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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28 matches:

  1.    wt: 8:   2 Natural Logarithms Exponentials Powers Roots/
  2.    wt: 3:   10 Examples of Algebraic Reasoning/
  3.    wt: 2:   5 Factored Polynomial Sign Analysis Examples/
  4.    wt: 2:   4 Functions/
  5.    wt: 2:   3 Quadratics Geometrically/
  6.    wt: 2:   1 Five Polynomial Operations/
  7.    wt: 2:   More Algebra/
  8.    wt: 2:   A Origins of Counting and Figuring Methods/
  9.    wt: 2:   8 Unifying Theme For Algebra/
  10.    wt: 2:   Step 2 Algebraic solutions for one unknown/
  11.    wt: 2:   1 Working With Sets/
  12.    wt: 1:   10 Intersecting Straight Lines and Transversals/
  13.    wt: 1:   B Real Numbers Extrinsic Development/
  14.    wt: 1:   9 Proportionality Backwards and Forwards/
  15.    wt: 1:   7 Axioms Logic and Equivalent Equations/
  16.    wt: 1:   6 More Less Greater Than Inequalities and Comparison/
  17.    wt: 1:   5 Real Numbers/
  18.    wt: 1:   4 Computation Rules and Function Notation/
  19.    wt: 1:   Step 4 Gaussian Elimination/
  20.    wt: 1:   Step 3 Easy systems in 2 or more unknowns/
  21.    wt: 1:   Step 1 Stick diagram and fractions/
  22.    wt: 1:   3 Solving Linear Equations/
  23.    wt: 1:   2 Formula Forward Use Evaluation/
  24.    wt: 1:   Algebra Starter Lessons/
  25.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  26.    wt: 1:   11 Squares and Square Roots/
  27.    wt: 1:   Volume 2 Three Skills For Algebra/
  28.    wt: 1:   Volume 1 Elements of Reason/

Web Page Search

229 matches:

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

Extended Search

466 matches:

  1.    wt: 9:   9 Formulas for Real Exponents with Logarithms
  2.    wt: 9:   8 Formulas for Fractional Exponents with Logarithms
  3.    wt: 8:   11 Growth and Decay in Biology
  4.    wt: 8:   10 Exponential Growth and Decay Models
  5.    wt: 8:   2 Square Root Simplification a prequel
  6.    wt: 8:   1 Calculator Starter Exercises
  7.    wt: 4:   2 Algebraic use of function notation
  8.    wt: 4:   5 Areas of Rectangles Revisited
  9.    wt: 4:   3 Inequalities Algebraically
  10.    wt: 4:   1 Decimals Modular and Remainder Arithmetic
  11.    wt: 3:   26 Function definitions done and coming
  12.    wt: 3:   21 Graphs of functions given by Horizontal Line Method
  13.    wt: 3:   15 Sign analysis of functions
  14.    wt: 3:   8 Set view of relations and functions
  15.    wt: 3:   1 Geometric Introduction of Function Notation
  16.    wt: 3:   8 quadratics backward use of various formulas
  17.    wt: 3:   4 quadratics difference of two squares
  18.    wt: 3:   Rewriting algebraic substitution as function substitutions
  19.    wt: 3:   7 arcsin left inverse of sine Definition
  20.    wt: 3:   3 Left Inverse of cosine arccos definition
  21.    wt: 3:   27 Logarithmic use of products of sines and cosines
  22.    wt: 3:   21 Logarithms Powers and Exponentials
  23.    wt: 3:   21 Addition of Multiples of a Single Vector
  24.    wt: 3:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  25.    wt: 3:   1 The Counting Origins of Numbers
  26.    wt: 3:   4 Fraction Operations Axiomatic Development
  27.    wt: 3:   2 Fraction Operations Physical Development
  28.    wt: 3:   7 Pythagorean Theorem Chinese Square Proof
  29.    wt: 3:   1 Changing Calculations
  30.    wt: 3:   1 Whole and Natural Numbers
  31.    wt: 3:   6 Algebraic Solution Example
  32.    wt: 3:   5 Algebraic Solutions Introduction
  33.    wt: 3:   11 Volume of Sphere
  34.    wt: 3:   10 Volume of Pyramid
  35.    wt: 3:   10 Set View of Wordy Extensions To Arithmetic
  36.    wt: 3:   8 Sets of Numbers
  37.    wt: 3:   1 Finite Sets
  38.    wt: 3:   4 A Brief Story of numbers and algebra
  39.    wt: 3:   3 Properties of Square Roots with example
