Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Development with How-TOs Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling; and for avid readers in school and out. See site volumes.

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

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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39 matches:

  1.    wt: 3:   4 Remainder Arithmetic and Divisibility/
  2.    wt: 3:   Volume 1 Elements of Reason/
  3.    wt: 2:   4 Functions/
  4.    wt: 2:   14 Degrees to Radians and Radians to Degrees/
  5.    wt: 2:   4 Lines and Slopes Take 1/
  6.    wt: 2:   10 Examples of Algebraic Reasoning/
  7.    wt: 2:   Step 4 Gaussian Elimination/
  8.    wt: 2:   12 Comparison of Unsigned and Signed Numbers/
  9.    wt: 2:   D Decimal Long Division Methods/
  10.    wt: 2:   5 Lessons on Integration/
  11.    wt: 2:   4 Lessons on Using Derivatives/
  12.    wt: 2:   Volume 2 Three Skills For Algebra/
  13.    wt: 2:   Volume 1A Pattern Based Reason/
  14.    wt: 1:   5 Factored Polynomial Sign Analysis Examples/
  15.    wt: 1:   A Origins of Counting and Figuring Methods/
  16.    wt: 1:   4 Computation Rules and Function Notation/
  17.    wt: 1:   11 Squares and Square Roots/
  18.    wt: 1:   10 LCM GCD and Euclid GCD Algorithm/
  19.    wt: 1:   9 Combinatorics Trees Tables and Products/
  20.    wt: 1:   8 Arithmetic with Signed Numbers/
  21.    wt: 1:   7 Arithmetic and Fractions with Units/
  22.    wt: 1:   6 Fractions and Ratios/
  23.    wt: 1:   5 Integers/
  24.    wt: 1:   3 Prime Factorization Skills/
  25.    wt: 1:   C Decimal Multiplication Methods/
  26.    wt: 1:   B Decimal Comparing and Subtracting Methods/
  27.    wt: 1:   A Decimal Counting and Adding Methods/
  28.    wt: 1:   2 Arithmetic with Decimals/
  29.    wt: 1:   1 Decimal Place Value/
  30.    wt: 1:   Arithmetic and Number Theory Skills/
  31.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  32.    wt: 1:   38 Lessons on Calculating Derivatives/
  33.    wt: 1:   13 Lessons on Limits and Continuity/
  34.    wt: 1:   70 Calculus Starter Lessons/
  35.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  36.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  37.    wt: 1:   Volume 1B Mathematics Curriculum Notes/
  38.    wt: 1:   Secondary Mathematics A Practical Approach/
  39.    wt: 1:   PreSchool and Primary Mathematics or Quantitative Skills/

Web Page Search

292 matches:

  1.    wt: 5:   Chapter 4 Longer Chains of Reason
  2.    wt: 4:   Chapter 7 Longer Chains of Reason
  3.    wt: 3:   4 Resultant of a Sum of Movements
  4.    wt: 3:   34 sines and cosines of 2A 3A 4A 5A
  5.    wt: 3:   14 video Factors of 24 Take II
  6.    wt: 3:   Chapter 3 Chains of Reason
  7.    wt: 3:   Chapter 6 Chains of Reason
  8.    wt: 2:   Different Kinds of Reasoning in maths
  9.    wt: 2:   three kinds of reason in mathematics
  10.    wt: 2:   chapitre 04 04 Parlons de la logique
  11.    wt: 2:   4 quadratics difference of two squares
  12.    wt: 2:   35 sines and cosines of 2A 3A 4A 5A
  13.    wt: 2:   33 sines and cosines of 2A 3A 4A 5A
  14.    wt: 2:   27 Logarithmic use of products of sines and cosines
  15.    wt: 2:   4 sines and cosines for reference angle 45 degrees
  16.    wt: 2:   14 Law of cosines
  17.    wt: 2:   5 An Easy Proof of the Distributive Law
  18.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  19.    wt: 2:   21 Addition of Multiples of a Single Vector
  20.    wt: 2:   4 Location of Point in Decimal Addition
  21.    wt: 2:   4 Comparison of Negative Numbers
  22.    wt: 2:   4 A Brief Story of numbers and algebra
  23.    wt: 2:   14 GCD of 650 110 via Primes LCM via Product Rule
  24.    wt: 2:   10 Euclid Algorithm with 129 125 and with 45 14
  25.    wt: 2:   4 LCM of 8 and 10 via Prime
  26.    wt: 2:   13 video Factors of 24 using prime
  27.    wt: 2:   4 Groups of 3 Place Value in Decimal Fractions
  28.    wt: 2:   4 Mixing and Changing Units of Time
  29.    wt: 2:   Example 4 with x function of y
  30.    wt: 2:   34 Derivative of exponential function
  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:   Chapter 14. Forward and Backward Use of a Formula
  34.    wt: 2:   Chapter 24 Direct and Indirect Reason
  35.    wt: 2:   Chapter 14 Deductive and Empirical Views of Mathematics
  36.    wt: 1:   Skills Chapter 4 Logic
  37.    wt: 1:   4 algebra
  38.    wt: 1:   Applied Maths Program14092009 POMME variant
  39.    wt: 1:   Mathematics Education Professors
  40.    wt: 1:   teaching tutoring algebraic reason
  41.    wt: 1:   04 29 New Mathematics Curriculum
  42.    wt: 1:   04 25 when to stop or suspend mathemat
  43.    wt: 1:   Theory of Knowledge
  44.    wt: 1:   chapitre 04 10 Etapes pour une meilleur raison
  45.    wt: 1:   chapitre 04 09 Regles accidentelles
  46.    wt: 1:   chapitre 04 08 Limitations et benefices
  47.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  48.    wt: 1:   chapitre 04 06 engagements
  49.    wt: 1:   chapitre 04 05 Implication versus suggestion
  50.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  51.    wt: 1:   chapitre 04 02 Deuxieme enigme
  52.    wt: 1:   chapitre 04 01 Premiere enigme
  53.    wt: 1:   chapitre 04 00 Les regles d implication
  54.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  55.    wt: 1:   Quebec cahiers d apprentissage en mathematiques pour 4 16
  56.    wt: 1:   4 Energy Power Heat09
  57.    wt: 1:   D Energy Power04
  58.    wt: 1:   F Wire Resistance Calculation04
  59.    wt: 1:   E Kirchoffs Second Law
  60.    wt: 1:   D Kirchoff First Law
  61.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  62.    wt: 1:   24 Standards For Skill Develoment Take II
  63.    wt: 1:   24 Standards For Skill Develoment
  64.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  65.    wt: 1:   14 Multiplication and Times Tables
  66.    wt: 1:   8 The Effect of Negative Remarks
  67.    wt: 1:   4 Learning Takes Time and Effort
  68.    wt: 1:   Ages 12 to 14 Skills with take home value
  69.    wt: 1:   Ages 12 to 14 Geometry
  70.    wt: 1:   Ages 12 to 14 Arithmetic
  71.    wt: 1:   Ages 4 plus to 5 plus
  72.    wt: 1:   Ages 3 plus to 4 plus
  73.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  74.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  75.    wt: 1:   sign monoticity analysis example 4
  76.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  77.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  78.    wt: 1:   15 Sign analysis of functions
  79.    wt: 1:   14 Surjections Injections Bijections
  80.    wt: 1:   8 Set view of relations and functions
  81.    wt: 1:   4 Function notation in and beyond mathematics
  82.    wt: 1:   2 Algebraic use of function notation
  83.    wt: 1:   1 Geometric Introduction of Function Notation
  84.    wt: 1:   8 quadratics backward use of various formulas
  85.    wt: 1:   4 Polynomials Long division linear divisor
  86.    wt: 1:   14 secant function Definition Graph and Inverse
  87.    wt: 1:   11 arctan left inverse of tangent Graph
  88.    wt: 1:   10 arctan left inverse of tangent Definition
  89.    wt: 1:   8 arcsin left inverse of sine Graph
  90.    wt: 1:   7 arcsin left inverse of sine Definition
  91.    wt: 1:   6 Graph of arccos function
  92.    wt: 1:   4 possible motivation for term arccos
