Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Development How-TOs Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling; and for avid readers not in school. See Site Map

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

Ages 15+: Why study slopes Polynomials Quadratics Why factor polynomials Logarithms Functions
What is similarity Euclidean geometry leanly Coordinates + complex no.s Vectors DC Electric Circuits
Ages 12+: Prime factorization Written work formats Decimal place value Extend arithmetic skills orally
What is a variable 5. Fraction Operations by Raising Terms Solving Linear Equations: Take I Take II

Online Volumes: 1 - Elements of Reason, 2 - 3 Skills For Algebra, 3 - Why Slopes and
More Math, 1A - Pattern Based Reason, 1B - Skill Development Principles + Troubles

Welcome: Site content may develop critical thinking, improve reading and writing, and build mathematics skills. See online chapters on on logic and pattern based reason.

Teachers: This December 2011, 5-phase framework offers a context for mathematics & logic instruction. Phases 1 to 3 focus on skills with actual or potential value for adult & daily life. College-oriented phases 5 & 4 focus on calculus & preparation for it. Phases 1 to 4 may also serve trades & professions not dependent on calculus.

Site Review: Math resources ... span ... arithmetic, logic, algebra, calculus, complex numbers, and Euclidean geometry. Lessons and how-tos .... provide a good foundation for high school and college ... mathematics. Read more.

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51 matches:

  1.    wt: 9:   12 Comparison of Unsigned and Signed Numbers/
  2.    wt: 7:   9 Combinatorics Trees Tables and Products/
  3.    wt: 7:   8 Arithmetic with Signed Numbers/
  4.    wt: 7:   3 Prime Factorization Skills/
  5.    wt: 7:   A Decimal Counting and Adding Methods/
  6.    wt: 6:   11 Squares and Square Roots/
  7.    wt: 6:   10 LCM GCD and Euclid GCD Algorithm/
  8.    wt: 6:   7 Arithmetic and Fractions with Units/
  9.    wt: 6:   6 Fractions and Ratios/
  10.    wt: 6:   4 Remainder Arithmetic and Divisibility/
  11.    wt: 6:   B Decimal Comparing and Subtracting 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: 4:   14 Degrees to Radians and Radians to Degrees/
  19.    wt: 2:   13 Vectors/
  20.    wt: 2:   12 Function Translating and Rescaling/
  21.    wt: 2:   11 Parallel Straight Lines and Transversals/
  22.    wt: 2:   10 Intersecting Straight Lines and Transversals/
  23.    wt: 2:   9 Lines and Slopes Take 2 with tangent function/
  24.    wt: 2:   7 Complex Numbers/
  25.    wt: 2:   4 Lines and Slopes Take 1/
  26.    wt: 2:   3 Cartesian and Polar Coordinates/
  27.    wt: 2:   2 Euclidean Geometry Constructions Theory extras/
  28.    wt: 2:   PreSchool and Primary Mathematics or Quantitative Skills/
  29.    wt: 1:   Mathematics Skills Year by Year/
  30.    wt: 1:   5 Factored Polynomial Sign Analysis Examples/
  31.    wt: 1:   15 Arc or Inverse Trigonometric Function/
  32.    wt: 1:   8 Unit Circle Trigonometry/
  33.    wt: 1:   6 Trigonometry first steps/
  34.    wt: 1:   5 What is Similarity/
  35.    wt: 1:   1 Maps Plans Measurement/
  36.    wt: 1:   Geometry maps plans trigonometry vectors/
  37.    wt: 1:   B Real Numbers Extrinsic Development/
  38.    wt: 1:   A Origins of Counting and Figuring Methods/
  39.    wt: 1:   9 Proportionality Backwards and Forwards/
  40.    wt: 1:   7 Axioms Logic and Equivalent Equations/
  41.    wt: 1:   6 More Less Greater Than Inequalities and Comparison/
  42.    wt: 1:   5 Real Numbers/
  43.    wt: 1:   4 Computation Rules and Function Notation/
  44.    wt: 1:   Step 1 Stick diagram and fractions/
  45.    wt: 1:   Time Date Matters/
  46.    wt: 1:   Skills with take home value/
  47.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  48.    wt: 1:   13 Lessons on Limits and Continuity/
  49.    wt: 1:   Volume 2 Three Skills For Algebra/
  50.    wt: 1:   Work and Study Tips/
  51.    wt: 1:   Resources and Reciprocal Links/

Web Page Search

462 matches:

  1.    wt: 5:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  2.    wt: 5:   11 Signed Number Addition and Addition Properties
  3.    wt: 4:   2 signed and unsigned numbers as coordinates
  4.    wt: 4:   How to Build Skills and Confidence
  5.    wt: 3:   How to be a better instructor
  6.    wt: 3:   13 Addition and Addition Tables
  7.    wt: 3:   13 From one to one to many to one
  8.    wt: 3:   Vector and Complex Number Applet
  9.    wt: 3:   14 Vector Head to Tail Sums and Resultants
  10.    wt: 3:   2 Combing Counts Addition Skills and Principles
  11.    wt: 3:   4 A Brief Story of numbers and algebra
  12.    wt: 3:   6 adding signed numbers
  13.    wt: 3:   17 Efficient Ways to Add and Subtract
  14.    wt: 3:   15 Adding and Subtracting with Unlike Denominators
  15.    wt: 3:   14 Adding and Subtracting with Like Denominators
  16.    wt: 3:   8 What skills and work habits to require
  17.    wt: 3:   6. Counting and adding units and mixed units
  18.    wt: 3:   5. How to add decimals C. Examples
  19.    wt: 3:   4. How to add with decimals B with conversions
  20.    wt: 3:   3. How to add with decimals A sans conversions
  21.    wt: 3:   Quick history of numbers and algebra
  22.    wt: 3:   Formula Evaluation how to show work
  23.    wt: 3:   Expression Evaluation how to show work
  24.    wt: 3:   Chapter 20 Vectors and Complex Numbers
  25.    wt: 3:   Appendix E. How To Study Mathematics and Why
  26.    wt: 3:   Q How Logic and Proofs extend Show Work Practices
  27.    wt: 3:   E. When and how to correct errors
  28.    wt: 3:   Primary and Secondary Skills and Practices with Take Home Value
  29.    wt: 3:   1 From Number Recognition and Counting to Arithmetic B
  30.    wt: 3:   1 From Number Recognition and Counting to Arithmetic A
  31.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  32.    wt: 2:   Ramblings Extrinsic numbers theory
  33.    wt: 2:   2 arithmetic with signed numbers
  34.    wt: 2:   1 arithmetic with unsigned numbers
  35.    wt: 2:   04 25 when to stop or suspend mathemat
  36.    wt: 2:   Home Tutoring and Home Schooling
  37.    wt: 2:   2 Reading and Writing Skills
  38.    wt: 2:   Ages 12 to 14 Skills with take home value
  39.    wt: 2:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  40.    wt: 2:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  41.    wt: 2:   25 Absolute Value greatest integer and saw tooth functions
  42.    wt: 2:   24 Monotoncity Injectivity and Inverse Functions
  43.    wt: 2:   8 Notes for instructors or tutors
  44.    wt: 2:   9 Summary Degrees to Radians and back
  45.    wt: 2:   4 Circle Sector Area proportional to Central Angle
  46.    wt: 2:   7 Coordinate Addition and Scalar Multiplication
  47.    wt: 2:   5 Head To Tail Arrow Addition
  48.    wt: 2:   Construction Methods and Criteria for Isometric and Similar Triangles
  49.    wt: 2:   14 cosine even and sine and tangent are odd
  50.    wt: 2:   13 Navigation Location from Angles to 2 Landmarks
  51.    wt: 2:   7 Exercises to test skill and concept mastery
  52.    wt: 2:   5 Cartesian Addition and Translation
  53.    wt: 2:   4 Polar Coordinates to and from
  54.    wt: 2:   5 Drawing to Scale Avoids Angle Distortions
  55.    wt: 2:   3 Lengths and Areas on Maps and Plans
  56.    wt: 2:   A Signed Number Arithmetic Review
  57.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  58.    wt: 2:   22 Multiplication of Signed Numbers
  59.    wt: 2:   21 Addition of Multiples of a Single Vector
  60.    wt: 2:   19 Signed Multiples of Vectors
  61.    wt: 2:   18 Geometrically Why Vector Addition Commutes
  62.    wt: 2:   15 Head to Tails in place Addition Associative
  63.    wt: 2:   13 Arrows and Vectors in a Plane
  64.    wt: 2:   12 Real Numbers Line Signed Coordinates
  65.    wt: 2:   2 Addition and Multiplication Axioms
  66.    wt: 2:   2 More and Less Than for Counts and Measures
  67.    wt: 2:   12 Real Number Additive Inverses or Negatives
  68.    wt: 2:   11 Real Number Addition
  69.    wt: 2:   10 Real Number Lengths and Signs
  70.    wt: 2:   6 Unsigned Real Numbers
  71.    wt: 2:   1 Whole and Natural Numbers
  72.    wt: 2:   3 GE III Equation Addition and Multiplication
  73.    wt: 2:   1 Written work formats for developing and showing skill
  74.    wt: 2:   5 Talking about Numbers and Quantities
  75.    wt: 2:   3 Adding Words To Arithmetic
  76.    wt: 2:   1 More and Less Than for Counts and Measures
  77.    wt: 2:   7 GCD and LCM from prime factorization
  78.    wt: 2:   11 What are real lengths and numbers
  79.    wt: 2:   10 dividing signed numbers
  80.    wt: 2:   9 subtracting signed numbers
  81.    wt: 2:   8 multiplying signed numbers
  82.    wt: 2:   7 negative and additive inverse
  83.    wt: 2:   5 lengths and signs of numbers
  84.    wt: 2:   3 signed coordinates for maps and planes
  85.    wt: 2:   3 Multiplying Units and Numbers
  86.    wt: 2:   1 Addition and Subtraction with Units
  87.    wt: 2:   C Equality for Fractions and Two Term Ratios and Fractions
  88.    wt: 2:   19 Dividing Fractions How TO
  89.    wt: 2:   9 Improper Fractions and Mixed Numbers
  90.    wt: 2:   11 Adding Integers Formulas and Examples
  91.    wt: 2:   8 Multiplication by Signed Numbers Integers
  92.    wt: 2:   5 Zero Movement and Additive Inverses
  93.    wt: 2:   18 video Count Factors given Prime Factorization
  94.    wt: 2:   17 Identify and Count Factors using Primes
  95.    wt: 2:   15 video Factors of 20 using Prime Factorization
  96.    wt: 2:   10 video Prime Factorization upto 23 squared
  97.    wt: 2:   9 video Prime Factorization upto 19 squared
  98.    wt: 2:   8 video Prime Factorization upto 19
  99.    wt: 2:   7 Calculator Usage Notes and Cautions
  100.    wt: 2:   6 Sieve of Eratosthenes and Square Rule
  101.    wt: 2:   5 Prime Factorization and a Square Rule
  102.    wt: 2:   1 video how Products are bigger than factor
  103.    wt: 2:   3 Harder Cases Convert to Compare and Subtract
  104.    wt: 2:   10 Names for Big Numbers and Powers of Ten Expansion
  105.    wt: 2:   8 Addition of Time Intervals via subtotaling
  106.    wt: 2:   1 Intro of Kids To Time Date Skills
  107.    wt: 2:   38 Formulas and derivatives for powers and roots
  108.    wt: 2:   D1 Sets and Sequences GLBs and LGBs
  109.    wt: 2:   Chapter 14 Limits and Continuity with and sans Decimals
  110.    wt: 2:   Appendix D. What to do in School and Why
  111.    wt: 2:   Appendix C. How to Read
  112.    wt: 2:   Appendix B. How To Learn
  113.    wt: 2:   Chapter 5 Islands and Divisions of Knowledge
  114.    wt: 2:   Chapter 1 Introduction to Chapters 2 to 6
  115.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  116.    wt: 2:   Postscript B More on Story Telling and Reason
  117.    wt: 2:   Chapter 16 Origins and Limitations of Rules and Patterns
  118.    wt: 2:   Chapter 12 Islands and Divisions of Knowledge
  119.    wt: 2:   V Reasons and Motivations for Logic and Mathematics
  120.    wt: 2:   S Adding words to algebra
  121.    wt: 2:   P Exact Arithmetic With Whole Numbers and Fractions
  122.    wt: 2:   J. More on written work and showing skill
  123.    wt: 2:   I. Logic and language skills
  124.    wt: 2:   G. Written work formats for developing and showing skill
  125.    wt: 2:   A. Skill has to be seen to believed
  126.    wt: 2:   Chapter 8 Skipped Topics and Why
  127.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  128.    wt: 2:   2 Identifying Size and Position Place and Spatial Sense
  129.    wt: 2:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  130.    wt: 2:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  131.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  132.    wt: 2:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  133.    wt: 2:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  134.    wt: 1:   Appendix 1 primary and preschool mathematic
  135.    wt: 1:   G LAMP Introduction Problem Solving Skills
  136.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  137.    wt: 1:   Skills Chapter 5 Calculus
  138.    wt: 1:   Skills Chapter 4 Logic
  139.    wt: 1:   Skills Chapter 3 Algebra
  140.    wt: 1:   Skills Chapter 2 Geometry
  141.    wt: 1:   Skills Chapter 1 Arithmetic
  142.    wt: 1:   Skills Chapter 0 Introduction
  143.    wt: 1:   9 combinatorics probability sets
  144.    wt: 1:   7 logic review and decimals an odd combination
  145.    wt: 1:   5 logarithms and exponentials etc
  146.    wt: 1:   which way to go
  147.    wt: 1:   three goals to set for students
  148.    wt: 1:   key notes and themes
  149.    wt: 1:   grouping students according to ability
  150.    wt: 1:   what should be learnt and When
  151.    wt: 1:   how letters appear
  152.    wt: 1:   What to Tell Students
  153.    wt: 1:   teaching tutoring algebraic reason
  154.    wt: 1:   standards for course material
  155.    wt: 1:   Operational Viewpoint to Value
  156.    wt: 1:   Theory of Knowledge
  157.    wt: 1:   Education in mathematics science and technology
  158.    wt: 1:   Four ways to improve education reform
  159.    wt: 1:   Motivation and Context Problem
  160.    wt: 1:   fairness and inductive principles for instruction
  161.    wt: 1:   words for mathematics instructor
  162.    wt: 1:   3 Like resistors in parallel
  163.    wt: 1:   2 Unlike resistors in parallel01
  164.    wt: 1:   1 Like resistors in series
  165.    wt: 1:   F Unlike Resistors in Series
  166.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  167.    wt: 1:   24 Standards For Skill Develoment Take II
  168.    wt: 1:   24 Standards For Skill Develoment
  169.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  170.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  171.    wt: 1:   17 Math Booklets for children and young teenagers
  172.    wt: 1:   14 Multiplication and Times Tables
  173.    wt: 1:   12 Goals and Objectives For Mathematics
  174.    wt: 1:   11 Help and Defend Your Child or Teens Education
  175.    wt: 1:   5 Patience Please for Yourself and Your Charges
  176.    wt: 1:   4 Learning Takes Time and Effort
  177.    wt: 1:   1 Speaking Skills
  178.    wt: 1:   Ages 12 to 14 Geometry
  179.    wt: 1:   Ages 12 to 14 Arithmetic
  180.    wt: 1:   Ages 10 to 12 Geometry
  181.    wt: 1:   Ages 10 to 12 Arithmetic
  182.    wt: 1:   Ages 9 to 10
  183.    wt: 1:   Ages 8 to 9
  184.    wt: 1:   Ages 7 to 8
  185.    wt: 1:   Ages 6 to 7
  186.    wt: 1:   Ages 4 plus to 5 plus
  187.    wt: 1:   Ages 3 plus to 4 plus
  188.    wt: 1:   26 Function definitions done and coming
  189.    wt: 1:   19 Horizontal line rule and method
  190.    wt: 1:   18 Vertical Line Rule and Method
  191.    wt: 1:   17 Function maxima minima and their location
  192.    wt: 1:   11 Function Domain Range Source and Targets
  193.    wt: 1:   9 Set theory term relation possible origins
  194.    wt: 1:   8 Set view of relations and functions
  195.    wt: 1:   6 Set Existence Formation and Notation
  196.    wt: 1:   4 Function notation in and beyond mathematics
  197.    wt: 1:   9 quadratics physical and further context
  198.    wt: 1:   3 quadratics factoring by inspection
  199.    wt: 1:   11 Growth and Decay in Biology
  200.    wt: 1:   10 Exponential Growth and Decay Models
  201.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  202.    wt: 1:   5 Natural Logarithm Calculator Exercises
  203.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  204.    wt: 1:   1 Calculator Starter Exercises
  205.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  206.    wt: 1:   3 Polynomials Multiplication Addition
  207.    wt: 1:   16 cotangent function Definition Graph and Inverse
  208.    wt: 1:   15 cosecant function Definition Graph and Inverse
  209.    wt: 1:   14 secant function Definition Graph and Inverse
  210.    wt: 1:   13 cosecant function Definition Graph and Inverse
  211.    wt: 1:   6 Radian Measure to Degrees
  212.    wt: 1:   5 Degrees to Radian Measure
  213.    wt: 1:   3 Circle Arclengh Proportional to Central Angle
  214.    wt: 1:   1 Degrees and Radians Introduction
  215.    wt: 1:   A Global Time and Navigation
  216.    wt: 1:   15 Dot and Cross Product
  217.    wt: 1:   13 Velocity Vectors in Physics
  218.    wt: 1:   12 From Applied To Pure Mathematics
  219.    wt: 1:   10 Parallelogram Addition Method
  220.    wt: 1:   9 Head to Tail Coordinate View
  221.    wt: 1:   8 Parallel Vectors
  222.    wt: 1:   6 Vectors with Coordinates
  223.    wt: 1:   3 Navigation with Arrows or Vectors
  224.    wt: 1:   2 Signed Coordinates
  225.    wt: 1:   1 Unsigned Coordinates
  226.    wt: 1:   Parallel Lines and Parallel Transversals
  227.    wt: 1:   Triangle Angles Sum To 180 Degrees
  228.    wt: 1:   Parallel Lines and Alternating Corresponding Angles
  229.    wt: 1:   Parallel Lines and Interior Angles
  230.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  231.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  232.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  233.    wt: 1:   29 secant cosecant and cotangent for acute angles