  40.    wt: 3:   Chapter 24 Logarithms Powers and Exponentials
  41.    wt: 3:   Chapter 19. Exponentials and Natural Logarithms
  42.    wt: 2:   5 logarithms and exponentials etc
  43.    wt: 2:   sign monoticity analysis example 4
  44.    wt: 2:   sign monoticity analysis example 3
  45.    wt: 2:   sign monoticity analysis example 2
  46.    wt: 2:   sign monoticity analysis example 1
  47.    wt: 2:   25 Absolute Value greatest integer and saw tooth functions
  48.    wt: 2:   24 Monotoncity Injectivity and Inverse Functions
  49.    wt: 2:   23 Inverse Functions
  50.    wt: 2:   22 Square Root function graphically
  51.    wt: 2:   20 Interchanging coordinates a reflection
  52.    wt: 2:   19 Horizontal line rule and method
  53.    wt: 2:   18 Vertical Line Rule and Method
  54.    wt: 2:   17 Function maxima minima and their location
  55.    wt: 2:   16 Increasing or decreasing on intervals
  56.    wt: 2:   14 Surjections Injections Bijections
  57.    wt: 2:   13 From one to one to many to one
  58.    wt: 2:   12 Function Domain Recognition Exercises
  59.    wt: 2:   11 Function Domain Range Source and Targets
  60.    wt: 2:   10 Interval Notation
  61.    wt: 2:   9 Set theory term relation possible origins
  62.    wt: 2:   7 Functions with finite domains
  63.    wt: 2:   6 Set Existence Formation and Notation
  64.    wt: 2:   5 Function notation for geometric transformations
  65.    wt: 2:   4 Function notation in and beyond mathematics
  66.    wt: 2:   3 Formula or function graphing exercise
  67.    wt: 2:   Introduction Reading Guide
  68.    wt: 2:   A Quadratics Summary
  69.    wt: 2:   10 quadratic exercises
  70.    wt: 2:   9 quadratics physical and further context
  71.    wt: 2:   7 quadratic formulla derivation
  72.    wt: 2:   6 quadratics numerical approach
  73.    wt: 2:   5 quadratics completing the square
  74.    wt: 2:   3 quadratics factoring by inspection
  75.    wt: 2:   2 quadratics graphing in general
  76.    wt: 2:   1 quadratics graphing exercises
  77.    wt: 2:   Quadratics in 10 steps
  78.    wt: 2:   8 Notes for instructors or tutors
  79.    wt: 2:   7 Links Lessons Elsewhere
  80.    wt: 2:   6 Polynomial Operations and Equivalent Computation Rules
  81.    wt: 2:   5 Polynomials Long division Nonlinear divisor
  82.    wt: 2:   4 Polynomials Long division linear divisor
  83.    wt: 2:   3 Polynomials Multiplication Addition
  84.    wt: 2:   2 Column Multiplication Method
  85.    wt: 2:   1 Polynomials Distributive Law
  86.    wt: 2:   10 arctan left inverse of tangent Definition
  87.    wt: 2:   8 arcsin left inverse of sine Graph
  88.    wt: 2:   6 Graph of arccos function
  89.    wt: 2:   4 Resultant of a Sum of Movements
  90.    wt: 2:   Analytic View of Triangle Construction or Line Instersection More
  91.    wt: 2:   Straight Lines Intersection of
  92.    wt: 2:   20 N th Roots of Complex Numbers
  93.    wt: 2:   19 N th Roots of Unity
  94.    wt: 2:   18 Sixth Roots of Unity
  95.    wt: 2:   17 Cube Roots of unity
  96.    wt: 2:   5 An Easy Proof of the Distributive Law
  97.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  98.    wt: 2:   10 Midpoint of [a b] and [b a]
  99.    wt: 2:   5 Algebraic View of Slopes
  100.    wt: 2:   22 Multiplication of Signed Numbers
  101.    wt: 2:   19 Signed Multiples of Vectors
  102.    wt: 2:   8 Division and Mulplication of Compound Fractions
  103.    wt: 2:   4 Location of Point in Decimal Addition
  104.    wt: 2:   3 Location of Point in Decimal Multiplication
  105.    wt: 2:   E Long Division Methods more
  106.    wt: 2:   D Long Division Methods
  107.    wt: 2:   C Three Decimal Subtraction Methods
  108.    wt: 2:   B Decimal Comparison and Subtraction
  109.    wt: 2:   A Decimal Addition Columm Methods
  110.    wt: 2:   8 Column Multiplication Methods in General
  111.    wt: 2:   7 Decimals Multiplication Methods Examples
