Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Development How-TOs Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling; and for avid readers not in school. See Site Map

Logic 5 Chapters Arithmetic 10 Steps Algebra 12 Starter Steps & 5 Advanced Steps
Work & Study 23 Tips Geometry 15 Steps Calculus 70 Lessons

Ages 15+: Why study slopes Polynomials Quadratics Why factor polynomials Logarithms Functions
What is similarity Euclidean geometry leanly Coordinates + complex no.s Vectors DC Electric Circuits
Ages 12+: Prime factorization Written work formats Decimal place value Extend arithmetic skills orally
What is a variable 5. Fraction Operations by Raising Terms Solving Linear Equations: Take I Take II

Online Volumes: 1 - Elements of Reason, 2 - 3 Skills For Algebra, 3 - Why Slopes and
More Math, 1A - Pattern Based Reason, 1B - Skill Development Principles + Troubles

Welcome: Site content may develop critical thinking, improve reading and writing, and build mathematics skills. See online chapters on on logic and pattern based reason.

Teachers: This December 2011, 5-phase framework offers a context for mathematics & logic instruction. Phases 1 to 3 focus on skills with actual or potential value for adult & daily life. College-oriented phases 5 & 4 focus on calculus & preparation for it. Phases 1 to 4 may also serve trades & professions not dependent on calculus.

Site Review: Math resources ... span ... arithmetic, logic, algebra, calculus, complex numbers, and Euclidean geometry. Lessons and how-tos .... provide a good foundation for high school and college ... mathematics. Read more.

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34 matches:

  1.    wt: 8:   2 Natural Logarithms Exponentials Powers Roots/
  2.    wt: 3:   3 Quadratics Geometrically/
  3.    wt: 3:   10 Examples of Algebraic Reasoning/
  4.    wt: 3:   Step 3 Easy systems in 2 or more unknowns/
  5.    wt: 3:   Step 2 Algebraic solutions for one unknown/
  6.    wt: 2:   5 Factored Polynomial Sign Analysis Examples/
  7.    wt: 2:   4 Functions/
  8.    wt: 2:   1 Five Polynomial Operations/
  9.    wt: 2:   More Algebra/
  10.    wt: 2:   3 Cartesian and Polar Coordinates/
  11.    wt: 2:   A Origins of Counting and Figuring Methods/
  12.    wt: 2:   8 Unifying Theme For Algebra/
  13.    wt: 2:   Step 4 Gaussian Elimination/
  14.    wt: 2:   Step 1 Stick diagram and fractions/
  15.    wt: 2:   3 Solving Linear Equations/
  16.    wt: 2:   2 Formula Forward Use Evaluation/
  17.    wt: 2:   3 Prime Factorization Skills/
  18.    wt: 1:   Direct Current Electric Circuits/
  19.    wt: 1:   B Real Numbers Extrinsic Development/
  20.    wt: 1:   9 Proportionality Backwards and Forwards/
  21.    wt: 1:   7 Axioms Logic and Equivalent Equations/
  22.    wt: 1:   6 More Less Greater Than Inequalities and Comparison/
  23.    wt: 1:   5 Real Numbers/
  24.    wt: 1:   4 Computation Rules and Function Notation/
  25.    wt: 1:   1 Working With Sets/
  26.    wt: 1:   Algebra Starter Lessons/
  27.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  28.    wt: 1:   11 Squares and Square Roots/
  29.    wt: 1:   C Decimal Multiplication Methods/
  30.    wt: 1:   4 Lessons on Using Derivatives/
  31.    wt: 1:   38 Lessons on Calculating Derivatives/
  32.    wt: 1:   Volume 2 Three Skills For Algebra/
  33.    wt: 1:   Volume 1 Elements of Reason/
  34.    wt: 1:   Mathematics Skill Development Framework/

Web Page Search

253 matches:

  1.    wt: 3:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  2.    wt: 3:   2 Algebraic use of function notation
  3.    wt: 3:   8 quadratics backward use of various formulas
  4.    wt: 3:   7 Formulas for Roots with Logarithms Derivation
  5.    wt: 3:   6 Formulas for Even and Odd Roots with Logarithms
  6.    wt: 3:   3 Natural Logarithms and Exponentials Basic Properties
  7.    wt: 3:   27 Logarithmic use of products of sines and cosines
  8.    wt: 3:   21 Logarithms Powers and Exponentials
  9.    wt: 3:   38 Formulas and derivatives for powers and roots
  10.    wt: 3:   Chapter 24 Logarithms Powers and Exponentials
  11.    wt: 3:   Chapter 19. Exponentials and Natural Logarithms
  12.    wt: 2:   5 logarithms and exponentials etc
  13.    wt: 2:   9 Formulas for Real Exponents with Logarithms
  14.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  15.    wt: 2:   4 Resultant of a Sum of Movements
  16.    wt: 2:   26 Formulas for products of sines and cosines
  17.    wt: 2:   22 sine of 22.5 degrees via half angle formulas
  18.    wt: 2:   20 N th Roots of Complex Numbers
  19.    wt: 2:   19 N th Roots of Unity
  20.    wt: 2:   18 Sixth Roots of Unity
  21.    wt: 2:   17 Cube Roots of unity
  22.    wt: 2:   5 An Easy Proof of the Distributive Law
  23.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  24.    wt: 2:   5 Algebraic View of Slopes
  25.    wt: 2:   8 More Use of Maps Not Drawn to Scale
  26.    wt: 2:   21 Addition of Multiples of a Single Vector
  27.    wt: 2:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  28.    wt: 2:   4 A Brief Story of numbers and algebra
  29.    wt: 2:   3 Properties of Square Roots with example
  30.    wt: 2:   C Counting Areas with Powers of Ten
  31.    wt: 2:   B Powers of Ten
  32.    wt: 2:   10 Names for Big Numbers and Powers of Ten Expansion
  33.    wt: 2:   Quick history of numbers and algebra
  34.    wt: 2:   17 Derivatives of quotients of sine and cosine
  35.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  36.    wt: 2:   E2 Algebraic Properties of Limits
  37.    wt: 2:   Chapter 15. Algebraic Evaluation of Limits
  38.    wt: 2:   Chapter 31 Direct and Indirect Reason
  39.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  40.    wt: 2:   Chapter 24 Direct and Indirect Reason
  41.    wt: 1:   Ramblings Introduction Algebra Essay
  42.    wt: 1:   Skills Chapter 3 Algebra
  43.    wt: 1:   4 algebra
  44.    wt: 1:   Mathematics Education Professors
  45.    wt: 1:   talk the algebra talk
  46.    wt: 1:   geometric implications for algebra
  47.    wt: 1:   teaching tutoring algebraic reason
  48.    wt: 1:   Lessening Algebra Difficulties
  49.    wt: 1:   the trouble with algebra
  50.    wt: 1:   Theory of Knowledge
  51.    wt: 1:   Different Kinds of Reasoning in maths
  52.    wt: 1:   three kinds of reason in mathematics
  53.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  54.    wt: 1:   C Energy Power03
  55.    wt: 1:   E Wire Resistance Calculation03
  56.    wt: 1:   E Kirchoffs Second Law
  57.    wt: 1:   D Kirchoff First Law
  58.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  59.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  60.    wt: 1:   8 The Effect of Negative Remarks
  61.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  62.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  63.    wt: 1:   15 Sign analysis of functions
  64.    wt: 1:   8 Set view of relations and functions
  65.    wt: 1:   1 Geometric Introduction of Function Notation
  66.    wt: 1:   4 quadratics difference of two squares
  67.    wt: 1:   5 Natural Logarithm Calculator Exercises
  68.    wt: 1:   Rewriting algebraic substitution as function substitutions
  69.    wt: 1:   11 arctan left inverse of tangent Graph
  70.    wt: 1:   10 arctan left inverse of tangent Definition
  71.    wt: 1:   8 arcsin left inverse of sine Graph
  72.    wt: 1:   7 arcsin left inverse of sine Definition
  73.    wt: 1:   6 Graph of arccos function
  74.    wt: 1:   3 Left Inverse of cosine arccos definition
  75.    wt: 1:   8 Radian Measures of Common Angles
  76.    wt: 1:   2 Radian Measure Numerical Value of one degree
  77.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  78.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  79.    wt: 1:   Straight Lines Intersection of
  80.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  81.    wt: 1:   17 tangent function angle sum formulas
  82.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  83.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  84.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  85.    wt: 1:   32 seven rows of pascals triangle
  86.    wt: 1:   30 unit circle calculation of six trigonometric functions
  87.    wt: 1:   28 Expressing products of sines cosines as sums
  88.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  89.    wt: 1:   21 sine and cosine Half Angle Formulas
  90.    wt: 1:   20 sine and cosine Double Angle Formulas
  91.    wt: 1:   18 sum of sinusoidal waves as a single wave
  92.    wt: 1:   17F Law of cosines
  93.    wt: 1:   17E Trig Formulas for dot and cross Products
  94.    wt: 1:   17D cis formulas for sine cosines and tangent
  95.    wt: 1:   17C sine and cosine double triple angle formulas
  96.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  97.    wt: 1:   13 Graph of tangent function many periods
  98.    wt: 1:   12 Graph of tangent function for one period
  99.    wt: 1:   10 Graphs of sines and cosines many periods
  100.    wt: 1:   9 Graphs of sine and cosine over one period
  101.    wt: 1:   8 period of tangent function
  102.    wt: 1:   7 period of sine and cosine
  103.    wt: 1:   Unit Circle Development of Trigonometry
  104.    wt: 1:   14 Law of cosines
  105.    wt: 1:   13 Trig Formulas for dot and cross Products
  106.    wt: 1:   12 cis formulas for sine cosines and tangent
  107.    wt: 1:   11 sine and cosine double triple angle formulas
  108.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  109.    wt: 1:   8 Unit Circle Development of Trigonometry
  110.    wt: 1:   6 Field Properties of Complex Number
  111.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  112.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  113.    wt: 1:   9 Similarity of Triangles Usual Criteria
  114.    wt: 1:   8 Similarity of Triangles and Polygons
  115.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  116.    wt: 1:   1 Early Concept of Like or Similar Shapes
  117.    wt: 1:   10 Midpoint of [a b] and [b a]
  118.    wt: 1:   6 Intersection of lines by solving linear systems
  119.    wt: 1:   1 Numerical view of lines and their equations
  120.    wt: 1:   13 Pythagorean spatial distance formulas
  121.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  122.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  123.    wt: 1:   17 Right Bisectors of Triangle Sides
  124.    wt: 1:   9 Construction of a right bisector
  125.    wt: 1:   3 Isometry of Triangles Congruence
  126.    wt: 1:   A Measurement with Ruler Proper Use
  127.    wt: 1:   2 Measuring Area Directly
  128.    wt: 1:   22 Multiplication of Signed Numbers
  129.    wt: 1:   19 Signed Multiples of Vectors
  130.    wt: 1:   8 Division and Mulplication of Compound Fractions
  131.    wt: 1:   4 Location of Point in Decimal Addition
  132.    wt: 1:   3 Location of Point in Decimal Multiplication
  133.    wt: 1:   1 The Counting Origins of Numbers
  134.    wt: 1:   5 Areas of Rectangles Revisited
  135.    wt: 1:   3 Inequalities Algebraically
  136.    wt: 1:   2 Algebraic View
  137.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  138.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  139.    wt: 1:   5 Equality in Algebra
  140.    wt: 1:   4 Comparison of Negative Numbers
  141.    wt: 1:   1 Whole and Natural Numbers
  142.    wt: 1:   3 Geometric Formulas and Function Notation
  143.    wt: 1:   1 Formulas Dependence and Function Notation
  144.    wt: 1:   6 Algebraic Solution Example
  145.    wt: 1:   5 Algebraic Solutions Introduction
  146.    wt: 1:   13 Naming Identifying Formulas with Words
  147.    wt: 1:   11 Volume of Sphere
  148.    wt: 1:   10 Volume of Pyramid
  149.    wt: 1:   9 Volume of Cone
  150.    wt: 1:   6 Pythagorean Hypotenuse Calculation Example
  151.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  152.    wt: 1:   8 Sets of Numbers
  153.    wt: 1:   6 Three Notions of What is a Variable
  154.    wt: 1:   1 Three Skills For Algebra
  155.    wt: 1:   3 Comparison of Negative Numbers
  156.    wt: 1:   5 Square Roots with primes more still
  157.    wt: 1:   4 Square Roots with primes more
  158.    wt: 1:   2 Square Roots with Prime
  159.    wt: 1:   1 Squares and Square Roots Introduction
  160.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  161.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  162.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  163.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  164.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  165.    wt: 1:   4 LCM of 8 and 10 via Prime
  166.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  167.    wt: 1:   5 lengths and signs of numbers
  168.    wt: 1:   6 Simplification of Fractions with Units
  169.    wt: 1:   13 Fraction Comparison Algebraic View
  170.    wt: 1:   11 Simplification an Algebraic View
  171.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  172.    wt: 1:   6 Multiplication of Mixed Numbers
  173.    wt: 1:   6 Multiplication Algebraically Take II
  174.    wt: 1:   3 Unit fraction of a fraction
  175.    wt: 1:   11 Adding Integers Formulas and Examples
  176.    wt: 1:   10 Integer Multiplication Formulas
  177.    wt: 1:   6 Multiplication by Natural Numbers
  178.    wt: 1:   4 Adding Movements wiht opposite directions
  179.    wt: 1:   3 Adding Movements with same direction
  180.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  181.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  182.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  183.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  184.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  185.    wt: 1:   20 Uniqueness of Prime Factorization
  186.    wt: 1:   16 video Factors of 980 using prime
  187.    wt: 1:   15 video Factors of 20 using Prime Factorization
  188.    wt: 1:   14 video Factors of 24 Take II
  189.    wt: 1:   13 video Factors of 24 using prime
  190.    wt: 1:   11 Efficient Square Rule Use
  191.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  192.    wt: 1:   8 Subtraction with Units of Measure
  193.    wt: 1:   1 Comparison and Subtraction Easy Direct Cases
  194.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  195.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  196.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  197.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  198.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  199.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  200.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  201.    wt: 1:   012 Division of Time Intervals by Time Intervals
  202.    wt: 1:   011 Division of Time Intervals By Numbers
  203.    wt: 1:   010 Repeated Addition of Time Intervals
  204.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  205.    wt: 1:   8 Addition of Time Intervals via subtotaling
  206.    wt: 1:   7 Addition of Time Intervals
  207.    wt: 1:   4 Mixing and Changing Units of Time
  208.    wt: 1:   3 Units and Lengths of Time
  209.    wt: 1:   1 Intro of Kids To Time Date Skills
  210.    wt: 1:   Example 2 volume of a cone
  211.    wt: 1:   Example 1 volume of a pyramid
  212.    wt: 1:   Volume of Solid by Cross Sections Lesson
  213.    wt: 1:   Example 4 with x function of y
  214.    wt: 1:   34 Derivative of exponential function
  215.    wt: 1:   31 Derivatives of inverse functions
  216.    wt: 1:   30Chain Rule A Proof
  217.    wt: 1:   28 Chain Rule Preparation for a Proof
  218.    wt: 1:   21 Chain Rule for powers
  219.    wt: 1:   8 Differentiation of polynomials
  220.    wt: 1:   5 Jumps and absence of unlimited error control
  221.    wt: 1:   2 Algebraic codification
  222.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  223.    wt: 1:   G.3 Constant Difference Theorem Proof
  224.    wt: 1:   D2 Limits of Monotone Sequences
  225.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  226.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  227.    wt: 1:   Chapter 18. Rules for Algebra
  228.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  229.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  230.    wt: 1:   Chapter 8 Three Skills For Algebra
  231.    wt: 1:   Chapter 6 Change of Language
  232.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  233.    wt: 1:   Chapter 4 Longer Chains of Reason
  234.    wt: 1:   Chapter 3 Chains of Reason
  235.    wt: 1:   Chapter 7 Two Treatments of Geometry
  236.    wt: 1:   Chapter 3 Algebra Difficulties
  237.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  238.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  239.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  240.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  241.    wt: 1:   Chapter 8 Change of Language
  242.    wt: 1:   Chapter 7 Longer Chains of Reason
  243.    wt: 1:   Chapter 6 Chains of Reason
  244.    wt: 1:   S Adding words to algebra
  245.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  246.    wt: 1:   C. Domino effect of being careful
  247.    wt: 1:   B. Domino effect of errors
  248.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  249.    wt: 1:   Chapter 6 More Algebra and Geometry
  250.    wt: 1:   Chapter 3 Algebra Starter Lessons
  251.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  252.    wt: 1:   More Algebra and Slope based Calculus Preview
  253.    wt: 1:   Systematic Algebra Skill Development Missing Links