  93.    wt: 1:   3 Left Inverse of cosine arccos definition
  94.    wt: 1:   8 Radian Measures of Common Angles
  95.    wt: 1:   4 Circle Sector Area proportional to Central Angle
  96.    wt: 1:   2 Radian Measure Numerical Value of one degree
  97.    wt: 1:   14 Why Scalar Multiplication Distributes Physical Argument
  98.    wt: 1:   4 graphing y=Asin(x c)
  99.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  100.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  101.    wt: 1:   Straight Lines Intersection of
  102.    wt: 1:   14 Straight Lines Equations General Case
  103.    wt: 1:   4 Tangent Function Properties
  104.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  105.    wt: 1:   32 seven rows of pascals triangle
  106.    wt: 1:   30 unit circle calculation of six trigonometric functions
  107.    wt: 1:   28 Expressing products of sines cosines as sums
  108.    wt: 1:   26 Formulas for products of sines and cosines
  109.    wt: 1:   24 tangent Angle Difference Formula
  110.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  111.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  112.    wt: 1:   18 sum of sinusoidal waves as a single wave
  113.    wt: 1:   17F Law of cosines
  114.    wt: 1:   14 cosine even and sine and tangent are odd
  115.    wt: 1:   13 Graph of tangent function many periods
  116.    wt: 1:   12 Graph of tangent function for one period
  117.    wt: 1:   10 Graphs of sines and cosines many periods
  118.    wt: 1:   9 Graphs of sine and cosine over one period
  119.    wt: 1:   8 period of tangent function
  120.    wt: 1:   7 period of sine and cosine
  121.    wt: 1:   Unit Circle Development of Trigonometry
  122.    wt: 1:   20 N th Roots of Complex Numbers
  123.    wt: 1:   19 N th Roots of Unity
  124.    wt: 1:   18 Sixth Roots of Unity
  125.    wt: 1:   17 Cube Roots of unity
  126.    wt: 1:   8 Unit Circle Development of Trigonometry
  127.    wt: 1:   6 Field Properties of Complex Number
  128.    wt: 1:   4 Multiplication Properties
  129.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  130.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  131.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  132.    wt: 1:   9 Similarity of Triangles Usual Criteria
  133.    wt: 1:   8 Similarity of Triangles and Polygons
  134.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  135.    wt: 1:   4 Similarity Definition with Coordinate
  136.    wt: 1:   1 Early Concept of Like or Similar Shapes
  137.    wt: 1:   10 Midpoint of [a b] and [b a]
  138.    wt: 1:   6 Intersection of lines by solving linear systems
  139.    wt: 1:   5 Algebraic View of Slopes
  140.    wt: 1:   4 Equations for lines three forms
  141.    wt: 1:   1 Numerical view of lines and their equations
  142.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  143.    wt: 1:   4 Polar Coordinates to and from
  144.    wt: 1:   17 Right Bisectors of Triangle Sides
  145.    wt: 1:   14 Parallel Lines Postulate
  146.    wt: 1:   9 Construction of a right bisector
  147.    wt: 1:   4 Side Side Side
  148.    wt: 1:   3 Isometry of Triangles Congruence
  149.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  150.    wt: 1:   4 Angles on Maps Plans drawn to scale
  151.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  152.    wt: 1:   22 Multiplication of Signed Numbers
  153.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  154.    wt: 1:   19 Signed Multiples of Vectors
  155.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  156.    wt: 1:   8 Division and Mulplication of Compound Fractions
  157.    wt: 1:   3 Location of Point in Decimal Multiplication
  158.    wt: 1:   4 Commutative Law Groups Counting Form
  159.    wt: 1:   1 The Counting Origins of Numbers
  160.    wt: 1:   5 Areas of Rectangles Revisited
  161.    wt: 1:   4 Fraction Operations Axiomatic Development
  162.    wt: 1:   4 Rates Ratios and Proporitionality
  163.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  164.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  165.    wt: 1:   4 Subtraction and Division Axioms
  166.    wt: 1:   14 Real Number Multiplication
  167.    wt: 1:   4 Rational Numbers
  168.    wt: 1:   4 Changing Letters
  169.    wt: 1:   4 GE III Animated Examples
  170.    wt: 1:   4 Solving a triangular system exercise
  171.    wt: 1:   4 Four Examples Fractional Coefficients
  172.    wt: 1:   4 Two Examples
  173.    wt: 1:   11 Volume of Sphere
  174.    wt: 1:   10 Volume of Pyramid
  175.    wt: 1:   9 Volume of Cone
  176.    wt: 1:   4 Circle Area Formula Example
  177.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  178.    wt: 1:   8 Sets of Numbers
  179.    wt: 1:   4 Subset Builder Notation
  180.    wt: 1:   6 Three Notions of What is a Variable
  181.    wt: 1:   4 Greater More Less Than Signs in General
  182.    wt: 1:   3 Comparison of Negative Numbers
  183.    wt: 1:   4 Square Roots with primes more
  184.    wt: 1:   3 Properties of Square Roots with example
  185.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  186.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  187.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  188.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  189.    wt: 1:   5 Common Divisors 60 45 via Prime
  190.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  191.    wt: 1:   4 Counting with Trees Product Rule Take I
  192.    wt: 1:   5 lengths and signs of numbers
  193.    wt: 1:   4 signed coordinates for regions in space
  194.    wt: 1:   6 Simplification of Fractions with Units
  195.    wt: 1:   4 Fractions with Units
  196.    wt: 1:   14 Adding and Subtracting with Like Denominators
  197.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  198.    wt: 1:   6 Multiplication of Mixed Numbers
  199.    wt: 1:   4 Fraction Multiplication
  200.    wt: 1:   3 Unit fraction of a fraction
  201.    wt: 1:   4 Adding Movements wiht opposite directions
  202.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  203.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  204.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  205.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  206.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  207.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  208.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  209.    wt: 1:   4 Remainder Arithmetic Modulo 10 in general
  210.    wt: 1:   20 Uniqueness of Prime Factorization
  211.    wt: 1:   16 video Factors of 980 using prime
  212.    wt: 1:   15 video Factors of 20 using Prime Factorization
  213.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  214.    wt: 1:   4 video Prime Factorization Introduction
  215.    wt: 1:   4 Division with 2 Digit Divsors
  216.    wt: 1:   C Counting Areas with Powers of Ten
  217.    wt: 1:   B Powers of Ten
  218.    wt: 1:   4 Two and Three Digit Multipliers
  219.    wt: 1:   8 Subtraction with Units of Measure
  220.    wt: 1:   4 Subtraction with Conversions Borrows and Letter J
  221.    wt: 1:   4. How to add with decimals B with conversions