  112.    wt: 2:   6 Column Methods for Decimal Multiplication
  113.    wt: 2:   5 Distributive Law for Whole Numbers
  114.    wt: 2:   4 Commutative Law Groups Counting Form
  115.    wt: 2:   3 Multiplicative Counting Skills Principles
  116.    wt: 2:   2 Combing Counts Addition Skills and Principles
  117.    wt: 2:   2 Algebraic View
  118.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  119.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  120.    wt: 2:   6 Compound Interest Forward and Backwards
  121.    wt: 2:   5 Triangle Area Formula Backwards
  122.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  123.    wt: 2:   3 Linear Equation Literal Solution More
  124.    wt: 2:   2 Linear Equation Literal Solution
  125.    wt: 2:   5 Equality in Algebra
  126.    wt: 2:   1 Equivalent Computation Rules
  127.    wt: 2:   4 Comparison of Negative Numbers
  128.    wt: 2:   1 Real Numbers Comparison
  129.    wt: 2:   4 Four Examples Fractional Coefficients
  130.    wt: 2:   3 Four Examples
  131.    wt: 2:   2 Three Examples
  132.    wt: 2:   1 Proper Equal Sign Usage
  133.    wt: 2:   10 One Example
  134.    wt: 2:   Using Letters for Physical Quantities
  135.    wt: 2:   13 Naming Identifying Formulas with Words
  136.    wt: 2:   12 Cone Cylinder Sphere Lesson Idea
  137.    wt: 2:   9 Volume of Cone
  138.    wt: 2:   1 Written work formats for developing and showing skill
  139.    wt: 2:   9 Sets in Probability and Statistics
  140.    wt: 2:   7 Cautious or Safe Set Construction
  141.    wt: 2:   6 Power Set Notation
  142.    wt: 2:   5 Product Builder Notation
  143.    wt: 2:   4 Subset Builder Notation
  144.    wt: 2:   3 Counting with Sets etc
  145.    wt: 2:   2 Venn Diagrams
  146.    wt: 2:   6 Three Notions of What is a Variable
  147.    wt: 2:   1 Three Skills For Algebra
  148.    wt: 2:   3 Comparison of Negative Numbers
  149.    wt: 2:   5 Square Roots with primes more still
  150.    wt: 2:   4 Square Roots with primes more
  151.    wt: 2:   2 Square Roots with Prime
  152.    wt: 2:   1 Squares and Square Roots Introduction
  153.    wt: 2:   C Counting Areas with Powers of Ten
  154.    wt: 2:   B Powers of Ten
  155.    wt: 2:   10 Names for Big Numbers and Powers of Ten Expansion
  156.    wt: 2:   Quick history of numbers and algebra
  157.    wt: 2:   012 Division of Time Intervals by Time Intervals
  158.    wt: 2:   011 Division of Time Intervals By Numbers
  159.    wt: 2:   010 Repeated Addition of Time Intervals
  160.    wt: 2:   1 Intro of Kids To Time Date Skills
  161.    wt: 2:   38 Formulas and derivatives for powers and roots
  162.    wt: 2:   17 Derivatives of quotients of sine and cosine
  163.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  164.    wt: 2:   E2 Algebraic Properties of Limits
  165.    wt: 2:   Chapter 15. Algebraic Evaluation of Limits
  166.    wt: 2:   Chapter 18. Rules for Algebra
  167.    wt: 2:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  168.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  169.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  170.    wt: 2:   Chapter 8 Three Skills For Algebra
  171.    wt: 2:   Chapter 6 Change of Language
  172.    wt: 2:   Chapter 5 Islands and Divisions of Knowledge
  173.    wt: 2:   Chapter 4 Longer Chains of Reason
  174.    wt: 2:   Chapter 3 Chains of Reason
  175.    wt: 1:   Ramblings Introduction Algebra Essay
  176.    wt: 1:   Skills Chapter 3 Algebra
  177.    wt: 1:   4 algebra
  178.    wt: 1:   1 arithmetic with unsigned numbers
  179.    wt: 1:   Mathematics Education Professors
  180.    wt: 1:   talk the algebra talk
  181.    wt: 1:   geometric implications for algebra
  182.    wt: 1:   teaching tutoring algebraic reason
  183.    wt: 1:   Lessening Algebra Difficulties
  184.    wt: 1:   the trouble with algebra