  234.    wt: 1:   27 Logarithmic use of products of sines and cosines
  235.    wt: 1:   26 Formulas for products of sines and cosines
  236.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  237.    wt: 1:   21 sine and cosine Half Angle Formulas
  238.    wt: 1:   20 sine and cosine Double Angle Formulas
  239.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  240.    wt: 1:   17E Trig Formulas for dot and cross Products
  241.    wt: 1:   17D cis formulas for sine cosines and tangent
  242.    wt: 1:   17C sine and cosine double triple angle formulas
  243.    wt: 1:   17A The complex number valued trig function cis
  244.    wt: 1:   10 Graphs of sines and cosines many periods
  245.    wt: 1:   9 Graphs of sine and cosine over one period
  246.    wt: 1:   7 period of sine and cosine
  247.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  248.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  249.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  250.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  251.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  252.    wt: 1:   21 Logarithms Powers and Exponentials
  253.    wt: 1:   20 N th Roots of Complex Numbers
  254.    wt: 1:   16 References and Originality Question
  255.    wt: 1:   13 Trig Formulas for dot and cross Products
  256.    wt: 1:   12 cis formulas for sine cosines and tangent
  257.    wt: 1:   11 sine and cosine double triple angle formulas
  258.    wt: 1:   9 The complex number valued trig function cis
  259.    wt: 1:   7 Second Way to Calculate Products
  260.    wt: 1:   6 Field Properties of Complex Number
  261.    wt: 1:   3 Addition Properties
  262.    wt: 1:   2 Complex Numbers made easier we hope
  263.    wt: 1:   Appetizer A Complex Number Applet
  264.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  265.    wt: 1:   3 Trigonometric Ratios sine and cosine
  266.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  267.    wt: 1:   8 Similarity of Triangles and Polygons
  268.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  269.    wt: 1:   10 Midpoint of [a b] and [b a]
  270.    wt: 1:   1 Numerical view of lines and their equations
  271.    wt: 1:   What is and is not here
  272.    wt: 1:   7 Complex Numbers Appetizer
  273.    wt: 1:   6 Polar Multiplication and Rotation
  274.    wt: 1:   PS H Distributive Law For Complex Numbers
  275.    wt: 1:   PS G Rotation Distributes over Addition
  276.    wt: 1:   PS F Scalar Multiplication Distributes over Addition
  277.    wt: 1:   PS D Addition with Cartesian Coordinates
  278.    wt: 1:   17 Right Bisectors of Triangle Sides
  279.    wt: 1:   16 Angles Subtended By Chords and Diameters
  280.    wt: 1:   10 Dropping a perpendicular to line
  281.    wt: 1:   9 Construction of a right bisector
  282.    wt: 1:   6 Ruler and compass Angle Bisection
  283.    wt: 1:   1 Initial Concepts and Terms
  284.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  285.    wt: 1:   6 Figuring with Maps Not to Scale
  286.    wt: 1:   4 Angles on Maps Plans drawn to scale
  287.    wt: 1:   musings do not puiblish real numbers
  288.    wt: 1:   A Modular and Remainder Arithmetic
  289.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  290.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  291.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  292.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  293.    wt: 1:   8 Division and Mulplication of Compound Fractions
  294.    wt: 1:   4 Location of Point in Decimal Addition
  295.    wt: 1:   B Decimal Comparison and Subtraction
  296.    wt: 1:   A Decimal Addition Columm Methods
  297.    wt: 1:   5 Distributive Law for Whole Numbers
  298.    wt: 1:   3 Multiplicative Counting Skills Principles
  299.    wt: 1:   1 The Counting Origins of Numbers
  300.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  301.    wt: 1:   4 Rates Ratios and Proporitionality
  302.    wt: 1:   9 Circle Area and Perimeter Formula Backwards Forwards
  303.    wt: 1:   6 Compound Interest Forward and Backwards
  304.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  305.    wt: 1:   6 Equations and Systems Equivalent or Implied
  306.    wt: 1:   4 Subtraction and Division Axioms
  307.    wt: 1:   4 Comparison of Negative Numbers
  308.    wt: 1:   3 More and Less Than with Unlike Signs
  309.    wt: 1:   1 Real Numbers Comparison
  310.    wt: 1:   16 Real Numbers Comparison
  311.    wt: 1:   15 Real Number Division
  312.    wt: 1:   14 Real Number Multiplication
  313.    wt: 1:   13 Real Number Subtraction
  314.    wt: 1:   8 Coordinates for Maps and Planes
  315.    wt: 1:   7 Real Numbers as Line Cordinates
  316.    wt: 1:   5 Rational Numbers More
  317.    wt: 1:   4 Rational Numbers
  318.    wt: 1:   3 Geometric Formulas and Function Notation
  319.    wt: 1:   1 Formulas Dependence and Function Notation
  320.    wt: 1:   Formula Usage Show Work Format
  321.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  322.    wt: 1:   9 Sets in Probability and Statistics
  323.    wt: 1:   8 Sets of Numbers
  324.    wt: 1:   1 Three Skills For Algebra
  325.    wt: 1:   3 Comparison of Negative Numbers
  326.    wt: 1:   2 More and Less Than with Unlike Signs
  327.    wt: 1:   1 Squares and Square Roots Introduction
  328.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  329.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  330.    wt: 1:   13 GCD from given Prime Factorization
  331.    wt: 1:   10 Euclid Algorithm with 129 125 and with 45 14
  332.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  333.    wt: 1:   4 LCM of 8 and 10 via Prime
  334.    wt: 1:   3 Counting with Tables and Trees II
  335.    wt: 1:   2 Counting with Tables and Trees I
  336.    wt: 1:   1 Counting and Counting Methods I
  337.    wt: 1:   4 signed coordinates for regions in space
  338.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  339.    wt: 1:   2 Equality and Units
  340.    wt: 1:   B Fractions and Two Term Ratios
  341.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  342.    wt: 1:   21 Reciprocals for Fractions and Wholes
  343.    wt: 1:   18 Efficient Ways to Multiply
  344.    wt: 1:   16 Addition Subtraction Comparision Compared
  345.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  346.    wt: 1:   6 Multiplication of Mixed Numbers
  347.    wt: 1:   13 Subtraction with Additive Inverse
  348.    wt: 1:   12 Adding Integers More Examples
  349.    wt: 1:   6 Multiplication by Natural Numbers
  350.    wt: 1:   4 Adding Movements wiht opposite directions
  351.    wt: 1:   3 Adding Movements with same direction
  352.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  353.    wt: 1:   20 Uniqueness of Prime Factorization
  354.    wt: 1:   19 video Prime Factorization Unique
  355.    wt: 1:   16 video Factors of 980 using prime
  356.    wt: 1:   14 video Factors of 24 Take II
  357.    wt: 1:   13 video Factors of 24 using prime
  358.    wt: 1:   12 LCD GCD and LCM using Primes
  359.    wt: 1:   4 video Prime Factorization Introduction
  360.    wt: 1:   3 video Primes and Composites from 9 times table
  361.    wt: 1:   2 Prime and Composites less than 16
  362.    wt: 1:   Division with Counts and Length
  363.    wt: 1:   Long Division forwards and backwards Example 3
  364.    wt: 1:   Long Division forwards and backwards Example 2
  365.    wt: 1:   Long Division forwards and backwards Example 1
  366.    wt: 1:   10 Division by Five Long and Short Ways
  367.    wt: 1:   4 Two and Three Digit Multipliers
  368.    wt: 1:   4 Subtraction with Conversions Borrows and Letter J
  369.    wt: 1:   1 Comparison and Subtraction Easy Direct Cases
  370.    wt: 1:   7 Adding decimal fractions using decimal point
  371.    wt: 1:   1. Explaining Addition Table
  372.    wt: 1:   11 Place Value SI Standard International way
  373.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  374.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  375.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  376.    wt: 1:   Exact Arithmetic Wholes and Fractions
  377.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  378.    wt: 1:   016 Numbering Occidental Calendar Days
  379.    wt: 1:   015 School and work day counting tables
  380.    wt: 1:   011 Division of Time Intervals By Numbers
  381.    wt: 1:   010 Repeated Addition of Time Intervals
  382.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  383.    wt: 1:   7 Addition of Time Intervals
  384.    wt: 1:   6 How long is a million seconds
  385.    wt: 1:   4 Mixing and Changing Units of Time
  386.    wt: 1:   3 Units and Lengths of Time
  387.    wt: 1:   2 Time and Date Matters in School
  388.    wt: 1:   Example 1. Area Between x and x squared
  389.    wt: 1:   17 Derivatives of quotients of sine and cosine
  390.    wt: 1:   16 Derivatives of reciprocals of sine and cosine
  391.    wt: 1:   15 sine and cosine derivatives 3rd step
  392.    wt: 1:   14 sine and cosine derivatives 2nd step
  393.    wt: 1:   13 sine and cosine derivatives 1st step
  394.    wt: 1:   13 Limits with Parameters and Derivatives Take II
  395.    wt: 1:   12 Limits with Parameters and Derivatives Take I
  396.    wt: 1:   9 Limits Continuity and Composition
  397.    wt: 1:   5 Jumps and absence of unlimited error control
  398.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  399.    wt: 1:   D2 Limits of Monotone Sequences
  400.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  401.    wt: 1:   PostScript For and Against Decimal Perspectives
  402.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  403.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  404.    wt: 1:   Chapter 23 Links To Trigonometry
  405.    wt: 1:   Chapter 22 Complex Numbers
  406.    wt: 1:   Chapter 21 Arrow Addition
  407.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  408.    wt: 1:   Chapter 12. Units and Slopes
  409.    wt: 1:   Chapter 10 Slopes and Units
  410.    wt: 1:   Chapter 7 Slopes and Velocity
  411.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  412.    wt: 1:   Chapter 2. Slopes and Ski Trails
  413.    wt: 1:   Chapter 31 Direct and Indirect Reason
  414.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  415.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  416.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  417.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  418.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  419.    wt: 1:   Chapter 20. Degrees and Radians
  420.    wt: 1:   Chapter 19. Functions and Sets
  421.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  422.    wt: 1:   Chapter 12. Shorthand Usage Guide
  423.    wt: 1:   Chapter 11. Why Shorthand
  424.    wt: 1:   Chapter 10 Describing and Changing Calculations
  425.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  426.    wt: 1:   Chapter 8 Three Skills For Algebra
  427.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  428.    wt: 1:   Annotated Links to Material Elsehwere
  429.    wt: 1:   Chapter 2 For and Against Mathematics
  430.    wt: 1:   Postscript C Consistency as a Tool for Reason
  431.    wt: 1:   Postscript A Story Telling
  432.    wt: 1:   Chapter 24 Direct and Indirect Reason
  433.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  434.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  435.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  436.    wt: 1:   Chapter 18 Sense and Knowledge
  437.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  438.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  439.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  440.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  441.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  442.    wt: 1:   1 Links to Online Resources Elsewhere Take 1
  443.    wt: 1:   R Why Learn Mathematics Skills
  444.    wt: 1:   O On Learning Mathematics and Science
  445.    wt: 1:   M Words to extend arithmetic
  446.    wt: 1:   L Skills with take home value
  447.    wt: 1:   N Improving Marks on Tests and Finals
  448.    wt: 1:   H more Routine to non routine problem solving
  449.    wt: 1:   H Jigsaw puzzles and problem solving
  450.    wt: 1:   F. The student teacher tutor feedback loop
  451.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  452.    wt: 1:   Chapter 6 More Algebra and Geometry
  453.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  454.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  455.    wt: 1:   7 Games and Activities for Instruction
  456.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  457.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  458.    wt: 1:   Helping the Blind in Logic and Mathematics
  459.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  460.    wt: 1:   More Algebra and Slope based Calculus Preview
  461.    wt: 1:   Which Way To Go
  462.    wt: 1:   The Math Forum and Site Content

