recognize, extend, and create repeating patterns with shapes, colors, and numbers.
Arithmetic and Geometric Series
Find sums of arithmetic and geometric sequences using series formulas and sigma notation.
Input-Output Tables
Find the rule that connects inputs to outputs in a function table.
Sequences and Mathematical Induction
Prove formulas and properties using mathematical induction with base case and inductive step.
Number Patterns
Recognize and extend patterns in sequences of numbers.
Sequences and Patterns
Identify arithmetic and geometric sequences, find nth terms, and recognize patterns.
Percentages
Discount and Sale Price
Calculate discounts, sale prices, and final costs with tax.
Finding a Percentage of a Number
Learn how to calculate percentages of numbers with practical examples.
Converting Fractions, Decimals, and Percentages
Learn to switch freely between fractions, decimals, and percentages.
Percent Increase and Decrease
Calculate percent change, markup, markdown, and percentage growth or decline.
Finding a Percent of a Number
Learn to calculate percentages of numbers using different methods.
Percentage Change
Calculate percentage increase and decrease in real-world situations.
Simple Interest
Calculate interest earned or paid using the formula I = PRT.
What is a Percentage?
Understand what percentages mean and how they show up in everyday life.
Ratios
Introduction to Ratios
Learn what ratios are and how to use them to compare quantities.
Proportions
Learn how to set up and solve proportions using cross-multiplication.
Ratio and Proportion Word Problems
Solve real-world problems using ratios and proportions.
Scale Drawings and Maps
Use scale factors to find real-world distances from drawings and maps.
Unit Rates
Learn what a unit rate is and how to use it to compare and calculate.
Word Problems
Word Problems: Addition and Subtraction
Practice turning word problems into addition and subtraction equations.
Draw a Picture Strategy
Learn to solve word problems by drawing pictures and diagrams.
Make a Table Strategy
Learn to solve problems by organizing information into tables with rows and columns.
Multi-Step Word Problems
Solve word problems that require two or more operations to find the answer.
Word Problems: Multiplication and Division
Learn to spot when a word problem needs multiplication or division.
Word Problem Strategies
Learn step-by-step strategies to solve any word problem with confidence.
Algebra
Absolute Value Equations and Inequalities
Solve absolute value equations and inequalities, understand distance interpretation.
Balance and Equality
Understand what the equals sign means and how to keep equations balanced.
Binomial Theorem
Expand binomial expressions using Pascal's triangle, binomial coefficients, and general term formula.
Combining Like Terms
Learn to simplify algebraic expressions by combining like terms.
Complex Numbers
Understand imaginary unit i, perform operations with complex numbers, and use the complex plane.
Determinants and Matrix Inverses
Calculate determinants, find inverse matrices, and solve systems using matrix algebra.
Determinants and Inverse Matrices
Calculate determinants, find inverse matrices, and understand their properties and applications.
Direct and Inverse Variation
Understand direct variation (y = kx) and inverse variation (y = k/x) relationships.
The Distributive Property
Learn to expand and simplify expressions using the distributive property.
Exponential Growth and Decay
Understand exponential functions and apply them to real-world growth and decay problems.
Factoring Expressions
Factor out the greatest common factor and recognize simple factoring patterns.
Function Composition and Inverse Functions
Compose functions f(g(x)), find and verify inverse functions fโปยน(x).
Graphing Linear Functions
Graph linear equations using slope-intercept form y = mx + b.
Graphing Quadratic Functions
Graph parabolas, identify vertex and axis of symmetry, understand transformations.
Imaginary & Complex Numbers
Discover numbers beyond real โ learn i, complex arithmetic, magnitude, and conjugates.
Introduction to Functions
Understand functions using input-output tables and function notation f(x).
Introduction to Matrices
Learn matrix notation, dimensions, and basic operations: addition, subtraction, and scalar multiplication.
Introduction to Polynomials
Understand polynomial terms, coefficients, and degrees. Add and subtract polynomials.
Linear Programming Basics
Graph systems of inequalities, identify feasible regions, and find optimal solutions at vertices.
Linear Relationships
Identify constant rates of change and understand slope in linear functions.
Literal Equations
Solve for a specific variable in formulas and multi-variable equations.
Logarithms
Understand logarithms as inverse of exponents, learn log properties and solve equations.
Matrix Multiplication
Multiply matrices, understand dimensions compatibility, and explore properties and applications.
Multiplying Polynomials
Multiply monomials, use distributive property with binomials, and apply the FOIL method.
Optimization Problems
Find maximum and minimum values using algebra, quadratic functions, and problem-solving strategies.
Order of Operations with Variables
Apply PEMDAS to expressions that contain variables.
Piecewise Functions
Evaluate and graph functions defined by different rules on different intervals.