Extended Search

610 matches:

  1.    wt: 9:   5 Natural Logarithm Calculator Exercises
  2.    wt: 8:   11 Growth and Decay in Biology
  3.    wt: 8:   10 Exponential Growth and Decay Models
  4.    wt: 8:   2 Square Root Simplification a prequel
  5.    wt: 8:   1 Calculator Starter Exercises
  6.    wt: 6:   8 quadratics backward use of various formulas
  7.    wt: 5:   2 Algebraic use of function notation
  8.    wt: 5:   3 Inequalities Algebraically
  9.    wt: 5:   3 Solving triangular system example
  10.    wt: 5:   3 Four Examples
  11.    wt: 5:   38 Formulas and derivatives for powers and roots
  12.    wt: 4:   3 Formula or function graphing exercise
  13.    wt: 4:   4 quadratics difference of two squares
  14.    wt: 4:   3 quadratics factoring by inspection
  15.    wt: 4:   3 Rectangular Coordinates Review
  16.    wt: 4:   3 Multiplicative Counting Skills Principles
  17.    wt: 4:   5 Areas of Rectangles Revisited
  18.    wt: 4:   3 Gaussian Elimination 3 unknowns first example
  19.    wt: 4:   3 GE III Equation Addition and Multiplication
  20.    wt: 4:   6 Algebraic Solution Example
  21.    wt: 4:   5 Algebraic Solutions Introduction
  22.    wt: 4:   3 Two Examples
  23.    wt: 4:   3 Comparison of Negative Numbers
  24.    wt: 4:   3 video Primes and Composites from 9 times table
  25.    wt: 4:   Systematic Algebra Skill Development Missing Links
  26.    wt: 3:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  27.    wt: 3:   21 Graphs of functions given by Horizontal Line Method
  28.    wt: 3:   15 Sign analysis of functions
  29.    wt: 3:   8 Set view of relations and functions
  30.    wt: 3:   1 Geometric Introduction of Function Notation
  31.    wt: 3:   A Quadratics Summary
  32.    wt: 3:   10 quadratic exercises
  33.    wt: 3:   9 quadratics physical and further context
  34.    wt: 3:   7 quadratic formulla derivation
  35.    wt: 3:   6 quadratics numerical approach
  36.    wt: 3:   5 quadratics completing the square
  37.    wt: 3:   2 quadratics graphing in general
  38.    wt: 3:   1 quadratics graphing exercises
  39.    wt: 3:   Quadratics in 10 steps
  40.    wt: 3:   3 Polynomials Multiplication Addition
  41.    wt: 3:   Rewriting algebraic substitution as function substitutions
  42.    wt: 3:   27 Logarithmic use of products of sines and cosines
  43.    wt: 3:   21 Logarithms Powers and Exponentials
  44.    wt: 3:   13 Pythagorean spatial distance formulas
  45.    wt: 3:   9 Pythagorean Theorem Chinese Square Proof
  46.    wt: 3:   3 Isometry of Triangles Congruence
  47.    wt: 3:   22 Multiplication of Signed Numbers
  48.    wt: 3:   21 Addition of Multiples of a Single Vector
  49.    wt: 3:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  50.    wt: 3:   3 Location of Point in Decimal Multiplication
  51.    wt: 3:   1 The Counting Origins of Numbers
  52.    wt: 3:   4 Fraction Operations Axiomatic Development
  53.    wt: 3:   2 Fraction Operations Physical Development
  54.    wt: 3:   1 Decimals Modular and Remainder Arithmetic
  55.    wt: 3:   3 Proportionality Examples
  56.    wt: 3:   7 Pythagorean Theorem Chinese Square Proof
  57.    wt: 3:   4 Rectangle Area and Like Formulas Backwards
  58.    wt: 3:   3 Linear Equation Literal Solution More
  59.    wt: 3:   3 Geometric Formulas and Function Notation
  60.    wt: 3:   4 Solving a triangular system exercise
  61.    wt: 3:   2 Essentially one exercises three with solution
  62.    wt: 3:   1 Essentially One Unknown
  63.    wt: 3:   4 Four Examples Fractional Coefficients
  64.    wt: 3:   2 Three Examples
  65.    wt: 3:   1 Proper Equal Sign Usage
  66.    wt: 3:   13 Naming Identifying Formulas with Words
  67.    wt: 3:   11 Volume of Sphere
  68.    wt: 3:   10 Volume of Pyramid
  69.    wt: 3:   9 Volume of Cone
  70.    wt: 3:   6 Pythagorean Hypotenuse Calculation Example
  71.    wt: 3:   3 Triangle Area Formula Example
  72.    wt: 3:   4 A Brief Story of numbers and algebra
  73.    wt: 3:   3 Properties of Square Roots with example
  74.    wt: 3:   3 Adding Movements with same direction
  75.    wt: 3:   20 Uniqueness of Prime Factorization
  76.    wt: 3:   16 video Factors of 980 using prime
  77.    wt: 3:   15 video Factors of 20 using Prime Factorization
  78.    wt: 3:   14 video Factors of 24 Take II
  79.    wt: 3:   13 video Factors of 24 using prime
  80.    wt: 3:   11 Efficient Square Rule Use
  81.    wt: 3:   6 Sieve of Eratosthenes and Square Rule
  82.    wt: 3:   C Counting Areas with Powers of Ten
  83.    wt: 3:   B Powers of Ten
  84.    wt: 3:   3 More One Digit Multipliers
  85.    wt: 3:   3 More on Groups of 3 Multi Digit Place Value
  86.    wt: 3:   34 Derivative of exponential function
  87.    wt: 3:   31 Derivatives of inverse functions
  88.    wt: 3:   30Chain Rule A Proof
  89.    wt: 3:   17 Derivatives of quotients of sine and cosine
  90.    wt: 3:   16 Derivatives of reciprocals of sine and cosine
  91.    wt: 3:   Chapter 24 Logarithms Powers and Exponentials
  92.    wt: 3:   Chapter 19. Exponentials and Natural Logarithms
  93.    wt: 3:   Chapter 31 Direct and Indirect Reason
  94.    wt: 3:   Chapter 14. Forward and Backward Use of a Formula
  95.    wt: 3:   Chapter 3 Chains of Reason
  96.    wt: 3:   More Algebra and Slope based Calculus Preview
  97.    wt: 2:   5 logarithms and exponentials etc
  98.    wt: 2:   teaching tutoring algebraic reason
  99.    wt: 2:   Different Kinds of Reasoning in maths
  100.    wt: 2:   3 Energy Power Heat08
  101.    wt: 2:   C Energy Power03
  102.    wt: 2:   E Wire Resistance Calculation03
  103.    wt: 2:   3 Like resistors in parallel
  104.    wt: 2:   E Kirchoffs Second Law
  105.    wt: 2:   D Kirchoff First Law
  106.    wt: 2:   B Electromotive force conventional current01
  107.    wt: 2:   3 Preparing for Science Studies
  108.    wt: 2:   sign monoticity analysis example 4
  109.    wt: 2:   sign monoticity analysis example 3
  110.    wt: 2:   sign monoticity analysis example 2
  111.    wt: 2:   sign monoticity analysis example 1
  112.    wt: 2:   26 Function definitions done and coming
  113.    wt: 2:   25 Absolute Value greatest integer and saw tooth functions
  114.    wt: 2:   24 Monotoncity Injectivity and Inverse Functions
  115.    wt: 2:   23 Inverse Functions
  116.    wt: 2:   22 Square Root function graphically
  117.    wt: 2:   20 Interchanging coordinates a reflection
  118.    wt: 2:   19 Horizontal line rule and method
  119.    wt: 2:   18 Vertical Line Rule and Method
  120.    wt: 2:   17 Function maxima minima and their location
  121.    wt: 2:   16 Increasing or decreasing on intervals
  122.    wt: 2:   14 Surjections Injections Bijections
  123.    wt: 2:   13 From one to one to many to one
  124.    wt: 2:   12 Function Domain Recognition Exercises
  125.    wt: 2:   11 Function Domain Range Source and Targets
  126.    wt: 2:   10 Interval Notation
  127.    wt: 2:   9 Set theory term relation possible origins
  128.    wt: 2:   7 Functions with finite domains
  129.    wt: 2:   6 Set Existence Formation and Notation
  130.    wt: 2:   5 Function notation for geometric transformations
  131.    wt: 2:   4 Function notation in and beyond mathematics
  132.    wt: 2:   Introduction Reading Guide
  133.    wt: 2:   8 Notes for instructors or tutors
  134.    wt: 2:   7 Links Lessons Elsewhere
  135.    wt: 2:   6 Polynomial Operations and Equivalent Computation Rules
  136.    wt: 2:   5 Polynomials Long division Nonlinear divisor
  137.    wt: 2:   4 Polynomials Long division linear divisor
  138.    wt: 2:   2 Column Multiplication Method
  139.    wt: 2:   1 Polynomials Distributive Law
  140.    wt: 2:   4 Resultant of a Sum of Movements
  141.    wt: 2:   3 Navigation with Arrows or Vectors
  142.    wt: 2:   Straight Lines Intersection of
  143.    wt: 2:   26 Formulas for products of sines and cosines
  144.    wt: 2:   22 sine of 22.5 degrees via half angle formulas
  145.    wt: 2:   20 N th Roots of Complex Numbers
  146.    wt: 2:   19 N th Roots of Unity
  147.    wt: 2:   18 Sixth Roots of Unity
  148.    wt: 2:   17 Cube Roots of unity
  149.    wt: 2:   5 An Easy Proof of the Distributive Law
  150.    wt: 2:   3 Addition Properties
