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: 7:   12 Comparison of Unsigned and Signed Numbers/
  3.    wt: 7:   7 Arithmetic and Fractions with Units/
  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

368 matches:

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

Extended Search

717 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:   21 Working With Signs
  5.    wt: 9:   18 Efficient Ways to Multiply
  6.    wt: 9:   16 Addition Subtraction Comparision Compared
  7.    wt: 9:   13 Fraction Comparison Algebraic View
  8.    wt: 9:   12 Fraction Comparison
  9.    wt: 9:   11 Simplification an Algebraic View
  10.    wt: 9:   8 Numerals Fractionals Quantals Take II
  11.    wt: 9:   7 Numerals Fractionals Quantals
  12.    wt: 9:   6 Multiplication Algebraically Take II
  13.    wt: 9:   4 Fraction Multiplication
  14.    wt: 9:   3 Unit fraction of a fraction
  15.    wt: 9:   2 Unit Fraction Multiplication
  16.    wt: 9:   1 What is a fraction Take II
  17.    wt: 9:   1 What is a fraction
  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 Simplification of Fractions with Units
  24.    wt: 8:   4 Fractions with Units
  25.    wt: 8:   2 Equality and Units
  26.    wt: 8:   1 Addition and Subtraction with Units
  27.    wt: 8:   6 Sieve of Eratosthenes and Square Rule
  28.    wt: 8:   8 What skills and work habits to require
  29.    wt: 8:   6. Counting and adding units and mixed units
  30.    wt: 7:   4 Greater More Less Than Signs in General
  31.    wt: 7:   1 Squares and Square Roots Introduction
  32.    wt: 7:   17 GCD LCM of 85 and 60 via Prime
  33.    wt: 7:   16 GCD and LCM of 650 225 via Prime
  34.    wt: 7:   10 Euclid Algorithm with 129 125 and with 45 14
  35.    wt: 7:   9 GCD of 360 110 via Primes and Euclid Algorithm
  36.    wt: 7:   7 GCD and LCM from prime factorization
  37.    wt: 7:   4 LCM of 8 and 10 via Prime
  38.    wt: 7:   2 Least Common Multiple LCM intro via list method
  39.    wt: 7:   1 Least Common Multiples LCM Introduction
  40.    wt: 7:   3 Counting with Tables and Trees II
  41.    wt: 7:   2 Counting with Tables and Trees I
  42.    wt: 7:   1 Counting and Counting Methods I
  43.    wt: 7:   10 dividing signed numbers
  44.    wt: 7:   9 subtracting signed numbers
  45.    wt: 7:   8 multiplying signed numbers
  46.    wt: 7:   7 negative and additive inverse
  47.    wt: 7:   6 adding signed numbers
  48.    wt: 7:   3 signed coordinates for maps and planes
  49.    wt: 7:   7 Converting or Changing Units
  50.    wt: 7:   6 Multiplication by Natural Numbers
  51.    wt: 7:   A Decimals Modular and Remainder Arithmetic
  52.    wt: 7:   17 Identify and Count Factors using Primes
  53.    wt: 7:   12 LCD GCD and LCM using Primes
  54.    wt: 7:   7 Calculator Usage Notes and Cautions
  55.    wt: 7:   5 Prime Factorization and a Square Rule
  56.    wt: 7:   3 video Primes and Composites from 9 times table
  57.    wt: 7:   2 Prime and Composites less than 16
  58.    wt: 7:   7 Subtraction for Decimal Fractions with Exercises
  59.    wt: 7:   6 Subtraction with Conversion Example with Exercises
  60.    wt: 7:   4 Subtraction with Conversions Borrows and Letter J
  61.    wt: 7:   3 Harder Cases Convert to Compare and Subtract
  62.    wt: 7:   1 Comparison and Subtraction Easy Direct Cases
  63.    wt: 7:   7 Adding decimal fractions using decimal point
  64.    wt: 7:   10 Names for Big Numbers and Powers of Ten Expansion
  65.    wt: 7:   Quick history of numbers and algebra
  66.    wt: 7:   Exact Arithmetic Wholes and Fractions
  67.    wt: 6:   5 Square Roots with primes more still
  68.    wt: 6:   4 Square Roots with primes more
  69.    wt: 6:   3 Properties of Square Roots with example
  70.    wt: 6:   2 Square Roots with Prime
  71.    wt: 6:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  72.    wt: 6:   14 GCD of 650 110 via Primes LCM via Product Rule
  73.    wt: 6:   13 GCD from given Prime Factorization
  74.    wt: 6:   11 GCD 2700 288 via Euclid Algorithm
  75.    wt: 6:   8 GCD from Euclidean Algorithm
  76.    wt: 6:   6 GCD from Prime
  77.    wt: 6:   5 Common Divisors 60 45 via Prime
  78.    wt: 6:   LCM 60 45 Avoid List Method Use Prime
  79.    wt: 6:   12 GCD 2700 288 via Prime
  80.    wt: 6:   5 Counting with Tables Trees Product Rule Take II
  81.    wt: 6:   4 Counting with Trees Product Rule Take I
  82.    wt: 6:   4 signed coordinates for regions in space
  83.    wt: 6:   B Integer Long Division Multiple Choices
  84.    wt: 6:   11 Adding Integers Formulas and Examples
  85.    wt: 6:   8 Multiplication by Signed Numbers Integers
