Lib Art

Liberal Arts Math Playlists

PROBLEM SOLVING

Introduction to Percent
Ex 1: Relating Fractions, Decimals, and Percents
Ex 2: Relating Fractions, Decimals, and Percents
The Percent Equation
Ex 1: Solve a Percent Problem Using a Percent Equation
Ex 2: Solve a Percent Problem Using a Percent Equation
Ex 3: Solve a Percent Problem Using a Percent Equation
Ex: Determine the Percent of a Number Using a Bar Graph
Ex: Change, Absolute Change, and Relative Change
Percent of Change
Ex 1: Determine a Percent of Change (decrease)
Ex 2: Determine a Percent of Change (increase)
Ex: Tax Percent Application - Find the Amount of FICA tax paid
Ex: Percent Applications - Changing Bases of Relative Change
Ex: Percent of Original Price Paid After Two Percentage Discounts
Ex: Weighted Average - Determine an Ending Percent or Grade of a Weighted Average
Ex: Proportion Application - Estimate Cost Based Upon Area
Ex: Proportion Application - Estimate Cost Based Upon Area
Rates and Unit Rates
American Unit Conversions
Perimeter and Area Formulas
Ex: Find the Number of Meters Traveled in 3 seconds Given Kilometers Per Hour
Unit Conversion Application - Number of Lemons for a Lemon Pie
Ex: Determine the Width of a Canyon Based Upon an Echo Time
Ex: Volume Conversion to Determine the Number of Cubic Yards of Soil Needed

GEOMETRY

Perimeter and Area

Volume / Surface Area / Misc

Introduction to Volume (1)
Introduction to Volume (2)
Determine the Volume of a Rectangular Prism (Whole Numbers)
Determine the Volume of a Cube (Decimals)
Volume of Stairs: Decomposing Volume (Right Rectangular Prisms)
Ex: Determine Volume of a Cone
Ex: Find the Surface Area of an Open Top Box
Find the Area of an Open Top Box
Ex: Volume of Pyramid
Find the Volume of a Cylinder
Volume of a Cylinder and a Pyramid
Find the Volume of a Sphere
Volume Between Two Spheres
Volume of the Empty Space in a Cubic Box with a Ball Inside
Determine the Percent of Volume of a Rectangular Pool (Box)
Will It Fit? Water Bottles and Volume of a Cylinder
Ex: Find the Volume of a Sphere When the Radius is a Fraction with a Radical
Ex: Determine the Surface Area of a Box (Right Rectangular Prism)
Determine the Surface Area of a Rectangular Prism (Whole Numbers)
Ex: Find the Surface Area of an Open Top Box
Find the Surface Area of an Open Top Box
Determine the Surface Area of a Cube (Decimals)
Find the surface Area of a Cylinder
Find the Surface Area of a Sphere

Geometric Applications

Ex: Builder's Level Application - Decimal Addition and Subtraction
Ex: Perimeter Application - Linear Feet of Baseboard Needed for a Room
Rectangle Perimeter Application: Feet of Fencing Required
Perimeter Application: Perimeter With and Without Edge
Circumference Application: Determine the Radius
Ex: Area Application - Area of an Inner Room with a Outer Footing
Application: Find the Radius of a Circle Given the Area