  151.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  152.    wt: 2:   5 Algebraic View of Slopes
  153.    wt: 2:   3 Slope product for perpendicular lines
  154.    wt: 2:   12 Spatial Coordinates
  155.    wt: 2:   11 Triangle Inequality
  156.    wt: 2:   10 Pythagorean plane distance formula
  157.    wt: 2:   8 Distance Between Points on a Line
  158.    wt: 2:   7 Complex Numbers Appetizer
  159.    wt: 2:   6 Polar Multiplication and Rotation
  160.    wt: 2:   5 Cartesian Addition and Translation
  161.    wt: 2:   4 Polar Coordinates to and from
  162.    wt: 2:   2 Cartesian Coordinates with signs
  163.    wt: 2:   1 Cartesian Coordinates sans signs
  164.    wt: 2:   8 More Use of Maps Not Drawn to Scale
  165.    wt: 2:   26 More Less Greater Than Comparison
  166.    wt: 2:   25 Mid way Convergence to Axiomatic Approach
  167.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  168.    wt: 2:   23 Distributive Law Two Derivations
  169.    wt: 2:   19 Signed Multiples of Vectors
  170.    wt: 2:   8 Division and Mulplication of Compound Fractions
  171.    wt: 2:   4 Location of Point in Decimal Addition
  172.    wt: 2:   E Long Division Methods more
  173.    wt: 2:   D Long Division Methods
  174.    wt: 2:   C Three Decimal Subtraction Methods
  175.    wt: 2:   B Decimal Comparison and Subtraction
  176.    wt: 2:   A Decimal Addition Columm Methods
  177.    wt: 2:   8 Column Multiplication Methods in General
  178.    wt: 2:   7 Decimals Multiplication Methods Examples
  179.    wt: 2:   6 Column Methods for Decimal Multiplication
  180.    wt: 2:   5 Distributive Law for Whole Numbers
  181.    wt: 2:   4 Commutative Law Groups Counting Form
  182.    wt: 2:   2 Combing Counts Addition Skills and Principles
  183.    wt: 2:   2 Algebraic View
  184.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  185.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  186.    wt: 2:   6 Compound Interest Forward and Backwards
  187.    wt: 2:   5 Triangle Area Formula Backwards
  188.    wt: 2:   2 Linear Equation Literal Solution
  189.    wt: 2:   1 Changing Calculations
  190.    wt: 2:   5 Equality in Algebra
  191.    wt: 2:   3 Product Axioms Two Forms
  192.    wt: 2:   4 Comparison of Negative Numbers
  193.    wt: 2:   3 More and Less Than with Unlike Signs
  194.    wt: 2:   3 Fractions
  195.    wt: 2:   1 Whole and Natural Numbers
  196.    wt: 2:   1 Formulas Dependence and Function Notation
  197.    wt: 2:   More Exercises
  198.    wt: 2:   Simple Exercises
  199.    wt: 2:   5 Gaussian Elimination for 3 unknowns 2nd example
  200.    wt: 2:   4 GE III Animated Examples
  201.    wt: 2:   2 GE II Comparison
  202.    wt: 2:   1 GE Substitution four examples
  203.    wt: 2:   Skill Development Notes
  204.    wt: 2:   10 One Example
  205.    wt: 2:   9 Three Examples
  206.    wt: 2:   8 One Example
  207.    wt: 2:   7 Two Examples
  208.    wt: 2:   6 Three Examples
  209.    wt: 2:   5 Three Examples
  210.    wt: 2:   4 Two Examples
  211.    wt: 2:   2 Three Examples
  212.    wt: 2:   Using Letters for Physical Quantities
  213.    wt: 2:   Formula Usage Show Work Format
  214.    wt: 2:   12 Cone Cylinder Sphere Lesson Idea
  215.    wt: 2:   8 Compound Interest Formula Evaluation
  216.    wt: 2:   7 Compound Interest Formula Introduction
  217.    wt: 2:   5 Box Volume Formula Example
  218.    wt: 2:   4 Circle Area Formula Example
  219.    wt: 2:   2 Another Rectangle Area Formula Example
  220.    wt: 2:   1 Written work formats for developing and showing skill
  221.    wt: 2:   10 Set View of Wordy Extensions To Arithmetic
  222.    wt: 2:   8 Sets of Numbers
  223.    wt: 2:   3 Counting with Sets etc
  224.    wt: 2:   6 Three Notions of What is a Variable
  225.    wt: 2:   3 Adding Words To Arithmetic
  226.    wt: 2:   1 Three Skills For Algebra
  227.    wt: 2:   5 Square Roots with primes more still
  228.    wt: 2:   4 Square Roots with primes more
  229.    wt: 2:   2 Square Roots with Prime
  230.    wt: 2:   1 Squares and Square Roots Introduction
  231.    wt: 2:   9 GCD of 360 110 via Primes and Euclid Algorithm
  232.    wt: 2:   3 Unit fraction of a fraction
  233.    wt: 2:   19 video Prime Factorization Unique
  234.    wt: 2:   18 video Count Factors given Prime Factorization
  235.    wt: 2:   17 Identify and Count Factors using Primes
  236.    wt: 2:   12 LCD GCD and LCM using Primes
  237.    wt: 2:   10 video Prime Factorization upto 23 squared
  238.    wt: 2:   9 video Prime Factorization upto 19 squared
  239.    wt: 2:   8 video Prime Factorization upto 19
  240.    wt: 2:   7 Calculator Usage Notes and Cautions
  241.    wt: 2:   5 Prime Factorization and a Square Rule
  242.    wt: 2:   4 video Prime Factorization Introduction
  243.    wt: 2:   2 Prime and Composites less than 16
  244.    wt: 2:   1 video how Products are bigger than factor
  245.    wt: 2:   3 Division Single Digit Divisor Example
  246.    wt: 2:   3 Harder Cases Convert to Compare and Subtract
  247.    wt: 2:   10 Names for Big Numbers and Powers of Ten Expansion
  248.    wt: 2:   Quick history of numbers and algebra
  249.    wt: 2:   3 Units and Lengths of Time
  250.    wt: 2:   Example 4 with x function of y
  251.    wt: 2:   3 Second derivative test
  252.    wt: 2:   2 Second derivative test prequel
  253.    wt: 2:   36 Cube root derivative animated
  254.    wt: 2:   33 Chain Rule Real Player video examples
  255.    wt: 2:   28 Chain Rule Preparation for a Proof
  256.    wt: 2:   21 Chain Rule for powers
  257.    wt: 2:   12 Quotient rule examples
  258.    wt: 2:   8 Differentiation of polynomials
  259.    wt: 2:   3 Motivation for Limit Definition Take 2
  260.    wt: 2:   E2 Algebraic Properties of Limits
  261.    wt: 2:   Chapter 15. Algebraic Evaluation of Limits
  262.    wt: 2:   Chapter 18. Rules for Algebra
  263.    wt: 2:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  264.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  265.    wt: 2:   Chapter 8 Three Skills For Algebra
  266.    wt: 2:   Chapter 6 Change of Language
  267.    wt: 2:   Chapter 5 Islands and Divisions of Knowledge
  268.    wt: 2:   Chapter 4 Longer Chains of Reason
  269.    wt: 2:   Chapter 3 Algebra Difficulties
  270.    wt: 2:   Chapter 24 Direct and Indirect Reason
  271.    wt: 2:   C. Domino effect of being careful
  272.    wt: 2:   Chapter 3 Algebra Starter Lessons
  273.    wt: 2:   Implementation Notes
  274.    wt: 2:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  275.    wt: 2:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  276.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  277.    wt: 1:   Ramblings Introduction Algebra Essay
  278.    wt: 1:   Skills Chapter 3 Algebra
  279.    wt: 1:   4 algebra
  280.    wt: 1:   3 Euclidean Geometry Leanly
  281.    wt: 1:   permissions for teachers
  282.    wt: 1:   Math Ed if it must be short make it lean effective
  283.    wt: 1:   Mathematics Education Professors
  284.    wt: 1:   Education Reform Inconsistencies
  285.    wt: 1:   talk the algebra talk
  286.    wt: 1:   geometric implications for algebra
  287.    wt: 1:   Lessening Algebra Difficulties
  288.    wt: 1:   the trouble with algebra
  289.    wt: 1:   Theory of Knowledge
  290.    wt: 1:   three kinds of reason in mathematics
  291.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  292.    wt: 1:   liens
  293.    wt: 1:   4 Energy Power Heat09
  294.    wt: 1:   2 Energy Power Heat07
  295.    wt: 1:   1 Energy Power Heat06
  296.    wt: 1:   E Energy Power05
  297.    wt: 1:   D Energy Power04
  298.    wt: 1:   B Energy Power02
  299.    wt: 1:   A Energy Power01
  300.    wt: 1:   2 Conductance Resistance Duality02
  301.    wt: 1:   1 Conductance Resistance Duality01
  302.    wt: 1:   F Wire Resistance Calculation04
  303.    wt: 1:   D Wire Resistance Calculation02
  304.    wt: 1:   C Wire Resistance Calculation01
  305.    wt: 1:   B Wire Resistance Qualitative02
  306.    wt: 1:   A Wire Resistance Qualitative01
  307.    wt: 1:   2 Unlike resistors in parallel01
  308.    wt: 1:   1 Like resistors in series
  309.    wt: 1:   H Series Circuit02
  310.    wt: 1:   G Series Circuit01
  311.    wt: 1:   F Unlike Resistors in Series