  222.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  223.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  224.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  225.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  226.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  227.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  228.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  229.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  230.    wt: 1:   Quick history of numbers and algebra
  231.    wt: 1:   014 Counting Days with Calendars
  232.    wt: 1:   012 Division of Time Intervals by Time Intervals
  233.    wt: 1:   011 Division of Time Intervals By Numbers
  234.    wt: 1:   010 Repeated Addition of Time Intervals
  235.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  236.    wt: 1:   8 Addition of Time Intervals via subtotaling
  237.    wt: 1:   7 Addition of Time Intervals
  238.    wt: 1:   3 Units and Lengths of Time
  239.    wt: 1:   1 Intro of Kids To Time Date Skills
  240.    wt: 1:   Example 2 volume of a cone
  241.    wt: 1:   Example 1 volume of a pyramid
  242.    wt: 1:   Volume of Solid by Cross Sections Lesson
  243.    wt: 1:   4 Definite Integrals Evaluation Exercises
  244.    wt: 1:   4 Second derivative test exercise example
  245.    wt: 1:   31 Derivatives of inverse functions
  246.    wt: 1:   30Chain Rule A Proof
  247.    wt: 1:   28 Chain Rule Preparation for a Proof
  248.    wt: 1:   24 Chain Rule Animated Examples
  249.    wt: 1:   14 sine and cosine derivatives 2nd step
  250.    wt: 1:   8 Differentiation of polynomials
  251.    wt: 1:   4 Sum Rule
  252.    wt: 1:   5 Jumps and absence of unlimited error control
  253.    wt: 1:   4 Numerical properties
  254.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  255.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  256.    wt: 1:   G.3 Constant Difference Theorem Proof
  257.    wt: 1:   F.4 Finite Covering Theorem
  258.    wt: 1:   E2 Algebraic Properties of Limits
  259.    wt: 1:   D2 Limits of Monotone Sequences
  260.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  261.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  262.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  263.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  264.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  265.    wt: 1:   Chapter 4. More Slope Sign Analysis
  266.    wt: 1:   Chapter 31 Direct and Indirect Reason
  267.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  268.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  269.    wt: 1:   Chapter 6 Change of Language
  270.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  271.    wt: 1:   Chapter 7 Two Treatments of Geometry
  272.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  273.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  274.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  275.    wt: 1:   Postscript C Consistency as a Tool for Reason
  276.    wt: 1:   Postscript B More on Story Telling and Reason
  277.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  278.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  279.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  280.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  281.    wt: 1:   Chapter 8 Change of Language
  282.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  283.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  284.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  285.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  286.    wt: 1:   C. Domino effect of being careful
  287.    wt: 1:   B. Domino effect of errors
  288.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  289.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  290.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  291.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  292.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year

Extended Search

722 matches:

  1.    wt: 8:   Chapter 4 Longer Chains of Reason
  2.    wt: 6:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  3.    wt: 6:   Chapter 7 Longer Chains of Reason
  4.    wt: 5:   24 Divisibility Tests for 2 3 5 9 10
  5.    wt: 5:   19 Remainder Arithmetic Rule of 9 for checking sums III
  6.    wt: 5:   18 Remainder Arithmetic Rule of 9 for checking sums II
  7.    wt: 5:   17 Remainder Arithmetic Rule of 9 for checking sums I
  8.    wt: 5:   14 video Factors of 24 Take II
  9.    wt: 5:   Chapter 14. Forward and Backward Use of a Formula
  10.    wt: 5:   Chapter 3 Chains of Reason
  11.    wt: 5:   Chapter 24 Direct and Indirect Reason
  12.    wt: 5:   Chapter 14 Deductive and Empirical Views of Mathematics
  13.    wt: 5:   Chapter 6 Chains of Reason
  14.    wt: 4:   24 Monotoncity Injectivity and Inverse Functions
  15.    wt: 4:   14 Surjections Injections Bijections
  16.    wt: 4:   4 Function notation in and beyond mathematics
  17.    wt: 4:   4 Circle Sector Area proportional to Central Angle
  18.    wt: 4:   4 Resultant of a Sum of Movements
  19.    wt: 4:   4 Equations for lines three forms
  20.    wt: 4:   4 GE III Animated Examples
  21.    wt: 4:   4 Greater More Less Than Signs in General
  22.    wt: 4:   10 Euclid Algorithm with 129 125 and with 45 14
  23.    wt: 4:   25 Divisibility Tests for 2 3 5 9 10 Example
  24.    wt: 4:   23 Remainder Arithmetic Modulo 2
  25.    wt: 4:   22 Remainder Arithmetic Modulo 3 more
  26.    wt: 4:   21 Remainder Arithmetic Modulo 3
  27.    wt: 4:   16 Remainder Arithmetic Modulo 9 Example 2
  28.    wt: 4:   14 Remainder Arithmetic Modulo 9 Example
  29.    wt: 4:   10 Remainder Arithmetic Long Division by 5 Quickly
  30.    wt: 4:   4 Remainder Arithmetic Modulo 10 in general
  31.    wt: 4:   4 Division with 2 Digit Divsors
  32.    wt: 4:   4 Groups of 3 Place Value in Decimal Fractions
  33.    wt: 4:   Example 4 with x function of y
  34.    wt: 4:   34 Derivative of exponential function
  35.    wt: 4:   17 Derivatives of quotients of sine and cosine
  36.    wt: 4:   Appendix D. What to do in School and Why
  37.    wt: 4:   Chapter 24. Personal Investment and Pension EGS
  38.    wt: 4:   Chapter 4 Implication Rules Forwards and Backwards
  39.    wt: 3:   sign monoticity analysis example 4
  40.    wt: 3:   21 Graphs of functions given by Horizontal Line Method
  41.    wt: 3:   15 Sign analysis of functions
  42.    wt: 3:   8 Set view of relations and functions
  43.    wt: 3:   2 Algebraic use of function notation
  44.    wt: 3:   1 Geometric Introduction of Function Notation
  45.    wt: 3:   8 Radian Measures of Common Angles
  46.    wt: 3:   2 Radian Measure Numerical Value of one degree
  47.    wt: 3:   35 sines and cosines of 2A 3A 4A 5A
  48.    wt: 3:   34 sines and cosines of 2A 3A 4A 5A
  49.    wt: 3:   14 Law of cosines
  50.    wt: 3:   Four Simple Exercises
  51.    wt: 3:   10 Midpoint of [a b] and [b a]
  52.    wt: 3:   6 Intersection of lines by solving linear systems
  53.    wt: 3:   5 Algebraic View of Slopes
  54.    wt: 3:   1 Numerical view of lines and their equations
  55.    wt: 3:   4 Commutative Law Groups Counting Form
  56.    wt: 3:   5 Areas of Rectangles Revisited
  57.    wt: 3:   4 Fraction Operations Axiomatic Development
  58.    wt: 3:   3 Comparison of Negative Numbers
  59.    wt: 3:   14 GCD of 650 110 via Primes LCM via Product Rule
  60.    wt: 3:   4 LCM of 8 and 10 via Prime
  61.    wt: 3:   LCM 60 45 Avoid List Method Use Prime
