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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43 matches:

  1.    wt: 7:   12 Comparison of Unsigned and Signed Numbers/
  2.    wt: 7:   7 Arithmetic and Fractions with Units/
  3.    wt: 7:   6 Fractions and Ratios/
  4.    wt: 6:   11 Squares and Square Roots/
  5.    wt: 6:   10 LCM GCD and Euclid GCD Algorithm/
  6.    wt: 6:   9 Combinatorics Trees Tables and Products/
  7.    wt: 6:   8 Arithmetic with Signed Numbers/
  8.    wt: 6:   4 Remainder Arithmetic and Divisibility/
  9.    wt: 6:   3 Prime Factorization Skills/
  10.    wt: 6:   B Decimal Comparing and Subtracting Methods/
  11.    wt: 6:   A Decimal Counting and Adding Methods/
  12.    wt: 5:   5 Integers/
  13.    wt: 5:   D Decimal Long Division Methods/
  14.    wt: 5:   C Decimal Multiplication Methods/
  15.    wt: 5:   2 Arithmetic with Decimals/
  16.    wt: 5:   1 Decimal Place Value/
  17.    wt: 5:   Arithmetic and Number Theory Skills/
  18.    wt: 2:   Step 1 Stick diagram and fractions/
  19.    wt: 2:   PreSchool and Primary Mathematics or Quantitative Skills/
  20.    wt: 1:   Mathematics Skills Year by Year/
  21.    wt: 1:   14 Degrees to Radians and Radians to Degrees/
  22.    wt: 1:   12 Function Translating and Rescaling/
  23.    wt: 1:   11 Parallel Straight Lines and Transversals/
  24.    wt: 1:   10 Intersecting Straight Lines and Transversals/
  25.    wt: 1:   9 Lines and Slopes Take 2 with tangent function/
  26.    wt: 1:   7 Complex Numbers/
  27.    wt: 1:   4 Lines and Slopes Take 1/
  28.    wt: 1:   3 Cartesian and Polar Coordinates/
  29.    wt: 1:   2 Euclidean Geometry Constructions Theory extras/
  30.    wt: 1:   B Real Numbers Extrinsic Development/
  31.    wt: 1:   A Origins of Counting and Figuring Methods/
  32.    wt: 1:   9 Proportionality Backwards and Forwards/
  33.    wt: 1:   7 Axioms Logic and Equivalent Equations/
  34.    wt: 1:   6 More Less Greater Than Inequalities and Comparison/
  35.    wt: 1:   5 Real Numbers/
  36.    wt: 1:   4 Computation Rules and Function Notation/
  37.    wt: 1:   Time Date Matters/
  38.    wt: 1:   Skills with take home value/
  39.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  40.    wt: 1:   13 Lessons on Limits and Continuity/
  41.    wt: 1:   Volume 2 Three Skills For Algebra/
  42.    wt: 1:   Work and Study Tips/
  43.    wt: 1:   Resources and Reciprocal Links/

Web Page Search

357 matches:

  1.    wt: 4:   C Equality for Fractions and Two Term Ratios and Fractions
  2.    wt: 3:   8 Division and Mulplication of Compound Fractions
  3.    wt: 3:   9 Improper Fractions and Mixed Numbers
  4.    wt: 3:   P Exact Arithmetic With Whole Numbers and Fractions
  5.    wt: 3:   Primary and Secondary Skills and Practices with Take Home Value
  6.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  7.    wt: 2:   Ramblings Extrinsic numbers theory
  8.    wt: 2:   2 Reading and Writing Skills
  9.    wt: 2:   Vector and Complex Number Applet
  10.    wt: 2:   Construction Methods and Criteria for Isometric and Similar Triangles
  11.    wt: 2:   14 cosine even and sine and tangent are odd
  12.    wt: 2:   3 Lengths and Areas on Maps and Plans
  13.    wt: 2:   11 Signed Number Addition and Addition Properties
  14.    wt: 2:   2 Combing Counts Addition Skills and Principles
  15.    wt: 2:   6 Compound Interest Forward and Backwards
  16.    wt: 2:   2 More and Less Than for Counts and Measures
  17.    wt: 2:   10 Real Number Lengths and Signs
  18.    wt: 2:   1 Whole and Natural Numbers
  19.    wt: 2:   5 Talking about Numbers and Quantities
  20.    wt: 2:   4 A Brief Story of numbers and algebra
  21.    wt: 2:   1 More and Less Than for Counts and Measures
  22.    wt: 2:   11 What are real lengths and numbers
  23.    wt: 2:   5 lengths and signs of numbers
  24.    wt: 2:   2 signed and unsigned numbers as coordinates
  25.    wt: 2:   5 Reciprocals and Division for Fractions with Units
  26.    wt: 2:   3 Multiplying Units and Numbers
  27.    wt: 2:   B Fractions and Two Term Ratios
  28.    wt: 2:   A Similarities between Fractions and Two Term Ratios
  29.    wt: 2:   22 Complex Compound Fractions
  30.    wt: 2:   21 Reciprocals for Fractions and Wholes
  31.    wt: 2:   10 Simplification of Fractions and Mixed Numerals
  32.    wt: 2:   8 What skills and work habits to require
  33.    wt: 2:   6. Counting and adding units and mixed units
  34.    wt: 2:   10 Names for Big Numbers and Powers of Ten Expansion
  35.    wt: 2:   Quick history of numbers and algebra
  36.    wt: 2:   Exact Arithmetic Wholes and Fractions
  37.    wt: 2:   38 Formulas and derivatives for powers and roots
  38.    wt: 2:   D1 Sets and Sequences GLBs and LGBs
  39.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  40.    wt: 2:   Chapter 14 Limits and Continuity with and sans Decimals
  41.    wt: 2:   Chapter 5 Islands and Divisions of Knowledge
  42.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  43.    wt: 2:   Chapter 16 Origins and Limitations of Rules and Patterns
  44.    wt: 2:   Chapter 12 Islands and Divisions of Knowledge
  45.    wt: 2:   V Reasons and Motivations for Logic and Mathematics
  46.    wt: 2:   I. Logic and language skills
  47.    wt: 2:   How to Build Skills and Confidence
  48.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  49.    wt: 2:   2 Identifying Size and Position Place and Spatial Sense
  50.    wt: 2:   1 From Number Recognition and Counting to Arithmetic B
  51.    wt: 2:   1 From Number Recognition and Counting to Arithmetic A
  52.    wt: 1:   Appendix 1 primary and preschool mathematic
  53.    wt: 1:   G LAMP Introduction Problem Solving Skills
  54.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  55.    wt: 1:   Skills Chapter 5 Calculus
  56.    wt: 1:   Skills Chapter 4 Logic
  57.    wt: 1:   Skills Chapter 3 Algebra
  58.    wt: 1:   Skills Chapter 2 Geometry
  59.    wt: 1:   Skills Chapter 1 Arithmetic
  60.    wt: 1:   Skills Chapter 0 Introduction
  61.    wt: 1:   7 logic review and decimals an odd combination
  62.    wt: 1:   5 logarithms and exponentials etc
  63.    wt: 1:   2 arithmetic with signed numbers
  64.    wt: 1:   1 arithmetic with unsigned numbers
  65.    wt: 1:   key notes and themes
  66.    wt: 1:   what should be learnt and When
  67.    wt: 1:   standards for course material
  68.    wt: 1:   Theory of Knowledge
  69.    wt: 1:   Education in mathematics science and technology
  70.    wt: 1:   Motivation and Context Problem
  71.    wt: 1:   fairness and inductive principles for instruction
  72.    wt: 1:   Home Tutoring and Home Schooling
  73.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  74.    wt: 1:   24 Standards For Skill Develoment Take II
  75.    wt: 1:   24 Standards For Skill Develoment
  76.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  77.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  78.    wt: 1:   17 Math Booklets for children and young teenagers
  79.    wt: 1:   14 Multiplication and Times Tables
  80.    wt: 1:   13 Addition and Addition Tables
  81.    wt: 1:   12 Goals and Objectives For Mathematics
  82.    wt: 1:   11 Help and Defend Your Child or Teens Education
  83.    wt: 1:   5 Patience Please for Yourself and Your Charges
  84.    wt: 1:   4 Learning Takes Time and Effort
  85.    wt: 1:   1 Speaking Skills
  86.    wt: 1:   Ages 12 to 14 Skills with take home value
  87.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  88.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  89.    wt: 1:   26 Function definitions done and coming
  90.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  91.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  92.    wt: 1:   19 Horizontal line rule and method