Extended Search

816 matches:

  1.    wt: 9:   4 Greater More Less Than Signs in General
  2.    wt: 9:   11 What are real lengths and numbers
  3.    wt: 9:   10 dividing signed numbers
  4.    wt: 9:   9 subtracting signed numbers
  5.    wt: 9:   8 multiplying signed numbers
  6.    wt: 9:   7 negative and additive inverse
  7.    wt: 9:   5 lengths and signs of numbers
  8.    wt: 9:   3 signed coordinates for maps and planes
  9.    wt: 9:   17 Efficient Ways to Add and Subtract
  10.    wt: 9:   15 Adding and Subtracting with Unlike Denominators
  11.    wt: 9:   14 Adding and Subtracting with Like Denominators
  12.    wt: 9:   18 video Count Factors given Prime Factorization
  13.    wt: 9:   17 Identify and Count Factors using Primes
  14.    wt: 9:   15 video Factors of 20 using Prime Factorization
  15.    wt: 9:   10 video Prime Factorization upto 23 squared
  16.    wt: 9:   9 video Prime Factorization upto 19 squared
  17.    wt: 9:   8 video Prime Factorization upto 19
  18.    wt: 9:   7 Calculator Usage Notes and Cautions
  19.    wt: 9:   6 Sieve of Eratosthenes and Square Rule
  20.    wt: 9:   5 Prime Factorization and a Square Rule
  21.    wt: 9:   1 video how Products are bigger than factor
  22.    wt: 8:   7 GCD and LCM from prime factorization
  23.    wt: 8:   3 Counting with Tables and Trees II
  24.    wt: 8:   2 Counting with Tables and Trees I
  25.    wt: 8:   1 Counting and Counting Methods I
  26.    wt: 8:   4 signed coordinates for regions in space
  27.    wt: 8:   3 Multiplying Units and Numbers
  28.    wt: 8:   1 Addition and Subtraction with Units
  29.    wt: 8:   C Equality for Fractions and Two Term Ratios and Fractions
  30.    wt: 8:   19 Dividing Fractions How TO
  31.    wt: 8:   9 Improper Fractions and Mixed Numbers
  32.    wt: 8:   20 Uniqueness of Prime Factorization
  33.    wt: 8:   19 video Prime Factorization Unique
  34.    wt: 8:   16 video Factors of 980 using prime
  35.    wt: 8:   14 video Factors of 24 Take II
  36.    wt: 8:   13 video Factors of 24 using prime
  37.    wt: 8:   12 LCD GCD and LCM using Primes
  38.    wt: 8:   4 video Prime Factorization Introduction
  39.    wt: 8:   3 video Primes and Composites from 9 times table
  40.    wt: 8:   2 Prime and Composites less than 16
  41.    wt: 8:   3 Harder Cases Convert to Compare and Subtract
  42.    wt: 8:   7 Adding decimal fractions using decimal point
  43.    wt: 8:   1. Explaining Addition Table
  44.    wt: 8:   Quick history of numbers and algebra
  45.    wt: 8:   Formula Evaluation how to show work
  46.    wt: 8:   Expression Evaluation how to show work
  47.    wt: 7:   1 Squares and Square Roots Introduction
  48.    wt: 7:   17 GCD LCM of 85 and 60 via Prime
  49.    wt: 7:   16 GCD and LCM of 650 225 via Prime
  50.    wt: 7:   13 GCD from given Prime Factorization
  51.    wt: 7:   10 Euclid Algorithm with 129 125 and with 45 14
  52.    wt: 7:   9 GCD of 360 110 via Primes and Euclid Algorithm
  53.    wt: 7:   4 LCM of 8 and 10 via Prime
  54.    wt: 7:   5 Counting with Tables Trees Product Rule Take II
  55.    wt: 7:   4 Counting with Trees Product Rule Take I
  56.    wt: 7:   5 Reciprocals and Division for Fractions with Units
  57.    wt: 7:   2 Equality and Units
  58.    wt: 7:   B Fractions and Two Term Ratios
  59.    wt: 7:   A Similarities between Fractions and Two Term Ratios
  60.    wt: 7:   21 Reciprocals for Fractions and Wholes
  61.    wt: 7:   18 Efficient Ways to Multiply
  62.    wt: 7:   16 Addition Subtraction Comparision Compared
  63.    wt: 7:   10 Simplification of Fractions and Mixed Numerals
  64.    wt: 7:   6 Multiplication of Mixed Numbers
  65.    wt: 7:   11 Adding Integers Formulas and Examples
  66.    wt: 7:   8 Multiplication by Signed Numbers Integers
  67.    wt: 7:   5 Zero Movement and Additive Inverses
  68.    wt: 7:   A Decimals Modular and Remainder Arithmetic
  69.    wt: 7:   11 Efficient Square Rule Use
  70.    wt: 7:   4 Subtraction with Conversions Borrows and Letter J
  71.    wt: 7:   1 Comparison and Subtraction Easy Direct Cases
  72.    wt: 7:   Appendix 1 Counting Revisited 15 minute video
  73.    wt: 7:   2 Decimal Counting Practices
  74.    wt: 7:   10 Names for Big Numbers and Powers of Ten Expansion
  75.    wt: 6:   9 Summary Degrees to Radians and back
  76.    wt: 6:   4 Circle Sector Area proportional to Central Angle
  77.    wt: 6:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  78.    wt: 6:   11 Signed Number Addition and Addition Properties
  79.    wt: 6:   5 Square Roots with primes more still
  80.    wt: 6:   4 Square Roots with primes more
  81.    wt: 6:   3 Properties of Square Roots with example
  82.    wt: 6:   2 Square Roots with Prime
  83.    wt: 6:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  84.    wt: 6:   14 GCD of 650 110 via Primes LCM via Product Rule
  85.    wt: 6:   11 GCD 2700 288 via Euclid Algorithm
  86.    wt: 6:   8 GCD from Euclidean Algorithm
  87.    wt: 6:   6 GCD from Prime
  88.    wt: 6:   5 Common Divisors 60 45 via Prime
  89.    wt: 6:   LCM 60 45 Avoid List Method Use Prime
  90.    wt: 6:   2 Least Common Multiple LCM intro via list method
  91.    wt: 6:   1 Least Common Multiples LCM Introduction
  92.    wt: 6:   12 GCD 2700 288 via Prime
  93.    wt: 6:   7 Converting or Changing Units
  94.    wt: 6:   6 Simplification of Fractions with Units
  95.    wt: 6:   4 Fractions with Units
  96.    wt: 6:   D Three Term Ratios
  97.    wt: 6:   22 Complex Compound Fractions
  98.    wt: 6:   21 Working With Signs
  99.    wt: 6:   20 Dividing Fractions the Why
  100.    wt: 6:   13 Fraction Comparison Algebraic View
  101.    wt: 6:   12 Fraction Comparison
  102.    wt: 6:   11 Simplification an Algebraic View
  103.    wt: 6:   8 Numerals Fractionals Quantals Take II
  104.    wt: 6:   7 Numerals Fractionals Quantals
  105.    wt: 6:   6 Multiplication Algebraically Take II
  106.    wt: 6:   5 Equivalent Fractions
  107.    wt: 6:   4 Fraction Multiplication
  108.    wt: 6:   3 Unit fraction of a fraction
  109.    wt: 6:   2 Unit Fraction Multiplication
  110.    wt: 6:   1 What is a fraction Take II
  111.    wt: 6:   1 What is a fraction
  112.    wt: 6:   Fraction Operations by Raising Terms A Simple Innovation
  113.    wt: 6:   13 Subtraction with Additive Inverse
  114.    wt: 6:   12 Adding Integers More Examples
  115.    wt: 6:   6 Multiplication by Natural Numbers
  116.    wt: 6:   4 Adding Movements wiht opposite directions
  117.    wt: 6:   3 Adding Movements with same direction
  118.    wt: 6:   27 Divisibility by 2 3 6 5 9 10 Example
  119.    wt: 6:   26 Divisibility by 2 3 5 Example
  120.    wt: 6:   25 Divisibility Tests for 2 3 5 9 10 Example
  121.    wt: 6:   24 Divisibility Tests for 2 3 5 9 10
  122.    wt: 6:   23 Remainder Arithmetic Modulo 2
  123.    wt: 6:   22 Remainder Arithmetic Modulo 3 more
  124.    wt: 6:   21 Remainder Arithmetic Modulo 3
  125.    wt: 6:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  126.    wt: 6:   19 Remainder Arithmetic Rule of 9 for checking sums III
  127.    wt: 6:   18 Remainder Arithmetic Rule of 9 for checking sums II
  128.    wt: 6:   17 Remainder Arithmetic Rule of 9 for checking sums I
  129.    wt: 6:   16 Remainder Arithmetic Modulo 9 Example 2
  130.    wt: 6:   15 Remainder Arithmetic Modulo 9 Example
  131.    wt: 6:   14 Remainder Arithmetic Modulo 9 Example
  132.    wt: 6:   13 Remainder Arithmetic Modulo 5 Example
  133.    wt: 6:   12 Remainder Arithmetic Modulo 10 Example
  134.    wt: 6:   11 Remainder Arithmetic Long Division by 5 Quickly more
  135.    wt: 6:   10 Remainder Arithmetic Long Division by 5 Quickly
  136.    wt: 6:   9 Remainder Arithmetic Divisibility by 5
  137.    wt: 6:   8 Remainder Arithmetic Morulo 5 Examples II
  138.    wt: 6:   7 Remainder Arithmetic Modulo 5 Examples I
  139.    wt: 6:   6 Remainder Arithmetic Modulo 5 Propertie
  140.    wt: 6:   5 Remainder Arithmetic Modulo 5
  141.    wt: 6:   4 Remainder Arithmetic Modulo 10 in general
  142.    wt: 6:   3 Remainder Arithmetic Modulos 10 more still
  143.    wt: 6:   2 Remainder Arithmetic Modulo 10 more
  144.    wt: 6:   1 Remainder Arithmetic Modulo 10
  145.    wt: 6:   Division with Counts and Length
  146.    wt: 6:   Long Division forwards and backwards Example 3
  147.    wt: 6:   Long Division forwards and backwards Example 2
  148.    wt: 6:   Long Division forwards and backwards Example 1
  149.    wt: 6:   10 Division by Five Long and Short Ways
  150.    wt: 6:   4 Two and Three Digit Multipliers
  151.    wt: 6:   Appendix 2 Three Decimal Subtraction Methods
  152.    wt: 6:   Appendix 1 Decimals Comparison Method Take II
  153.    wt: 6:   Subtraction with J Conversions Example
  154.    wt: 6:   Subtraction Another Video Lesson
  155.    wt: 6:   9 22 Minute Subtraction Review Video
  156.    wt: 6:   8 Subtraction with Units of Measure
  157.    wt: 6:   7 Subtraction for Decimal Fractions with Exercises
  158.    wt: 6:   6 Subtraction with Conversion Example with Exercises
  159.    wt: 6:   5 A Tip for Efficent Subtraction
  160.    wt: 6:   2 Subtraction Easy Case Examples
  161.    wt: 6:   11 Place Value SI Standard International way
  162.    wt: 6:   9 Place Value Review Decimal form of Avogrados number included
  163.    wt: 6:   8 Review Lesson 1 2 4 and 6 All in One
  164.    wt: 6:   1 Place Value in Three Digit Whole Numbers
  165.    wt: 6:   Exact Arithmetic Wholes and Fractions
  166.    wt: 6:   Practical Methods Ends and Values for Arithmetic
  167.    wt: 5:   6 Radian Measure to Degrees
  168.    wt: 5:   5 Degrees to Radian Measure
  169.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  170.    wt: 5:   1 Degrees and Radians Introduction
  171.    wt: 5:   Vector and Complex Number Applet
  172.    wt: 5:   arithmetic videos Real Player Format
  173.    wt: 5:   D Remainders Modulo 11 Pair Rule
  174.    wt: 5:   C Divisibility by 11 Integer Recognition Method
  175.    wt: 5:   B Integer Long Division Multiple Choices
  176.    wt: 5:   A Associative Law Theorectical Note
  177.    wt: 5:   10 Integer Multiplication Formulas
  178.    wt: 5:   9 Multiplying Integers
  179.    wt: 5:   7 Multiplication by Signs
  180.    wt: 5:   2 Integers Multiplies of a Unit Moverment
  181.    wt: 5:   1 Integers as Coordinates
  182.    wt: 5:   Long Division Backwards more
  183.    wt: 5:   Long Division Backward
  184.    wt: 5:   12 Why Long Division Works Take III
  185.    wt: 5:   11 Another Single Digit Divisor Example
  186.    wt: 5:   9 Why Long Division Works Take II
  187.    wt: 5:   8 Correcting the Mistake
  188.    wt: 5:   7 Long Divison Mistake Catching
  189.    wt: 5:   6 Why Decimal Long Division Methods Works Take I
  190.    wt: 5:   5 Long Division Include Zeroes or not
  191.    wt: 5:   4 Division with 2 Digit Divsors
  192.    wt: 5:   3 Division Single Digit Divisor Example
  193.    wt: 5:   2 Division with Single Digit Divisors
  194.    wt: 5:   1 Divsion Physical Examples
  195.    wt: 5:   D Decimal Multiplication Methods Derived
  196.    wt: 5:   C Counting Areas with Powers of Ten
  197.    wt: 5:   B Powers of Ten
  198.    wt: 5:   A Elementary Basis for Multiplication Methods
  199.    wt: 5:   6 Multiplication Commutes Order Not Important
  200.    wt: 5:   5 Decimal Fraction Multiplication
  201.    wt: 5:   3 More One Digit Multipliers