  312.    wt: 1:   C Electromotive force conventional current02
  313.    wt: 1:   A Circuit Elements
  314.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  315.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  316.    wt: 1:   8 The Effect of Negative Remarks
  317.    wt: 1:   Ages 3 plus to 4 plus
  318.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  319.    wt: 1:   11 arctan left inverse of tangent Graph
  320.    wt: 1:   10 arctan left inverse of tangent Definition
  321.    wt: 1:   8 arcsin left inverse of sine Graph
  322.    wt: 1:   7 arcsin left inverse of sine Definition
  323.    wt: 1:   6 Graph of arccos function
  324.    wt: 1:   3 Left Inverse of cosine arccos definition
  325.    wt: 1:   8 Radian Measures of Common Angles
  326.    wt: 1:   2 Radian Measure Numerical Value of one degree
  327.    wt: 1:   3 graphing y=f(x c) plus K
  328.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  329.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  330.    wt: 1:   14 Straight Lines Equations General Case
  331.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  332.    wt: 1:   12 Straight Lines Graphing mx plus b
  333.    wt: 1:   11 Straight Lines Graphing y=mx
  334.    wt: 1:   10 Straight Lines through Origin Equations More
  335.    wt: 1:   9 Straight Lines through Origin Equations
  336.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  337.    wt: 1:   17 tangent function angle sum formulas
  338.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  339.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  340.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  341.    wt: 1:   32 seven rows of pascals triangle
  342.    wt: 1:   31 basic secant cosecant cotangent trig identities
  343.    wt: 1:   30 unit circle calculation of six trigonometric functions
  344.    wt: 1:   28 Expressing products of sines cosines as sums
  345.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  346.    wt: 1:   21 sine and cosine Half Angle Formulas
  347.    wt: 1:   20 sine and cosine Double Angle Formulas
  348.    wt: 1:   18 sum of sinusoidal waves as a single wave
  349.    wt: 1:   17F Law of cosines
  350.    wt: 1:   17E Trig Formulas for dot and cross Products
  351.    wt: 1:   17D cis formulas for sine cosines and tangent
  352.    wt: 1:   17C sine and cosine double triple angle formulas
  353.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  354.    wt: 1:   13 Graph of tangent function many periods
  355.    wt: 1:   12 Graph of tangent function for one period
  356.    wt: 1:   10 Graphs of sines and cosines many periods
  357.    wt: 1:   9 Graphs of sine and cosine over one period
  358.    wt: 1:   8 period of tangent function
  359.    wt: 1:   7 period of sine and cosine
  360.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  361.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  362.    wt: 1:   Unit Circle Development of Trigonometry
  363.    wt: 1:   14 Law of cosines
  364.    wt: 1:   13 Trig Formulas for dot and cross Products
  365.    wt: 1:   12 cis formulas for sine cosines and tangent
  366.    wt: 1:   11 sine and cosine double triple angle formulas
  367.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  368.    wt: 1:   8 Unit Circle Development of Trigonometry
  369.    wt: 1:   6 Field Properties of Complex Number
  370.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  371.    wt: 1:   3 Trigonometric Ratios sine and cosine
  372.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  373.    wt: 1:   9 Similarity of Triangles Usual Criteria
  374.    wt: 1:   8 Similarity of Triangles and Polygons
  375.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  376.    wt: 1:   3 Similarity by Design with coordinates
  377.    wt: 1:   1 Early Concept of Like or Similar Shapes
  378.    wt: 1:   10 Midpoint of [a b] and [b a]
  379.    wt: 1:   6 Intersection of lines by solving linear systems
  380.    wt: 1:   1 Numerical view of lines and their equations
  381.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  382.    wt: 1:   17 Right Bisectors of Triangle Sides
  383.    wt: 1:   9 Construction of a right bisector
  384.    wt: 1:   A Measurement with Ruler Proper Use
  385.    wt: 1:   3 Lengths and Areas on Maps and Plans
  386.    wt: 1:   2 Measuring Area Directly
  387.    wt: 1:   musings do not puiblish real numbers
  388.    wt: 1:   A Modular and Remainder Arithmetic
  389.    wt: 1:   A Signed Number Arithmetic Review
  390.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  391.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  392.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  393.    wt: 1:   15 Head to Tails in place Addition Associative
  394.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  395.    wt: 1:   13 Arrows and Vectors in a Plane
  396.    wt: 1:   12 Real Numbers Line Signed Coordinates
  397.    wt: 1:   11 Signed Number Addition and Addition Properties
  398.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  399.    wt: 1:   9 Division with Digits after Decimal Point
  400.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  401.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  402.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  403.    wt: 1:   2 Counting Digits in Decimal Multiplication
  404.    wt: 1:   1 Fractions with Finite Decimal Expansions
  405.    wt: 1:   5 Proportionality in Equivalent Fractions
  406.    wt: 1:   4 Rates Ratios and Proporitionality
  407.    wt: 1:   1 What is Proportionality
  408.    wt: 1:   6 Equations and Systems Equivalent or Implied
  409.    wt: 1:   4 Subtraction and Division Axioms
  410.    wt: 1:   2 Addition and Multiplication Axioms
  411.    wt: 1:   1 Equivalent Computation Rules
  412.    wt: 1:   5 Greater More Less Than Signs in General
  413.    wt: 1:   2 More and Less Than for Counts and Measures
  414.    wt: 1:   1 Real Numbers Comparison
  415.    wt: 1:   16 Real Numbers Comparison
  416.    wt: 1:   15 Real Number Division
  417.    wt: 1:   14 Real Number Multiplication
  418.    wt: 1:   13 Real Number Subtraction
  419.    wt: 1:   12 Real Number Additive Inverses or Negatives
  420.    wt: 1:   11 Real Number Addition
  421.    wt: 1:   10 Real Number Lengths and Signs
  422.    wt: 1:   9 Coordinates for Regions in Space
  423.    wt: 1:   8 Coordinates for Maps and Planes
  424.    wt: 1:   7 Real Numbers as Line Cordinates
  425.    wt: 1:   6 Unsigned Real Numbers
  426.    wt: 1:   5 Rational Numbers More
  427.    wt: 1:   4 Rational Numbers
  428.    wt: 1:   2 Integers
  429.    wt: 1:   5 Independent versus Dependent Variables
  430.    wt: 1:   4 Changing Letters
  431.    wt: 1:   2 Computation Rules Evaluation
  432.    wt: 1:   9 Sets in Probability and Statistics
  433.    wt: 1:   7 Cautious or Safe Set Construction
  434.    wt: 1:   6 Power Set Notation
  435.    wt: 1:   5 Product Builder Notation
  436.    wt: 1:   4 Subset Builder Notation
  437.    wt: 1:   2 Venn Diagrams
  438.    wt: 1:   1 Finite Sets
  439.    wt: 1:   5 Talking about Numbers and Quantities
  440.    wt: 1:   2 What is a Variable
  441.    wt: 1:   About Folder Contents
  442.    wt: 1:   4 Greater More Less Than Signs in General
  443.    wt: 1:   2 More and Less Than with Unlike Signs
  444.    wt: 1:   1 More and Less Than for Counts and Measures
  445.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  446.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  447.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  448.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  449.    wt: 1:   4 LCM of 8 and 10 via Prime
  450.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  451.    wt: 1:   5 lengths and signs of numbers
  452.    wt: 1:   3 signed coordinates for maps and planes
  453.    wt: 1:   6 Simplification of Fractions with Units
  454.    wt: 1:   13 Fraction Comparison Algebraic View
  455.    wt: 1:   11 Simplification an Algebraic View
  456.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  457.    wt: 1:   6 Multiplication of Mixed Numbers
  458.    wt: 1:   6 Multiplication Algebraically Take II
  459.    wt: 1:   11 Adding Integers Formulas and Examples
  460.    wt: 1:   10 Integer Multiplication Formulas