  93.    wt: 1:   18 Vertical Line Rule and Method
  94.    wt: 1:   17 Function maxima minima and their location
  95.    wt: 1:   11 Function Domain Range Source and Targets
  96.    wt: 1:   9 Set theory term relation possible origins
  97.    wt: 1:   8 Set view of relations and functions
  98.    wt: 1:   6 Set Existence Formation and Notation
  99.    wt: 1:   4 Function notation in and beyond mathematics
  100.    wt: 1:   9 quadratics physical and further context
  101.    wt: 1:   11 Growth and Decay in Biology
  102.    wt: 1:   10 Exponential Growth and Decay Models
  103.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  104.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  105.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  106.    wt: 1:   16 cotangent function Definition Graph and Inverse
  107.    wt: 1:   15 cosecant function Definition Graph and Inverse
  108.    wt: 1:   14 secant function Definition Graph and Inverse
  109.    wt: 1:   13 cosecant function Definition Graph and Inverse
  110.    wt: 1:   9 Summary Degrees to Radians and back
  111.    wt: 1:   1 Degrees and Radians Introduction
  112.    wt: 1:   A Global Time and Navigation
  113.    wt: 1:   15 Dot and Cross Product
  114.    wt: 1:   7 Coordinate Addition and Scalar Multiplication
  115.    wt: 1:   Parallel Lines and Parallel Transversals
  116.    wt: 1:   Parallel Lines and Alternating Corresponding Angles
  117.    wt: 1:   Parallel Lines and Interior Angles
  118.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  119.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  120.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  121.    wt: 1:   29 secant cosecant and cotangent for acute angles
  122.    wt: 1:   27 Logarithmic use of products of sines and cosines
  123.    wt: 1:   26 Formulas for products of sines and cosines
  124.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  125.    wt: 1:   21 sine and cosine Half Angle Formulas
  126.    wt: 1:   20 sine and cosine Double Angle Formulas
  127.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  128.    wt: 1:   17E Trig Formulas for dot and cross Products
  129.    wt: 1:   17D cis formulas for sine cosines and tangent
  130.    wt: 1:   17C sine and cosine double triple angle formulas
  131.    wt: 1:   17A The complex number valued trig function cis
  132.    wt: 1:   10 Graphs of sines and cosines many periods
  133.    wt: 1:   9 Graphs of sine and cosine over one period
  134.    wt: 1:   7 period of sine and cosine
  135.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  136.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  137.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  138.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  139.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  140.    wt: 1:   21 Logarithms Powers and Exponentials
  141.    wt: 1:   20 N th Roots of Complex Numbers
  142.    wt: 1:   16 References and Originality Question
  143.    wt: 1:   13 Trig Formulas for dot and cross Products
  144.    wt: 1:   12 cis formulas for sine cosines and tangent
  145.    wt: 1:   11 sine and cosine double triple angle formulas
  146.    wt: 1:   9 The complex number valued trig function cis
  147.    wt: 1:   6 Field Properties of Complex Number
  148.    wt: 1:   2 Complex Numbers made easier we hope
  149.    wt: 1:   Appetizer A Complex Number Applet
  150.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  151.    wt: 1:   3 Trigonometric Ratios sine and cosine
  152.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  153.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  154.    wt: 1:   8 Similarity of Triangles and Polygons
  155.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  156.    wt: 1:   10 Midpoint of [a b] and [b a]
  157.    wt: 1:   7 Exercises to test skill and concept mastery
  158.    wt: 1:   1 Numerical view of lines and their equations
  159.    wt: 1:   What is and is not here
  160.    wt: 1:   7 Complex Numbers Appetizer
  161.    wt: 1:   6 Polar Multiplication and Rotation
  162.    wt: 1:   5 Cartesian Addition and Translation
  163.    wt: 1:   4 Polar Coordinates to and from
  164.    wt: 1:   PS H Distributive Law For Complex Numbers
  165.    wt: 1:   16 Angles Subtended By Chords and Diameters
  166.    wt: 1:   6 Ruler and compass Angle Bisection
  167.    wt: 1:   1 Initial Concepts and Terms
  168.    wt: 1:   musings do not puiblish real numbers
  169.    wt: 1:   A Modular and Remainder Arithmetic
  170.    wt: 1:   A Signed Number Arithmetic Review
  171.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  172.    wt: 1:   22 Multiplication of Signed Numbers
  173.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  174.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  175.    wt: 1:   13 Arrows and Vectors in a Plane
  176.    wt: 1:   12 Real Numbers Line Signed Coordinates
  177.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  178.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  179.    wt: 1:   1 Fractions with Finite Decimal Expansions
  180.    wt: 1:   B Decimal Comparison and Subtraction
  181.    wt: 1:   5 Distributive Law for Whole Numbers
  182.    wt: 1:   3 Multiplicative Counting Skills Principles
  183.    wt: 1:   1 The Counting Origins of Numbers
  184.    wt: 1:   5 Areas of Rectangles Revisited
  185.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  186.    wt: 1:   5 Proportionality in Equivalent Fractions
  187.    wt: 1:   4 Rates Ratios and Proporitionality
  188.    wt: 1:   9 Circle Area and Perimeter Formula Backwards Forwards
  189.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  190.    wt: 1:   6 Equations and Systems Equivalent or Implied
  191.    wt: 1:   4 Subtraction and Division Axioms
  192.    wt: 1:   2 Addition and Multiplication Axioms
  193.    wt: 1:   4 Comparison of Negative Numbers
  194.    wt: 1:   3 More and Less Than with Unlike Signs
  195.    wt: 1:   1 Real Numbers Comparison
  196.    wt: 1:   16 Real Numbers Comparison
  197.    wt: 1:   15 Real Number Division
  198.    wt: 1:   14 Real Number Multiplication
  199.    wt: 1:   13 Real Number Subtraction
  200.    wt: 1:   12 Real Number Additive Inverses or Negatives
  201.    wt: 1:   11 Real Number Addition
  202.    wt: 1:   8 Coordinates for Maps and Planes
  203.    wt: 1:   7 Real Numbers as Line Cordinates
  204.    wt: 1:   6 Unsigned Real Numbers
  205.    wt: 1:   5 Rational Numbers More
  206.    wt: 1:   4 Rational Numbers
  207.    wt: 1:   3 Fractions
  208.    wt: 1:   3 Geometric Formulas and Function Notation
  209.    wt: 1:   1 Formulas Dependence and Function Notation
  210.    wt: 1:   3 GE III Equation Addition and Multiplication
  211.    wt: 1:   8 Compound Interest Formula Evaluation
  212.    wt: 1:   7 Compound Interest Formula Introduction
  213.    wt: 1:   1 Written work formats for developing and showing skill
  214.    wt: 1:   9 Sets in Probability and Statistics
  215.    wt: 1:   8 Sets of Numbers
  216.    wt: 1:   1 Three Skills For Algebra
  217.    wt: 1:   3 Comparison of Negative Numbers
  218.    wt: 1:   2 More and Less Than with Unlike Signs
  219.    wt: 1:   1 Squares and Square Roots Introduction
  220.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  221.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  222.    wt: 1:   10 Euclid Algorithm with 129 125 and with 45 14
  223.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  224.    wt: 1:   7 GCD and LCM from prime factorization
  225.    wt: 1:   4 LCM of 8 and 10 via Prime
  226.    wt: 1:   3 Counting with Tables and Trees II
  227.    wt: 1:   2 Counting with Tables and Trees I
  228.    wt: 1:   1 Counting and Counting Methods I
  229.    wt: 1:   10 dividing signed numbers
