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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44 matches:

  1.    wt: 9:   6 Fractions and Ratios/
  2.    wt: 8:   7 Arithmetic and Fractions with Units/
  3.    wt: 7:   12 Comparison of Unsigned and Signed Numbers/
  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:   6 Trigonometry first steps/
  28.    wt: 1:   4 Lines and Slopes Take 1/
  29.    wt: 1:   3 Cartesian and Polar Coordinates/
  30.    wt: 1:   2 Euclidean Geometry Constructions Theory extras/
  31.    wt: 1:   B Real Numbers Extrinsic Development/
  32.    wt: 1:   A Origins of Counting and Figuring Methods/
  33.    wt: 1:   9 Proportionality Backwards and Forwards/
  34.    wt: 1:   7 Axioms Logic and Equivalent Equations/
  35.    wt: 1:   6 More Less Greater Than Inequalities and Comparison/
  36.    wt: 1:   5 Real Numbers/
  37.    wt: 1:   4 Computation Rules and Function Notation/
  38.    wt: 1:   Time Date Matters/
  39.    wt: 1:   Skills with take home value/
  40.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  41.    wt: 1:   13 Lessons on Limits and Continuity/
  42.    wt: 1:   Volume 2 Three Skills For Algebra/
  43.    wt: 1:   Work and Study Tips/
  44.    wt: 1:   Resources and Reciprocal Links/

Web Page Search

361 matches:

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

Extended Search

712 matches:

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

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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