  461.    wt: 1:   6 Multiplication by Natural Numbers
  462.    wt: 1:   4 Adding Movements wiht opposite directions
  463.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  464.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  465.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  466.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  467.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  468.    wt: 1:   15 Remainder Arithmetic Modulo 9 Example
  469.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  470.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  471.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  472.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  473.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  474.    wt: 1:   9 Remainder Arithmetic Divisibility by 5
  475.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  476.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  477.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  478.    wt: 1:   D Decimal Multiplication Methods Derived
  479.    wt: 1:   A Elementary Basis for Multiplication Methods
  480.    wt: 1:   6 Multiplication Commutes Order Not Important
  481.    wt: 1:   5 Decimal Fraction Multiplication
  482.    wt: 1:   4 Two and Three Digit Multipliers
  483.    wt: 1:   2 One Digit Multipliers
  484.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  485.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  486.    wt: 1:   Video Power Notation in Decimal Expansion
  487.    wt: 1:   1 Why 3 times 5 gives 15
  488.    wt: 1:   8 Subtraction with Units of Measure
  489.    wt: 1:   1 Comparison and Subtraction Easy Direct Cases
  490.    wt: 1:   3. How to add with decimals A sans conversions
  491.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  492.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  493.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  494.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  495.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  496.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  497.    wt: 1:   012 Division of Time Intervals by Time Intervals
  498.    wt: 1:   011 Division of Time Intervals By Numbers
  499.    wt: 1:   010 Repeated Addition of Time Intervals
  500.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  501.    wt: 1:   8 Addition of Time Intervals via subtotaling
  502.    wt: 1:   7 Addition of Time Intervals
  503.    wt: 1:   4 Mixing and Changing Units of Time
  504.    wt: 1:   1 Intro of Kids To Time Date Skills
  505.    wt: 1:   Example 2 volume of a cone
  506.    wt: 1:   Example 1 volume of a pyramid
  507.    wt: 1:   Volume of Solid by Cross Sections Lesson
  508.    wt: 1:   Example 3
  509.    wt: 1:   Example 2
  510.    wt: 1:   Example 1
  511.    wt: 1:   3 Two Chain Rule Method Exercises
  512.    wt: 1:   A Related lessons in Volume 3
  513.    wt: 1:   4 Second derivative test exercise example
  514.    wt: 1:   1 Two cubic sketching exercises with 1st derivative
  515.    wt: 1:   A Chain Rule Real Player video examples
  516.    wt: 1:   29 Chain Rule Optional Reading
  517.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  518.    wt: 1:   26 Chain Rule Recognising outer inner functions
  519.    wt: 1:   25 Chain Rule Animated Examples Continued
  520.    wt: 1:   24 Chain Rule Animated Examples
  521.    wt: 1:   23 Chain Rule in general
  522.    wt: 1:   22 Chain Rule for polynomials
  523.    wt: 1:   20 Chain Rule for Pulley Systems
  524.    wt: 1:   19 Chain Rule for linear functions
  525.    wt: 1:   18 Chain Rule Introduction
  526.    wt: 1:   15 sine and cosine derivatives 3rd step
  527.    wt: 1:   14 sine and cosine derivatives 2nd step
  528.    wt: 1:   13 sine and cosine derivatives 1st step
  529.    wt: 1:   11 Quotient rule
  530.    wt: 1:   10 Power rule for negative integers
  531.    wt: 1:   9 Reciprocal rule
  532.    wt: 1:   7 Animated Differentiation Examples
  533.    wt: 1:   6 Power rule from product rule
  534.    wt: 1:   5 Product Rule
  535.    wt: 1:   4 Sum Rule
  536.    wt: 1:   2 Motivation for Limit Definition Take 1
  537.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  538.    wt: 1:   5 Jumps and absence of unlimited error control
  539.    wt: 1:   4 Numerical properties
  540.    wt: 1:   2 Algebraic codification
  541.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  542.    wt: 1:   G.3 Constant Difference Theorem Proof
  543.    wt: 1:   D2 Limits of Monotone Sequences
  544.    wt: 1:   B3 Bolzano Weierstrass Theorem
  545.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  546.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  547.    wt: 1:   Chapter 3. Slope Sign Analysis
  548.    wt: 1:   Postscript More on Better Performance
  549.    wt: 1:   Postscript For Better Performance
  550.    wt: 1:   Appendix E. How To Study Mathematics and Why
  551.    wt: 1:   Appendix D. What to do in School and Why
  552.    wt: 1:   Appendix C. How to Read
  553.    wt: 1:   Appendix B. How To Learn
  554.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  555.    wt: 1:   Chapter 30 Truth Tables
  556.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  557.    wt: 1:   Chapter 28 Occurrence Tables
  558.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  559.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  560.    wt: 1:   Chapter 25. Mathematical Induction Examples
  561.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  562.    wt: 1:   Chapter 23. Notation For Sums
  563.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  564.    wt: 1:   Chapter 21. Third Reading Guide
  565.    wt: 1:   Chapter 20. Degrees and Radians
  566.    wt: 1:   Chapter 19. Functions and Sets
  567.    wt: 1:   Chapter 16. Painless Theorem Proving
  568.    wt: 1:   Chapter 15. Solving Linear Equations
  569.    wt: 1:   Chapter 13. Second Reading Guide
  570.    wt: 1:   Chapter 12. Shorthand Usage Guide
  571.    wt: 1:   Chapter 11. Why Shorthand
  572.    wt: 1:   Chapter 10 Describing and Changing Calculations
  573.    wt: 1:   Postscript What is a Variable
  574.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  575.    wt: 1:   Solutions For Arithmetic Exercises
  576.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  577.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  578.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  579.    wt: 1:   Foreword
  580.    wt: 1:   Chapter 7 Two Treatments of Geometry
  581.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  582.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  583.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  584.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  585.    wt: 1:   Chapter 8 Change of Language
  586.    wt: 1:   Chapter 7 Longer Chains of Reason
  587.    wt: 1:   Chapter 6 Chains of Reason
  588.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  589.    wt: 1:   S Adding words to algebra
  590.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  591.    wt: 1:   B. Domino effect of errors
  592.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  593.    wt: 1:   Chapter 6 More Algebra and Geometry
  594.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  595.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  596.    wt: 1:   Helping the Blind in Logic and Mathematics
  597.    wt: 1:   Mathematics Education References
  598.    wt: 1:   Mathematics Education References
  599.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  600.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  601.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  602.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  603.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  604.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  605.    wt: 1:   Which Way To Go
  606.    wt: 13:   3 Natural Logarithms and Exponentials Basic Properties
  607.    wt: 11:   7 Formulas for Roots with Logarithms Derivation
  608.    wt: 11:   6 Formulas for Even and Odd Roots with Logarithms
  609.    wt: 10:   9 Formulas for Real Exponents with Logarithms
  610.    wt: 10:   8 Formulas for Fractional Exponents with Logarithms