  202.    wt: 5:   2 One Digit Multipliers
  203.    wt: 5:   Video Decimal Multiplication Geometric View Example 2
  204.    wt: 5:   Video Decimal Multiplication Geometric View Example 2
  205.    wt: 5:   Video Power Notation in Decimal Expansion
  206.    wt: 5:   1 Why 3 times 5 gives 15
  207.    wt: 5:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  208.    wt: 5:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  209.    wt: 5:   5 More on Groups of 3 Place Value in Decimal Fractions
  210.    wt: 5:   4 Groups of 3 Place Value in Decimal Fractions
  211.    wt: 5:   3 More on Groups of 3 Multi Digit Place Value
  212.    wt: 5:   2 Groups of Three Place Value for Multidigit Decimals
  213.    wt: 5:   The 20 Times Table
  214.    wt: 5:   The 12 Times Table Visually
  215.    wt: 5:   About folder contents
  216.    wt: 5:   How to Build Skills and Confidence
  217.    wt: 5:   Primary and Secondary Skills and Practices with Take Home Value
  218.    wt: 5:   1 From Number Recognition and Counting to Arithmetic B
  219.    wt: 5:   1 From Number Recognition and Counting to Arithmetic A
  220.    wt: 4:   8 Radian Measures of Common Angles
  221.    wt: 4:   7 Radian Measures in special Triangles
  222.    wt: 4:   2 Radian Measure Numerical Value of one degree
  223.    wt: 4:   7 Coordinate Addition and Scalar Multiplication
  224.    wt: 4:   5 Head To Tail Arrow Addition
  225.    wt: 4:   Construction Methods and Criteria for Isometric and Similar Triangles
  226.    wt: 4:   7 Exercises to test skill and concept mastery
  227.    wt: 4:   5 Cartesian Addition and Translation
  228.    wt: 4:   4 Polar Coordinates to and from
  229.    wt: 4:   14 Vector Head to Tail Sums and Resultants
  230.    wt: 4:   2 Combing Counts Addition Skills and Principles
  231.    wt: 4:   Appendix E. How To Study Mathematics and Why
  232.    wt: 4:   Q How Logic and Proofs extend Show Work Practices
  233.    wt: 4:   E. When and how to correct errors
  234.    wt: 4:   5 Interpreting and Drawing Maps and Plans.
  235.    wt: 4:   2 Identifying Size and Position Place and Spatial Sense
  236.    wt: 3:   How to be a better instructor
  237.    wt: 3:   13 Addition and Addition Tables
  238.    wt: 3:   Ages 12 to 14 Skills with take home value
  239.    wt: 3:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  240.    wt: 3:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  241.    wt: 3:   13 From one to one to many to one
  242.    wt: 3:   A Global Time and Navigation
  243.    wt: 3:   15 Dot and Cross Product
  244.    wt: 3:   13 Velocity Vectors in Physics
  245.    wt: 3:   12 From Applied To Pure Mathematics
  246.    wt: 3:   10 Parallelogram Addition Method
  247.    wt: 3:   9 Head to Tail Coordinate View
  248.    wt: 3:   8 Parallel Vectors
  249.    wt: 3:   6 Vectors with Coordinates
  250.    wt: 3:   3 Navigation with Arrows or Vectors
  251.    wt: 3:   2 Signed Coordinates
  252.    wt: 3:   1 Unsigned Coordinates
  253.    wt: 3:   Parallel Lines and Parallel Transversals
  254.    wt: 3:   Triangle Angles Sum To 180 Degrees
  255.    wt: 3:   Parallel Lines and Alternating Corresponding Angles
  256.    wt: 3:   Parallel Lines and Interior Angles
  257.    wt: 3:   14 cosine even and sine and tangent are odd
  258.    wt: 3:   21 Logarithms Powers and Exponentials
  259.    wt: 3:   20 N th Roots of Complex Numbers
  260.    wt: 3:   16 References and Originality Question
  261.    wt: 3:   13 Trig Formulas for dot and cross Products
  262.    wt: 3:   12 cis formulas for sine cosines and tangent
  263.    wt: 3:   11 sine and cosine double triple angle formulas
  264.    wt: 3:   9 The complex number valued trig function cis
  265.    wt: 3:   7 Second Way to Calculate Products
  266.    wt: 3:   6 Field Properties of Complex Number
  267.    wt: 3:   3 Addition Properties
  268.    wt: 3:   2 Complex Numbers made easier we hope
  269.    wt: 3:   Appetizer A Complex Number Applet
  270.    wt: 3:   13 Navigation Location from Angles to 2 Landmarks
  271.    wt: 3:   10 Midpoint of [a b] and [b a]
  272.    wt: 3:   1 Numerical view of lines and their equations
  273.    wt: 3:   What is and is not here
  274.    wt: 3:   7 Complex Numbers Appetizer
  275.    wt: 3:   6 Polar Multiplication and Rotation
  276.    wt: 3:   PS H Distributive Law For Complex Numbers
  277.    wt: 3:   PS G Rotation Distributes over Addition
  278.    wt: 3:   PS F Scalar Multiplication Distributes over Addition
  279.    wt: 3:   PS D Addition with Cartesian Coordinates
  280.    wt: 3:   17 Right Bisectors of Triangle Sides
  281.    wt: 3:   16 Angles Subtended By Chords and Diameters
  282.    wt: 3:   10 Dropping a perpendicular to line
  283.    wt: 3:   9 Construction of a right bisector
  284.    wt: 3:   6 Ruler and compass Angle Bisection
  285.    wt: 3:   1 Initial Concepts and Terms
  286.    wt: 3:   5 Drawing to Scale Avoids Angle Distortions
  287.    wt: 3:   3 Lengths and Areas on Maps and Plans
  288.    wt: 3:   A Signed Number Arithmetic Review
  289.    wt: 3:   24 Signed Numbers Arithmmetic Properties
  290.    wt: 3:   22 Multiplication of Signed Numbers
  291.    wt: 3:   21 Addition of Multiples of a Single Vector
  292.    wt: 3:   19 Signed Multiples of Vectors
  293.    wt: 3:   18 Geometrically Why Vector Addition Commutes
  294.    wt: 3:   15 Head to Tails in place Addition Associative
  295.    wt: 3:   13 Arrows and Vectors in a Plane
  296.    wt: 3:   12 Real Numbers Line Signed Coordinates
  297.    wt: 3:   2 Addition and Multiplication Axioms
  298.    wt: 3:   2 More and Less Than for Counts and Measures
  299.    wt: 3:   12 Real Number Additive Inverses or Negatives
  300.    wt: 3:   11 Real Number Addition
  301.    wt: 3:   10 Real Number Lengths and Signs
  302.    wt: 3:   6 Unsigned Real Numbers
  303.    wt: 3:   1 Whole and Natural Numbers
  304.    wt: 3:   4 A Brief Story of numbers and algebra
  305.    wt: 3:   8 Addition of Time Intervals via subtotaling
  306.    wt: 3:   1 Intro of Kids To Time Date Skills
  307.    wt: 3:   Chapter 20 Vectors and Complex Numbers
  308.    wt: 3:   Appendix D. What to do in School and Why
  309.    wt: 3:   Appendix C. How to Read
  310.    wt: 3:   Appendix B. How To Learn
  311.    wt: 3:   Chapter 5 Islands and Divisions of Knowledge
  312.    wt: 3:   Chapter 1 Introduction to Chapters 2 to 6
  313.    wt: 3:   V Reasons and Motivations for Logic and Mathematics
  314.    wt: 3:   S Adding words to algebra
  315.    wt: 3:   P Exact Arithmetic With Whole Numbers and Fractions
  316.    wt: 3:   J. More on written work and showing skill
  317.    wt: 3:   I. Logic and language skills
  318.    wt: 3:   G. Written work formats for developing and showing skill
  319.    wt: 3:   A. Skill has to be seen to believed
  320.    wt: 3:   7 Games and Activities for Instruction
  321.    wt: 3:   4 Money Matters Saving Earning Buying Selling and Budgets
  322.    wt: 3:   3 Telling Tracking Time Temporal and More Place Sense
  323.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  324.    wt: 2:   Ramblings Extrinsic numbers theory
  325.    wt: 2:   2 arithmetic with signed numbers
  326.    wt: 2:   1 arithmetic with unsigned numbers
  327.    wt: 2:   04 25 when to stop or suspend mathemat
  328.    wt: 2:   Home Tutoring and Home Schooling
  329.    wt: 2:   2 Reading and Writing Skills
  330.    wt: 2:   Ages 12 to 14 Geometry
  331.    wt: 2:   Ages 12 to 14 Arithmetic
  332.    wt: 2:   Ages 10 to 12 Geometry
  333.    wt: 2:   Ages 10 to 12 Arithmetic
  334.    wt: 2:   Ages 9 to 10
  335.    wt: 2:   Ages 8 to 9
  336.    wt: 2:   Ages 7 to 8
  337.    wt: 2:   Ages 6 to 7
  338.    wt: 2:   Ages 4 plus to 5 plus
  339.    wt: 2:   Ages 3 plus to 4 plus
  340.    wt: 2:   25 Absolute Value greatest integer and saw tooth functions
  341.    wt: 2:   24 Monotoncity Injectivity and Inverse Functions
  342.    wt: 2:   8 Notes for instructors or tutors
  343.    wt: 2:   16 cotangent function Definition Graph and Inverse
  344.    wt: 2:   15 cosecant function Definition Graph and Inverse
  345.    wt: 2:   14 secant function Definition Graph and Inverse
  346.    wt: 2:   13 cosecant function Definition Graph and Inverse
  347.    wt: 2:   14 Why Scalar Multiplication Distributes Physical Argument
  348.    wt: 2:   11 Component Method
  349.    wt: 2:   4 Resultant of a Sum of Movements
  350.    wt: 2:   4 graphing y=Asin(x c)
  351.    wt: 2:   3 graphing y=f(x c) plus K
  352.    wt: 2:   2 Graphing y=Af(x) Vertical Scaling
  353.    wt: 2:   1 graphing y=f(x a)
  354.    wt: 2:   Proportionality of Line Segments From Parallel Transversals
  355.    wt: 2:   SAS Method For Isometric Or Proportional Triangle Construction
  356.    wt: 2:   Analytic View of Triangle Construction or Line Instersection More
  357.    wt: 2:   Straight Lines ASA Intersection Study More
  358.    wt: 2:   Straight Lines ASA Intersection Study
  359.    wt: 2:   Straight Lines Instersection Solving Equations
  360.    wt: 2:   Straight Lines Intersection of
  361.    wt: 2:   D Straight Lines Slope from Coordinates Examples
  362.    wt: 2:   C Straight Lines Slope from Coordinates
  363.    wt: 2:   B Straight Line Slope Scaling Properties More
  364.    wt: 2:   A Straight Line Slope Scaling Properties
  365.    wt: 2:   14 Straight Lines Equations General Case
  366.    wt: 2:   13 Straight Lines Finding Equations from 2 points
  367.    wt: 2:   12 Straight Lines Graphing mx plus b
  368.    wt: 2:   11 Straight Lines Graphing y=mx
  369.    wt: 2:   10 Straight Lines through Origin Equations More
  370.    wt: 2:   9 Straight Lines through Origin Equations
  371.    wt: 2:   8 Straight Lines Equation for vertical
  372.    wt: 2:   7 Tangent Function is odd on this domain
  373.    wt: 2:   6 Tangent Function Inclination Angle Take 2
  374.    wt: 2:   5 Tangent Function Graph
  375.    wt: 2:   4 Tangent Function Properties
  376.    wt: 2:   3 Straight Lines Slope as Tangent of Inclination Angle
  377.    wt: 2:   2 Straight Lines Slopes As Rise Over Run
  378.    wt: 2:   1 Straight Lines Slope Concept
  379.    wt: 2:   35 sines and cosines of 2A 3A 4A 5A
  380.    wt: 2:   34 sines and cosines of 2A 3A 4A 5A
  381.    wt: 2:   33 sines and cosines of 2A 3A 4A 5A
  382.    wt: 2:   29 secant cosecant and cotangent for acute angles
  383.    wt: 2:   27 Logarithmic use of products of sines and cosines
  384.    wt: 2:   26 Formulas for products of sines and cosines
  385.    wt: 2:   23 sine and cosine of 180 plus 22.5 degrees
  386.    wt: 2:   21 sine and cosine Half Angle Formulas
  387.    wt: 2:   20 sine and cosine Double Angle Formulas
  388.    wt: 2:   19 Pythagorean Identity For sine and cosine functions
  389.    wt: 2:   17E Trig Formulas for dot and cross Products
  390.    wt: 2:   17D cis formulas for sine cosines and tangent
  391.    wt: 2:   17C sine and cosine double triple angle formulas
  392.    wt: 2:   17A The complex number valued trig function cis
  393.    wt: 2:   10 Graphs of sines and cosines many periods
  394.    wt: 2:   9 Graphs of sine and cosine over one period
  395.    wt: 2:   7 period of sine and cosine
  396.    wt: 2:   6 sines and cosines for reference angle 30 degrees
  397.    wt: 2:   5 sines and cosines for reference angle 60 degrees