  86.    wt: 6:   5 Zero Movement and Additive Inverses
  87.    wt: 6:   27 Divisibility by 2 3 6 5 9 10 Example
  88.    wt: 6:   26 Divisibility by 2 3 5 Example
  89.    wt: 6:   25 Divisibility Tests for 2 3 5 9 10 Example
  90.    wt: 6:   24 Divisibility Tests for 2 3 5 9 10
  91.    wt: 6:   23 Remainder Arithmetic Modulo 2
  92.    wt: 6:   22 Remainder Arithmetic Modulo 3 more
  93.    wt: 6:   21 Remainder Arithmetic Modulo 3
  94.    wt: 6:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  95.    wt: 6:   19 Remainder Arithmetic Rule of 9 for checking sums III
  96.    wt: 6:   18 Remainder Arithmetic Rule of 9 for checking sums II
  97.    wt: 6:   17 Remainder Arithmetic Rule of 9 for checking sums I
  98.    wt: 6:   16 Remainder Arithmetic Modulo 9 Example 2
  99.    wt: 6:   15 Remainder Arithmetic Modulo 9 Example
  100.    wt: 6:   14 Remainder Arithmetic Modulo 9 Example
  101.    wt: 6:   13 Remainder Arithmetic Modulo 5 Example
  102.    wt: 6:   12 Remainder Arithmetic Modulo 10 Example
  103.    wt: 6:   11 Remainder Arithmetic Long Division by 5 Quickly more
  104.    wt: 6:   10 Remainder Arithmetic Long Division by 5 Quickly
  105.    wt: 6:   9 Remainder Arithmetic Divisibility by 5
  106.    wt: 6:   8 Remainder Arithmetic Morulo 5 Examples II
  107.    wt: 6:   7 Remainder Arithmetic Modulo 5 Examples I
  108.    wt: 6:   6 Remainder Arithmetic Modulo 5 Propertie
  109.    wt: 6:   5 Remainder Arithmetic Modulo 5
  110.    wt: 6:   4 Remainder Arithmetic Modulo 10 in general
  111.    wt: 6:   3 Remainder Arithmetic Modulos 10 more still
  112.    wt: 6:   2 Remainder Arithmetic Modulo 10 more
  113.    wt: 6:   1 Remainder Arithmetic Modulo 10
  114.    wt: 6:   20 Uniqueness of Prime Factorization
  115.    wt: 6:   19 video Prime Factorization Unique
  116.    wt: 6:   18 video Count Factors given Prime Factorization
  117.    wt: 6:   16 video Factors of 980 using prime
  118.    wt: 6:   15 video Factors of 20 using Prime Factorization
  119.    wt: 6:   14 video Factors of 24 Take II
  120.    wt: 6:   13 video Factors of 24 using prime
  121.    wt: 6:   11 Efficient Square Rule Use
  122.    wt: 6:   10 video Prime Factorization upto 23 squared
  123.    wt: 6:   9 video Prime Factorization upto 19 squared
  124.    wt: 6:   8 video Prime Factorization upto 19
  125.    wt: 6:   4 video Prime Factorization Introduction
  126.    wt: 6:   1 video how Products are bigger than factor
  127.    wt: 6:   Division with Counts and Length
  128.    wt: 6:   Long Division forwards and backwards Example 3
  129.    wt: 6:   Long Division forwards and backwards Example 2
  130.    wt: 6:   Long Division forwards and backwards Example 1
  131.    wt: 6:   10 Division by Five Long and Short Ways
  132.    wt: 6:   6 Why Decimal Long Division Methods Works Take I
  133.    wt: 6:   6 Multiplication Commutes Order Not Important
  134.    wt: 6:   4 Two and Three Digit Multipliers
  135.    wt: 6:   Appendix 2 Three Decimal Subtraction Methods
  136.    wt: 6:   Appendix 1 Decimals Comparison Method Take II
  137.    wt: 6:   Subtraction with J Conversions Example
  138.    wt: 6:   Subtraction Another Video Lesson
  139.    wt: 6:   9 22 Minute Subtraction Review Video
  140.    wt: 6:   8 Subtraction with Units of Measure
  141.    wt: 6:   5 A Tip for Efficent Subtraction
  142.    wt: 6:   2 Subtraction Easy Case Examples
  143.    wt: 6:   Appendix 1 Counting Revisited 15 minute video
  144.    wt: 6:   5. How to add decimals C. Examples
  145.    wt: 6:   4. How to add with decimals B with conversions
  146.    wt: 6:   3. How to add with decimals A sans conversions
  147.    wt: 6:   2 Decimal Counting Practices
  148.    wt: 6:   1. Explaining Addition Table
  149.    wt: 6:   11 Place Value SI Standard International way
  150.    wt: 6:   9 Place Value Review Decimal form of Avogrados number included
  151.    wt: 6:   8 Review Lesson 1 2 4 and 6 All in One
  152.    wt: 6:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  153.    wt: 6:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  154.    wt: 6:   5 More on Groups of 3 Place Value in Decimal Fractions
  155.    wt: 6:   4 Groups of 3 Place Value in Decimal Fractions
  156.    wt: 6:   1 Place Value in Three Digit Whole Numbers
  157.    wt: 6:   Practical Methods Ends and Values for Arithmetic
  158.    wt: 5:   arithmetic videos Real Player Format
  159.    wt: 5:   D Remainders Modulo 11 Pair Rule
  160.    wt: 5:   C Divisibility by 11 Integer Recognition Method
  161.    wt: 5:   A Associative Law Theorectical Note
  162.    wt: 5:   13 Subtraction with Additive Inverse