  185.    wt: 1:   Theory of Knowledge
  186.    wt: 1:   Different Kinds of Reasoning in maths
  187.    wt: 1:   three kinds of reason in mathematics
  188.    wt: 1:   deux definitions pour variable
  189.    wt: 1:   E Kirchoffs Second Law
  190.    wt: 1:   D Kirchoff First Law
  191.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  192.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  193.    wt: 1:   10 Ends values for work study instruction
  194.    wt: 1:   8 The Effect of Negative Remarks
  195.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  196.    wt: 1:   16 cotangent function Definition Graph and Inverse
  197.    wt: 1:   15 cosecant function Definition Graph and Inverse
  198.    wt: 1:   14 secant function Definition Graph and Inverse
  199.    wt: 1:   13 cosecant function Definition Graph and Inverse
  200.    wt: 1:   11 arctan left inverse of tangent Graph
  201.    wt: 1:   9 motivation for name arcsin
  202.    wt: 1:   5 Swapping Coordinates is a reflection
  203.    wt: 1:   4 possible motivation for term arccos
  204.    wt: 1:   2 cosine function more properties
  205.    wt: 1:   1 cosine function properties
  206.    wt: 1:   8 Radian Measures of Common Angles
  207.    wt: 1:   2 Radian Measure Numerical Value of one degree
  208.    wt: 1:   1 Degrees and Radians Introduction
  209.    wt: 1:   10 Parallelogram Addition Method
  210.    wt: 1:   1 graphing y=f(x a)
  211.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  212.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  213.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  214.    wt: 1:   Straight Lines ASA Intersection Study More
  215.    wt: 1:   Straight Lines ASA Intersection Study
  216.    wt: 1:   Straight Lines Instersection Solving Equations
  217.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  218.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  219.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  220.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  221.    wt: 1:   32 seven rows of pascals triangle
  222.    wt: 1:   30 unit circle calculation of six trigonometric functions
  223.    wt: 1:   28 Expressing products of sines cosines as sums
  224.    wt: 1:   26 Formulas for products of sines and cosines
  225.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  226.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  227.    wt: 1:   18 sum of sinusoidal waves as a single wave
  228.    wt: 1:   17F Law of cosines
  229.    wt: 1:   13 Graph of tangent function many periods
  230.    wt: 1:   12 Graph of tangent function for one period
  231.    wt: 1:   10 Graphs of sines and cosines many periods
  232.    wt: 1:   9 Graphs of sine and cosine over one period
  233.    wt: 1:   8 period of tangent function
  234.    wt: 1:   7 period of sine and cosine
  235.    wt: 1:   Unit Circle Development of Trigonometry
  236.    wt: 1:   14 Law of cosines
  237.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  238.    wt: 1:   8 Unit Circle Development of Trigonometry
  239.    wt: 1:   6 Field Properties of Complex Number
  240.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  241.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  242.    wt: 1:   9 Similarity of Triangles Usual Criteria
  243.    wt: 1:   8 Similarity of Triangles and Polygons
  244.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  245.    wt: 1:   4 Similarity Definition with Coordinate
  246.    wt: 1:   1 Early Concept of Like or Similar Shapes
  247.    wt: 1:   6 Intersection of lines by solving linear systems
  248.    wt: 1:   1 Numerical view of lines and their equations
  249.    wt: 1:   10 Pythagorean plane distance formula
  250.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  251.    wt: 1:   17 Right Bisectors of Triangle Sides
  252.    wt: 1:   10 Dropping a perpendicular to line
