Chycho – The Language of Mathematics

Content on this page is geared towards teaching the syntax of the language of mathematics, the rules and principles that we use in math. See Math in Real Life for a look at how we can use this information to enhance our lives.

Lessons:
Series I

Section 1: Introduction and Instructions
Videos: (1): Introduction and (2): Instructions

Section 2: The Real Number Set
Videos: (3): The Real Number Set – Part 1, (4): The Real Number Set – Part 2, and (22): Instructions for Exercises – 1

Section 3: Zero and Infinity
Videos: (5): Zero and Infinity

Section 4: Basic Operations
Lesson 1: Adding and Subtracting
Videos: (6): Adding and Subtracting
Lesson 2: Multiplying and Dividing
Videos: (8): Multiplying and Dividing
Lesson 3: Dealing with Negative Numbers
Videos: (7): Dealing with Negative Numbers

Section 5: Prime Numbers
Lesson 1: Understanding Prime Numbers
Videos: (9): Prime Numbers
Lesson 2: Finding Prime Factors
Videos: (10): Finding Prime Factors

Section 6: Fractions
Lesson 1: Reducing Fractions
Videos: (11): Reducing Fractions
Lesson 2: Multiplying and Dividing Fractions
Videos: (12): Multiply and Divide Fractions
Lesson 3: Adding and Subtracting Fraction
Videos: (13): Adding and Subtracting Fraction

Section 7: Trigonometry
Lesson 1: Introduction to Trigonometry and Geometry
Videos: (14): Introduction to Trigonometry
Lesson 2: Understanding Right Triangles
Videos: (15): Right Triangles Part 1, (16): Right Triangles Part 2, and (17): Right Triangles Part 3
Lesson 3: Solving Right Triangles
Videos: (18): Solving Right Triangles 1 and (19): Solving Right Triangles 2

Section 8: Basic Geometry
Lesson 1: Parallel Lines
Videos: (31): Parallel Lines
Lesson 2: Congruent and Similar Triangles
Videos: (20): Congruent Similar Triangles 1 and (21): Congruent Similar Triangles 2

Section 9: Coordinate Geometry
Lesson 1: Cartesian Coordinate System
Videos: (23): Cartesian Coordinate System
Lesson 2: Slope and Midpoint of a Line
Videos: (24): Slope and Midpoint of a Line
Lesson 3: Distance of a Line
Videos: (25): Distance of a Line

Section 10: Proofs
Lesson 1: Introductions to Proofs
Videos: (26): Introductions to Proofs
Lesson 2: Proofs Involving Triangles
Videos: (30): Proofs Involving Triangles
Lesson 3: Proofs Involving a Line
Videos: (27): Proofs Involving a Line 1, (28): Proofs Involving a Line 2, and (29): Proofs Involving a Line 3
Lesson 4: Coordinate Geometry Proof
Videos: (32): Coordinate Geometry Proof 1 and (33): Coordinate Geometry Proof 2

Section 11: Why a negative and a negative makes a positive
Videos: (35): why 2 negatives make a positive

Section 12: Book Recommendations
Videos: (57): Book Recommendations (Part 1 of 2) and (58): Book Recommendations (Part 2 of 2)

Section 13: Miscellaneous Videos
Videos: (34): Prepping for next set of videos (update 1) and (36): First Series Montage with SPM and (37): Update for Series II (update 2)

Series II

Section 1: Exponents and Radicals
Lesson 1: Introduction and Layout
Videos: (38): Exponents and Radicals (intro) and (39): Exponents and Radicals Layout

Lesson 2: Exponents and Radicals with Real Number Set (Introduction)
Videos: (40): Exponents and Radicals (Real 1 of 2) and (41): Exponents and Radicals (Real 2 of 2)

Lesson 3: Exponents and Radicals with Examples (Introduction)
Videos: (42): Exponents and Radicals (1 of 3), (43): Exponents and Radicals (2 of 3), and (44): Exponents and Radicals (3 of 3)

Lesson 4: Rules for Adding and Subtracting
Videos: (45): Rules for Adding and Subtracting Exponents and Radicals

Lesson 5: Rules for Multiplying and Dividing
Videos: (46): Rules for Multiplying and Dividing Exponents and Radicals

Lesson 6: Rules for Exponents to Exponents
Videos: (47): Rules for Exponents to Exponents

Lesson 7: Reducing Radicals
Videos: (48): Reducing Radicals

Lesson 8: Multiplying Radicals Example
Videos: (49): Multiplying Radicals (example 1)