  163.    wt: 5:   12 Adding Integers More Examples
  164.    wt: 5:   10 Integer Multiplication Formulas
  165.    wt: 5:   9 Multiplying Integers
  166.    wt: 5:   7 Multiplication by Signs
  167.    wt: 5:   4 Adding Movements wiht opposite directions
  168.    wt: 5:   3 Adding Movements with same direction
  169.    wt: 5:   2 Integers Multiplies of a Unit Moverment
  170.    wt: 5:   1 Integers as Coordinates
  171.    wt: 5:   Long Division Backwards more
  172.    wt: 5:   Long Division Backward
  173.    wt: 5:   12 Why Long Division Works Take III
  174.    wt: 5:   11 Another Single Digit Divisor Example
  175.    wt: 5:   9 Why Long Division Works Take II
  176.    wt: 5:   8 Correcting the Mistake
  177.    wt: 5:   7 Long Divison Mistake Catching
  178.    wt: 5:   5 Long Division Include Zeroes or not
  179.    wt: 5:   4 Division with 2 Digit Divsors
  180.    wt: 5:   3 Division Single Digit Divisor Example
  181.    wt: 5:   2 Division with Single Digit Divisors
  182.    wt: 5:   1 Divsion Physical Examples
  183.    wt: 5:   D Decimal Multiplication Methods Derived
  184.    wt: 5:   C Counting Areas with Powers of Ten
  185.    wt: 5:   B Powers of Ten
  186.    wt: 5:   A Elementary Basis for Multiplication Methods
  187.    wt: 5:   5 Decimal Fraction Multiplication
  188.    wt: 5:   3 More One Digit Multipliers
  189.    wt: 5:   2 One Digit Multipliers
  190.    wt: 5:   Video Decimal Multiplication Geometric View Example 2
  191.    wt: 5:   Video Decimal Multiplication Geometric View Example 2
  192.    wt: 5:   Video Power Notation in Decimal Expansion
  193.    wt: 5:   1 Why 3 times 5 gives 15
  194.    wt: 5:   3 More on Groups of 3 Multi Digit Place Value
  195.    wt: 5:   2 Groups of Three Place Value for Multidigit Decimals
  196.    wt: 5:   Formula Evaluation how to show work
  197.    wt: 5:   Expression Evaluation how to show work
  198.    wt: 5:   The 20 Times Table
  199.    wt: 5:   The 12 Times Table Visually
  200.    wt: 5:   About folder contents
  201.    wt: 5:   Primary and Secondary Skills and Practices with Take Home Value
  202.    wt: 4:   P Exact Arithmetic With Whole Numbers and Fractions
  203.    wt: 4:   5 Interpreting and Drawing Maps and Plans.
  204.    wt: 4:   2 Identifying Size and Position Place and Spatial Sense
  205.    wt: 4:   1 From Number Recognition and Counting to Arithmetic B
  206.    wt: 4:   1 From Number Recognition and Counting to Arithmetic A
  207.    wt: 3:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  208.    wt: 3:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  209.    wt: 3:   Construction Methods and Criteria for Isometric and Similar Triangles
  210.    wt: 3:   6 Field Properties of Complex Number
  211.    wt: 3:   5 Trigonometric Ratios For Tangent and Special Triangles
  212.    wt: 3:   3 Trigonometric Ratios sine and cosine
  213.    wt: 3:   6 Polar Multiplication and Rotation
  214.    wt: 3:   6 Ruler and compass Angle Bisection
  215.    wt: 3:   1 Initial Concepts and Terms
  216.    wt: 3:   11 Signed Number Addition and Addition Properties
  217.    wt: 3:   8 Division and Mulplication of Compound Fractions
  218.    wt: 3:   2 Combing Counts Addition Skills and Principles
  219.    wt: 3:   4 Rates Ratios and Proporitionality
  220.    wt: 3:   2 More and Less Than for Counts and Measures
  221.    wt: 3:   10 Real Number Lengths and Signs
  222.    wt: 3:   1 Whole and Natural Numbers
  223.    wt: 3:   6 Three Examples
  224.    wt: 3:   Chapter 5 Islands and Divisions of Knowledge
  225.    wt: 3:   V Reasons and Motivations for Logic and Mathematics
  226.    wt: 3:   I. Logic and language skills
  227.    wt: 3:   How to Build Skills and Confidence
  228.    wt: 3:   7 Games and Activities for Instruction
  229.    wt: 3:   6 Measuring via counting or arithmetic the role of fractions
  230.    wt: 3:   4 Money Matters Saving Earning Buying Selling and Budgets
  231.    wt: 3:   3 Telling Tracking Time Temporal and More Place Sense
  232.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  233.    wt: 2:   Ramblings Extrinsic numbers theory
  234.    wt: 2:   2 Reading and Writing Skills
  235.    wt: 2:   Ages 12 to 14 Skills with take home value
  236.    wt: 2:   9 Set theory term relation possible origins
  237.    wt: 2:   9 Summary Degrees to Radians and back
  238.    wt: 2:   1 Degrees and Radians Introduction
  239.    wt: 2:   Vector and Complex Number Applet
  240.    wt: 2:   Parallel Lines and Parallel Transversals
  241.    wt: 2:   Parallel Lines and Alternating Corresponding Angles