  230.    wt: 1:   9 subtracting signed numbers
  231.    wt: 1:   8 multiplying signed numbers
  232.    wt: 1:   7 negative and additive inverse
  233.    wt: 1:   6 adding signed numbers
  234.    wt: 1:   3 signed coordinates for maps and planes
  235.    wt: 1:   6 Simplification of Fractions with Units
  236.    wt: 1:   4 Fractions with Units
  237.    wt: 1:   2 Equality and Units
  238.    wt: 1:   1 Addition and Subtraction with Units
  239.    wt: 1:   20 Dividing Fractions the Why
  240.    wt: 1:   19 Dividing Fractions How TO
  241.    wt: 1:   17 Efficient Ways to Add and Subtract
  242.    wt: 1:   15 Adding and Subtracting with Unlike Denominators
  243.    wt: 1:   14 Adding and Subtracting with Like Denominators
  244.    wt: 1:   6 Multiplication of Mixed Numbers
  245.    wt: 1:   5 Equivalent Fractions
  246.    wt: 1:   11 Adding Integers Formulas and Examples
  247.    wt: 1:   8 Multiplication by Signed Numbers Integers
  248.    wt: 1:   6 Multiplication by Natural Numbers
  249.    wt: 1:   5 Zero Movement and Additive Inverses
  250.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  251.    wt: 1:   17 Identify and Count Factors using Primes
  252.    wt: 1:   12 LCD GCD and LCM using Primes
  253.    wt: 1:   7 Calculator Usage Notes and Cautions
  254.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  255.    wt: 1:   5 Prime Factorization and a Square Rule
  256.    wt: 1:   3 video Primes and Composites from 9 times table
  257.    wt: 1:   2 Prime and Composites less than 16
  258.    wt: 1:   Division with Counts and Length
  259.    wt: 1:   Long Division forwards and backwards Example 3
  260.    wt: 1:   Long Division forwards and backwards Example 2
  261.    wt: 1:   Long Division forwards and backwards Example 1
  262.    wt: 1:   10 Division by Five Long and Short Ways
  263.    wt: 1:   4 Two and Three Digit Multipliers
  264.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  265.    wt: 1:   4 Subtraction with Conversions Borrows and Letter J
  266.    wt: 1:   3 Harder Cases Convert to Compare and Subtract
  267.    wt: 1:   1 Comparison and Subtraction Easy Direct Cases
  268.    wt: 1:   Appendix 1 Counting Revisited 15 minute video
  269.    wt: 1:   7 Adding decimal fractions using decimal point
  270.    wt: 1:   11 Place Value SI Standard International way
  271.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  272.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  273.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  274.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  275.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  276.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  277.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  278.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  279.    wt: 1:   016 Numbering Occidental Calendar Days
  280.    wt: 1:   015 School and work day counting tables
  281.    wt: 1:   011 Division of Time Intervals By Numbers
  282.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  283.    wt: 1:   4 Mixing and Changing Units of Time
  284.    wt: 1:   3 Units and Lengths of Time
  285.    wt: 1:   2 Time and Date Matters in School
  286.    wt: 1:   1 Intro of Kids To Time Date Skills
  287.    wt: 1:   Example 1. Area Between x and x squared
  288.    wt: 1:   17 Derivatives of quotients of sine and cosine
  289.    wt: 1:   16 Derivatives of reciprocals of sine and cosine
  290.    wt: 1:   15 sine and cosine derivatives 3rd step
  291.    wt: 1:   14 sine and cosine derivatives 2nd step
  292.    wt: 1:   13 sine and cosine derivatives 1st step
  293.    wt: 1:   13 Limits with Parameters and Derivatives Take II
  294.    wt: 1:   12 Limits with Parameters and Derivatives Take I
  295.    wt: 1:   9 Limits Continuity and Composition
  296.    wt: 1:   5 Jumps and absence of unlimited error control
  297.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  298.    wt: 1:   PostScript For and Against Decimal Perspectives
  299.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  300.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  301.    wt: 1:   Chapter 22 Complex Numbers
  302.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  303.    wt: 1:   Chapter 12. Units and Slopes
  304.    wt: 1:   Chapter 10 Slopes and Units
  305.    wt: 1:   Chapter 7 Slopes and Velocity
  306.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  307.    wt: 1:   Chapter 2. Slopes and Ski Trails
  308.    wt: 1:   Appendix E. How To Study Mathematics and Why
  309.    wt: 1:   Appendix D. What to do in School and Why
  310.    wt: 1:   Chapter 31 Direct and Indirect Reason
  311.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  312.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  313.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  314.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  315.    wt: 1:   Chapter 20. Degrees and Radians
  316.    wt: 1:   Chapter 19. Functions and Sets
  317.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  318.    wt: 1:   Chapter 12. Shorthand Usage Guide
  319.    wt: 1:   Chapter 11. Why Shorthand
  320.    wt: 1:   Chapter 10 Describing and Changing Calculations
  321.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  322.    wt: 1:   Chapter 8 Three Skills For Algebra
  323.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  324.    wt: 1:   Chapter 2 For and Against Mathematics
  325.    wt: 1:   Postscript B More on Story Telling and Reason
  326.    wt: 1:   Chapter 24 Direct and Indirect Reason
  327.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  328.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  329.    wt: 1:   Chapter 18 Sense and Knowledge
  330.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  331.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  332.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  333.    wt: 1:   R Why Learn Mathematics Skills
  334.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  335.    wt: 1:   O On Learning Mathematics and Science
  336.    wt: 1:   L Skills with take home value
  337.    wt: 1:   N Improving Marks on Tests and Finals
  338.    wt: 1:   J. More on written work and showing skill
  339.    wt: 1:   H Jigsaw puzzles and problem solving
  340.    wt: 1:   G. Written work formats for developing and showing skill
  341.    wt: 1:   E. When and how to correct errors
  342.    wt: 1:   Chapter 8 Skipped Topics and Why
  343.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  344.    wt: 1:   Chapter 6 More Algebra and Geometry
  345.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  346.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  347.    wt: 1:   7 Games and Activities for Instruction
  348.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  349.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  350.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  351.    wt: 1:   Helping the Blind in Logic and Mathematics
  352.    wt: 1:   More Algebra and Slope based Calculus Preview
  353.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  354.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  355.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  356.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  357.    wt: 1:   The Math Forum and Site Content

Extended Search

706 matches:

  1.    wt: 9:   1 More and Less Than for Counts and Measures
  2.    wt: 9:   5 Reciprocals and Division for Fractions with Units
  3.    wt: 9:   3 Multiplying Units and Numbers
  4.    wt: 9:   B Fractions and Two Term Ratios
  5.    wt: 9:   A Similarities between Fractions and Two Term Ratios
  6.    wt: 9:   22 Complex Compound Fractions
  7.    wt: 9:   21 Reciprocals for Fractions and Wholes