Teachers, Tutors, Parents: Site material offers better or best practices for mathematics skill building - simpler than expected and comprehensive. Your duty is to study them alone or with help. Start now.

Secondary Mathematics for Ages 11+, A Practical Approach for home-tutoring or -schooling, or for schools & colleges with local curriculum control. Study how to include site content - its skill development how-TOs and innovations into present or future lesson plans - some reading required.

Road Safety Messages and Questions: When and why should you face traffic when walking along a road or cycle path? Is it a good idea to hang limbs outside of cars etc? What gives more protection in a crash: a car, motorbike or bicycle? See too, the BBC-Belgium story Texting and Driving - texting & the impossible test - the article links to a gruesome utube video on the subject

The Logic of Injustice: How Texas sent an innocent man to his death - The wrong Carlos. Some judgments are irreversible. Procescution: Where and when prosectors play to win rather than for justice, guilt beyond a reasonable doubt goes unrespected due to prosecutors who putting winning first, those innocence before the law may be convicted. Some procescutors offices in continuing to accuse after a pardon due to reasonable doubt or innocent being shown, may sucessfully oppose compensaton for false convictions by asserting a pardon individual is still under suspicion. Then the pardoned individual or the latter's estate is not compensation for years or decade of improper or false imprisonment, or for execution. Site chapters on Logic
and some in Pattern Based Reason may slowly lead to greater precision in reading, applying and writing laws.