  398.    wt: 2:   4 sines and cosines for reference angle 45 degrees
  399.    wt: 2:   3 sines and cosines for reference angle 90 degrees
  400.    wt: 2:   Right Triangle and Unit Circle Trigonometry
  401.    wt: 2:   19 N th Roots of Unity
  402.    wt: 2:   18 Sixth Roots of Unity
  403.    wt: 2:   17 Cube Roots of unity
  404.    wt: 2:   15 Pythagorean Theorem Converse
  405.    wt: 2:   14 Law of cosines
  406.    wt: 2:   10 sine cosine Angle Sum Formulas via cis
  407.    wt: 2:   8 Unit Circle Development of Trigonometry
  408.    wt: 2:   5 An Easy Proof of the Distributive Law
  409.    wt: 2:   4 Multiplication Properties
  410.    wt: 2:   1 Rectangular Polar Coordinates Review
  411.    wt: 2:   5 Trigonometric Ratios For Tangent and Special Triangles
  412.    wt: 2:   3 Trigonometric Ratios sine and cosine
  413.    wt: 2:   Right Triangle and Unit Circle Trigonometry
  414.    wt: 2:   8 Similarity of Triangles and Polygons
  415.    wt: 2:   5 Similarity of Circles Squares and Rectangles
  416.    wt: 2:   Four Simple Exercises
  417.    wt: 2:   12 Links Lessons elsewhere
  418.    wt: 2:   11 A Partial Summary
  419.    wt: 2:   9 Midpoint Coordinates Half Endpoint Sum
  420.    wt: 2:   8 Mid Point Formula
  421.    wt: 2:   6 Intersection of lines by solving linear systems
  422.    wt: 2:   5 Algebraic View of Slopes
  423.    wt: 2:   4 Equations for lines three forms
  424.    wt: 2:   3 Slope product for perpendicular lines
  425.    wt: 2:   2 point slope equation for a line
  426.    wt: 2:   13 Pythagorean spatial distance formulas
  427.    wt: 2:   12 Spatial Coordinates
  428.    wt: 2:   11 Triangle Inequality
  429.    wt: 2:   10 Pythagorean plane distance formula
  430.    wt: 2:   9 Pythagorean Theorem Chinese Square Proof
  431.    wt: 2:   8 Distance Between Points on a Line
  432.    wt: 2:   3 Rectangular Coordinates Review
  433.    wt: 2:   2 Cartesian Coordinates with signs
  434.    wt: 2:   1 Cartesian Coordinates sans signs
  435.    wt: 2:   Euclidean Geometry Elsewhere LINKS
  436.    wt: 2:   PS E Multiplication with Polar Coordinates
  437.    wt: 2:   PS C Similarity Use Recognize it in Trigonometry
  438.    wt: 2:   PS B Parallelogram Construction Methods
  439.    wt: 2:   PS A Kite Construction Methods
  440.    wt: 2:   21 Parallelograms
  441.    wt: 2:   19 Right Triangle Similarity
  442.    wt: 2:   18 Triangle Similarity Take 1
  443.    wt: 2:   15 Triangle Angle Sum is 180 degrees
  444.    wt: 2:   14 Parallel Lines Postulate
  445.    wt: 2:   13 Angle Side Angle Failure
  446.    wt: 2:   12 Side Angle Side Failure
  447.    wt: 2:   11 Triangle Construction Fails
  448.    wt: 2:   8 Isoceles Triangles
  449.    wt: 2:   7 Angle Side Angle
  450.    wt: 2:   5 Side Angle Side
  451.    wt: 2:   4 Side Side Side
  452.    wt: 2:   3 Isometry of Triangles Congruence
  453.    wt: 2:   2 Correspondence between Triangles
  454.    wt: 2:   Short Course on Euclidean Geometry
  455.    wt: 2:   8 More Use of Maps Not Drawn to Scale
  456.    wt: 2:   6 Figuring with Maps Not to Scale
  457.    wt: 2:   4 Angles on Maps Plans drawn to scale
  458.    wt: 2:   musings do not puiblish real numbers
  459.    wt: 2:   A Modular and Remainder Arithmetic
  460.    wt: 2:   25 Mid way Convergence to Axiomatic Approach
  461.    wt: 2:   17 Arrows Rotate to Reverse with Length Unchanged
  462.    wt: 2:   16 Collinear Horizontal Arrows Vectors
  463.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  464.    wt: 2:   8 Division and Mulplication of Compound Fractions
  465.    wt: 2:   4 Location of Point in Decimal Addition
  466.    wt: 2:   B Decimal Comparison and Subtraction
  467.    wt: 2:   A Decimal Addition Columm Methods
  468.    wt: 2:   5 Distributive Law for Whole Numbers
  469.    wt: 2:   3 Multiplicative Counting Skills Principles
  470.    wt: 2:   1 The Counting Origins of Numbers
  471.    wt: 2:   4 Rates Ratios and Proporitionality
  472.    wt: 2:   6 Equations and Systems Equivalent or Implied
  473.    wt: 2:   4 Subtraction and Division Axioms
  474.    wt: 2:   4 Comparison of Negative Numbers
  475.    wt: 2:   3 More and Less Than with Unlike Signs
  476.    wt: 2:   1 Real Numbers Comparison
  477.    wt: 2:   16 Real Numbers Comparison
  478.    wt: 2:   15 Real Number Division
  479.    wt: 2:   14 Real Number Multiplication
  480.    wt: 2:   13 Real Number Subtraction
  481.    wt: 2:   8 Coordinates for Maps and Planes
  482.    wt: 2:   7 Real Numbers as Line Cordinates
  483.    wt: 2:   5 Rational Numbers More
  484.    wt: 2:   4 Rational Numbers
  485.    wt: 2:   3 Geometric Formulas and Function Notation
  486.    wt: 2:   1 Formulas Dependence and Function Notation
  487.    wt: 2:   3 GE III Equation Addition and Multiplication
  488.    wt: 2:   1 Written work formats for developing and showing skill
  489.    wt: 2:   5 Talking about Numbers and Quantities
  490.    wt: 2:   3 Adding Words To Arithmetic
  491.    wt: 2:   016 Numbering Occidental Calendar Days
  492.    wt: 2:   015 School and work day counting tables
  493.    wt: 2:   011 Division of Time Intervals By Numbers
  494.    wt: 2:   010 Repeated Addition of Time Intervals
  495.    wt: 2:   9 Comparison and Subtraction of Time Intervals
  496.    wt: 2:   7 Addition of Time Intervals
  497.    wt: 2:   6 How long is a million seconds
  498.    wt: 2:   4 Mixing and Changing Units of Time
  499.    wt: 2:   3 Units and Lengths of Time
  500.    wt: 2:   2 Time and Date Matters in School
  501.    wt: 2:   Example 1. Area Between x and x squared
  502.    wt: 2:   38 Formulas and derivatives for powers and roots
  503.    wt: 2:   13 Limits with Parameters and Derivatives Take II
  504.    wt: 2:   12 Limits with Parameters and Derivatives Take I
  505.    wt: 2:   9 Limits Continuity and Composition
  506.    wt: 2:   5 Jumps and absence of unlimited error control
  507.    wt: 2:   D1 Sets and Sequences GLBs and LGBs
  508.    wt: 2:   Chapter 14 Limits and Continuity with and sans Decimals
  509.    wt: 2:   Chapter 31 Direct and Indirect Reason
  510.    wt: 2:   Chapter 29 Contrapositive and Vacuously True Implications
  511.    wt: 2:   Chapter 27 Shorthand Symbols as Pronouns
  512.    wt: 2:   Chapter 26 What is in chapters 27 to 31
  513.    wt: 2:   Chapter 24. Personal Investment and Pension EGS
  514.    wt: 2:   Chapter 22. Geometric Sums and Sequences
  515.    wt: 2:   Chapter 20. Degrees and Radians
  516.    wt: 2:   Chapter 19. Functions and Sets
  517.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  518.    wt: 2:   Chapter 12. Shorthand Usage Guide
  519.    wt: 2:   Chapter 11. Why Shorthand
  520.    wt: 2:   Chapter 10 Describing and Changing Calculations
  521.    wt: 2:   Chapter 9 Talking about Numbers or Quantities
  522.    wt: 2:   Chapter 8 Three Skills For Algebra
  523.    wt: 2:   Chapter 2 Implication Rules Forwards and Backwards
  524.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  525.    wt: 2:   Postscript B More on Story Telling and Reason
  526.    wt: 2:   Chapter 16 Origins and Limitations of Rules and Patterns
  527.    wt: 2:   Chapter 12 Islands and Divisions of Knowledge
  528.    wt: 2:   1 Links to Online Resources Elsewhere Take 1
  529.    wt: 2:   R Why Learn Mathematics Skills
  530.    wt: 2:   O On Learning Mathematics and Science
  531.    wt: 2:   M Words to extend arithmetic
  532.    wt: 2:   L Skills with take home value
  533.    wt: 2:   N Improving Marks on Tests and Finals
  534.    wt: 2:   H more Routine to non routine problem solving
  535.    wt: 2:   H Jigsaw puzzles and problem solving
  536.    wt: 2:   F. The student teacher tutor feedback loop
  537.    wt: 2:   Chapter 8 Skipped Topics and Why
  538.    wt: 2:   6 Measuring via counting or arithmetic the role of fractions
  539.    wt: 2:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  540.    wt: 2:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  541.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  542.    wt: 2:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  543.    wt: 2:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  544.    wt: 1:   Appendix 1 primary and preschool mathematic
  545.    wt: 1:   G LAMP Introduction Problem Solving Skills
  546.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  547.    wt: 1:   Skills Chapter 5 Calculus
  548.    wt: 1:   Skills Chapter 4 Logic
  549.    wt: 1:   Skills Chapter 3 Algebra
  550.    wt: 1:   Skills Chapter 2 Geometry
  551.    wt: 1:   Skills Chapter 1 Arithmetic
  552.    wt: 1:   Skills Chapter 0 Introduction
  553.    wt: 1:   9 combinatorics probability sets
  554.    wt: 1:   7 logic review and decimals an odd combination
  555.    wt: 1:   5 logarithms and exponentials etc
  556.    wt: 1:   which way to go
  557.    wt: 1:   three goals to set for students
  558.    wt: 1:   key notes and themes
  559.    wt: 1:   grouping students according to ability
  560.    wt: 1:   what should be learnt and When
  561.    wt: 1:   how letters appear
  562.    wt: 1:   What to Tell Students
  563.    wt: 1:   teaching tutoring algebraic reason
  564.    wt: 1:   standards for course material
  565.    wt: 1:   Operational Viewpoint to Value
  566.    wt: 1:   Theory of Knowledge
  567.    wt: 1:   Education in mathematics science and technology
  568.    wt: 1:   Four ways to improve education reform
  569.    wt: 1:   Motivation and Context Problem
  570.    wt: 1:   fairness and inductive principles for instruction
  571.    wt: 1:   words for mathematics instructor
  572.    wt: 1:   3 Like resistors in parallel
  573.    wt: 1:   2 Unlike resistors in parallel01
  574.    wt: 1:   1 Like resistors in series
  575.    wt: 1:   F Unlike Resistors in Series
  576.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  577.    wt: 1:   24 Standards For Skill Develoment Take II
  578.    wt: 1:   24 Standards For Skill Develoment
  579.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  580.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  581.    wt: 1:   17 Math Booklets for children and young teenagers
  582.    wt: 1:   14 Multiplication and Times Tables
  583.    wt: 1:   12 Goals and Objectives For Mathematics
  584.    wt: 1:   11 Help and Defend Your Child or Teens Education
  585.    wt: 1:   5 Patience Please for Yourself and Your Charges
  586.    wt: 1:   4 Learning Takes Time and Effort
  587.    wt: 1:   1 Speaking Skills
  588.    wt: 1:   sign monoticity analysis example 4
  589.    wt: 1:   sign monoticity analysis example 3
  590.    wt: 1:   sign monoticity analysis example 2
  591.    wt: 1:   sign monoticity analysis example 1
  592.    wt: 1:   26 Function definitions done and coming
  593.    wt: 1:   19 Horizontal line rule and method
  594.    wt: 1:   18 Vertical Line Rule and Method
  595.    wt: 1:   17 Function maxima minima and their location
  596.    wt: 1:   11 Function Domain Range Source and Targets
  597.    wt: 1:   9 Set theory term relation possible origins
  598.    wt: 1:   8 Set view of relations and functions
  599.    wt: 1:   6 Set Existence Formation and Notation
  600.    wt: 1:   4 Function notation in and beyond mathematics
  601.    wt: 1:   9 quadratics physical and further context
  602.    wt: 1:   3 quadratics factoring by inspection
  603.    wt: 1:   11 Growth and Decay in Biology
  604.    wt: 1:   10 Exponential Growth and Decay Models