  8.    wt: 9:   10 Simplification of Fractions and Mixed Numerals
  9.    wt: 8:   3 Comparison of Negative Numbers
  10.    wt: 8:   2 More and Less Than with Unlike Signs
  11.    wt: 8:   11 What are real lengths and numbers
  12.    wt: 8:   5 lengths and signs of numbers
  13.    wt: 8:   2 signed and unsigned numbers as coordinates
  14.    wt: 8:   6 Simplification of Fractions with Units
  15.    wt: 8:   4 Fractions with Units
  16.    wt: 8:   2 Equality and Units
  17.    wt: 8:   1 Addition and Subtraction with Units
  18.    wt: 8:   20 Dividing Fractions the Why
  19.    wt: 8:   19 Dividing Fractions How TO
  20.    wt: 8:   17 Efficient Ways to Add and Subtract
  21.    wt: 8:   15 Adding and Subtracting with Unlike Denominators
  22.    wt: 8:   14 Adding and Subtracting with Like Denominators
  23.    wt: 8:   6 Multiplication of Mixed Numbers
  24.    wt: 8:   5 Equivalent Fractions
  25.    wt: 8:   8 What skills and work habits to require
  26.    wt: 8:   6. Counting and adding units and mixed units
  27.    wt: 7:   4 Greater More Less Than Signs in General
  28.    wt: 7:   1 Squares and Square Roots Introduction
  29.    wt: 7:   17 GCD LCM of 85 and 60 via Prime
  30.    wt: 7:   16 GCD and LCM of 650 225 via Prime
  31.    wt: 7:   10 Euclid Algorithm with 129 125 and with 45 14
  32.    wt: 7:   9 GCD of 360 110 via Primes and Euclid Algorithm
  33.    wt: 7:   7 GCD and LCM from prime factorization
  34.    wt: 7:   4 LCM of 8 and 10 via Prime
  35.    wt: 7:   3 Counting with Tables and Trees II
  36.    wt: 7:   2 Counting with Tables and Trees I
  37.    wt: 7:   1 Counting and Counting Methods I
  38.    wt: 7:   10 dividing signed numbers
  39.    wt: 7:   9 subtracting signed numbers
  40.    wt: 7:   8 multiplying signed numbers
  41.    wt: 7:   7 negative and additive inverse
  42.    wt: 7:   6 adding signed numbers
  43.    wt: 7:   3 signed coordinates for maps and planes
  44.    wt: 7:   7 Converting or Changing Units
  45.    wt: 7:   D Three Term Ratios
  46.    wt: 7:   21 Working With Signs
  47.    wt: 7:   18 Efficient Ways to Multiply
  48.    wt: 7:   16 Addition Subtraction Comparision Compared
  49.    wt: 7:   13 Fraction Comparison Algebraic View
  50.    wt: 7:   12 Fraction Comparison
  51.    wt: 7:   11 Simplification an Algebraic View
  52.    wt: 7:   8 Numerals Fractionals Quantals Take II
  53.    wt: 7:   7 Numerals Fractionals Quantals
  54.    wt: 7:   6 Multiplication Algebraically Take II
  55.    wt: 7:   4 Fraction Multiplication
  56.    wt: 7:   3 Unit fraction of a fraction
  57.    wt: 7:   2 Unit Fraction Multiplication
  58.    wt: 7:   1 What is a fraction Take II
  59.    wt: 7:   1 What is a fraction
  60.    wt: 7:   Fraction Operations by Raising Terms A Simple Innovation
  61.    wt: 7:   A Decimals Modular and Remainder Arithmetic
  62.    wt: 7:   17 Identify and Count Factors using Primes
  63.    wt: 7:   12 LCD GCD and LCM using Primes
  64.    wt: 7:   7 Calculator Usage Notes and Cautions
  65.    wt: 7:   6 Sieve of Eratosthenes and Square Rule
  66.    wt: 7:   5 Prime Factorization and a Square Rule
  67.    wt: 7:   3 video Primes and Composites from 9 times table
  68.    wt: 7:   2 Prime and Composites less than 16
  69.    wt: 7:   7 Subtraction for Decimal Fractions with Exercises
  70.    wt: 7:   4 Subtraction with Conversions Borrows and Letter J
  71.    wt: 7:   3 Harder Cases Convert to Compare and Subtract
  72.    wt: 7:   1 Comparison and Subtraction Easy Direct Cases
  73.    wt: 7:   Appendix 1 Counting Revisited 15 minute video
  74.    wt: 7:   7 Adding decimal fractions using decimal point
  75.    wt: 7:   10 Names for Big Numbers and Powers of Ten Expansion
  76.    wt: 7:   Quick history of numbers and algebra
  77.    wt: 7:   Exact Arithmetic Wholes and Fractions
  78.    wt: 6:   5 Square Roots with primes more still
  79.    wt: 6:   4 Square Roots with primes more
  80.    wt: 6:   3 Properties of Square Roots with example
  81.    wt: 6:   2 Square Roots with Prime
  82.    wt: 6:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  83.    wt: 6:   14 GCD of 650 110 via Primes LCM via Product Rule
  84.    wt: 6:   13 GCD from given Prime Factorization
  85.    wt: 6:   11 GCD 2700 288 via Euclid Algorithm
  86.    wt: 6:   8 GCD from Euclidean Algorithm
  87.    wt: 6:   6 GCD from Prime
  88.    wt: 6:   5 Common Divisors 60 45 via Prime
  89.    wt: 6:   LCM 60 45 Avoid List Method Use Prime
  90.    wt: 6:   2 Least Common Multiple LCM intro via list method
  91.    wt: 6:   1 Least Common Multiples LCM Introduction
  92.    wt: 6:   12 GCD 2700 288 via Prime
  93.    wt: 6:   5 Counting with Tables Trees Product Rule Take II
  94.    wt: 6:   4 Counting with Trees Product Rule Take I
  95.    wt: 6:   4 signed coordinates for regions in space
  96.    wt: 6:   11 Adding Integers Formulas and Examples
  97.    wt: 6:   8 Multiplication by Signed Numbers Integers
  98.    wt: 6:   6 Multiplication by Natural Numbers
  99.    wt: 6:   5 Zero Movement and Additive Inverses
  100.    wt: 6:   27 Divisibility by 2 3 6 5 9 10 Example
  101.    wt: 6:   26 Divisibility by 2 3 5 Example
  102.    wt: 6:   25 Divisibility Tests for 2 3 5 9 10 Example
  103.    wt: 6:   24 Divisibility Tests for 2 3 5 9 10
  104.    wt: 6:   23 Remainder Arithmetic Modulo 2
  105.    wt: 6:   22 Remainder Arithmetic Modulo 3 more
  106.    wt: 6:   21 Remainder Arithmetic Modulo 3
  107.    wt: 6:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  108.    wt: 6:   19 Remainder Arithmetic Rule of 9 for checking sums III
  109.    wt: 6:   18 Remainder Arithmetic Rule of 9 for checking sums II
  110.    wt: 6:   17 Remainder Arithmetic Rule of 9 for checking sums I
  111.    wt: 6:   16 Remainder Arithmetic Modulo 9 Example 2
  112.    wt: 6:   15 Remainder Arithmetic Modulo 9 Example
  113.    wt: 6:   14 Remainder Arithmetic Modulo 9 Example
  114.    wt: 6:   13 Remainder Arithmetic Modulo 5 Example
  115.    wt: 6:   12 Remainder Arithmetic Modulo 10 Example
  116.    wt: 6:   11 Remainder Arithmetic Long Division by 5 Quickly more
  117.    wt: 6:   10 Remainder Arithmetic Long Division by 5 Quickly
  118.    wt: 6:   9 Remainder Arithmetic Divisibility by 5
  119.    wt: 6:   8 Remainder Arithmetic Morulo 5 Examples II
  120.    wt: 6:   7 Remainder Arithmetic Modulo 5 Examples I
  121.    wt: 6:   6 Remainder Arithmetic Modulo 5 Propertie
  122.    wt: 6:   5 Remainder Arithmetic Modulo 5
  123.    wt: 6:   4 Remainder Arithmetic Modulo 10 in general
  124.    wt: 6:   3 Remainder Arithmetic Modulos 10 more still
  125.    wt: 6:   2 Remainder Arithmetic Modulo 10 more
  126.    wt: 6:   1 Remainder Arithmetic Modulo 10
  127.    wt: 6:   20 Uniqueness of Prime Factorization
  128.    wt: 6:   19 video Prime Factorization Unique
  129.    wt: 6:   18 video Count Factors given Prime Factorization
  130.    wt: 6:   16 video Factors of 980 using prime
  131.    wt: 6:   15 video Factors of 20 using Prime Factorization
  132.    wt: 6:   14 video Factors of 24 Take II
  133.    wt: 6:   13 video Factors of 24 using prime
  134.    wt: 6:   11 Efficient Square Rule Use
  135.    wt: 6:   10 video Prime Factorization upto 23 squared
  136.    wt: 6:   9 video Prime Factorization upto 19 squared
  137.    wt: 6:   8 video Prime Factorization upto 19
  138.    wt: 6:   4 video Prime Factorization Introduction
  139.    wt: 6:   1 video how Products are bigger than factor
  140.    wt: 6:   Division with Counts and Length
  141.    wt: 6:   Long Division forwards and backwards Example 3
  142.    wt: 6:   Long Division forwards and backwards Example 2
  143.    wt: 6:   Long Division forwards and backwards Example 1
  144.    wt: 6:   10 Division by Five Long and Short Ways