  242.    wt: 2:   Parallel Lines and Interior Angles
  243.    wt: 2:   14 cosine even and sine and tangent are odd
  244.    wt: 2:   21 Logarithms Powers and Exponentials
  245.    wt: 2:   20 N th Roots of Complex Numbers
  246.    wt: 2:   16 References and Originality Question
  247.    wt: 2:   13 Trig Formulas for dot and cross Products
  248.    wt: 2:   12 cis formulas for sine cosines and tangent
  249.    wt: 2:   11 sine and cosine double triple angle formulas
  250.    wt: 2:   9 The complex number valued trig function cis
  251.    wt: 2:   2 Complex Numbers made easier we hope
  252.    wt: 2:   Appetizer A Complex Number Applet
  253.    wt: 2:   7 Trignometric Ratios Unit Circle
  254.    wt: 2:   4 Trigonometric Ratios For Two Special Triangles
  255.    wt: 2:   2 Similar Triangles Equality of Corresponding Side Ratios
  256.    wt: 2:   Right Triangle and Unit Circle Trigonometry
  257.    wt: 2:   10 Midpoint of [a b] and [b a]
  258.    wt: 2:   7 Exercises to test skill and concept mastery
  259.    wt: 2:   6 Intersection of lines by solving linear systems
  260.    wt: 2:   1 Numerical view of lines and their equations
  261.    wt: 2:   What is and is not here
  262.    wt: 2:   7 Complex Numbers Appetizer
  263.    wt: 2:   5 Cartesian Addition and Translation
  264.    wt: 2:   4 Polar Coordinates to and from
  265.    wt: 2:   PS H Distributive Law For Complex Numbers
  266.    wt: 2:   16 Angles Subtended By Chords and Diameters
  267.    wt: 2:   3 Lengths and Areas on Maps and Plans
  268.    wt: 2:   musings do not puiblish real numbers
  269.    wt: 2:   A Modular and Remainder Arithmetic
  270.    wt: 2:   A Signed Number Arithmetic Review
  271.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  272.    wt: 2:   22 Multiplication of Signed Numbers
  273.    wt: 2:   21 Addition of Multiples of a Single Vector
  274.    wt: 2:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  275.    wt: 2:   19 Signed Multiples of Vectors
  276.    wt: 2:   14 Vector Head to Tail Sums and Resultants
  277.    wt: 2:   13 Arrows and Vectors in a Plane
  278.    wt: 2:   12 Real Numbers Line Signed Coordinates
  279.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  280.    wt: 2:   5 Fractions with Infinite Decimal Expansions
  281.    wt: 2:   1 Fractions with Finite Decimal Expansions
  282.    wt: 2:   B Decimal Comparison and Subtraction
  283.    wt: 2:   6 Column Methods for Decimal Multiplication
  284.    wt: 2:   5 Distributive Law for Whole Numbers
  285.    wt: 2:   3 Multiplicative Counting Skills Principles
  286.    wt: 2:   1 The Counting Origins of Numbers
  287.    wt: 2:   5 Proportionality in Equivalent Fractions
  288.    wt: 2:   6 Equations and Systems Equivalent or Implied
  289.    wt: 2:   4 Subtraction and Division Axioms
  290.    wt: 2:   2 Addition and Multiplication Axioms
  291.    wt: 2:   4 Comparison of Negative Numbers
  292.    wt: 2:   3 More and Less Than with Unlike Signs
  293.    wt: 2:   1 Real Numbers Comparison
  294.    wt: 2:   16 Real Numbers Comparison
  295.    wt: 2:   15 Real Number Division
  296.    wt: 2:   14 Real Number Multiplication
  297.    wt: 2:   13 Real Number Subtraction
  298.    wt: 2:   12 Real Number Additive Inverses or Negatives
  299.    wt: 2:   11 Real Number Addition
  300.    wt: 2:   8 Coordinates for Maps and Planes
  301.    wt: 2:   7 Real Numbers as Line Cordinates
  302.    wt: 2:   6 Unsigned Real Numbers
  303.    wt: 2:   5 Rational Numbers More
  304.    wt: 2:   4 Rational Numbers
  305.    wt: 2:   3 Fractions
  306.    wt: 2:   3 Geometric Formulas and Function Notation
  307.    wt: 2:   1 Formulas Dependence and Function Notation
  308.    wt: 2:   Skill Development Notes
  309.    wt: 2:   10 One Example
  310.    wt: 2:   9 Three Examples
  311.    wt: 2:   8 One Example
  312.    wt: 2:   7 Two Examples
  313.    wt: 2:   5 Three Examples
  314.    wt: 2:   4 Two Examples
  315.    wt: 2:   3 Two Examples
  316.    wt: 2:   2 Three Examples
  317.    wt: 2:   5 Talking about Numbers and Quantities
  318.    wt: 2:   4 A Brief Story of numbers and algebra
  319.    wt: 2:   016 Numbering Occidental Calendar Days
  320.    wt: 2:   015 School and work day counting tables
  321.    wt: 2:   011 Division of Time Intervals By Numbers
  322.    wt: 2:   9 Comparison and Subtraction of Time Intervals
  323.    wt: 2:   4 Mixing and Changing Units of Time
  324.    wt: 2:   3 Units and Lengths of Time
  325.    wt: 2:   2 Time and Date Matters in School
  326.    wt: 2:   1 Intro of Kids To Time Date Skills
  327.    wt: 2:   Example 1. Area Between x and x squared