MEASUREMENT

American or Standard Units

American Unit Conversions
Household Measurements and Conversions
Non-Standard Unit Conversions (Unit Fractions)
Single Step Unit Conversion (US Standard - Unit Fractions)
Single Step Unit Conversion Applications (US Standard - Unit Fractions)
Common Customary Length Conversions Using Unit Fractions
Common Customary Weight Conversions Using Unit Fractions
Convert Inches to Feet and Feet to Inches
Convert Fluid Ounces to Half-Gallons Using Unit Fractions and Proportions
Convert Gallons and Quarts to Cups: Lemonade
Add Pounds and Ounces (Basic)
Multi-Step Unit Conversions (US Standard - Unit Fractions)
Convert Hours and Days to Seconds using Unit Fractions
Add and Subtract Time (Hours and Minutes)
Application: Subtract Hours and Minutes
Add and Subtract Gallons and Quarts
Ex: Determine Square Yards from Square Feet Application
Convert Square Feet to Square Yards (Unit Fractions)
Ex: Converting Between Different Units of Volume in Standard or American System
Ex: Converting Between Different Units of Weight in Standard or American System
Convert Between Ounces and Grams Using a Unit Fraction
Ex: Convert Between Different Units of Lengths Using Standard or American System
Ex: Convert Feet Per Second to Miles Per Hour
Ex: Convert Mile Per Hour to Feet Per Second
Ex: Convert Yards Per Second to Miles Per Hour
Ex: Unit Conversion / Proportion Application - Cost of Carpet
Unit Conversions of Area and Volume
Convert Area Units in Square Inches, Square Feet, and Square Yards
Determine Area in Square Inches and Square Feet
App: Determine a Volume of a Box in Cubic Inches and Cubic Feet
Determine Volume in Cubic Feet and Convert to Cubic Yards (Topsoil App)
Determine Volume in Cubic Feet and Cubic Yards (Conversion)

Currency Conversions

Convert U.S. Dollars to Euros Using a Unit Fraction
Convert Euros Per Liter to Dollar Per Gallon Using Unit Fractions
Converting Between Pesos and Dollars Using a Unit Fraction

Metric Units

Introduction to Metric Conversions
Metric Unit Conversions
Common Metric Length Conversions Using Unit Fractions
Common Metric Volume Conversions Using Unit Fractions
Common Metric Weight Conversions Using Unit Fractions
Compare Metric Units using Metric Conversions (Unit Fractions)
Convert Metric Units to US Standard Units (Unit Fractions)
Ex: Converting Between Metric Units
Ex: Metric Conversions Using Unit Fractions - Length
Ex: Metric Conversions Using Unit Fractions - Volume / Capacity
Ex: Metric Conversions Using Unit Fractions - Weight

Converting Between Standard and Metric Units

American to Metric and Metric to American Conversions
Convert Between Inches and Centimeters Using a Unit Fraction
Convert Between Gallons and Liters Using a Unit Fraction
Ex: Convert Lengths Between the Standard and Metric System
Ex: Convert Weight Between the Standard and Metric System
Converting Between Meters and Feet Using a Unit Fraction
Ex: Convert Volume Between the Standard and Metric System
Ex: Convert Height in Feet and Inches to Inches, Centimeters, and Meters
Convert Kiloliters to Quarts and Cups to Milliliters
Equations to convert between Celsius and Fahrenheit
Ex: Convert Temperature from Celsius to Fahrenheit
Ex: Convert Temperature from Fahrenheit to Celsius
Time Conversions
Convert Between Celsius and Fahrenheit Using an Equation
Convert Between Pounds and Kilograms Using a Unit Fraction

Unit Scale and Scale Factor

Unit Scale
Scale Factor
Proportion Applications: Map Scale Factor (Clear Fractions, No Cross Products)
Determine the Height of a Building Using a Scale Factor (Proportion)

VOTING THEORY

Introduction to Voting Theory and Preference Tables
Ex: Reading a Preference Table (Voting Theory)
Voting Theory: Fairness Criterion
Voting Theory: Plurality Method and Condorcet Criterion
Ex: Determine the Least Number of Votes Needed Using the Plurality Method
Voting Theory: Insincere Voting / Strategic Voting
Voting Theory: Instant Runoff Voting
Voting Theory: Monotonicity Criterion Using Instant Runoff Voting
Voting Theory: Borda count
Voting Theory: Copeland's Method
Voting Theory: Approval Voting

WEIGHTED VOTING

Introduction to Weighted Voting
Weighted Voting: Coalitions and Critical Players
Weighted Voting: The Banzhaf Power Index
Weighted Voting: The Shapley-Shubik Power Index

FAIR DIVISION

Introduction to Fair Division
Fair Division: The Divider-Chooser Method
The Divider-Chooser Method of Fair Division – Why It Is Meant Only for 2 Players
Fair Division: The Lone Divider Method
The Lone Divider Method: Why It Doesn't Pay To Be Greedy
Fair Division: The Last Diminisher Method
Fair Division: The Moving Knife Method
Fair Division: The Sealed Bid Method