  605.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  606.    wt: 1:   5 Natural Logarithm Calculator Exercises
  607.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  608.    wt: 1:   1 Calculator Starter Exercises
  609.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  610.    wt: 1:   3 Polynomials Multiplication Addition
  611.    wt: 1:   12 motivation for term arctan
  612.    wt: 1:   11 arctan left inverse of tangent Graph
  613.    wt: 1:   10 arctan left inverse of tangent Definition
  614.    wt: 1:   9 motivation for name arcsin
  615.    wt: 1:   8 arcsin left inverse of sine Graph
  616.    wt: 1:   7 arcsin left inverse of sine Definition
  617.    wt: 1:   6 Graph of arccos function
  618.    wt: 1:   5 Swapping Coordinates is a reflection
  619.    wt: 1:   4 possible motivation for term arccos
  620.    wt: 1:   3 Left Inverse of cosine arccos definition
  621.    wt: 1:   2 cosine function more properties
  622.    wt: 1:   1 cosine function properties
  623.    wt: 1:   17 tangent function angle sum formulas
  624.    wt: 1:   32 seven rows of pascals triangle
  625.    wt: 1:   31 basic secant cosecant cotangent trig identities
  626.    wt: 1:   30 unit circle calculation of six trigonometric functions
  627.    wt: 1:   28 Expressing products of sines cosines as sums
  628.    wt: 1:   25 tangent double angle formula Slope connection
  629.    wt: 1:   24 tangent Angle Difference Formula
  630.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  631.    wt: 1:   18 sum of sinusoidal waves as a single wave
  632.    wt: 1:   17G Pythagorean Theorem Converse
  633.    wt: 1:   17F Law of cosines
  634.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  635.    wt: 1:   16 Right Triangle Complementary Angle Relations
  636.    wt: 1:   15 sine cosine Complementary Angle Relations
  637.    wt: 1:   13 Graph of tangent function many periods
  638.    wt: 1:   12 Graph of tangent function for one period
  639.    wt: 1:   11 tangent function undefined when terminal side vertical
  640.    wt: 1:   8 period of tangent function
  641.    wt: 1:   2 Quadrant I reference Angles
  642.    wt: 1:   1 Unit Points Reflections Rotations
  643.    wt: 1:   Unit Circle Development of Trigonometry
  644.    wt: 1:   8 Triangles Cascade Problem Solving
  645.    wt: 1:   7 Trignometric Ratios Unit Circle
  646.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  647.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  648.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  649.    wt: 1:   1 Angle Measurement with Degrees
  650.    wt: 1:   Why Trigonometry the whyslopes view
  651.    wt: 1:   12 Triangles Similarity More Problems
  652.    wt: 1:   11 Triangle Similarity Missing Side Problem
  653.    wt: 1:   10 Similarity of Triangles Equivalent of Two Criteria
  654.    wt: 1:   9 Similarity of Triangles Usual Criteria
  655.    wt: 1:   7 Translations Rotations Reflections Dilatations
  656.    wt: 1:   6 Geometric Diagrams in Class
  657.    wt: 1:   4 Similarity Definition with Coordinate
  658.    wt: 1:   3 Similarity by Design with coordinates
  659.    wt: 1:   2 Similarity By Design
  660.    wt: 1:   1 Early Concept of Like or Similar Shapes
  661.    wt: 1:   A Measurement with Ruler Proper Use
  662.    wt: 1:   2 Measuring Area Directly
  663.    wt: 1:   1 Length Measurement
  664.    wt: 1:   About Folder Contents
  665.    wt: 1:   26 More Less Greater Than Comparison
  666.    wt: 1:   23 Distributive Law Two Derivations
  667.    wt: 1:   9 Division with Digits after Decimal Point
  668.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  669.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  670.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  671.    wt: 1:   3 Location of Point in Decimal Multiplication
  672.    wt: 1:   2 Counting Digits in Decimal Multiplication
  673.    wt: 1:   1 Fractions with Finite Decimal Expansions
  674.    wt: 1:   E Long Division Methods more
  675.    wt: 1:   D Long Division Methods
  676.    wt: 1:   C Three Decimal Subtraction Methods
  677.    wt: 1:   8 Column Multiplication Methods in General
  678.    wt: 1:   7 Decimals Multiplication Methods Examples
  679.    wt: 1:   6 Column Methods for Decimal Multiplication
  680.    wt: 1:   4 Commutative Law Groups Counting Form
  681.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  682.    wt: 1:   5 Proportionality in Equivalent Fractions
  683.    wt: 1:   3 Proportionality Examples
  684.    wt: 1:   2 Algebraic View
  685.    wt: 1:   1 What is Proportionality
  686.    wt: 1:   9 Circle Area and Perimeter Formula Backwards Forwards
  687.    wt: 1:   6 Compound Interest Forward and Backwards
  688.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  689.    wt: 1:   5 Equality in Algebra
  690.    wt: 1:   3 Product Axioms Two Forms
  691.    wt: 1:   1 Equivalent Computation Rules
  692.    wt: 1:   5 Greater More Less Than Signs in General
  693.    wt: 1:   9 Coordinates for Regions in Space
  694.    wt: 1:   3 Fractions
  695.    wt: 1:   2 Integers
  696.    wt: 1:   5 Independent versus Dependent Variables
  697.    wt: 1:   4 Changing Letters
  698.    wt: 1:   2 Computation Rules Evaluation
  699.    wt: 1:   Skill Development Notes
  700.    wt: 1:   10 One Example
  701.    wt: 1:   9 Three Examples
  702.    wt: 1:   8 One Example
  703.    wt: 1:   7 Two Examples
  704.    wt: 1:   6 Three Examples
  705.    wt: 1:   5 Three Examples
  706.    wt: 1:   4 Two Examples
  707.    wt: 1:   3 Two Examples
  708.    wt: 1:   2 Three Examples
  709.    wt: 1:   Formula Usage Show Work Format
  710.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  711.    wt: 1:   9 Sets in Probability and Statistics
  712.    wt: 1:   8 Sets of Numbers
  713.    wt: 1:   1 Three Skills For Algebra
  714.    wt: 1:   014 Counting Days with Calendars
  715.    wt: 1:   013 Travel Time Tables
  716.    wt: 1:   012 Division of Time Intervals by Time Intervals
  717.    wt: 1:   5 Conversion Arithmetic
  718.    wt: 1:   Example 2 volume of a cone
  719.    wt: 1:   Example 1 volume of a pyramid
  720.    wt: 1:   Volume of Solid by Cross Sections Lesson
  721.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  722.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  723.    wt: 1:   Example 4 with x function of y
  724.    wt: 1:   Example 3
  725.    wt: 1:   Example 2
  726.    wt: 1:   Example 1
  727.    wt: 1:   Area Between Curves Lesson Take 2
  728.    wt: 1:   Area Between Curves Lesson Take 1
  729.    wt: 1:   Summary
  730.    wt: 1:   17 Derivatives of quotients of sine and cosine
  731.    wt: 1:   16 Derivatives of reciprocals of sine and cosine
  732.    wt: 1:   15 sine and cosine derivatives 3rd step
  733.    wt: 1:   14 sine and cosine derivatives 2nd step
  734.    wt: 1:   13 sine and cosine derivatives 1st step
  735.    wt: 1:   11 Limits at infinity Three Examples
  736.    wt: 1:   10 Three one sided limits with infinite values
  737.    wt: 1:   8 Four Animated Examples
  738.    wt: 1:   7 Evaluation by immediate or delayed substitution
  739.    wt: 1:   6 Continuity at a point
  740.    wt: 1:   4 Numerical properties
  741.    wt: 1:   3 Decimal insights for limits continuity convergence
  742.    wt: 1:   2 Algebraic codification
  743.    wt: 1:   1 Numerical introduction
  744.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  745.    wt: 1:   D2 Limits of Monotone Sequences
  746.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  747.    wt: 1:   PostScript For and Against Decimal Perspectives
  748.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  749.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  750.    wt: 1:   Chapter 23 Links To Trigonometry
  751.    wt: 1:   Chapter 22 Complex Numbers
  752.    wt: 1:   Chapter 21 Arrow Addition
  753.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  754.    wt: 1:   Chapter 12. Units and Slopes
  755.    wt: 1:   Chapter 10 Slopes and Units
  756.    wt: 1:   Chapter 7 Slopes and Velocity
  757.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  758.    wt: 1:   Chapter 2. Slopes and Ski Trails
  759.    wt: 1:   Postscript More on Better Performance
  760.    wt: 1:   Postscript For Better Performance
  761.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  762.    wt: 1:   Chapter 30 Truth Tables
  763.    wt: 1:   Chapter 28 Occurrence Tables
  764.    wt: 1:   Chapter 25. Mathematical Induction Examples
  765.    wt: 1:   Chapter 23. Notation For Sums
  766.    wt: 1:   Chapter 21. Third Reading Guide
  767.    wt: 1:   Chapter 18. Rules for Algebra
  768.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  769.    wt: 1:   Chapter 16. Painless Theorem Proving
  770.    wt: 1:   Chapter 15. Solving Linear Equations
  771.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  772.    wt: 1:   Chapter 13. Second Reading Guide
  773.    wt: 1:   Postscript What is a Variable
  774.    wt: 1:   Solutions For Arithmetic Exercises
  775.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  776.    wt: 1:   Chapter 6 Change of Language
  777.    wt: 1:   Chapter 4 Longer Chains of Reason
  778.    wt: 1:   Chapter 3 Chains of Reason
  779.    wt: 1:   Foreword
  780.    wt: 1:   Annotated Links to Material Elsehwere
  781.    wt: 1:   Chapter 2 For and Against Mathematics
  782.    wt: 1:   Postscript C Consistency as a Tool for Reason
  783.    wt: 1:   Postscript A Story Telling
  784.    wt: 1:   Chapter 24 Direct and Indirect Reason
  785.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  786.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  787.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  788.    wt: 1:   Chapter 18 Sense and Knowledge
  789.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  790.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  791.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  792.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  793.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  794.    wt: 1:   N Mathematics Prepare for College Studies
  795.    wt: 1:   D. Check work a must with a caution
  796.    wt: 1:   C. Domino effect of being careful
  797.    wt: 1:   B. Domino effect of errors
  798.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  799.    wt: 1:   Chapter 6 More Algebra and Geometry
  800.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  801.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  802.    wt: 1:   Helping the Blind in Logic and Mathematics
  803.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  804.    wt: 1:   More Algebra and Slope based Calculus Preview
  805.    wt: 1:   Which Way To Go
  806.    wt: 1:   The Math Forum and Site Content
  807.    wt: 11:   1 More and Less Than for Counts and Measures
  808.    wt: 11:   2 signed and unsigned numbers as coordinates
  809.    wt: 10:   3 Comparison of Negative Numbers
  810.    wt: 10:   2 More and Less Than with Unlike Signs
  811.    wt: 10:   6 adding signed numbers
  812.    wt: 10:   8 What skills and work habits to require
  813.    wt: 10:   6. Counting and adding units and mixed units
  814.    wt: 10:   5. How to add decimals C. Examples
  815.    wt: 10:   4. How to add with decimals B with conversions
  816.    wt: 10:   3. How to add with decimals A sans conversions