  253.    wt: 1:   9 Construction of a right bisector
  254.    wt: 1:   3 Isometry of Triangles Congruence
  255.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  256.    wt: 1:   1 Length Measurement
  257.    wt: 1:   musings do not puiblish real numbers
  258.    wt: 1:   A Modular and Remainder Arithmetic
  259.    wt: 1:   A Signed Number Arithmetic Review
  260.    wt: 1:   26 More Less Greater Than Comparison
  261.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  262.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  263.    wt: 1:   23 Distributive Law Two Derivations
  264.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  265.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  266.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  267.    wt: 1:   15 Head to Tails in place Addition Associative
  268.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  269.    wt: 1:   13 Arrows and Vectors in a Plane
  270.    wt: 1:   12 Real Numbers Line Signed Coordinates
  271.    wt: 1:   11 Signed Number Addition and Addition Properties
  272.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  273.    wt: 1:   9 Division with Digits after Decimal Point
  274.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  275.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  276.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  277.    wt: 1:   2 Counting Digits in Decimal Multiplication
  278.    wt: 1:   1 Fractions with Finite Decimal Expansions
  279.    wt: 1:   5 Proportionality in Equivalent Fractions
  280.    wt: 1:   4 Rates Ratios and Proporitionality
  281.    wt: 1:   3 Proportionality Examples
  282.    wt: 1:   1 What is Proportionality
  283.    wt: 1:   6 Equations and Systems Equivalent or Implied
  284.    wt: 1:   4 Subtraction and Division Axioms
  285.    wt: 1:   3 Product Axioms Two Forms
  286.    wt: 1:   2 Addition and Multiplication Axioms
  287.    wt: 1:   5 Greater More Less Than Signs in General
  288.    wt: 1:   3 More and Less Than with Unlike Signs
  289.    wt: 1:   2 More and Less Than for Counts and Measures
  290.    wt: 1:   16 Real Numbers Comparison
  291.    wt: 1:   15 Real Number Division
  292.    wt: 1:   14 Real Number Multiplication
  293.    wt: 1:   13 Real Number Subtraction
  294.    wt: 1:   12 Real Number Additive Inverses or Negatives
  295.    wt: 1:   11 Real Number Addition
  296.    wt: 1:   10 Real Number Lengths and Signs
  297.    wt: 1:   9 Coordinates for Regions in Space
  298.    wt: 1:   8 Coordinates for Maps and Planes
  299.    wt: 1:   7 Real Numbers as Line Cordinates
  300.    wt: 1:   6 Unsigned Real Numbers
  301.    wt: 1:   5 Rational Numbers More
  302.    wt: 1:   4 Rational Numbers
  303.    wt: 1:   3 Fractions
  304.    wt: 1:   2 Integers
  305.    wt: 1:   5 Independent versus Dependent Variables
  306.    wt: 1:   4 Changing Letters
  307.    wt: 1:   3 Geometric Formulas and Function Notation
  308.    wt: 1:   2 Computation Rules Evaluation
  309.    wt: 1:   1 Formulas Dependence and Function Notation
  310.    wt: 1:   More Exercises
  311.    wt: 1:   Simple Exercises
  312.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  313.    wt: 1:   4 GE III Animated Examples
  314.    wt: 1:   3 Gaussian Elimination 3 unknowns first example
  315.    wt: 1:   3 GE III Equation Addition and Multiplication
  316.    wt: 1:   2 GE II Comparison
  317.    wt: 1:   1 GE Substitution four examples
  318.    wt: 1:   4 Solving a triangular system exercise
  319.    wt: 1:   3 Solving triangular system example
  320.    wt: 1:   2 Essentially one exercises three with solution
  321.    wt: 1:   1 Essentially One Unknown
  322.    wt: 1:   Skill Development Notes
  323.    wt: 1:   9 Three Examples
  324.    wt: 1:   8 One Example
  325.    wt: 1:   7 Two Examples
  326.    wt: 1:   6 Three Examples