  145.    wt: 6:   4 Two and Three Digit Multipliers
  146.    wt: 6:   Appendix 2 Three Decimal Subtraction Methods
  147.    wt: 6:   Appendix 1 Decimals Comparison Method Take II
  148.    wt: 6:   Subtraction with J Conversions Example
  149.    wt: 6:   Subtraction Another Video Lesson
  150.    wt: 6:   9 22 Minute Subtraction Review Video
  151.    wt: 6:   8 Subtraction with Units of Measure
  152.    wt: 6:   6 Subtraction with Conversion Example with Exercises
  153.    wt: 6:   5 A Tip for Efficent Subtraction
  154.    wt: 6:   2 Subtraction Easy Case Examples
  155.    wt: 6:   5. How to add decimals C. Examples
  156.    wt: 6:   4. How to add with decimals B with conversions
  157.    wt: 6:   3. How to add with decimals A sans conversions
  158.    wt: 6:   2 Decimal Counting Practices
  159.    wt: 6:   1. Explaining Addition Table
  160.    wt: 6:   11 Place Value SI Standard International way
  161.    wt: 6:   9 Place Value Review Decimal form of Avogrados number included
  162.    wt: 6:   8 Review Lesson 1 2 4 and 6 All in One
  163.    wt: 6:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  164.    wt: 6:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  165.    wt: 6:   5 More on Groups of 3 Place Value in Decimal Fractions
  166.    wt: 6:   4 Groups of 3 Place Value in Decimal Fractions
  167.    wt: 6:   1 Place Value in Three Digit Whole Numbers
  168.    wt: 6:   Practical Methods Ends and Values for Arithmetic
  169.    wt: 5:   arithmetic videos Real Player Format
  170.    wt: 5:   D Remainders Modulo 11 Pair Rule
  171.    wt: 5:   C Divisibility by 11 Integer Recognition Method
  172.    wt: 5:   B Integer Long Division Multiple Choices
  173.    wt: 5:   A Associative Law Theorectical Note
  174.    wt: 5:   13 Subtraction with Additive Inverse
  175.    wt: 5:   12 Adding Integers More Examples
  176.    wt: 5:   10 Integer Multiplication Formulas
  177.    wt: 5:   9 Multiplying Integers
  178.    wt: 5:   7 Multiplication by Signs
  179.    wt: 5:   4 Adding Movements wiht opposite directions
  180.    wt: 5:   3 Adding Movements with same direction
  181.    wt: 5:   2 Integers Multiplies of a Unit Moverment
  182.    wt: 5:   1 Integers as Coordinates
  183.    wt: 5:   Long Division Backwards more
  184.    wt: 5:   Long Division Backward
  185.    wt: 5:   12 Why Long Division Works Take III
  186.    wt: 5:   11 Another Single Digit Divisor Example
  187.    wt: 5:   9 Why Long Division Works Take II
  188.    wt: 5:   8 Correcting the Mistake
  189.    wt: 5:   7 Long Divison Mistake Catching
  190.    wt: 5:   6 Why Decimal Long Division Methods Works Take I
  191.    wt: 5:   5 Long Division Include Zeroes or not
  192.    wt: 5:   4 Division with 2 Digit Divsors
  193.    wt: 5:   3 Division Single Digit Divisor Example
  194.    wt: 5:   2 Division with Single Digit Divisors
  195.    wt: 5:   1 Divsion Physical Examples
  196.    wt: 5:   D Decimal Multiplication Methods Derived
  197.    wt: 5:   C Counting Areas with Powers of Ten
  198.    wt: 5:   B Powers of Ten
  199.    wt: 5:   A Elementary Basis for Multiplication Methods
  200.    wt: 5:   6 Multiplication Commutes Order Not Important
  201.    wt: 5:   5 Decimal Fraction Multiplication
  202.    wt: 5:   3 More One Digit Multipliers
  203.    wt: 5:   2 One Digit Multipliers
  204.    wt: 5:   Video Decimal Multiplication Geometric View Example 2
  205.    wt: 5:   Video Decimal Multiplication Geometric View Example 2
  206.    wt: 5:   Video Power Notation in Decimal Expansion
  207.    wt: 5:   1 Why 3 times 5 gives 15
  208.    wt: 5:   3 More on Groups of 3 Multi Digit Place Value
  209.    wt: 5:   2 Groups of Three Place Value for Multidigit Decimals
  210.    wt: 5:   Formula Evaluation how to show work
  211.    wt: 5:   Expression Evaluation how to show work
  212.    wt: 5:   The 20 Times Table
  213.    wt: 5:   The 12 Times Table Visually
  214.    wt: 5:   About folder contents
  215.    wt: 5:   Primary and Secondary Skills and Practices with Take Home Value
  216.    wt: 4:   8 Division and Mulplication of Compound Fractions
  217.    wt: 4:   P Exact Arithmetic With Whole Numbers and Fractions
  218.    wt: 4:   5 Interpreting and Drawing Maps and Plans.
  219.    wt: 4:   2 Identifying Size and Position Place and Spatial Sense
  220.    wt: 4:   1 From Number Recognition and Counting to Arithmetic B
  221.    wt: 4:   1 From Number Recognition and Counting to Arithmetic A
  222.    wt: 3:   Construction Methods and Criteria for Isometric and Similar Triangles
  223.    wt: 3:   11 Signed Number Addition and Addition Properties
  224.    wt: 3:   2 Combing Counts Addition Skills and Principles
  225.    wt: 3:   2 More and Less Than for Counts and Measures
  226.    wt: 3:   10 Real Number Lengths and Signs
  227.    wt: 3:   1 Whole and Natural Numbers
  228.    wt: 3:   Chapter 5 Islands and Divisions of Knowledge
  229.    wt: 3:   V Reasons and Motivations for Logic and Mathematics
  230.    wt: 3:   I. Logic and language skills
  231.    wt: 3:   How to Build Skills and Confidence
  232.    wt: 3:   7 Games and Activities for Instruction
  233.    wt: 3:   6 Measuring via counting or arithmetic the role of fractions
  234.    wt: 3:   4 Money Matters Saving Earning Buying Selling and Budgets
  235.    wt: 3:   3 Telling Tracking Time Temporal and More Place Sense
  236.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  237.    wt: 2:   Ramblings Extrinsic numbers theory
  238.    wt: 2:   2 Reading and Writing Skills
  239.    wt: 2:   Ages 12 to 14 Skills with take home value
  240.    wt: 2:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  241.    wt: 2:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  242.    wt: 2:   9 Summary Degrees to Radians and back
  243.    wt: 2:   1 Degrees and Radians Introduction
  244.    wt: 2:   Vector and Complex Number Applet
  245.    wt: 2:   Parallel Lines and Parallel Transversals
  246.    wt: 2:   Parallel Lines and Alternating Corresponding Angles
  247.    wt: 2:   Parallel Lines and Interior Angles
  248.    wt: 2:   14 cosine even and sine and tangent are odd
  249.    wt: 2:   21 Logarithms Powers and Exponentials
  250.    wt: 2:   20 N th Roots of Complex Numbers
  251.    wt: 2:   16 References and Originality Question
  252.    wt: 2:   13 Trig Formulas for dot and cross Products
  253.    wt: 2:   12 cis formulas for sine cosines and tangent
  254.    wt: 2:   11 sine and cosine double triple angle formulas
  255.    wt: 2:   9 The complex number valued trig function cis
  256.    wt: 2:   6 Field Properties of Complex Number
  257.    wt: 2:   2 Complex Numbers made easier we hope
  258.    wt: 2:   Appetizer A Complex Number Applet
  259.    wt: 2:   10 Midpoint of [a b] and [b a]
  260.    wt: 2:   7 Exercises to test skill and concept mastery
  261.    wt: 2:   1 Numerical view of lines and their equations
  262.    wt: 2:   What is and is not here
  263.    wt: 2:   7 Complex Numbers Appetizer
  264.    wt: 2:   6 Polar Multiplication and Rotation
  265.    wt: 2:   5 Cartesian Addition and Translation
  266.    wt: 2:   4 Polar Coordinates to and from
  267.    wt: 2:   PS H Distributive Law For Complex Numbers
  268.    wt: 2:   16 Angles Subtended By Chords and Diameters
  269.    wt: 2:   6 Ruler and compass Angle Bisection
  270.    wt: 2:   1 Initial Concepts and Terms
  271.    wt: 2:   3 Lengths and Areas on Maps and Plans
  272.    wt: 2:   musings do not puiblish real numbers
  273.    wt: 2:   A Modular and Remainder Arithmetic
  274.    wt: 2:   A Signed Number Arithmetic Review
  275.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  276.    wt: 2:   22 Multiplication of Signed Numbers
  277.    wt: 2:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  278.    wt: 2:   14 Vector Head to Tail Sums and Resultants