Lesson 9: Adding and Subtracting Radicals Example
Videos: (50): Adding and Subtracting Radicals (example 1)

Lesson 10: Simplifying Radicals Examples
Videos: (51): Simplifying Radicals (3 examples)

Lesson 11: Creating Large Radicals
Videos: (52): Creating a Large Radicals Problem (Part 1 of 4), (53): Creating a Large Radicals Problem (Part 2 of 4), (54): Creating a Large Radicals Problem (Part 3 of 4), and (55): Creating a Large Radicals Problem (Part 4 of 4)

Lesson 12: Simplifying Large Radicals
Videos: (56): Simplifying Large Radicals

Series 3a

Section 1: Summary of Series I and II, and Introduction to Series III
Videos: (61): Summary of Series I and II, and Introduction to the Equal Sign

Section 2: Black Holes and Elementary Particles
Videos: (62): Black holes and elementary particles (Part 1) and (63): Black holes and elementary particles (Part 2)

Section 3: Techniques for Solving Equations
Lesson 1: The Equal Sign: The difference between solving an equation and simplifying an expression
Videos: (64): The equal sign allows us to enter the world of applied mathematics
Lesson 2: Addition and Subtraction
Videos: (65): Solving Equations – Addition and Subtraction
Lesson 3: Multiplying and Dividing
Videos: (67): Solving Equations – Multiplication and Division
Lesson 4: Exponents and Radicals
Videos: (68): Solving Equations – Exponents and Radicals
Lesson 5: Cross Multiplication
Videos: (69): Solving Equations – Cross Multiplication

Section 4: Solving Equations and Checking Solutions
Lesson 1: Introduction to Examples and Methods
Videos: (70): Solving Equations – Introduction to Examples and Methods and (71): Solving Equations – What are we solving for?
Lesson 2: Examples 1: Solving and Checking
Videos: (72): Solving Equations – Example 1, Part 1 of 3, (73): Solving Equations – Example 1, Part 2 of 3, and (74): Checking the Solution – Example 1, Part 3 of 3
Lesson 3: Examples 2 & 3: Solving Using Two Methods
Videos: (75): Solving Equations – Example 2, Two Methods and (76): Solving Equations – Example 3, Using Two Methods
Lesson 4: Four Examples of Simple Equations
Videos: (77): Solving Equations – Four Examples of Simple Equations
Lesson 5: How not to solve an equation: Do not eliminate solutions
Videos: (83): How not to solve an equation: Do not eliminate solutions
Lesson 6: Finding Restrictions for Equations: No Dividing by Zero
Videos: (87): Finding Restrictions for Equations – No Dividing by Zero (Part 1) and (88): Finding Restrictions for Equations – No Dividing by Zero (Part 2)

Section 5: Solving Quadratic Equations: Factoring Techniques
Lesson 1: Introduction to Quadratic Equations and Functions
Videos: (78): Introduction to Solving Quadratic Equations (Part 1) and (79): Introduction to Solving Quadratic Equations (Part 2)
Lesson 2: Factoring: Greatest Common Factor
Videos: (80): Factoring: Part 1 – Greatest Common Factor (GCF), (81): Factoring: Part 2 – Greatest Common Factor (GCF), and (82): Factoring: Part 3 – Greatest Common Factor (GCF)
Lesson 3: Solving and Graphing Solutions: GCF
Videos: (84): Solving and Graphing Equations – Greatest Common Factor (GCF)
Lesson 4: Factoring: Simple Trinomial Factoring
Videos: (85): Factoring: Part 4 – Simple Trinomial Factoring and (86): Factoring: Part 5 – Three examples of Simple Trinomial Factoring

Factoring polynomials continues in Series IIIb

Section 6: Introduction to Polynomial Functions
Videos: (89): Understanding Polynomials and Defining Terms (Part 1 of 3), (90): Understanding Polynomials and Defining Terms (Part 2 of 3), and (91): Understanding Polynomials and Defining Terms (Part 3 of 3)

Section 7: Miscellaneous

Series IIIb

Section 1: Recaps and Introductions
Video: (97): Recap of Series I, II, and IIIa

Video: (98): Introduction to Series IIIb

Video: (105): Why Do We Factor? Introduction to Factoring Polynomials

Video: (122): Factoring Polynomials, a Graphical Representation

Section 2: Difference of Squares
Continues from Section 5 of Series IIIa

Lesson 1: Videos: (99): Factoring: Part 6 – Difference of Squares (Part 1) , (100): Factoring: Part 7 – Difference of Squares (Part 2), 6 Examples, and (101): Factoring: Part 8 – Difference of Squares (Part 3), Be Careful With The Following