Polynomial Division and Remainder Theorem
Divide polynomials using long division and synthetic division; apply Remainder and Factor Theorems.
Rational Expressions
Simplify, multiply, divide, add, and subtract algebraic fractions.
Rational Functions and Asymptotes
Graph rational functions; find vertical, horizontal, and slant asymptotes; identify holes.
Solving One-Step Equations
Learn how to solve simple equations with one operation.
Solving Quadratic Equations
Solve quadratic equations using factoring, square roots, and introduction to quadratic formula.
Solving Systems with Matrices
Solve systems of linear equations using matrix equations, row operations, and Gaussian elimination.
Solving Two-Step Equations
Learn how to solve equations that require two operations to isolate the variable.
Systems of Linear Equations
Solve systems using graphing and substitution methods to find where lines intersect.
Systems of Linear Equations
Solve systems with 3+ variables using substitution, elimination, and matrix methods.
Variables and Expressions
Learn what variables are and how to read and write algebraic expressions.
Writing Algebraic Expressions
Learn to translate words into mathematical expressions using variables and operations.
Writing Linear Equations
Write equations from two points, point-slope form, and real-world applications.
Combinatorics
Combinations and Permutations Deep Dive
Master counting principles, permutations with repetition, circular arrangements, and advanced combinations.
The Counting Principle
Learn the Fundamental Counting Principle to count outcomes of multi-step events using multiplication.
Pascal's Triangle
Explore Pascal's Triangle โ its construction, patterns, and connection to combinations and the binomial theorem.
Coordinate Geometry
Conic Sections Introduction
Understand circles, parabolas, ellipses, and hyperbolas as conic sections with standard equations.
Distance Between Points
Calculate the distance between two points on the coordinate plane.
The Distance Formula
Find the distance between two points on the coordinate plane using the distance formula.
The Coordinate Plane (All Four Quadrants)
Plot and identify points in all four quadrants using positive and negative coordinates.
Graphing Linear Equations
Learn to graph lines on the coordinate plane using tables and slope-intercept form.
The Midpoint Formula
Find the midpoint of a line segment on the coordinate plane.
Parametric Equations
Represent curves using parameters, convert between parametric and rectangular forms, graph parametric curves.
Polar Coordinates
Understand r and ฮธ notation, convert between polar and rectangular coordinates, graph polar equations.
The Coordinate Plane
Learn to plot and read points using the x-axis and y-axis.
Vectors in the Plane
Understand vector notation, magnitude, direction, component form, and vector operations.
Exponents
Exponent Basics
Learn what exponents mean and how to evaluate powers of numbers.
Introduction to Radicals
Understand square roots, simplify radicals, and perform basic radical operations.
Laws of Exponents
Learn the rules for multiplying, dividing, and raising powers to powers.
Negative Exponents
Understand negative exponents and how they relate to fractions and reciprocals.
Scientific Notation Basics
Learn to write very large and very small numbers in scientific notation.
Squares and Square Roots
Understand perfect squares and how to find square roots.
Geometry
3D Shapes
Learn to identify and describe three-dimensional shapes like cubes, spheres, cylinders, and cones.
Angle Relationships
Identify and work with complementary, supplementary, and vertical angles.
Angles Basics
Learn what angles are, how they are measured, and the main types.
Area Basics
Understand what area is and how to find it for rectangles, squares, and triangles.
Area of Triangles and Parallelograms
Calculate area using base and height formulas.
Basic 2D Shapes
Learn to identify and describe common shapes like circles, squares, triangles, and rectangles.
Circles - Advanced Topics
Learn about arcs, sectors, central angles, and arc length in circles.
Circles: Circumference and Area
Learn to calculate the distance around and space inside a circle.
Congruent and Similar Figures
Identify congruent and similar shapes, use scale factors, and find corresponding parts.
Geometric Proofs
Learn two-column proofs, triangle congruence postulates (SSS, SAS, ASA, AAS), and logical reasoning.
Introduction to Trigonometry
Learn basic trigonometric ratios: sine, cosine, and tangent for right triangles.
Law of Sines and Law of Cosines
Solve non-right triangles using Law of Sines and Law of Cosines.
Measuring Angles with a Protractor
Learn to use a protractor to measure and draw angles in degrees.
Parallel and Perpendicular Lines
Learn to identify parallel lines that never meet and perpendicular lines that form right angles.
Perimeter Basics
Learn what perimeter is and how to calculate it for common shapes.
Position and Direction
Learn to describe where things are using position words like left, right, above, below, and between.
The Pythagorean Theorem
Learn the relationship between the sides of a right triangle.
Quadrilaterals
Learn about four-sided shapes including squares, rectangles, trapezoids, rhombuses, and parallelograms.