APPORTIONMENT

Introduction to Apportionment
Apportionment: Hamilton's Method
Apportionment: The Alabama Paradox
Apportionment: The New States Paradox
Apportionment: The Population Paradox
Apportionment: Jefferson's Method
Apportionment: Webster's Method
Apportionment: Huntington-Hill Method
Apportionment: Lowndes' Method

GRAPH THEORY

Introduction to Graph Theory
Graph Theory: Dijkstra's Algorithm
Graph Theory: Euler Paths and Euler Circuits
Graph Theory: Fleury's Algorthim
Graph Theory: Eulerization
Graph Theory: Hamiltonian Circuits and Paths
Graph Theory: The Brute Force Algorithm
Graph Theory: Number of Routes and Circuits of a Complete Graph
Graph Theory: Nearest Neighbor Algorithm (NNA)
Graph Theory: Repeated Nearest Neighbor Algorithm (RNNA)
Graph Theory: Sorted Edges Algorithm (Cheapest Link Algorithm)
Graph Theory: Spanning Trees
Graph Theory: Kruskal's Algorithm

SCHEDULING

Introduction to Scheduling
Scheduling: The List Processing Algorithm Part 1
Ex: Scheduling - Create a Priority List Using the Decreasing Time Algorithm
Ex: Scheduling - Create a Priority List Using the Critical Path Algorithm
Scheduling: The List Processing Algorithm Part 2
Ex: Create a Schedule with Three Processors Using the List Processing Algorithm
Scheduling: The Decreasing Time Algorithm
Ex: Create a Priority List and Schedule Using the Decreasing Time Algorithm and List Processing Algorithm
Scheduling: The Critical Path Algorithm Version 1 (Part 1)
Scheduling: The Critical Path Algorithm Version1 (Part 2)
Scheduling: The Back Flow Algorithm Part 1
Scheduling: The Back Flow Algorithm Part 2

Finance: Simple and Compounded Interest

The Simple Interest Formula
Ex: Determine an Account Balance Using Simple Interest
Complete a Simple Interest Table Over 5 Years
Simple Interest: Find a Deposit Needed for a Balance in the Future
Simple Interest: Determine Doubling Time
Simple Interest: Determine the Interest Rate Needed for Doubling an Investment
Compounded Interest
Compare Simple Interest and Interest Compounded Annually
Compare Simple Interest and Interest Compounded Annually, Quarterly, and Monthly
Compounded Interest Table: Monthly Over 5 Months
Ex 1: Compounded Interest Formula – Quarterly
Ex: Compounded Interest Formula - Determine Deposit Needed (Present Value)
Lesson: Solving Compounded Interest Problems Using a TVM Solver
Compounded Interest Problems Using a TVM Solver: Solving for Time
Compounded Interest Problems Using a TVM Solver: Solving for Interest Rate
Account Balance and Interest Earned with Simple and Compounded Interest
Compounded Interest: Solve for Principal (Present Value)
Ex: TI84 TVM Solver - Present Value with Compounded Interest
Annual Percentage Yield (APY) Using a Formula (Monthly)
Annual Percentage Yield (APY) Using the TVM Solver on the TI-84 (Monthly)
Annual Percentage Yield (APY) Using a Formula (Quarterly)
Annual Percentage Yield (APY) Using the TVM Solver on the TI-84 (Quarterly)
Effective Yield for Compounded Interest
Compounded Interest (Slightly Different Form of Equation): Find Future Value
Effective Yield for Continuous Interest
Effective Interest Rate (Effective Yield)
Solving Exponential Equations for Time using Common Logs
Ex 2: Compounded Interest with Logarithms
Annual Rate of Return Need for Loss Recover and Additional Return on Investment
Determine the Annual Rate of Return Needed to Breakeven and Reach a Financial Goal After a Loss (1 Year Recover)
Determine the Annual Rate of Return Needed to Breakeven and Reach a Financial Goal After a Loss (2 Year Recover)

STATISTICS

Introduction to Statistics
Statistics: Sampling Methods
Statistics Control Groups and the Placebo Effect
Statistics: Introduction to Experiments and Confounding
Statistics: Sources of Bias
Statistics: Collecting Data Exercises