  279.    wt: 2:   13 Arrows and Vectors in a Plane
  280.    wt: 2:   12 Real Numbers Line Signed Coordinates
  281.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  282.    wt: 2:   5 Fractions with Infinite Decimal Expansions
  283.    wt: 2:   1 Fractions with Finite Decimal Expansions
  284.    wt: 2:   B Decimal Comparison and Subtraction
  285.    wt: 2:   5 Distributive Law for Whole Numbers
  286.    wt: 2:   3 Multiplicative Counting Skills Principles
  287.    wt: 2:   1 The Counting Origins of Numbers
  288.    wt: 2:   5 Proportionality in Equivalent Fractions
  289.    wt: 2:   4 Rates Ratios and Proporitionality
  290.    wt: 2:   6 Compound Interest Forward and Backwards
  291.    wt: 2:   6 Equations and Systems Equivalent or Implied
  292.    wt: 2:   4 Subtraction and Division Axioms
  293.    wt: 2:   2 Addition and Multiplication Axioms
  294.    wt: 2:   4 Comparison of Negative Numbers
  295.    wt: 2:   3 More and Less Than with Unlike Signs
  296.    wt: 2:   1 Real Numbers Comparison
  297.    wt: 2:   16 Real Numbers Comparison
  298.    wt: 2:   15 Real Number Division
  299.    wt: 2:   14 Real Number Multiplication
  300.    wt: 2:   13 Real Number Subtraction
  301.    wt: 2:   12 Real Number Additive Inverses or Negatives
  302.    wt: 2:   11 Real Number Addition
  303.    wt: 2:   8 Coordinates for Maps and Planes
  304.    wt: 2:   7 Real Numbers as Line Cordinates
  305.    wt: 2:   6 Unsigned Real Numbers
  306.    wt: 2:   5 Rational Numbers More
  307.    wt: 2:   4 Rational Numbers
  308.    wt: 2:   3 Fractions
  309.    wt: 2:   3 Geometric Formulas and Function Notation
  310.    wt: 2:   1 Formulas Dependence and Function Notation
  311.    wt: 2:   Skill Development Notes
  312.    wt: 2:   10 One Example
  313.    wt: 2:   9 Three Examples
  314.    wt: 2:   8 One Example
  315.    wt: 2:   7 Two Examples
  316.    wt: 2:   6 Three Examples
  317.    wt: 2:   5 Three Examples
  318.    wt: 2:   4 Two Examples
  319.    wt: 2:   3 Two Examples
  320.    wt: 2:   2 Three Examples
  321.    wt: 2:   5 Talking about Numbers and Quantities
  322.    wt: 2:   4 A Brief Story of numbers and algebra
  323.    wt: 2:   016 Numbering Occidental Calendar Days
  324.    wt: 2:   015 School and work day counting tables
  325.    wt: 2:   011 Division of Time Intervals By Numbers
  326.    wt: 2:   9 Comparison and Subtraction of Time Intervals
  327.    wt: 2:   4 Mixing and Changing Units of Time
  328.    wt: 2:   3 Units and Lengths of Time
  329.    wt: 2:   2 Time and Date Matters in School
  330.    wt: 2:   1 Intro of Kids To Time Date Skills
  331.    wt: 2:   Example 1. Area Between x and x squared
  332.    wt: 2:   38 Formulas and derivatives for powers and roots
  333.    wt: 2:   13 Limits with Parameters and Derivatives Take II
  334.    wt: 2:   12 Limits with Parameters and Derivatives Take I
  335.    wt: 2:   9 Limits Continuity and Composition
  336.    wt: 2:   5 Jumps and absence of unlimited error control
  337.    wt: 2:   D1 Sets and Sequences GLBs and LGBs
  338.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  339.    wt: 2:   Chapter 14 Limits and Continuity with and sans Decimals
  340.    wt: 2:   Appendix E. How To Study Mathematics and Why
  341.    wt: 2:   Appendix D. What to do in School and Why
  342.    wt: 2:   Chapter 31 Direct and Indirect Reason
  343.    wt: 2:   Chapter 29 Contrapositive and Vacuously True Implications
  344.    wt: 2:   Chapter 27 Shorthand Symbols as Pronouns
  345.    wt: 2:   Chapter 24. Personal Investment and Pension EGS
  346.    wt: 2:   Chapter 22. Geometric Sums and Sequences
  347.    wt: 2:   Chapter 20. Degrees and Radians
  348.    wt: 2:   Chapter 19. Functions and Sets
  349.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  350.    wt: 2:   Chapter 12. Shorthand Usage Guide
  351.    wt: 2:   Chapter 11. Why Shorthand
  352.    wt: 2:   Chapter 10 Describing and Changing Calculations
  353.    wt: 2:   Chapter 9 Talking about Numbers or Quantities
  354.    wt: 2:   Chapter 8 Three Skills For Algebra
  355.    wt: 2:   Chapter 2 Implication Rules Forwards and Backwards
  356.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  357.    wt: 2:   Chapter 16 Origins and Limitations of Rules and Patterns
  358.    wt: 2:   Chapter 12 Islands and Divisions of Knowledge
  359.    wt: 2:   R Why Learn Mathematics Skills
  360.    wt: 2:   Q How Logic and Proofs extend Show Work Practices
  361.    wt: 2:   O On Learning Mathematics and Science
  362.    wt: 2:   L Skills with take home value
  363.    wt: 2:   N Improving Marks on Tests and Finals
  364.    wt: 2:   J. More on written work and showing skill
  365.    wt: 2:   H Jigsaw puzzles and problem solving
  366.    wt: 2:   G. Written work formats for developing and showing skill
  367.    wt: 2:   E. When and how to correct errors
  368.    wt: 1:   Appendix 1 primary and preschool mathematic
  369.    wt: 1:   G LAMP Introduction Problem Solving Skills
  370.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  371.    wt: 1:   Skills Chapter 5 Calculus
  372.    wt: 1:   Skills Chapter 4 Logic
  373.    wt: 1:   Skills Chapter 3 Algebra
  374.    wt: 1:   Skills Chapter 2 Geometry
  375.    wt: 1:   Skills Chapter 1 Arithmetic
  376.    wt: 1:   Skills Chapter 0 Introduction
  377.    wt: 1:   7 logic review and decimals an odd combination
  378.    wt: 1:   5 logarithms and exponentials etc
  379.    wt: 1:   2 arithmetic with signed numbers
  380.    wt: 1:   1 arithmetic with unsigned numbers
  381.    wt: 1:   key notes and themes
  382.    wt: 1:   what should be learnt and When
  383.    wt: 1:   standards for course material
  384.    wt: 1:   Theory of Knowledge
  385.    wt: 1:   Education in mathematics science and technology
  386.    wt: 1:   Motivation and Context Problem
  387.    wt: 1:   fairness and inductive principles for instruction
  388.    wt: 1:   Home Tutoring and Home Schooling
  389.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  390.    wt: 1:   24 Standards For Skill Develoment Take II
  391.    wt: 1:   24 Standards For Skill Develoment
  392.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  393.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  394.    wt: 1:   17 Math Booklets for children and young teenagers
  395.    wt: 1:   14 Multiplication and Times Tables
  396.    wt: 1:   13 Addition and Addition Tables
  397.    wt: 1:   12 Goals and Objectives For Mathematics
  398.    wt: 1:   11 Help and Defend Your Child or Teens Education
  399.    wt: 1:   5 Patience Please for Yourself and Your Charges
  400.    wt: 1:   4 Learning Takes Time and Effort
  401.    wt: 1:   1 Speaking Skills
  402.    wt: 1:   Ages 12 to 14 Geometry
  403.    wt: 1:   Ages 12 to 14 Arithmetic
  404.    wt: 1:   Ages 10 to 12 Geometry
  405.    wt: 1:   Ages 10 to 12 Arithmetic
  406.    wt: 1:   Ages 9 to 10
  407.    wt: 1:   Ages 8 to 9
  408.    wt: 1:   Ages 7 to 8
  409.    wt: 1:   Ages 6 to 7
  410.    wt: 1:   Ages 4 plus to 5 plus
  411.    wt: 1:   Ages 3 plus to 4 plus
  412.    wt: 1:   26 Function definitions done and coming
  413.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  414.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  415.    wt: 1:   19 Horizontal line rule and method
  416.    wt: 1:   18 Vertical Line Rule and Method
  417.    wt: 1:   17 Function maxima minima and their location
  418.    wt: 1:   11 Function Domain Range Source and Targets
  419.    wt: 1:   9 Set theory term relation possible origins
  420.    wt: 1:   8 Set view of relations and functions
  421.    wt: 1:   6 Set Existence Formation and Notation
  422.    wt: 1:   4 Function notation in and beyond mathematics
  423.    wt: 1:   9 quadratics physical and further context