  327.    wt: 1:   5 Three Examples
  328.    wt: 1:   4 Two Examples
  329.    wt: 1:   3 Two Examples
  330.    wt: 1:   2 Three Examples
  331.    wt: 1:   Formula Usage Show Work Format
  332.    wt: 1:   8 Compound Interest Formula Evaluation
  333.    wt: 1:   7 Compound Interest Formula Introduction
  334.    wt: 1:   6 Pythagorean Hypotenuse Calculation Example
  335.    wt: 1:   5 Box Volume Formula Example
  336.    wt: 1:   4 Circle Area Formula Example
  337.    wt: 1:   3 Triangle Area Formula Example
  338.    wt: 1:   2 Another Rectangle Area Formula Example
  339.    wt: 1:   5 Talking about Numbers and Quantities
  340.    wt: 1:   3 Adding Words To Arithmetic
  341.    wt: 1:   2 What is a Variable
  342.    wt: 1:   About Folder Contents
  343.    wt: 1:   4 Greater More Less Than Signs in General
  344.    wt: 1:   2 More and Less Than with Unlike Signs
  345.    wt: 1:   1 More and Less Than for Counts and Measures
  346.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  347.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  348.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  349.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  350.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  351.    wt: 1:   4 LCM of 8 and 10 via Prime
  352.    wt: 1:   5 lengths and signs of numbers
  353.    wt: 1:   6 Simplification of Fractions with Units
  354.    wt: 1:   13 Fraction Comparison Algebraic View
  355.    wt: 1:   11 Simplification an Algebraic View
  356.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  357.    wt: 1:   6 Multiplication of Mixed Numbers
  358.    wt: 1:   6 Multiplication Algebraically Take II
  359.    wt: 1:   3 Unit fraction of a fraction
  360.    wt: 1:   10 Integer Multiplication Formulas
  361.    wt: 1:   6 Multiplication by Natural Numbers
  362.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  363.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  364.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  365.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  366.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  367.    wt: 1:   20 Uniqueness of Prime Factorization
  368.    wt: 1:   16 video Factors of 980 using prime
  369.    wt: 1:   15 video Factors of 20 using Prime Factorization
  370.    wt: 1:   14 video Factors of 24 Take II
  371.    wt: 1:   13 video Factors of 24 using prime
  372.    wt: 1:   10 video Prime Factorization upto 23 squared
  373.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  374.    wt: 1:   10 Division by Five Long and Short Ways
  375.    wt: 1:   8 Subtraction with Units of Measure
  376.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  377.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  378.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  379.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  380.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  381.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  382.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  383.    wt: 1:   016 Numbering Occidental Calendar Days
  384.    wt: 1:   015 School and work day counting tables
  385.    wt: 1:   014 Counting Days with Calendars
  386.    wt: 1:   013 Travel Time Tables
  387.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  388.    wt: 1:   8 Addition of Time Intervals via subtotaling
  389.    wt: 1:   7 Addition of Time Intervals
  390.    wt: 1:   4 Mixing and Changing Units of Time
  391.    wt: 1:   3 Units and Lengths of Time
  392.    wt: 1:   Example 2 volume of a cone
  393.    wt: 1:   Example 1 volume of a pyramid
  394.    wt: 1:   Volume of Solid by Cross Sections Lesson
  395.    wt: 1:   Example 4 with x function of y
  396.    wt: 1:   34 Derivative of exponential function
  397.    wt: 1:   31 Derivatives of inverse functions
  398.    wt: 1:   30Chain Rule A Proof