Normal Distribution / Sampling Distribution and Estimations

BINOMIAL DISTRIBUTION

Graph a Binomial Distribution and Find Probabilities Using Desmos (Definition)
Graph a Binomial Distribution and Find Probabilities Using Desmos
Complete a Binomial Distribution Table and Find Probabilities (By Hand)
Determine Binomial Probabilities Using Formulas: P(x=k)
Determine Binomial Probabilities Using the TI-84: P(x=k)
Determine Binomial Probabilities Using the TI-84: P(x=k), P(x<=k), P(x>=k)
Determine Binomial Probabilities Using Desmos P(x=k)
Determine Binomial Probabilities Using Desmos: P(x=k), P(x<=k)
Determine Binomial Probabilities of One Color from a Multinomial Probability Distribution
Find a Probability of a Binormal Distribution (Survival from Disease)
Find Probabilities of a Binormal Distribution (Coin Tosses)
Introduction to Multinomial Probabilities

PROBABILITY

Introduction to Probability Lesson
Introduction to Probability
Ex: Basic Example of Finding Probability - Running a Red Light
Ex: Basic Example of Finding Probability From a Table
Probability from a Table: Grades and Gender
Ex: Basic Probability Review Using Marbles
Probability Using 3 Colored and Numbered Marbles
Determine Basic Probability with Three Different Colored Marbles
Ex: Find Basic Probabilities When Rolling One Fair Die
Ex: Find Basic Probabilities Using a Deck of Cards
The Probability of a Roulette Wheel
Probability of Selecting a Card from a Deck of Playing Cards
Probability of Select a Letter, Consonant, and Vowel from a Sentence
Determine Probability from a Venn Diagram with Cardinality
Determine the Probability of the Complement of an Event (Percent)
Probability: The Probability of the Complement of an Event
Probability: The Probability of Independent Events
Probability of Independent Events: Weather

And, Or, and Conditional Probability Lesson
Counting, Permutations, Combinations, and Probability Lesson
Probability of Two Independent Events: Two Rolls of a Fair Die
Probability of Two Independent Events: Socks and Shirts
Probability: Determine the Probability of the Union of Events
Probability: Probability of Mutually Exclusive Events
"OR" Probability with Cards: Mutually Exclusive and Not - No Formulas
"OR" Probability with Cards: Mutually Exclusive and Not - Formulas
Determine P(A or B) Given Other Probabilities as Decimals
Introduction to Probability With and Without Replacement
Probability With and Without Replacement: Marbles
Probability With and Without Replacement: Draw 2 cards, One at a Time
Probability with Rolling Two Dice: And , Or (No Formulas)
Probability Without Replacement (Dependent): Selecting Students in Order
Conditional Probability Without Replacement: Draw 2 Cards, One at a Time
Conditional Probability of a Second Roll on a Fair Die Given a First Roll (Independent)
Probability: Probability of Events Not Mutually Exclusive
Determine Probability from a Venn Diagram (Basic, And, Or, Complement)
Ex: Determine a Probability with AND using a Table
Ex: Determine the Probability of a Union Using a Table (Not Mutually Exclusive - No Formula)
Ex: Determine the Probability of the Union of Two Events (OR)
Ex: Determine the Probability of a Union Using a Table (Not Mutually Exclusive)
Ex: Find the Probability of a Complement Using a Table
Ex: Find the Probability of Dependent Events Two Ways
Ex 2: Find the Probability of Dependent Events
Introduction to Conditional Probability
Ex: Find Conditional Probability Using a Table
Conditional Probability Using a Table: Pass a Course and Doing Homework