  62.    wt: 3:   4 signed coordinates for regions in space
  63.    wt: 3:   4 Fraction Multiplication
  64.    wt: 3:   4 Adding Movements wiht opposite directions
  65.    wt: 3:   A Decimals Modular and Remainder Arithmetic
  66.    wt: 3:   27 Divisibility by 2 3 6 5 9 10 Example
  67.    wt: 3:   26 Divisibility by 2 3 5 Example
  68.    wt: 3:   15 Remainder Arithmetic Modulo 9 Example
  69.    wt: 3:   13 Remainder Arithmetic Modulo 5 Example
  70.    wt: 3:   12 Remainder Arithmetic Modulo 10 Example
  71.    wt: 3:   11 Remainder Arithmetic Long Division by 5 Quickly more
  72.    wt: 3:   9 Remainder Arithmetic Divisibility by 5
  73.    wt: 3:   8 Remainder Arithmetic Morulo 5 Examples II
  74.    wt: 3:   7 Remainder Arithmetic Modulo 5 Examples I
  75.    wt: 3:   6 Remainder Arithmetic Modulo 5 Propertie
  76.    wt: 3:   5 Remainder Arithmetic Modulo 5
  77.    wt: 3:   3 Remainder Arithmetic Modulos 10 more still
  78.    wt: 3:   2 Remainder Arithmetic Modulo 10 more
  79.    wt: 3:   1 Remainder Arithmetic Modulo 10
  80.    wt: 3:   13 video Factors of 24 using prime
  81.    wt: 3:   4 video Prime Factorization Introduction
  82.    wt: 3:   Long Division Backwards more
  83.    wt: 3:   4 Two and Three Digit Multipliers
  84.    wt: 3:   4 Subtraction with Conversions Borrows and Letter J
  85.    wt: 3:   4. How to add with decimals B with conversions
  86.    wt: 3:   4 Definite Integrals Evaluation Exercises
  87.    wt: 3:   2 Indefinite Integrals Exercises
  88.    wt: 3:   4 Second derivative test exercise example
  89.    wt: 3:   3 Second derivative test
  90.    wt: 3:   24 Chain Rule Animated Examples
  91.    wt: 3:   16 Derivatives of reciprocals of sine and cosine
  92.    wt: 3:   14 sine and cosine derivatives 2nd step
  93.    wt: 3:   Chapter 24 Logarithms Powers and Exponentials
  94.    wt: 3:   Chapter 14 Limits and Continuity with and sans Decimals
  95.    wt: 3:   Chapter 4. More Slope Sign Analysis
  96.    wt: 3:   Appendix E. How To Study Mathematics and Why
  97.    wt: 3:   Appendix C. How to Read
  98.    wt: 3:   Appendix B. How To Learn
  99.    wt: 3:   Appendix A. Reading Guide For Next Appendices
  100.    wt: 3:   Chapter 31 Direct and Indirect Reason
  101.    wt: 3:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  102.    wt: 3:   Chapter 6 Change of Language
  103.    wt: 3:   Chapter 5 Islands and Divisions of Knowledge
  104.    wt: 3:   Chapter 4 Complex Numbers and Why Slopes
  105.    wt: 3:   Postscript D Reflections on Law of the Excluded Middle
  106.    wt: 3:   Postscript C Consistency as a Tool for Reason
  107.    wt: 3:   Postscript B More on Story Telling and Reason
  108.    wt: 3:   Chapter 19 What is in chapters 20 to 24
  109.    wt: 3:   Chapter 16 Origins and Limitations of Rules and Patterns
  110.    wt: 3:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  111.    wt: 3:   Chapter 12 Islands and Divisions of Knowledge
  112.    wt: 3:   Chapter 8 Change of Language
  113.    wt: 3:   Chapter 3 What is in chapters 4 to 8
  114.    wt: 3:   Chapter 4 Logic for Reading Writing and Geometry etc
  115.    wt: 3:   4 Money Matters Saving Earning Buying Selling and Budgets
  116.    wt: 2:   Skills Chapter 4 Logic
  117.    wt: 2:   4 algebra
  118.    wt: 2:   Mathematics Education Professors
  119.    wt: 2:   Different Kinds of Reasoning in maths
  120.    wt: 2:   three kinds of reason in mathematics
  121.    wt: 2:   chapitre 04 04 Parlons de la logique
  122.    wt: 2:   D Energy Power04
  123.    wt: 2:   24 Standards For Skill Develoment Take II
  124.    wt: 2:   24 Standards For Skill Develoment
  125.    wt: 2:   14 Multiplication and Times Tables
  126.    wt: 2:   4 Learning Takes Time and Effort
  127.    wt: 2:   Ages 4 plus to 5 plus
  128.    wt: 2:   26 Function definitions done and coming
  129.    wt: 2:   25 Absolute Value greatest integer and saw tooth functions
  130.    wt: 2:   23 Inverse Functions
  131.    wt: 2:   22 Square Root function graphically
  132.    wt: 2:   20 Interchanging coordinates a reflection
  133.    wt: 2:   19 Horizontal line rule and method
  134.    wt: 2:   18 Vertical Line Rule and Method
  135.    wt: 2:   17 Function maxima minima and their location
  136.    wt: 2:   16 Increasing or decreasing on intervals
  137.    wt: 2:   13 From one to one to many to one
  138.    wt: 2:   12 Function Domain Recognition Exercises
  139.    wt: 2:   11 Function Domain Range Source and Targets
  140.    wt: 2:   10 Interval Notation
  141.    wt: 2:   9 Set theory term relation possible origins
  142.    wt: 2:   7 Functions with finite domains
  143.    wt: 2:   6 Set Existence Formation and Notation
  144.    wt: 2:   5 Function notation for geometric transformations
  145.    wt: 2:   3 Formula or function graphing exercise
  146.    wt: 2:   Introduction Reading Guide
  147.    wt: 2:   4 quadratics difference of two squares
  148.    wt: 2:   9 Summary Degrees to Radians and back
  149.    wt: 2:   7 Radian Measures in special Triangles
  150.    wt: 2:   6 Radian Measure to Degrees
  151.    wt: 2:   5 Degrees to Radian Measure
  152.    wt: 2:   3 Circle Arclengh Proportional to Central Angle
  153.    wt: 2:   1 Degrees and Radians Introduction
  154.    wt: 2:   14 Why Scalar Multiplication Distributes Physical Argument
  155.    wt: 2:   Analytic View of Triangle Construction or Line Instersection More
  156.    wt: 2:   33 sines and cosines of 2A 3A 4A 5A
  157.    wt: 2:   27 Logarithmic use of products of sines and cosines
  158.    wt: 2:   7 period of sine and cosine
  159.    wt: 2:   4 sines and cosines for reference angle 45 degrees
  160.    wt: 2:   5 An Easy Proof of the Distributive Law
  161.    wt: 2:   4 Multiplication Properties
  162.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  163.    wt: 2:   8 Similarity of Triangles and Polygons
  164.    wt: 2:   4 Similarity Definition with Coordinate
  165.    wt: 2:   12 Links Lessons elsewhere
  166.    wt: 2:   11 A Partial Summary
  167.    wt: 2:   9 Midpoint Coordinates Half Endpoint Sum
  168.    wt: 2:   8 Mid Point Formula
  169.    wt: 2:   7 Exercises to test skill and concept mastery
  170.    wt: 2:   3 Slope product for perpendicular lines
  171.    wt: 2:   2 point slope equation for a line
  172.    wt: 2:   What is and is not here
  173.    wt: 2:   4 Polar Coordinates to and from
  174.    wt: 2:   14 Parallel Lines Postulate
  175.    wt: 2:   4 Side Side Side
  176.    wt: 2:   21 Addition of Multiples of a Single Vector
  177.    wt: 2:   4 Location of Point in Decimal Addition
  178.    wt: 2:   1 The Counting Origins of Numbers
  179.    wt: 2:   3 Inequalities Algebraically
  180.    wt: 2:   2 Fraction Operations Physical Development
  181.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  182.    wt: 2:   4 Rates Ratios and Proporitionality
  183.    wt: 2:   4 Comparison of Negative Numbers
  184.    wt: 2:   4 Changing Letters
  185.    wt: 2:   5 Gaussian Elimination for 3 unknowns 2nd example
  186.    wt: 2:   3 Gaussian Elimination 3 unknowns first example
  187.    wt: 2:   3 GE III Equation Addition and Multiplication
  188.    wt: 2:   2 GE II Comparison
  189.    wt: 2:   1 GE Substitution four examples
  190.    wt: 2:   4 Solving a triangular system exercise
  191.    wt: 2:   4 Four Examples Fractional Coefficients