  424.    wt: 1:   11 Growth and Decay in Biology
  425.    wt: 1:   10 Exponential Growth and Decay Models
  426.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  427.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  428.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  429.    wt: 1:   16 cotangent function Definition Graph and Inverse
  430.    wt: 1:   15 cosecant function Definition Graph and Inverse
  431.    wt: 1:   14 secant function Definition Graph and Inverse
  432.    wt: 1:   13 cosecant function Definition Graph and Inverse
  433.    wt: 1:   8 Radian Measures of Common Angles
  434.    wt: 1:   7 Radian Measures in special Triangles
  435.    wt: 1:   6 Radian Measure to Degrees
  436.    wt: 1:   5 Degrees to Radian Measure
  437.    wt: 1:   4 Circle Sector Area proportional to Central Angle
  438.    wt: 1:   3 Circle Arclengh Proportional to Central Angle
  439.    wt: 1:   2 Radian Measure Numerical Value of one degree
  440.    wt: 1:   A Global Time and Navigation
  441.    wt: 1:   15 Dot and Cross Product
  442.    wt: 1:   7 Coordinate Addition and Scalar Multiplication
  443.    wt: 1:   4 graphing y=Asin(x c)
  444.    wt: 1:   3 graphing y=f(x c) plus K
  445.    wt: 1:   2 Graphing y=Af(x) Vertical Scaling
  446.    wt: 1:   1 graphing y=f(x a)
  447.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  448.    wt: 1:   Triangle Angles Sum To 180 Degrees
  449.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  450.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  451.    wt: 1:   Straight Lines ASA Intersection Study More
  452.    wt: 1:   Straight Lines ASA Intersection Study
  453.    wt: 1:   Straight Lines Instersection Solving Equations
  454.    wt: 1:   Straight Lines Intersection of
  455.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  456.    wt: 1:   C Straight Lines Slope from Coordinates
  457.    wt: 1:   B Straight Line Slope Scaling Properties More
  458.    wt: 1:   A Straight Line Slope Scaling Properties
  459.    wt: 1:   14 Straight Lines Equations General Case
  460.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  461.    wt: 1:   12 Straight Lines Graphing mx plus b
  462.    wt: 1:   11 Straight Lines Graphing y=mx
  463.    wt: 1:   10 Straight Lines through Origin Equations More
  464.    wt: 1:   9 Straight Lines through Origin Equations
  465.    wt: 1:   8 Straight Lines Equation for vertical
  466.    wt: 1:   7 Tangent Function is odd on this domain
  467.    wt: 1:   6 Tangent Function Inclination Angle Take 2
  468.    wt: 1:   5 Tangent Function Graph
  469.    wt: 1:   4 Tangent Function Properties
  470.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  471.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  472.    wt: 1:   1 Straight Lines Slope Concept
  473.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  474.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  475.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  476.    wt: 1:   29 secant cosecant and cotangent for acute angles
  477.    wt: 1:   27 Logarithmic use of products of sines and cosines
  478.    wt: 1:   26 Formulas for products of sines and cosines
  479.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  480.    wt: 1:   21 sine and cosine Half Angle Formulas
  481.    wt: 1:   20 sine and cosine Double Angle Formulas
  482.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  483.    wt: 1:   17E Trig Formulas for dot and cross Products
  484.    wt: 1:   17D cis formulas for sine cosines and tangent
  485.    wt: 1:   17C sine and cosine double triple angle formulas
  486.    wt: 1:   17A The complex number valued trig function cis
  487.    wt: 1:   10 Graphs of sines and cosines many periods
  488.    wt: 1:   9 Graphs of sine and cosine over one period
  489.    wt: 1:   7 period of sine and cosine
  490.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  491.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  492.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  493.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  494.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  495.    wt: 1:   19 N th Roots of Unity
  496.    wt: 1:   18 Sixth Roots of Unity
  497.    wt: 1:   17 Cube Roots of unity
  498.    wt: 1:   15 Pythagorean Theorem Converse
  499.    wt: 1:   14 Law of cosines
  500.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  501.    wt: 1:   8 Unit Circle Development of Trigonometry
  502.    wt: 1:   7 Second Way to Calculate Products
  503.    wt: 1:   5 An Easy Proof of the Distributive Law
  504.    wt: 1:   4 Multiplication Properties
  505.    wt: 1:   3 Addition Properties
  506.    wt: 1:   1 Rectangular Polar Coordinates Review
  507.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  508.    wt: 1:   3 Trigonometric Ratios sine and cosine
  509.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  510.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  511.    wt: 1:   8 Similarity of Triangles and Polygons
  512.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  513.    wt: 1:   Four Simple Exercises
  514.    wt: 1:   12 Links Lessons elsewhere
  515.    wt: 1:   11 A Partial Summary
  516.    wt: 1:   9 Midpoint Coordinates Half Endpoint Sum
  517.    wt: 1:   8 Mid Point Formula
  518.    wt: 1:   6 Intersection of lines by solving linear systems
  519.    wt: 1:   5 Algebraic View of Slopes
  520.    wt: 1:   4 Equations for lines three forms
  521.    wt: 1:   3 Slope product for perpendicular lines
  522.    wt: 1:   2 point slope equation for a line
  523.    wt: 1:   13 Pythagorean spatial distance formulas
  524.    wt: 1:   12 Spatial Coordinates
  525.    wt: 1:   11 Triangle Inequality
  526.    wt: 1:   10 Pythagorean plane distance formula
  527.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  528.    wt: 1:   8 Distance Between Points on a Line
  529.    wt: 1:   3 Rectangular Coordinates Review
  530.    wt: 1:   2 Cartesian Coordinates with signs
  531.    wt: 1:   1 Cartesian Coordinates sans signs
  532.    wt: 1:   Euclidean Geometry Elsewhere LINKS
  533.    wt: 1:   PS G Rotation Distributes over Addition
  534.    wt: 1:   PS F Scalar Multiplication Distributes over Addition
  535.    wt: 1:   PS E Multiplication with Polar Coordinates
  536.    wt: 1:   PS D Addition with Cartesian Coordinates
  537.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  538.    wt: 1:   PS B Parallelogram Construction Methods
  539.    wt: 1:   PS A Kite Construction Methods
  540.    wt: 1:   21 Parallelograms
  541.    wt: 1:   19 Right Triangle Similarity
  542.    wt: 1:   18 Triangle Similarity Take 1
  543.    wt: 1:   17 Right Bisectors of Triangle Sides
  544.    wt: 1:   15 Triangle Angle Sum is 180 degrees
  545.    wt: 1:   14 Parallel Lines Postulate
  546.    wt: 1:   13 Angle Side Angle Failure
  547.    wt: 1:   12 Side Angle Side Failure
  548.    wt: 1:   11 Triangle Construction Fails
  549.    wt: 1:   10 Dropping a perpendicular to line
  550.    wt: 1:   9 Construction of a right bisector
  551.    wt: 1:   8 Isoceles Triangles
  552.    wt: 1:   7 Angle Side Angle
  553.    wt: 1:   5 Side Angle Side
  554.    wt: 1:   4 Side Side Side
  555.    wt: 1:   3 Isometry of Triangles Congruence
  556.    wt: 1:   2 Correspondence between Triangles
  557.    wt: 1:   Short Course on Euclidean Geometry
  558.    wt: 1:   26 More Less Greater Than Comparison
  559.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  560.    wt: 1:   23 Distributive Law Two Derivations
  561.    wt: 1:   21 Addition of Multiples of a Single Vector
  562.    wt: 1:   19 Signed Multiples of Vectors