Find P(notB|notA) Given P(A), P(B), P(A and B) (Venn Diagram)
Conditional Probability with Marbles
Conditional, AND, and OR Probability Using a Table: Car Color and Tickets
Ex: Determine Conditional Probability from a Table
Conditional Probability Using a Table: Pregnancy Test
Conditional Probability Using a Venn Diagram: Dance Categories
Basic and Conditional Probability Using a Table: Car Color and Tickets
Probability Mixed Review: Bingo (Conditional, And, OR, and NOT)
Probability: Bayes’ Theorem
Conditional Probability Using a Table and Bayes' Theorem: Insurance
Conditional Probability Using a Table and Bayes' Theorem: Hospital Visits
Conditional Probability: Bayes’ Theorem – Disease Testing (Table and Formula)
The Counting Principle
The Counting Principle: Cars, Outfits, and Pizza
The Counting Principle: License Plates, Tests, Codes
Probability: The Counting Principle and Dependent Events
Counting: The Number of 4 Letter Codes from 6 Letters with Various Conditions
Counting: The Number of 5 Letter Passwords With and Without Repetition
Probability of 6 Letters With No Repetition
Probability of 3 letters With No Repetition are Vowels
Simplifying Factorial Expressions
Permutations
Combinations
Evaluate Combinations by Hand (No Calculator)
Permutation Examples
Combination Examples
Evaluate Factorials, Permutations, and Combinations Using a Free Online Tool (MOER/Mathas)
Evaluate Factorials, Permutations, and Combinations Using a Free Online Calculator
Factorials, Permutations and Combinations on the Desmos Scientific Calculator
Evaluate Factorials, Permutations, and Combinations Using Desmos
Combinations: The Number of 3 Member Committees from 34 People
Counting: Find the Number of 5 1 Digit Number Picks (Perm and Comb)
Counting Problems
Probability of 4 letters With No Repetition are Vowels
Probability of 3 letters With Repetition are Vowels
Probability a 5 Digit PIN has No Repeated Digits
Probability: Determining Probability Using Combinations
Determining Probability with Combinations
Probability with Combinations
Probability of Drawing Two Hearts (Combinations and Conditional)
Probability of Drawing Two Aces (Combinations and Conditional)
Probability of Drawing Two Face Cards (Combinations and Conditional)
Probability of 5 Card Hands Using Combinations: Part 1
Probability of 5 Card Hands Using Combinations: Part 2
Conditional, AND, and OR Probability Using a Table: Car Color and Tickets
Probability of Male/Female Committee Members Using Combinations

Expected Value Lesson
Expected Value
Ex: Expected Value
Expected Value: Life Insurance
Expected Value: Raffle
Expected Value of a Discrete Probability Distribution
Find Probabilities and Expected Value of a Discrete Probability Distribution
Find a Probability of a Binormal Distribution (Survival from Disease)
Find Probabilities of a Binormal Distribution (Coin Tosses)

Introduction to Odds Lesson
Ex: Determine Odds from Given Information (Basic)
Ex: Determine Probability Given Odds
Odds of a Roll when Rolling a Single Die
Find Probability from Odds
Probability and Odds of Selecting a Card Face from a Deck of Playing Cards
Determine Odds of a Roulette Wheel
Determine the Complement and Odds of an Event Given Probability (Decimal)
Determine the Complement and Odds of an Event Given Probability (Percent)

HISTORICAL COUNTING SYSTEMS

Inca Counting Boards
The Inca Quipu
Convert Numbers in Different Bases to Base Ten
Ex: Convert Base-12 to Base-10
Convert Numbers in Base Ten to Different Bases: Remainder Method
Convert Numbers in Base Ten to Different Bases: Calculator Method
Convert a Base-10 Number to Base 12
Convert a Base-10 Number to Base-60
Convert a Base-10 Number to a Decimal to Base-60
Convert a Base-12 Number to Base-10
Convert a Base-60 Number to Base-10
Convert a Base-60 Number to Base-10 with a Decimal
The Mayan Number System: Writing Mayan Number in Base 10
The Mayan Number System: Writing Base 10 Numbers as Mayan Number (base 20)
The Mayan Number System: Addition of Mayan Numbers

CRYPTOGRAPHY

Cryptograph: Substitution Cipher (Caeser Cipher)
Cryptography: Transposition Cipher
Cryptography: Caesar Cipher With Shift
Modular Arithmetic