  192.    wt: 2:   4 Two Examples
  193.    wt: 2:   4 A Brief Story of numbers and algebra
  194.    wt: 2:   2 More and Less Than with Unlike Signs
  195.    wt: 2:   1 More and Less Than for Counts and Measures
  196.    wt: 2:   4 Square Roots with primes more
  197.    wt: 2:   3 Properties of Square Roots with example
  198.    wt: 2:   1 Squares and Square Roots Introduction
  199.    wt: 2:   17 GCD LCM of 85 and 60 via Prime
  200.    wt: 2:   16 GCD and LCM of 650 225 via Prime
  201.    wt: 2:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  202.    wt: 2:   9 GCD of 360 110 via Primes and Euclid Algorithm
  203.    wt: 2:   5 Common Divisors 60 45 via Prime
  204.    wt: 2:   4 Counting with Trees Product Rule Take I
  205.    wt: 2:   5 lengths and signs of numbers
  206.    wt: 2:   6 Simplification of Fractions with Units
  207.    wt: 2:   4 Fractions with Units
  208.    wt: 2:   14 Adding and Subtracting with Like Denominators
  209.    wt: 2:   10 Simplification of Fractions and Mixed Numerals
  210.    wt: 2:   6 Multiplication of Mixed Numbers
  211.    wt: 2:   3 Unit fraction of a fraction
  212.    wt: 2:   B Integer Long Division Multiple Choices
  213.    wt: 2:   2 Integers Multiplies of a Unit Moverment
  214.    wt: 2:   20 Uniqueness of Prime Factorization
  215.    wt: 2:   16 video Factors of 980 using prime
  216.    wt: 2:   15 video Factors of 20 using Prime Factorization
  217.    wt: 2:   6 Sieve of Eratosthenes and Square Rule
  218.    wt: 2:   Long Division Backward
  219.    wt: 2:   Division with Counts and Length
  220.    wt: 2:   Long Division forwards and backwards Example 3
  221.    wt: 2:   Long Division forwards and backwards Example 2
  222.    wt: 2:   Long Division forwards and backwards Example 1
  223.    wt: 2:   12 Why Long Division Works Take III
  224.    wt: 2:   11 Another Single Digit Divisor Example
  225.    wt: 2:   10 Division by Five Long and Short Ways
  226.    wt: 2:   9 Why Long Division Works Take II
  227.    wt: 2:   8 Correcting the Mistake
  228.    wt: 2:   7 Long Divison Mistake Catching
  229.    wt: 2:   6 Why Decimal Long Division Methods Works Take I
  230.    wt: 2:   5 Long Division Include Zeroes or not
  231.    wt: 2:   3 Division Single Digit Divisor Example
  232.    wt: 2:   2 Division with Single Digit Divisors
  233.    wt: 2:   1 Divsion Physical Examples
  234.    wt: 2:   C Counting Areas with Powers of Ten
  235.    wt: 2:   B Powers of Ten
  236.    wt: 2:   Video Decimal Multiplication Geometric View Example 2
  237.    wt: 2:   Subtraction with J Conversions Example
  238.    wt: 2:   8 Subtraction with Units of Measure
  239.    wt: 2:   10 Names for Big Numbers and Powers of Ten Expansion
  240.    wt: 2:   9 Place Value Review Decimal form of Avogrados number included
  241.    wt: 2:   8 Review Lesson 1 2 4 and 6 All in One
  242.    wt: 2:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  243.    wt: 2:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  244.    wt: 2:   5 More on Groups of 3 Place Value in Decimal Fractions
  245.    wt: 2:   3 More on Groups of 3 Multi Digit Place Value
  246.    wt: 2:   2 Groups of Three Place Value for Multidigit Decimals
  247.    wt: 2:   Quick history of numbers and algebra
  248.    wt: 2:   Formula Evaluation how to show work
  249.    wt: 2:   4 Mixing and Changing Units of Time
  250.    wt: 2:   Example 2 volume of a cone
  251.    wt: 2:   Example 1 volume of a pyramid
  252.    wt: 2:   Volume of Solid by Cross Sections Lesson
  253.    wt: 2:   Area Between Crossing Curves Lesson Take 2
  254.    wt: 2:   Area Between Crossing Curves Lesson Take 1
  255.    wt: 2:   A Related Material in Volume 3
  256.    wt: 2:   5 Area Under Curve Exercise
  257.    wt: 2:   3 Two Chain Rule Method Exercises
  258.    wt: 2:   1 Chain Rule in Reverse Integration Method
  259.    wt: 2:   A Related lessons in Volume 3
  260.    wt: 2:   2 Second derivative test prequel
  261.    wt: 2:   1 Two cubic sketching exercises with 1st derivative
  262.    wt: 2:   33 Chain Rule Real Player video examples
  263.    wt: 2:   31 Derivatives of inverse functions
  264.    wt: 2:   30Chain Rule A Proof
  265.    wt: 2:   28 Chain Rule Preparation for a Proof
  266.    wt: 2:   25 Chain Rule Animated Examples Continued
  267.    wt: 2:   23 Chain Rule in general
  268.    wt: 2:   13 sine and cosine derivatives 1st step
  269.    wt: 2:   8 Differentiation of polynomials
  270.    wt: 2:   6 Power rule from product rule
  271.    wt: 2:   4 Sum Rule
  272.    wt: 2:   12 Limits with Parameters and Derivatives Take I
  273.    wt: 2:   5 Jumps and absence of unlimited error control
  274.    wt: 2:   4 Numerical properties
  275.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  276.    wt: 2:   G.4 Lipschitz Continuity implies EquiContinuity
  277.    wt: 2:   G.3 Constant Difference Theorem Proof
  278.    wt: 2:   F.5b Extreme Value Theorem
  279.    wt: 2:   F.4 Finite Covering Theorem
  280.    wt: 2:   E2 Algebraic Properties of Limits
  281.    wt: 2:   D2 Limits of Monotone Sequences
  282.    wt: 2:   C Triangle Inequalities
  283.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  284.    wt: 2:   Postscript Pythagorean Theorem yet another proof
  285.    wt: 2:   Chapter 15. Algebraic Evaluation of Limits
  286.    wt: 2:   Postscript More on Better Performance
  287.    wt: 2:   Postscript For Better Performance
  288.    wt: 2:   Chapter 30 Truth Tables
  289.    wt: 2:   Chapter 29 Contrapositive and Vacuously True Implications
  290.    wt: 2:   Chapter 28 Occurrence Tables
  291.    wt: 2:   Chapter 27 Shorthand Symbols as Pronouns
  292.    wt: 2:   Chapter 26 What is in chapters 27 to 31
  293.    wt: 2:   Chapter 25. Mathematical Induction Examples
  294.    wt: 2:   Chapter 23. Notation For Sums
  295.    wt: 2:   Chapter 22. Geometric Sums and Sequences
  296.    wt: 2:   Chapter 21. Third Reading Guide
  297.    wt: 2:   Chapter 20. Degrees and Radians
  298.    wt: 2:   Chapter 19. Functions and Sets
  299.    wt: 2:   Chapter 18. Rules for Algebra
  300.    wt: 2:   Chapter 16. Painless Theorem Proving
  301.    wt: 2:   Chapter 15. Solving Linear Equations
  302.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  303.    wt: 2:   Chapter 13. Second Reading Guide
  304.    wt: 2:   Chapter 12. Shorthand Usage Guide
  305.    wt: 2:   Chapter 11. Why Shorthand
  306.    wt: 2:   Chapter 10 Describing and Changing Calculations
  307.    wt: 2:   Postscript What is a Variable
  308.    wt: 2:   Chapter 9 Talking about Numbers or Quantities
  309.    wt: 2:   Chapter 8 Three Skills For Algebra
  310.    wt: 2:   Solutions For Arithmetic Exercises
  311.    wt: 2:   Chapter 7 Prep for Calculus Arithmetic Exercises
  312.    wt: 2:   Chapter 2 Implication Rules Forwards and Backwards
  313.    wt: 2:   Chapter 1 Introduction to Chapters 2 to 6
  314.    wt: 2:   Foreword
  315.    wt: 2:   Postscript B Mathematics Education References
  316.    wt: 2:   Chapter 7 Two Treatments of Geometry
  317.    wt: 2:   Chapter 6 Rule Based Reason in Mathematics
  318.    wt: 2:   Postscript A Story Telling
  319.    wt: 2:   Chapter 23 Truth Tables
  320.    wt: 2:   Chapter 22 Contrapositive and Vacuously True Implications
  321.    wt: 2:   Chapter 21 Occurrence Tables