Solving Trigonometric Equations
Solve equations involving trig functions using algebra, identities, and inverse functions.
Special Right Triangles
Master 45-45-90 and 30-60-90 triangles with their special side ratios.
Surface Area of 3D Shapes
Calculate surface areas of cylinders, cones, spheres, and composite shapes.
Surface Area of Rectangular Prisms
Calculate the total area of all faces of 3D rectangular boxes.
Symmetry and Transformations
Identify line symmetry and rotational symmetry using transformation rules.
Symmetry
Learn about lines of symmetry and rotational symmetry in shapes.
Transformations on the Coordinate Plane
Perform translations, reflections, and rotations on coordinate points and shapes.
Triangle Inequality Theorem
Understand which side lengths can form triangles and find possible ranges.
Trigonometric Graphs
Graph sine, cosine, and tangent functions; understand amplitude, period, phase shift, and vertical shift.
Trigonometric Identities
Learn and apply Pythagorean, reciprocal, quotient, sum/difference, and double-angle identities.
Types of Triangles
Classify triangles by their sides and angles.
Volume Basics
Learn what volume is and how to calculate it for boxes and cubes.
Volume of Cylinders, Cones, and Spheres
Calculate volumes of 3D curved shapes: cylinders, cones, and spheres.
Volume of Rectangular Prisms
Calculate the space inside 3D rectangular boxes using length, width, and height.
Precalculus
Introduction to Limits
Understand limits intuitively, evaluate limits, and explore one-sided limits and continuity.
Polar Coordinates and Parametric Equations
Convert between polar and Cartesian coordinates, graph polar equations, and understand parametric curves.
Probability
Binomial Distribution
Calculate binomial probabilities, understand trials and success probability, find expected value.
Compound Events
Learn how to find probabilities when two or more events are combined.
Compound Probability
Calculate probabilities of independent and dependent events using tree diagrams.
Conditional Probability
Understand P(A|B), independent vs dependent events, and Bayes' theorem.
Permutations and Combinations
Learn counting principles, permutations (order matters), and combinations (order doesn't matter).
Probability with AND and OR
Calculate probabilities of compound events using AND (multiplication) and OR (addition) rules.
Probability Basics
Understand what probability is and how to calculate simple probabilities.
Statistics
Box-and-Whisker Plots
Display data using five-number summary and identify quartiles and outliers.
Data Analysis and Regression
Analyze data using linear regression, correlation coefficients, and predictive modeling.
Data Analysis and Interpretation
Choose appropriate displays, analyze trends, and draw conclusions from data.
Double Bar Graphs
Learn to read and create double bar graphs that compare two sets of data side by side.
Line Plots (Dot Plots)
Learn to read and create line plots that show frequency data using X's or dots above a number line.
Mean, Median, Mode, and Range
Learn the four measures of central tendency and spread to describe data sets.
Mean, Median, and Mode
Learn the three main ways to find the center of a data set.
Normal Distribution and Z-Scores
Understand the bell curve, calculate z-scores, use the empirical rule, and find probabilities.
Normal Distribution Basics
Understand bell curves, z-scores, the 68-95-99.7 rule, and applications of normal distribution.
Reading Pictographs
Learn to read and understand pictographs โ graphs that use pictures to show data.
Probability from Data
Use frequency tables and collected data to calculate experimental probabilities.
Range and Outliers
Learn how to find the range of a data set and identify outliers.
Reading Bar Graphs
Learn how to read, interpret, and compare data using bar graphs.
Reading Simple Tables
Learn to find information in tables using rows, columns, and labels.
Scatter Plots
Plot data points to identify correlation, trends, and relationships between variables.
Standard Deviation and Variance
Measure data spread using range, variance, and standard deviation; understand ฯ notation.
Stem-and-Leaf Plots
Organize and display numerical data using stems and leaves to see distribution.
Tally Marks
Learn to count and record data using tally marks, an easy way to keep track.
Calculus
Applications of Derivatives
Apply derivatives to related rates, optimization, motion problems, and curve sketching.
Applications of Integrals
Calculate areas between curves, volumes of revolution, arc length, and real-world applications.
Integration Techniques
Master u-substitution, integration by parts, partial fractions, and trigonometric substitutions.
Introduction to Derivatives
Understand derivatives as rates of change, find slopes of tangent lines, and learn basic derivative rules.
Introduction to Integrals
Understand integrals as area under curves, learn antiderivatives, and explore Riemann sums basics.
Discrete Math
Graph Theory Introduction
Explore vertices, edges, paths, circuits, trees, and Euler paths in graph theory.
Number Bases: Binary, Hex & Decimal
Learn to convert between binary (base-2), hexadecimal (base-16), and decimal (base-10).