  328.    wt: 2:   38 Formulas and derivatives for powers and roots
  329.    wt: 2:   13 Limits with Parameters and Derivatives Take II
  330.    wt: 2:   12 Limits with Parameters and Derivatives Take I
  331.    wt: 2:   9 Limits Continuity and Composition
  332.    wt: 2:   5 Jumps and absence of unlimited error control
  333.    wt: 2:   Postscript One Sided and Intermediate Value Theorems
  334.    wt: 2:   D1 Sets and Sequences GLBs and LGBs
  335.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  336.    wt: 2:   Chapter 14 Limits and Continuity with and sans Decimals
  337.    wt: 2:   Appendix E. How To Study Mathematics and Why
  338.    wt: 2:   Appendix D. What to do in School and Why
  339.    wt: 2:   Chapter 31 Direct and Indirect Reason
  340.    wt: 2:   Chapter 29 Contrapositive and Vacuously True Implications
  341.    wt: 2:   Chapter 27 Shorthand Symbols as Pronouns
  342.    wt: 2:   Chapter 24. Personal Investment and Pension EGS
  343.    wt: 2:   Chapter 22. Geometric Sums and Sequences
  344.    wt: 2:   Chapter 20. Degrees and Radians
  345.    wt: 2:   Chapter 19. Functions and Sets
  346.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  347.    wt: 2:   Chapter 12. Shorthand Usage Guide
  348.    wt: 2:   Chapter 11. Why Shorthand
  349.    wt: 2:   Chapter 10 Describing and Changing Calculations
  350.    wt: 2:   Chapter 9 Talking about Numbers or Quantities
  351.    wt: 2:   Chapter 8 Three Skills For Algebra
  352.    wt: 2:   Chapter 2 Implication Rules Forwards and Backwards
  353.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  354.    wt: 2:   Chapter 16 Origins and Limitations of Rules and Patterns
  355.    wt: 2:   Chapter 12 Islands and Divisions of Knowledge
  356.    wt: 2:   R Why Learn Mathematics Skills
  357.    wt: 2:   Q How Logic and Proofs extend Show Work Practices
  358.    wt: 2:   O On Learning Mathematics and Science
  359.    wt: 2:   L Skills with take home value
  360.    wt: 2:   N Improving Marks on Tests and Finals
  361.    wt: 2:   J. More on written work and showing skill
  362.    wt: 2:   H Jigsaw puzzles and problem solving
  363.    wt: 2:   G. Written work formats for developing and showing skill
  364.    wt: 2:   E. When and how to correct errors
  365.    wt: 2:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  366.    wt: 1:   Appendix 1 primary and preschool mathematic
  367.    wt: 1:   G LAMP Introduction Problem Solving Skills
  368.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  369.    wt: 1:   Skills Chapter 5 Calculus
  370.    wt: 1:   Skills Chapter 4 Logic
  371.    wt: 1:   Skills Chapter 3 Algebra
  372.    wt: 1:   Skills Chapter 2 Geometry
  373.    wt: 1:   Skills Chapter 1 Arithmetic
  374.    wt: 1:   Skills Chapter 0 Introduction
  375.    wt: 1:   7 logic review and decimals an odd combination
  376.    wt: 1:   5 logarithms and exponentials etc
  377.    wt: 1:   2 arithmetic with signed numbers
  378.    wt: 1:   1 arithmetic with unsigned numbers
  379.    wt: 1:   key notes and themes
  380.    wt: 1:   what should be learnt and When
  381.    wt: 1:   standards for course material
  382.    wt: 1:   Theory of Knowledge
  383.    wt: 1:   Education in mathematics science and technology
  384.    wt: 1:   Motivation and Context Problem
  385.    wt: 1:   fairness and inductive principles for instruction
  386.    wt: 1:   Home Tutoring and Home Schooling
  387.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  388.    wt: 1:   24 Standards For Skill Develoment Take II
  389.    wt: 1:   24 Standards For Skill Develoment
  390.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  391.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  392.    wt: 1:   17 Math Booklets for children and young teenagers
  393.    wt: 1:   14 Multiplication and Times Tables
  394.    wt: 1:   13 Addition and Addition Tables
  395.    wt: 1:   12 Goals and Objectives For Mathematics
  396.    wt: 1:   11 Help and Defend Your Child or Teens Education
  397.    wt: 1:   6 Discipline Who is in Charge Conserving Authority
  398.    wt: 1:   5 Patience Please for Yourself and Your Charges
  399.    wt: 1:   4 Learning Takes Time and Effort
  400.    wt: 1:   1 Speaking Skills
  401.    wt: 1:   Ages 12 to 14 Geometry
  402.    wt: 1:   Ages 12 to 14 Arithmetic
  403.    wt: 1:   Ages 10 to 12 Geometry
  404.    wt: 1:   Ages 10 to 12 Arithmetic
  405.    wt: 1:   Ages 9 to 10
  406.    wt: 1:   Ages 8 to 9
  407.    wt: 1:   Ages 7 to 8
  408.    wt: 1:   Ages 6 to 7
  409.    wt: 1:   Ages 4 plus to 5 plus
  410.    wt: 1:   Ages 3 plus to 4 plus