  322.    wt: 2:   Chapter 20 Shorthand Symbols as Pronouns
  323.    wt: 2:   Chapter 18 Sense and Knowledge
  324.    wt: 2:   Chapter 17 Objective Ways Trial and Error Discovery
  325.    wt: 2:   Chapter 15 Objective Processes
  326.    wt: 2:   Chapter 11 Accidental Patterns
  327.    wt: 2:   Chapter 10 Responsibility
  328.    wt: 2:   Chapter 9 What is in Chapters 10 to 18
  329.    wt: 2:   Chapter 5 Deception
  330.    wt: 2:   Chapter 2 Skill Development
  331.    wt: 2:   Chapter 1 Introduction
  332.    wt: 2:   Three Remarks
  333.    wt: 2:   Foreword
  334.    wt: 2:   Appendix A Calculus with Proofs for Keen or Gifted
  335.    wt: 2:   6 Measuring via counting or arithmetic the role of fractions
  336.    wt: 2:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  337.    wt: 1:   K LAMP Musings Science Education
  338.    wt: 1:   J LAMP Introduction Extrinsic Origins
  339.    wt: 1:   I LAMP Introduction Study Habits
  340.    wt: 1:   H LAMP Introduction Instructional Concepts
  341.    wt: 1:   G LAMP Introduction Problem Solving Skills
  342.    wt: 1:   F LAMP Introduction Prerequisites
  343.    wt: 1:   E LAMP Introduction Modern Mathematics
  344.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  345.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  346.    wt: 1:   A Introduction Objectives
  347.    wt: 1:   Teach the teachers plus goals
  348.    wt: 1:   Applied Maths Program14092009 POMME variant
  349.    wt: 1:   site eurekas
  350.    wt: 1:   teacher certification
  351.    wt: 1:   modern education
  352.    wt: 1:   how letters appear
  353.    wt: 1:   geometric implications for algebra
  354.    wt: 1:   teaching tutoring algebraic reason
  355.    wt: 1:   04 29 New Mathematics Curriculum
  356.    wt: 1:   04 25 when to stop or suspend mathemat
  357.    wt: 1:   Theory of Knowledge
  358.    wt: 1:   Education in mathematics science and technology
  359.    wt: 1:   Leaner mathematics curriculum
  360.    wt: 1:   chapitre 04 10 Etapes pour une meilleur raison
  361.    wt: 1:   chapitre 04 09 Regles accidentelles
  362.    wt: 1:   chapitre 04 08 Limitations et benefices
  363.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  364.    wt: 1:   chapitre 04 06 engagements
  365.    wt: 1:   chapitre 04 05 Implication versus suggestion
  366.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  367.    wt: 1:   chapitre 04 02 Deuxieme enigme
  368.    wt: 1:   chapitre 04 01 Premiere enigme
  369.    wt: 1:   chapitre 04 00 Les regles d implication
  370.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  371.    wt: 1:   Quebec cahiers d apprentissage en mathematiques pour 4 16
  372.    wt: 1:   4 Energy Power Heat09
  373.    wt: 1:   F Wire Resistance Calculation04
  374.    wt: 1:   B Wire Resistance Qualitative02
  375.    wt: 1:   E Kirchoffs Second Law
  376.    wt: 1:   D Kirchoff First Law
  377.    wt: 1:   C Electromotive force conventional current02
  378.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  379.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  380.    wt: 1:   8 The Effect of Negative Remarks
  381.    wt: 1:   Ages 12 to 14 Skills with take home value
  382.    wt: 1:   Ages 12 to 14 Geometry
  383.    wt: 1:   Ages 12 to 14 Arithmetic
  384.    wt: 1:   Ages 3 plus to 4 plus
  385.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  386.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  387.    wt: 1:   sign monoticity analysis example 3
  388.    wt: 1:   sign monoticity analysis example 2
  389.    wt: 1:   sign monoticity analysis example 1
  390.    wt: 1:   8 quadratics backward use of various formulas
  391.    wt: 1:   4 Polynomials Long division linear divisor
  392.    wt: 1:   14 secant function Definition Graph and Inverse
  393.    wt: 1:   11 arctan left inverse of tangent Graph
  394.    wt: 1:   10 arctan left inverse of tangent Definition
  395.    wt: 1:   8 arcsin left inverse of sine Graph
  396.    wt: 1:   7 arcsin left inverse of sine Definition
  397.    wt: 1:   6 Graph of arccos function
  398.    wt: 1:   4 possible motivation for term arccos
  399.    wt: 1:   3 Left Inverse of cosine arccos definition
  400.    wt: 1:   5 Head To Tail Arrow Addition
  401.    wt: 1:   4 graphing y=Asin(x c)
  402.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  403.    wt: 1:   Triangle Angles Sum To 180 Degrees
  404.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  405.    wt: 1:   Straight Lines ASA Intersection Study More
  406.    wt: 1:   Straight Lines ASA Intersection Study
  407.    wt: 1:   Straight Lines Instersection Solving Equations
  408.    wt: 1:   Straight Lines Intersection of
  409.    wt: 1:   14 Straight Lines Equations General Case
  410.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  411.    wt: 1:   4 Tangent Function Properties
  412.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  413.    wt: 1:   32 seven rows of pascals triangle
  414.    wt: 1:   30 unit circle calculation of six trigonometric functions
  415.    wt: 1:   28 Expressing products of sines cosines as sums
  416.    wt: 1:   26 Formulas for products of sines and cosines
  417.    wt: 1:   25 tangent double angle formula Slope connection
  418.    wt: 1:   24 tangent Angle Difference Formula
  419.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  420.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  421.    wt: 1:   18 sum of sinusoidal waves as a single wave
  422.    wt: 1:   17F Law of cosines
  423.    wt: 1:   16 Right Triangle Complementary Angle Relations
  424.    wt: 1:   14 cosine even and sine and tangent are odd
  425.    wt: 1:   13 Graph of tangent function many periods
  426.    wt: 1:   12 Graph of tangent function for one period
  427.    wt: 1:   10 Graphs of sines and cosines many periods
  428.    wt: 1:   9 Graphs of sine and cosine over one period
  429.    wt: 1:   8 period of tangent function
  430.    wt: 1:   Unit Circle Development of Trigonometry
  431.    wt: 1:   20 N th Roots of Complex Numbers
  432.    wt: 1:   19 N th Roots of Unity
  433.    wt: 1:   18 Sixth Roots of Unity
  434.    wt: 1:   17 Cube Roots of unity
  435.    wt: 1:   8 Unit Circle Development of Trigonometry
  436.    wt: 1:   6 Field Properties of Complex Number
  437.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  438.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  439.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  440.    wt: 1:   9 Similarity of Triangles Usual Criteria
  441.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  442.    wt: 1:   1 Early Concept of Like or Similar Shapes
  443.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  444.    wt: 1:   PS D Addition with Cartesian Coordinates
  445.    wt: 1:   17 Right Bisectors of Triangle Sides
  446.    wt: 1:   9 Construction of a right bisector
  447.    wt: 1:   3 Isometry of Triangles Congruence
  448.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  449.    wt: 1:   4 Angles on Maps Plans drawn to scale
  450.    wt: 1:   A Modular and Remainder Arithmetic
  451.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  452.    wt: 1:   22 Multiplication of Signed Numbers
  453.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  454.    wt: 1:   19 Signed Multiples of Vectors