Lesson 2: Videos: (102): Difference of Squares: Solving Equations, a Graphical Representation (Part 1) , (103): Difference of Squares: Solving Equations, a Graphical Representation (Part 2), and (104): Difference of Squares: Solving Equations, a Graphical Representation (Part 3)

Section 3: Factoring Complex Trinomials using the 4-Step Method
Videos: (106): Factoring: Part 9 – Complex Trinomials (Part 1), 4-Step Method , (107): Factoring: Part 10 – Complex Trinomials (Part 2), 4-Step Method, (108): Factoring: Part 11 – Complex Trinomials (Part 3), 4-Step Method – Ex. #2, and (109): Factoring: Part 12 – Complex Trinomials (Part 4), 4-Step Method – Ex. #3

Section 4: The Quadratic Formula
Videos: (110): Factoring: Part 13 – Quadratic Formula (Part 1): Introduction , (111): Factoring: Part 14 – Quadratic Formula (Part 2): Ex. #1, and (112): Factoring: Part 15 – Quadratic Formula (Part 3): Ex. #2 & #3

Section 5: The Let Statement
Videos: (113): Factoring: Part 16: Let Statement (Part 1): Substitution , (114): Factoring: Part 17: Let Statement (Part 2): Quadratic Formula, (115): Factoring: Part 18: Let Statement (Part 3): Quadratic Formula,and (116): Factoring: Part 19: Let Statement (Part 4): Quadratic Formula, Checking Solutions

Section 6: Synthetic Division and The Division Statement

Lesson 1: Introduction, Long Division, and The Division Statement
Videos: (117): Factoring Part 20: Synthetic Division Part 1: Introduction , (118): Factoring Part 21: Synthetic Division Part 2: Long Division, The Division Statement, and (119): Factoring Part 22: Synthetic Division Part 3: The Division Statement

Lesson 2: Polynomial Long Division
Videos: (120): Factoring Part 23: Synthetic Division Part 4: Polynomial Long Division (Part 1) , (121): Factoring Part 24: Synthetic Division Part 5: Polynomial Long Division (Part 2), (123): Factoring Part 25: Synthetic Division Part 6: Polynomial Long Division (Part 3), and (124): Factoring Part 26: Synthetic Division Part 7: Polynomial Long Division (Part 4)

Lesson 3: Video: (125): The Division Statement, a Graphical Representation

Lesson 4: Synthetic Division
Videos: (126): Factoring Part 27: Synthetic Division Part 8: Part 1 – When to Use It , (127): Factoring Part 28: Synthetic Division Part 9: Part 2 – Be Careful With the Following, (128): Factoring Part 29: Synthetic Division Part 10: Part 3 – A Simple Example #1, and (129): Factoring Part 30: Synthetic Division Part 11: Part 4 – A Simple Example #2

Lesson 5: Factoring Large Polynomials
Videos: (130): Factoring Part 31: Synthetic Division Part 12: Part 5 – Introduction to Factoring Large Polynomials , (131): Factoring Part 32: Synthetic Division Part 13: Part 6 – Factoring Large Polynomials, Ex1, (132): Factoring Part 33: Synthetic Division Part 14: Part 7 – Factoring Large Polynomials, 2a, (133): Factoring Part 34: Synthetic Division Part 15: Part 8 – Factoring Large Polynomials, 2b, (134): Factoring Part 35: Synthetic Division Part 16: Part 9 – Factoring Large Polynomials, 3a, and (135): Factoring Part 36: Synthetic Division Part 17: Part 10 – Factoring Large Polynomials, 3b

Section 7: The Remainder Theorem and The Factor Theorem
Video: (142): The Remainder Theorem and The Factor Theorem

Section 8: Why Math is Important
Videos: (137): Why is Math Important? Part 1: Five Reasons Why Math is Important , and (138): Why is Math Important? Part 2: Because it’s part of evolution, part of what makes us human

Section 9: Study Tips
Lesson 1: Videos: (139): How to Study: Introduction , (140): How to Study: Tip #1: Why Are You Here?, and (141): How to Study: Tip #2: Longer is Better (Introduction to Efficiency)