  411.    wt: 1:   26 Function definitions done and coming
  412.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  413.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  414.    wt: 1:   19 Horizontal line rule and method
  415.    wt: 1:   18 Vertical Line Rule and Method
  416.    wt: 1:   17 Function maxima minima and their location
  417.    wt: 1:   11 Function Domain Range Source and Targets
  418.    wt: 1:   8 Set view of relations and functions
  419.    wt: 1:   6 Set Existence Formation and Notation
  420.    wt: 1:   4 Function notation in and beyond mathematics
  421.    wt: 1:   9 quadratics physical and further context
  422.    wt: 1:   11 Growth and Decay in Biology
  423.    wt: 1:   10 Exponential Growth and Decay Models
  424.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  425.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  426.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  427.    wt: 1:   16 cotangent function Definition Graph and Inverse
  428.    wt: 1:   15 cosecant function Definition Graph and Inverse
  429.    wt: 1:   14 secant function Definition Graph and Inverse
  430.    wt: 1:   13 cosecant function Definition Graph and Inverse
  431.    wt: 1:   12 motivation for term arctan
  432.    wt: 1:   4 possible motivation for term arccos
  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:   11 tangent function undefined when terminal side vertical
  488.    wt: 1:   10 Graphs of sines and cosines many periods
  489.    wt: 1:   9 Graphs of sine and cosine over one period
  490.    wt: 1:   7 period of sine and cosine
  491.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  492.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  493.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  494.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  495.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  496.    wt: 1:   19 N th Roots of Unity
  497.    wt: 1:   18 Sixth Roots of Unity
  498.    wt: 1:   17 Cube Roots of unity
  499.    wt: 1:   15 Pythagorean Theorem Converse
  500.    wt: 1:   14 Law of cosines
  501.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  502.    wt: 1:   8 Unit Circle Development of Trigonometry
  503.    wt: 1:   7 Second Way to Calculate Products
  504.    wt: 1:   5 An Easy Proof of the Distributive Law
  505.    wt: 1:   4 Multiplication Properties
  506.    wt: 1:   3 Addition Properties
  507.    wt: 1:   1 Rectangular Polar Coordinates Review
  508.    wt: 1:   8 Triangles Cascade Problem Solving
  509.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  510.    wt: 1:   1 Angle Measurement with Degrees
  511.    wt: 1:   Why Trigonometry the whyslopes view
  512.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  513.    wt: 1:   8 Similarity of Triangles and Polygons
  514.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  515.    wt: 1:   Four Simple Exercises
  516.    wt: 1:   12 Links Lessons elsewhere
  517.    wt: 1:   11 A Partial Summary
  518.    wt: 1:   9 Midpoint Coordinates Half Endpoint Sum
  519.    wt: 1:   8 Mid Point Formula
  520.    wt: 1:   5 Algebraic View of Slopes
  521.    wt: 1:   4 Equations for lines three forms
  522.    wt: 1:   3 Slope product for perpendicular lines
  523.    wt: 1:   2 point slope equation for a line
  524.    wt: 1:   13 Pythagorean spatial distance formulas
  525.    wt: 1:   12 Spatial Coordinates
  526.    wt: 1:   11 Triangle Inequality
  527.    wt: 1:   10 Pythagorean plane distance formula
  528.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  529.    wt: 1:   8 Distance Between Points on a Line
  530.    wt: 1:   3 Rectangular Coordinates Review
  531.    wt: 1:   2 Cartesian Coordinates with signs
  532.    wt: 1:   1 Cartesian Coordinates sans signs
  533.    wt: 1:   Euclidean Geometry Elsewhere LINKS
  534.    wt: 1:   PS G Rotation Distributes over Addition
  535.    wt: 1:   PS F Scalar Multiplication Distributes over Addition
  536.    wt: 1:   PS E Multiplication with Polar Coordinates
  537.    wt: 1:   PS D Addition with Cartesian Coordinates
  538.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  539.    wt: 1:   PS B Parallelogram Construction Methods
  540.    wt: 1:   PS A Kite Construction Methods
  541.    wt: 1:   21 Parallelograms
  542.    wt: 1:   19 Right Triangle Similarity
  543.    wt: 1:   18 Triangle Similarity Take 1
  544.    wt: 1:   17 Right Bisectors of Triangle Sides
  545.    wt: 1:   15 Triangle Angle Sum is 180 degrees
  546.    wt: 1:   14 Parallel Lines Postulate
  547.    wt: 1:   13 Angle Side Angle Failure