  455.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  456.    wt: 1:   8 Division and Mulplication of Compound Fractions
  457.    wt: 1:   3 Location of Point in Decimal Multiplication
  458.    wt: 1:   E Long Division Methods more
  459.    wt: 1:   D Long Division Methods
  460.    wt: 1:   C Three Decimal Subtraction Methods
  461.    wt: 1:   B Decimal Comparison and Subtraction
  462.    wt: 1:   A Decimal Addition Columm Methods
  463.    wt: 1:   8 Column Multiplication Methods in General
  464.    wt: 1:   7 Decimals Multiplication Methods Examples
  465.    wt: 1:   6 Column Methods for Decimal Multiplication
  466.    wt: 1:   5 Distributive Law for Whole Numbers
  467.    wt: 1:   3 Multiplicative Counting Skills Principles
  468.    wt: 1:   2 Combing Counts Addition Skills and Principles
  469.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  470.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  471.    wt: 1:   4 Subtraction and Division Axioms
  472.    wt: 1:   14 Real Number Multiplication
  473.    wt: 1:   4 Rational Numbers
  474.    wt: 1:   5 Independent versus Dependent Variables
  475.    wt: 1:   3 Geometric Formulas and Function Notation
  476.    wt: 1:   2 Computation Rules Evaluation
  477.    wt: 1:   1 Formulas Dependence and Function Notation
  478.    wt: 1:   Simple Exercises
  479.    wt: 1:   11 Volume of Sphere
  480.    wt: 1:   10 Volume of Pyramid
  481.    wt: 1:   9 Volume of Cone
  482.    wt: 1:   4 Circle Area Formula Example
  483.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  484.    wt: 1:   8 Sets of Numbers
  485.    wt: 1:   4 Subset Builder Notation
  486.    wt: 1:   6 Three Notions of What is a Variable
  487.    wt: 1:   arithmetic videos Real Player Format
  488.    wt: 1:   5 Square Roots with primes more still
  489.    wt: 1:   2 Square Roots with Prime
  490.    wt: 1:   13 GCD from given Prime Factorization
  491.    wt: 1:   11 GCD 2700 288 via Euclid Algorithm
  492.    wt: 1:   8 GCD from Euclidean Algorithm
  493.    wt: 1:   7 GCD and LCM from prime factorization
  494.    wt: 1:   6 GCD from Prime
  495.    wt: 1:   2 Least Common Multiple LCM intro via list method
  496.    wt: 1:   1 Least Common Multiples LCM Introduction
  497.    wt: 1:   12 GCD 2700 288 via Prime
  498.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  499.    wt: 1:   3 Counting with Tables and Trees II
  500.    wt: 1:   2 Counting with Tables and Trees I
  501.    wt: 1:   1 Counting and Counting Methods I
  502.    wt: 1:   11 What are real lengths and numbers
  503.    wt: 1:   10 dividing signed numbers
  504.    wt: 1:   9 subtracting signed numbers
  505.    wt: 1:   8 multiplying signed numbers
  506.    wt: 1:   7 negative and additive inverse
  507.    wt: 1:   6 adding signed numbers
  508.    wt: 1:   3 signed coordinates for maps and planes
  509.    wt: 1:   2 signed and unsigned numbers as coordinates
  510.    wt: 1:   7 Converting or Changing Units
  511.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  512.    wt: 1:   3 Multiplying Units and Numbers
  513.    wt: 1:   2 Equality and Units
  514.    wt: 1:   1 Addition and Subtraction with Units
  515.    wt: 1:   D Three Term Ratios
  516.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  517.    wt: 1:   B Fractions and Two Term Ratios
  518.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  519.    wt: 1:   22 Complex Compound Fractions
  520.    wt: 1:   21 Working With Signs
  521.    wt: 1:   21 Reciprocals for Fractions and Wholes
  522.    wt: 1:   20 Dividing Fractions the Why
  523.    wt: 1:   19 Dividing Fractions How TO
  524.    wt: 1:   18 Efficient Ways to Multiply
  525.    wt: 1:   17 Efficient Ways to Add and Subtract
  526.    wt: 1:   16 Addition Subtraction Comparision Compared
  527.    wt: 1:   15 Adding and Subtracting with Unlike Denominators
  528.    wt: 1:   13 Fraction Comparison Algebraic View
  529.    wt: 1:   12 Fraction Comparison
  530.    wt: 1:   11 Simplification an Algebraic View
  531.    wt: 1:   9 Improper Fractions and Mixed Numbers
  532.    wt: 1:   8 Numerals Fractionals Quantals Take II
  533.    wt: 1:   7 Numerals Fractionals Quantals
  534.    wt: 1:   6 Multiplication Algebraically Take II
  535.    wt: 1:   5 Equivalent Fractions
  536.    wt: 1:   2 Unit Fraction Multiplication
  537.    wt: 1:   1 What is a fraction Take II
  538.    wt: 1:   1 What is a fraction
  539.    wt: 1:   Fraction Operations by Raising Terms A Simple Innovation
  540.    wt: 1:   D Remainders Modulo 11 Pair Rule
  541.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  542.    wt: 1:   A Associative Law Theorectical Note
  543.    wt: 1:   13 Subtraction with Additive Inverse
  544.    wt: 1:   12 Adding Integers More Examples
  545.    wt: 1:   11 Adding Integers Formulas and Examples
  546.    wt: 1:   10 Integer Multiplication Formulas
  547.    wt: 1:   9 Multiplying Integers
  548.    wt: 1:   8 Multiplication by Signed Numbers Integers
  549.    wt: 1:   7 Multiplication by Signs
  550.    wt: 1:   6 Multiplication by Natural Numbers
  551.    wt: 1:   5 Zero Movement and Additive Inverses
  552.    wt: 1:   3 Adding Movements with same direction
  553.    wt: 1:   1 Integers as Coordinates
  554.    wt: 1:   19 video Prime Factorization Unique
  555.    wt: 1:   18 video Count Factors given Prime Factorization
  556.    wt: 1:   17 Identify and Count Factors using Primes
  557.    wt: 1:   12 LCD GCD and LCM using Primes
  558.    wt: 1:   11 Efficient Square Rule Use
  559.    wt: 1:   10 video Prime Factorization upto 23 squared
  560.    wt: 1:   9 video Prime Factorization upto 19 squared
  561.    wt: 1:   8 video Prime Factorization upto 19
  562.    wt: 1:   7 Calculator Usage Notes and Cautions
  563.    wt: 1:   5 Prime Factorization and a Square Rule
  564.    wt: 1:   3 video Primes and Composites from 9 times table
  565.    wt: 1:   2 Prime and Composites less than 16
  566.    wt: 1:   1 video how Products are bigger than factor
  567.    wt: 1:   D Decimal Multiplication Methods Derived
  568.    wt: 1:   A Elementary Basis for Multiplication Methods
  569.    wt: 1:   6 Multiplication Commutes Order Not Important
  570.    wt: 1:   5 Decimal Fraction Multiplication
  571.    wt: 1:   3 More One Digit Multipliers
  572.    wt: 1:   2 One Digit Multipliers
  573.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  574.    wt: 1:   Video Power Notation in Decimal Expansion
  575.    wt: 1:   1 Why 3 times 5 gives 15
  576.    wt: 1:   Appendix 2 Three Decimal Subtraction Methods
  577.    wt: 1:   Appendix 1 Decimals Comparison Method Take II
  578.    wt: 1:   Subtraction Another Video Lesson
  579.    wt: 1:   9 22 Minute Subtraction Review Video
  580.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  581.    wt: 1:   6 Subtraction with Conversion Example with Exercises
  582.    wt: 1:   5 A Tip for Efficent Subtraction
  583.    wt: 1:   3 Harder Cases Convert to Compare and Subtract
  584.    wt: 1:   2 Subtraction Easy Case Examples
  585.    wt: 1:   1 Comparison and Subtraction Easy Direct Cases
  586.    wt: 1:   Appendix 1 Counting Revisited 15 minute video
  587.    wt: 1:   8 What skills and work habits to require
  588.    wt: 1:   7 Adding decimal fractions using decimal point
  589.    wt: 1:   6. Counting and adding units and mixed units
  590.    wt: 1:   5. How to add decimals C. Examples