  399.    wt: 1:   28 Chain Rule Preparation for a Proof
  400.    wt: 1:   21 Chain Rule for powers
  401.    wt: 1:   8 Differentiation of polynomials
  402.    wt: 1:   3 Motivation for Limit Definition Take 2
  403.    wt: 1:   2 Motivation for Limit Definition Take 1
  404.    wt: 1:   5 Jumps and absence of unlimited error control
  405.    wt: 1:   2 Algebraic codification
  406.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  407.    wt: 1:   G.3 Constant Difference Theorem Proof
  408.    wt: 1:   D2 Limits of Monotone Sequences
  409.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  410.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  411.    wt: 1:   Postscript More on Better Performance
  412.    wt: 1:   Postscript For Better Performance
  413.    wt: 1:   Appendix E. How To Study Mathematics and Why
  414.    wt: 1:   Appendix D. What to do in School and Why
  415.    wt: 1:   Appendix C. How to Read
  416.    wt: 1:   Appendix B. How To Learn
  417.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  418.    wt: 1:   Chapter 31 Direct and Indirect Reason
  419.    wt: 1:   Chapter 30 Truth Tables
  420.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  421.    wt: 1:   Chapter 28 Occurrence Tables
  422.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  423.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  424.    wt: 1:   Chapter 25. Mathematical Induction Examples
  425.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  426.    wt: 1:   Chapter 23. Notation For Sums
  427.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  428.    wt: 1:   Chapter 21. Third Reading Guide
  429.    wt: 1:   Chapter 20. Degrees and Radians
  430.    wt: 1:   Chapter 19. Functions and Sets
  431.    wt: 1:   Chapter 16. Painless Theorem Proving
  432.    wt: 1:   Chapter 15. Solving Linear Equations
  433.    wt: 1:   Chapter 13. Second Reading Guide
  434.    wt: 1:   Chapter 12. Shorthand Usage Guide
  435.    wt: 1:   Chapter 11. Why Shorthand
  436.    wt: 1:   Chapter 10 Describing and Changing Calculations
  437.    wt: 1:   Postscript What is a Variable
  438.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  439.    wt: 1:   Solutions For Arithmetic Exercises
  440.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  441.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  442.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  443.    wt: 1:   Foreword
  444.    wt: 1:   Chapter 7 Two Treatments of Geometry
  445.    wt: 1:   Chapter 3 Algebra Difficulties
  446.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  447.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  448.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  449.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  450.    wt: 1:   Chapter 8 Change of Language
  451.    wt: 1:   Chapter 7 Longer Chains of Reason
  452.    wt: 1:   Chapter 6 Chains of Reason
  453.    wt: 1:   S Adding words to algebra
  454.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  455.    wt: 1:   C. Domino effect of being careful
  456.    wt: 1:   B. Domino effect of errors
  457.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  458.    wt: 1:   Chapter 6 More Algebra and Geometry
  459.    wt: 1:   Chapter 3 Algebra Starter Lessons
  460.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  461.    wt: 1:   More Algebra and Slope based Calculus Preview
  462.    wt: 1:   Systematic Algebra Skill Development Missing Links
  463.    wt: 11:   3 Natural Logarithms and Exponentials Basic Properties
  464.    wt: 10:   7 Formulas for Roots with Logarithms Derivation
  465.    wt: 10:   6 Formulas for Even and Odd Roots with Logarithms
  466.    wt: 10:   5 Natural Logarithm Calculator Exercises

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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