  548.    wt: 1:   12 Side Angle Side Failure
  549.    wt: 1:   11 Triangle Construction Fails
  550.    wt: 1:   10 Dropping a perpendicular to line
  551.    wt: 1:   9 Construction of a right bisector
  552.    wt: 1:   8 Isoceles Triangles
  553.    wt: 1:   7 Angle Side Angle
  554.    wt: 1:   5 Side Angle Side
  555.    wt: 1:   4 Side Side Side
  556.    wt: 1:   3 Isometry of Triangles Congruence
  557.    wt: 1:   2 Correspondence between Triangles
  558.    wt: 1:   Short Course on Euclidean Geometry
  559.    wt: 1:   26 More Less Greater Than Comparison
  560.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  561.    wt: 1:   23 Distributive Law Two Derivations
  562.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  563.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  564.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  565.    wt: 1:   15 Head to Tails in place Addition Associative
  566.    wt: 1:   9 Division with Digits after Decimal Point
  567.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  568.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  569.    wt: 1:   4 Location of Point in Decimal Addition
  570.    wt: 1:   3 Location of Point in Decimal Multiplication
  571.    wt: 1:   2 Counting Digits in Decimal Multiplication
  572.    wt: 1:   E Long Division Methods more
  573.    wt: 1:   D Long Division Methods
  574.    wt: 1:   C Three Decimal Subtraction Methods
  575.    wt: 1:   A Decimal Addition Columm Methods
  576.    wt: 1:   8 Column Multiplication Methods in General
  577.    wt: 1:   7 Decimals Multiplication Methods Examples
  578.    wt: 1:   4 Commutative Law Groups Counting Form
  579.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  580.    wt: 1:   3 Proportionality Examples
  581.    wt: 1:   2 Algebraic View
  582.    wt: 1:   1 What is Proportionality
  583.    wt: 1:   9 Circle Area and Perimeter Formula Backwards Forwards
  584.    wt: 1:   6 Compound Interest Forward and Backwards
  585.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  586.    wt: 1:   5 Equality in Algebra
  587.    wt: 1:   3 Product Axioms Two Forms
  588.    wt: 1:   1 Equivalent Computation Rules
  589.    wt: 1:   5 Greater More Less Than Signs in General
  590.    wt: 1:   9 Coordinates for Regions in Space
  591.    wt: 1:   2 Integers
  592.    wt: 1:   5 Independent versus Dependent Variables
  593.    wt: 1:   4 Changing Letters
  594.    wt: 1:   2 Computation Rules Evaluation
  595.    wt: 1:   3 GE III Equation Addition and Multiplication
  596.    wt: 1:   6 Algebraic Solution Example
  597.    wt: 1:   1 Written work formats for developing and showing skill
  598.    wt: 1:   9 Sets in Probability and Statistics
  599.    wt: 1:   8 Sets of Numbers
  600.    wt: 1:   1 Three Skills For Algebra
  601.    wt: 1:   014 Counting Days with Calendars
  602.    wt: 1:   013 Travel Time Tables
  603.    wt: 1:   012 Division of Time Intervals by Time Intervals
  604.    wt: 1:   010 Repeated Addition of Time Intervals
  605.    wt: 1:   8 Addition of Time Intervals via subtotaling
  606.    wt: 1:   7 Addition of Time Intervals
  607.    wt: 1:   6 How long is a million seconds
  608.    wt: 1:   5 Conversion Arithmetic
  609.    wt: 1:   Example 2 volume of a cone
  610.    wt: 1:   Example 1 volume of a pyramid
  611.    wt: 1:   Volume of Solid by Cross Sections Lesson
  612.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  613.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  614.    wt: 1:   Example 4 with x function of y
  615.    wt: 1:   Example 3
  616.    wt: 1:   Example 2
  617.    wt: 1:   Example 1
  618.    wt: 1:   Area Between Curves Lesson Take 2
  619.    wt: 1:   Area Between Curves Lesson Take 1
  620.    wt: 1:   Summary
  621.    wt: 1:   17 Derivatives of quotients of sine and cosine
  622.    wt: 1:   16 Derivatives of reciprocals of sine and cosine
  623.    wt: 1:   15 sine and cosine derivatives 3rd step
  624.    wt: 1:   14 sine and cosine derivatives 2nd step
  625.    wt: 1:   13 sine and cosine derivatives 1st step
  626.    wt: 1:   11 Limits at infinity Three Examples
  627.    wt: 1:   10 Three one sided limits with infinite values
  628.    wt: 1:   8 Four Animated Examples
  629.    wt: 1:   7 Evaluation by immediate or delayed substitution
  630.    wt: 1:   6 Continuity at a point
  631.    wt: 1:   4 Numerical properties
  632.    wt: 1:   3 Decimal insights for limits continuity convergence
  633.    wt: 1:   2 Algebraic codification
  634.    wt: 1:   1 Numerical introduction
  635.    wt: 1:   F.3 Intermediate Value Theorem
  636.    wt: 1:   PostScript For and Against Decimal Perspectives