SETS

Sets and Venn Diagrams In Class Exercises
Introduction to Set Theory
Finite and Infinite Sets
Introduction to Subsets
Sets: Elements Of and Subsets
Determining Subsets Using a Venn Diagram
Determine the Cardinality of Sets From a List of Set
Equal and Equivalent Sets
Set Operations and Venn Diagrams - Part 1 of 2
Set Operations and Venn Diagrams - Part 2 of 2
Solving Problems Using Venn Diagrams
Ex: Find the Union and Intersection of Two Sets Using a Venn Diagram
Ex: Find the Union and Intersection of Two Sets Without a Venn Diagram
Ex: Find the Intersection of a Set and A Complement Using a Venn Diagram
Ex: Find Intersections and Unions of Three Sets Using a Venn diagram (short)
Ex: Find Intersections and Unions of Three Sets Without Using a Venn diagram (short)
Ex: Find Intersections and Unions of Three Sets Using a Venn diagram (long)
Ex: Find Intersections and Unions of Three Sets Without Using a Venn diagram (long)
Ex: Determine Cardinality of the Intersection of Two Sets Using a Venn Diagram
Ex: Determine Cardinality of the Intersection of Two Sets Without Using Venn Diagram
Ex: Determine Cardinality of Various Sets Given a Venn Diagram of Three Sets
Ex: Determine Cardinality of the Intersection of Three Sets Using a Venn Diagram
Ex: Determine Cardinality of the Intersection of Three Sets Without Using Venn Diagram
Problem Solving with Venn Diagrams: Cardinality of a Universal Set
Use a Venn Diagram to Determine the Cardinality of a Set: n(not C and not D)
Ex: Find the Number of Element in the Intersection of Two Sets Using a Venn Diagram
Ex: Set Problem Solving - Find the Number of Element in the Intersection of Two Sets Using a Formula
Ex 1: Set Problem Solving - Find the Number of Element in the Union of Two Sets Using a Venn Diagram
Ex 1: Set Problem Solving - Find the Number of Element in the Union of Two Sets Using a Formula
Ex 2: Find the Number of Element in the Union of Two Sets Using a Venn Diagram
Ex 2: Set Problem Solving - Find the Number of Element in the Union of Two Sets Using a Formula
Ex: Determine How Many Elements in a Set With a Venn Diagram (Movies)
Ex: Determine How Many Elements in a Set Without a Venn Diagram (Movies)
Ex 1: Problem Solving With Venn Diagrams (Cardinality of Intersection)
Ex 2: Problem Solving With Venn Diagrams (Cardinality of A Intersect B Complement)
Ex 3: Problem Solving With Venn Diagrams (Cardinality of Complement of (A Union B)
Ex 4: Problem Solving With Venn Diagrams (Cardinality of A Intersect B Complement)
Determine the Number Elements in a Set From a Venn Diagram
Use a Venn diagram to Determine Cardinality of Sets (Level 1)
Use a Venn diagram to Determine Cardinality of Sets (Level 2)
Find Complement, Union, and Intersection of 2 Sets as Lists
Find the Intersections and Union of Three Sets as Lists
Venn Diagrams and Percentages: Survey Results Social Media
Venn Diagrams and Cardinality: Tea or Coffee Survey Results
Determine Cardinality of Sets Using a Venn Diagram
Determine Cardinality of Sets Using a Completed Venn Diagram: 3 Subjects
Determine Cardinality of Sets Using a Completed Venn Diagram: Vehicles
Determine the Cardinality of an Intersection of Two Sets
Complete a Venn Diagram With Cardinality: Math, English, History
Complete a Venn Diagram With Cardinality: Brand, Color, Size
Complete a Venn Diagram From Survey: Coffee and Tea
Determine the Cardinality of an Universal Set Using a Venn Diagram
Determine the Cardinality of a Set Given Cardinality of Union and Intersection

Logic

If-Then Statements and Converses
The Converse, Contrapositive, and Inverse of an If-Then Statement
Truth Tables for Compound Statements
Truth Tables for Conditional Statements
Truth Table for the Biconditional Statement
Truth Tables: Showing Statements are Equivalent

Miscellaneous

Introduction to Contact Tracing: Tracing the Exposure to a Virus
Math and Medicine: Intro to Calculating Dosages
Intro to Power Usage and Cost
Math and Sports: The Number of Games In a Round-Robin Tournament
Math and Sports: The Number of Games In a Single-Elimination Tournament