  591.    wt: 1:   3. How to add with decimals A sans conversions
  592.    wt: 1:   2 Decimal Counting Practices
  593.    wt: 1:   1. Explaining Addition Table
  594.    wt: 1:   11 Place Value SI Standard International way
  595.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  596.    wt: 1:   Exact Arithmetic Wholes and Fractions
  597.    wt: 1:   Expression Evaluation how to show work
  598.    wt: 1:   The 20 Times Table
  599.    wt: 1:   The 12 Times Table Visually
  600.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  601.    wt: 1:   About folder contents
  602.    wt: 1:   014 Counting Days with Calendars
  603.    wt: 1:   012 Division of Time Intervals by Time Intervals
  604.    wt: 1:   011 Division of Time Intervals By Numbers
  605.    wt: 1:   010 Repeated Addition of Time Intervals
  606.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  607.    wt: 1:   8 Addition of Time Intervals via subtotaling
  608.    wt: 1:   7 Addition of Time Intervals
  609.    wt: 1:   3 Units and Lengths of Time
  610.    wt: 1:   1 Intro of Kids To Time Date Skills
  611.    wt: 1:   Example 1. Area Between x and x squared
  612.    wt: 1:   Example 3
  613.    wt: 1:   Example 2
  614.    wt: 1:   Example 1
  615.    wt: 1:   Area Between Curves Lesson Take 2
  616.    wt: 1:   Area Between Curves Lesson Take 1
  617.    wt: 1:   Summary
  618.    wt: 1:   A Chain Rule Real Player video examples
  619.    wt: 1:   38 Formulas and derivatives for powers and roots
  620.    wt: 1:   36 Cube root derivative animated
  621.    wt: 1:   29 Chain Rule Optional Reading
  622.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  623.    wt: 1:   26 Chain Rule Recognising outer inner functions
  624.    wt: 1:   22 Chain Rule for polynomials
  625.    wt: 1:   21 Chain Rule for powers
  626.    wt: 1:   20 Chain Rule for Pulley Systems
  627.    wt: 1:   19 Chain Rule for linear functions
  628.    wt: 1:   18 Chain Rule Introduction
  629.    wt: 1:   15 sine and cosine derivatives 3rd step
  630.    wt: 1:   12 Quotient rule examples
  631.    wt: 1:   11 Quotient rule
  632.    wt: 1:   10 Power rule for negative integers
  633.    wt: 1:   9 Reciprocal rule
  634.    wt: 1:   7 Animated Differentiation Examples
  635.    wt: 1:   5 Product Rule
  636.    wt: 1:   3 Motivation for Limit Definition Take 2
  637.    wt: 1:   2 Motivation for Limit Definition Take 1
  638.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  639.    wt: 1:   13 Limits with Parameters and Derivatives Take II
  640.    wt: 1:   11 Limits at infinity Three Examples
  641.    wt: 1:   10 Three one sided limits with infinite values
  642.    wt: 1:   9 Limits Continuity and Composition
  643.    wt: 1:   8 Four Animated Examples
  644.    wt: 1:   7 Evaluation by immediate or delayed substitution
  645.    wt: 1:   6 Continuity at a point
  646.    wt: 1:   3 Decimal insights for limits continuity convergence
  647.    wt: 1:   2 Algebraic codification
  648.    wt: 1:   1 Numerical introduction
  649.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  650.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  651.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  652.    wt: 1:   G.5 Motions With Bounded Velocities
  653.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  654.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  655.    wt: 1:   F.5a Equicontinuity Theorems
  656.    wt: 1:   F.3 Intermediate Value Theorem
  657.    wt: 1:   F.2 Closed Range Theorem
  658.    wt: 1:   F.1 What Functions are Continuous
  659.    wt: 1:   E1 Error Control Inequalities
  660.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  661.    wt: 1:   B3 Bolzano Weierstrass Theorem
  662.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  663.    wt: 1:   PostScript For and Against Decimal Perspectives
  664.    wt: 1:   A1. Introduction
  665.    wt: 1:   Chapter 23 Links To Trigonometry
  666.    wt: 1:   Chapter 22 Complex Numbers
  667.    wt: 1:   Chapter 21 Arrow Addition
  668.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  669.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  670.    wt: 1:   Chapter 18. Slopes Areas Integration
  671.    wt: 1:   Chapter 17. Area Approximation
  672.    wt: 1:   Chapter 16. Velocity Approximation
  673.    wt: 1:   Chapter 15. Slope Approximation
  674.    wt: 1:   Chapter 13. Acceleration
  675.    wt: 1:   Chapter 12. Units and Slopes
  676.    wt: 1:   Chapter 11. Graphing Slope versus Position
  677.    wt: 1:   Chapter 10 Slopes and Units
  678.    wt: 1:   Chapter 9 About First Courses in Calculus
  679.    wt: 1:   Chapter 8. Slope Interpretation
  680.    wt: 1:   Chapter 7 Slopes and Velocity
  681.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  682.    wt: 1:   Chapter 5. Slope Sign Tests
  683.    wt: 1:   Chapter 3. Slope Sign Analysis
  684.    wt: 1:   Chapter 2. Slopes and Ski Trails
  685.    wt: 1:   Chapter 1.Introduction
  686.    wt: 1:   Fall 1983 Calculus Appetizer
  687.    wt: 1:   Foreword
  688.    wt: 1:   Annotated Links to Material Elsehwere
  689.    wt: 1:   Postscript A Three Remarks
  690.    wt: 1:   Chapter 12 Four Phases
  691.    wt: 1:   Chapter 11 Elementary Instruction
  692.    wt: 1:   Chapter 10 Transition
  693.    wt: 1:   Chapter 9 The Two Ends
  694.    wt: 1:   Chapter 8 Modern Instruction
  695.    wt: 1:   Chapter 5 Four References
  696.    wt: 1:   Chapter 3 Algebra Difficulties
  697.    wt: 1:   Chapter 2 For and Against Mathematics
  698.    wt: 1:   Chapter 1 Introduction
  699.    wt: 1:   Foreword
  700.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  701.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  702.    wt: 1:   N Mathematics Prepare for College Studies
  703.    wt: 1:   D. Check work a must with a caution
  704.    wt: 1:   C. Domino effect of being careful
  705.    wt: 1:   B. Domino effect of errors
  706.    wt: 1:   Chapter 8 Skipped Topics and Why
  707.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  708.    wt: 1:   Chapter 6 More Algebra and Geometry
  709.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  710.    wt: 1:   Chapter 3 Algebra Starter Lessons
  711.    wt: 1:   Chapter 2 Why Sets
  712.    wt: 1:   Chapter 1 Arithmetic
  713.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  714.    wt: 1:   7 Games and Activities for Instruction
  715.    wt: 1:   5 Interpreting and Drawing Maps and Plans.
  716.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  717.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  718.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  719.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  720.    wt: 1:   Mathematics Education References
  721.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  722.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry

Teachers & Tutors: Site pages offer better or best practices for providing skills - simpler than expected & comprehensive but for exercises. For your charges, your duty is to study them alone or in groups and develop skill building exercises & activities to share. Start now. The effort here is the best I can do. Others are welcome to refine or exceed it. Please do.

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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