  637.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  638.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  639.    wt: 1:   Chapter 22 Complex Numbers
  640.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  641.    wt: 1:   Chapter 12. Units and Slopes
  642.    wt: 1:   Chapter 10 Slopes and Units
  643.    wt: 1:   Chapter 7 Slopes and Velocity
  644.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  645.    wt: 1:   Chapter 2. Slopes and Ski Trails
  646.    wt: 1:   Postscript More on Better Performance
  647.    wt: 1:   Postscript For Better Performance
  648.    wt: 1:   Appendix C. How to Read
  649.    wt: 1:   Appendix B. How To Learn
  650.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  651.    wt: 1:   Chapter 30 Truth Tables
  652.    wt: 1:   Chapter 28 Occurrence Tables
  653.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  654.    wt: 1:   Chapter 25. Mathematical Induction Examples
  655.    wt: 1:   Chapter 23. Notation For Sums
  656.    wt: 1:   Chapter 21. Third Reading Guide
  657.    wt: 1:   Chapter 18. Rules for Algebra
  658.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  659.    wt: 1:   Chapter 16. Painless Theorem Proving
  660.    wt: 1:   Chapter 15. Solving Linear Equations
  661.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  662.    wt: 1:   Chapter 13. Second Reading Guide
  663.    wt: 1:   Postscript What is a Variable
  664.    wt: 1:   Solutions For Arithmetic Exercises
  665.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  666.    wt: 1:   Chapter 6 Change of Language
  667.    wt: 1:   Chapter 4 Longer Chains of Reason
  668.    wt: 1:   Chapter 3 Chains of Reason
  669.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  670.    wt: 1:   Foreword
  671.    wt: 1:   Chapter 2 For and Against Mathematics
  672.    wt: 1:   Postscript B More on Story Telling and Reason
  673.    wt: 1:   Chapter 24 Direct and Indirect Reason
  674.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  675.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  676.    wt: 1:   Chapter 18 Sense and Knowledge
  677.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  678.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  679.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  680.    wt: 1:   1 Links to Online Resources Elsewhere Take 1
  681.    wt: 1:   S Adding words to algebra
  682.    wt: 1:   N Mathematics Prepare for College Studies
  683.    wt: 1:   M Words to extend arithmetic
  684.    wt: 1:   H more Routine to non routine problem solving
  685.    wt: 1:   F. The student teacher tutor feedback loop
  686.    wt: 1:   D. Check work a must with a caution
  687.    wt: 1:   C. Domino effect of being careful
  688.    wt: 1:   B. Domino effect of errors
  689.    wt: 1:   A. Skill has to be seen to believed
  690.    wt: 1:   Chapter 8 Skipped Topics and Why
  691.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  692.    wt: 1:   Chapter 6 More Algebra and Geometry
  693.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  694.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  695.    wt: 1:   Helping the Blind in Logic and Mathematics
  696.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  697.    wt: 1:   More Algebra and Slope based Calculus Preview
  698.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  699.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  700.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  701.    wt: 1:   The Math Forum and Site Content
  702.    wt: 15:   C Equality for Fractions and Two Term Ratios and Fractions
  703.    wt: 13:   B Fractions and Two Term Ratios
  704.    wt: 13:   A Similarities between Fractions and Two Term Ratios
  705.    wt: 12:   9 Improper Fractions and Mixed Numbers
  706.    wt: 11:   D Three Term Ratios
  707.    wt: 11:   21 Reciprocals for Fractions and Wholes
  708.    wt: 11:   10 Simplification of Fractions and Mixed Numerals
  709.    wt: 10:   22 Complex Compound Fractions
  710.    wt: 10:   20 Dividing Fractions the Why
  711.    wt: 10:   19 Dividing Fractions How TO
  712.    wt: 10:   17 Efficient Ways to Add and Subtract
  713.    wt: 10:   15 Adding and Subtracting with Unlike Denominators
  714.    wt: 10:   14 Adding and Subtracting with Like Denominators
  715.    wt: 10:   6 Multiplication of Mixed Numbers
  716.    wt: 10:   5 Equivalent Fractions
  717.    wt: 10:   Fraction Operations by Raising Terms A Simple Innovation

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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