May 2012, Composition Starting: Pre-School and Primary Mathematics - Quantitative Skills, An Intellectual View, Feedback Welcome:

The 8 Most Popular Site Inlinks

20 Times Table - the most popular site page - popular pages - unexpected.
Fractions & Ratios - with lesson on raising terms to introduce & justify times, division & comparison as well addition & subtraction
Parent Center - See below
Volume 1, Elements of Reason - Intro to all site books.
What is a Variable - best for ages 13+
Written work formats for Arithmetic and Algebra - a skill method and standard!
Complex Numbers Visually - best for ages 13+
Natural Logs, Exponentials, Powers, Roots

Division of Labour: This site offers advice and directions with pointers to resources elsewhere, if known, when they help or lessen the need to write more.

Parent Center: Help your child or teen learn:

Parent-friendly Work Booklets for ages 3+ to 13 Use these or others to check or build skills. Other booklets are available but these booklets allow parents unsure of themselves in mathematics to help their children. The selection acquired in Canada is published in the USA. So it has a US orientation. In retrospect, the selection shows parents what to check with the booklets or by other ways, the choice is theirs. But in retrospect, the selection does not cover integral and fractions liquid weights and measures - ask the publishers to correct that! For ages 9 to 12 say, parents may compensate by showing boys and girls how to use weights or mass, and further measures in food preparation. Beyond that children may be shown how to measure and calculate angles, lengths and areas [proportional amounts too] directly or by using maps and plans drawns to scale. Learning how to gather and measure all the ingredients, pots and pans for a dish or a meal, along with cleaning up sets the stage for like activities or experiments in science courses, and in developing organizational skills, gives boys and girls a head start. Good luck. At the other extreme, more comprehensive than light, if your motto is McCainian: drill, drill, drill then Toronto mathematician and actor John Mighton's jump math organization has jump math workbooks for at least grades 3 to 8 for at-home and in-school use - training sessions for teachers available. Jump math has been expanding to cover older students. Jump Math Samples: plus Fractions for Grades 3-4 & Grades 5-6 [Read] Free Resources grades 1 to 8 [unread - likely to be good]. and

Mathematics Skills For Ages 3 to 14 - technical!

Skills with take home value - A few ideas

Basic skills include time-date-calendar Matters; money matters; map, plan and scale diagram matters;counting, measuring and figuring; decision making with logic and likelyhood; being careful and being aware of the domino effect of mistakes; reading and writing with precision.

Is your child able to add, subtract and multiply amounts of money, work with fractions, work with clocks and calendars, work with maps and plans, and measure length, weight-mass and volume? Schools may promote your son or daughter without providing basic skills in reading, writing and arithmetic.

Arithmetic and Number Theory Skills

Algebra Starter Lessons

1 Working With Sets
2 Formula Forward Use - Evaluation
3 Solving Linear Equations - Skip first step with students able to solve 1 eqn in 1 unknown.
4 Computation Rules and Function Notation
5 Real Numbers
6 More Less Greater Than Inequalities and Comparison
7 Axioms Logic and Equivalent Equations
8 Unifying Theme For Algebra
9 Proportionality Backwards and Forwards
10 Examples of Algebraic Reasoning
A Origins of Counting and Figuring Methods
B Real Numbers Extrinsic Development


Site coverage of formuala evaluation format, of computation rules and axioms, and of the forward and backward use of formulas and proportionality relations lessens the amount of natural talent needed to understand and explain algebra.

Geometry - maps plans trigonometry vectors

1 Maps Plans Measurement
2 Euclidean Geometry - Constructions + extras
3 Cartesian and Polar Coordinates
4 Lines and Slopes Take 1
5 What is Similarity
6 Trigonometry first steps
7 Complex Numbers
8 Unit-Circle Trigonometry
9 Lines and Slopes Take 2 with tangent function
10 Intersecting Straight Lines and Transversals
11 Parallel Straight Lines and Transversals
12 Function Translating and Rescaling
13 Vectors
14 Degrees to Radians and Radians to Degrees
15 Arc or Inverse Trigonometric Function

Pre-Teen and young teen mastery of skills and practices which should be common with map-plans-diagrams drawn to scale, contour interpretation included, has actual or potential take-home value for daily- and adult-life in solving routine problems. Elevating some practices to principles, axioms or postualates, provides a base for analytic and Euclidean geometry, an analytic view of similarity, and an efficient mastery of trigonometry and complex numbers. Right triangle trigonometry provide an analytic alternative to solving geometric problems by drawing diagrams to scale.

More Algebra

Natural-Logarithms Exponentials Powers Roots
Five Polynomial Operations
Quadratics Geometrically
Functions
5 Factored Polynomial Sign Analysis Examples
Rewriting algebraic substitution as function substitutions

The first topic leads to a full high school level theory for the forward and backward mastery of growth and decay models and for definition, range and domains of radicals, roots and powers. The next two topics make quadratics and polynomials easier to learn and teach. Site coverage of functions turns vertical and horizontal line rules into computation methods for evaluating functions.

70 Calculus Starter Lessons

Calculus Lessons Elsewhere:

  1. How to Ace Calculus: Street Wise Guide - Mostly Text.

  2. Flash Video for Calculus Phobics

They cover basic topics in ways likely to complement your notes, your textbooks and site material. When Goldilocks trespassed in the house of the three bears, she found three bowls of porridge, two not to her liking, and one just right. Different bears have different tastes. As invited guest here and elsewhere, if one or more explanations is not to liking, try another. It may be better or just right.

Unsolicited Advice

Learning to do and high marks if it comes to easy is often deceptive - light rather than deep. For that reason, students with learning difficulties determined not to let it get in their way may go deeper and farther than those with none. High marks, if the come easy, may be deceptive - provide a too light and not a deep mastery. That could have been your problem in secondary school, one that leads to comprehension shock or difficulties in calculus and more generally in the first year of college. Bon Appetite.

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Logic-Reason for all
Careful Thinking
Chains of Reason
Mathematical Induction
Responsibility
Bodies-of-Knowledge

Arithmetic - Ages 10+
1. Deciml Place Value - fun
2. Decimals for Tutors
3. Prime Factors - quickly
4. Fractions + Ratios
5. Arith with units - science

Geometry
1 Maps + Plans Use
2 Euclidean Geometry
3 Rct +Polr Coordinates
4 Lines-Slopes [I]
5. What is Similarity 		Algebra Starters - the base
1. Better Work Format
2. Solve Linear Eqns
3. Computation Rules
4. Axioms, Item 3 Viewpnt
5. Formulas Backwards 		More Algebra
Logarithms-ax & m/nth roots
Five Polynomial Operations
Quadratics Geometrically
Functions || Vectors too
Arith. Skill Check+Answers 		Calculus Prep/Preview
What is a Variable
Why study slopes
Why factor polynomials
Complex Numbers
Limits + Continuity

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