  563.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  564.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  565.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  566.    wt: 1:   15 Head to Tails in place Addition Associative
  567.    wt: 1:   9 Division with Digits after Decimal Point
  568.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  569.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  570.    wt: 1:   4 Location of Point in Decimal Addition
  571.    wt: 1:   3 Location of Point in Decimal Multiplication
  572.    wt: 1:   2 Counting Digits in Decimal Multiplication
  573.    wt: 1:   E Long Division Methods more
  574.    wt: 1:   D Long Division Methods
  575.    wt: 1:   C Three Decimal Subtraction Methods
  576.    wt: 1:   A Decimal Addition Columm Methods
  577.    wt: 1:   8 Column Multiplication Methods in General
  578.    wt: 1:   7 Decimals Multiplication Methods Examples
  579.    wt: 1:   6 Column Methods for Decimal Multiplication
  580.    wt: 1:   4 Commutative Law Groups Counting Form
  581.    wt: 1:   5 Areas of Rectangles Revisited
  582.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  583.    wt: 1:   3 Proportionality Examples
  584.    wt: 1:   2 Algebraic View
  585.    wt: 1:   1 What is Proportionality
  586.    wt: 1:   9 Circle Area and Perimeter Formula Backwards Forwards
  587.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  588.    wt: 1:   5 Equality in Algebra
  589.    wt: 1:   3 Product Axioms Two Forms
  590.    wt: 1:   1 Equivalent Computation Rules
  591.    wt: 1:   5 Greater More Less Than Signs in General
  592.    wt: 1:   9 Coordinates for Regions in Space
  593.    wt: 1:   2 Integers
  594.    wt: 1:   5 Independent versus Dependent Variables
  595.    wt: 1:   4 Changing Letters
  596.    wt: 1:   2 Computation Rules Evaluation
  597.    wt: 1:   3 GE III Equation Addition and Multiplication
  598.    wt: 1:   8 Compound Interest Formula Evaluation
  599.    wt: 1:   7 Compound Interest Formula Introduction
  600.    wt: 1:   1 Written work formats for developing and showing skill
  601.    wt: 1:   9 Sets in Probability and Statistics
  602.    wt: 1:   8 Sets of Numbers
  603.    wt: 1:   1 Three Skills For Algebra
  604.    wt: 1:   014 Counting Days with Calendars
  605.    wt: 1:   013 Travel Time Tables
  606.    wt: 1:   012 Division of Time Intervals by Time Intervals
  607.    wt: 1:   010 Repeated Addition of Time Intervals
  608.    wt: 1:   8 Addition of Time Intervals via subtotaling
  609.    wt: 1:   7 Addition of Time Intervals
  610.    wt: 1:   6 How long is a million seconds
  611.    wt: 1:   5 Conversion Arithmetic
  612.    wt: 1:   Example 2 volume of a cone
  613.    wt: 1:   Example 1 volume of a pyramid
  614.    wt: 1:   Volume of Solid by Cross Sections Lesson
  615.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  616.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  617.    wt: 1:   Example 4 with x function of y
  618.    wt: 1:   Example 3
  619.    wt: 1:   Example 2
  620.    wt: 1:   Example 1
  621.    wt: 1:   Area Between Curves Lesson Take 2
  622.    wt: 1:   Area Between Curves Lesson Take 1
  623.    wt: 1:   Summary
  624.    wt: 1:   17 Derivatives of quotients of sine and cosine
  625.    wt: 1:   16 Derivatives of reciprocals of sine and cosine
  626.    wt: 1:   15 sine and cosine derivatives 3rd step
  627.    wt: 1:   14 sine and cosine derivatives 2nd step
  628.    wt: 1:   13 sine and cosine derivatives 1st step
  629.    wt: 1:   11 Limits at infinity Three Examples
  630.    wt: 1:   10 Three one sided limits with infinite values
  631.    wt: 1:   8 Four Animated Examples
  632.    wt: 1:   7 Evaluation by immediate or delayed substitution
  633.    wt: 1:   6 Continuity at a point
  634.    wt: 1:   4 Numerical properties
  635.    wt: 1:   3 Decimal insights for limits continuity convergence
  636.    wt: 1:   2 Algebraic codification
  637.    wt: 1:   1 Numerical introduction
  638.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  639.    wt: 1:   PostScript For and Against Decimal Perspectives
  640.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  641.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  642.    wt: 1:   Chapter 22 Complex Numbers
  643.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  644.    wt: 1:   Chapter 12. Units and Slopes
  645.    wt: 1:   Chapter 10 Slopes and Units
  646.    wt: 1:   Chapter 7 Slopes and Velocity
  647.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  648.    wt: 1:   Chapter 2. Slopes and Ski Trails
  649.    wt: 1:   Postscript More on Better Performance
  650.    wt: 1:   Postscript For Better Performance
  651.    wt: 1:   Appendix C. How to Read
  652.    wt: 1:   Appendix B. How To Learn
  653.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  654.    wt: 1:   Chapter 30 Truth Tables
  655.    wt: 1:   Chapter 28 Occurrence Tables
  656.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  657.    wt: 1:   Chapter 25. Mathematical Induction Examples
  658.    wt: 1:   Chapter 23. Notation For Sums
  659.    wt: 1:   Chapter 21. Third Reading Guide
  660.    wt: 1:   Chapter 18. Rules for Algebra
  661.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  662.    wt: 1:   Chapter 16. Painless Theorem Proving
  663.    wt: 1:   Chapter 15. Solving Linear Equations
  664.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  665.    wt: 1:   Chapter 13. Second Reading Guide
  666.    wt: 1:   Postscript What is a Variable
  667.    wt: 1:   Solutions For Arithmetic Exercises
  668.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  669.    wt: 1:   Chapter 6 Change of Language
  670.    wt: 1:   Chapter 4 Longer Chains of Reason
  671.    wt: 1:   Chapter 3 Chains of Reason
  672.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  673.    wt: 1:   Foreword
  674.    wt: 1:   Chapter 2 For and Against Mathematics
  675.    wt: 1:   Postscript B More on Story Telling and Reason
  676.    wt: 1:   Chapter 24 Direct and Indirect Reason
  677.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  678.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  679.    wt: 1:   Chapter 18 Sense and Knowledge
  680.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  681.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  682.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  683.    wt: 1:   1 Links to Online Resources Elsewhere Take 1
  684.    wt: 1:   S Adding words to algebra
  685.    wt: 1:   N Mathematics Prepare for College Studies
  686.    wt: 1:   M Words to extend arithmetic
  687.    wt: 1:   H more Routine to non routine problem solving
  688.    wt: 1:   F. The student teacher tutor feedback loop
  689.    wt: 1:   D. Check work a must with a caution
  690.    wt: 1:   C. Domino effect of being careful
  691.    wt: 1:   B. Domino effect of errors
  692.    wt: 1:   A. Skill has to be seen to believed
  693.    wt: 1:   Chapter 8 Skipped Topics and Why
  694.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  695.    wt: 1:   Chapter 6 More Algebra and Geometry
  696.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  697.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  698.    wt: 1:   Helping the Blind in Logic and Mathematics
  699.    wt: 1:   More Algebra and Slope based Calculus Preview
  700.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  701.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  702.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  703.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  704.    wt: 1:   The Math Forum and Site Content
  705.    wt: 11:   C Equality for Fractions and Two Term Ratios and Fractions
  706.    wt: 10:   9 Improper Fractions and Mixed Numbers

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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