Teachers, Tutors, Parents: Site material offers better or best practices for mathematics skill building - simpler than expected and comprehensive. Your duty is to study them alone or with help. Start now.

Secondary Mathematics for Ages 11+, A Practical Approach for home-tutoring or -schooling, or for schools & colleges with local curriculum control. Study how to include site content - its skill development how-TOs and innovations into present or future lesson plans - some reading required.

Road Safety Messages and Questions: When and why should you face traffic when walking along a road or cycle path? Is it a good idea to hang limbs outside of cars etc? What gives more protection in a crash: a car, motorbike or bicycle? See too, the BBC-Belgium story Texting and Driving - texting & the impossible test - the article links to a gruesome utube video on the subject

The Logic of Injustice: How Texas sent an innocent man to his death - The wrong Carlos. Some judgments are irreversible. Procescution: Where and when prosectors play to win rather than for justice, guilt beyond a reasonable doubt goes unrespected due to prosecutors who putting winning first, those innocence before the law may be convicted. Some procescutors offices in continuing to accuse after a pardon due to reasonable doubt or innocent being shown, may sucessfully oppose compensaton for false convictions by asserting a pardon individual is still under suspicion. Then the pardoned individual or the latter's estate is not compensation for years or decade of improper or false imprisonment, or for execution. Site chapters on Logic
and some in Pattern Based Reason may slowly lead to greater precision in reading, applying and writing laws.

May 2012, Composition Starting: Pre-School and Primary Mathematics - Quantitative Skills, An Intellectual View, Feedback Welcome:

The 8 Most Popular Site Inlinks

20 Times Table - the most popular site page - popular pages - unexpected.
Fractions & Ratios - with lesson on raising terms to introduce & justify times, division & comparison as well addition & subtraction
Parent Center - See below
Volume 1, Elements of Reason - Intro to all site books.
What is a Variable - best for ages 13+
Written work formats for Arithmetic and Algebra - a skill method and standard!
Complex Numbers Visually - best for ages 13+
Natural Logs, Exponentials, Powers, Roots

Division of Labour: This site offers advice and directions with pointers to resources elsewhere, if known, when they help or lessen the need to write more.

Parent Center: Help your child or teen learn:

Parent-friendly Work Booklets for ages 3+ to 13 Use these or others to check or build skills. Other booklets are available but these booklets allow parents unsure of themselves in mathematics to help their children. The selection acquired in Canada is published in the USA. So it has a US orientation. In retrospect, the selection shows parents what to check with the booklets or by other ways, the choice is theirs. But in retrospect, the selection does not cover integral and fractions liquid weights and measures - ask the publishers to correct that! For ages 9 to 12 say, parents may compensate by showing boys and girls how to use weights or mass, and further measures in food preparation. Beyond that children may be shown how to measure and calculate angles, lengths and areas [proportional amounts too] directly or by using maps and plans drawns to scale. Learning how to gather and measure all the ingredients, pots and pans for a dish or a meal, along with cleaning up sets the stage for like activities or experiments in science courses, and in developing organizational skills, gives boys and girls a head start. Good luck. At the other extreme, more comprehensive than light, if your motto is McCainian: drill, drill, drill then Toronto mathematician and actor John Mighton's jump math organization has jump math workbooks for at least grades 3 to 8 for at-home and in-school use - training sessions for teachers available. Jump math has been expanding to cover older students. Jump Math Samples: plus Fractions for Grades 3-4 & Grades 5-6 [Read] Free Resources grades 1 to 8 [unread - likely to be good]. and

Mathematics Skills For Ages 3 to 14 - technical!

Skills with take home value - A few ideas

Basic skills include time-date-calendar Matters; money matters; map, plan and scale diagram matters;counting, measuring and figuring; decision making with logic and likelyhood; being careful and being aware of the domino effect of mistakes; reading and writing with precision.

Is your child able to add, subtract and multiply amounts of money, work with fractions, work with clocks and calendars, work with maps and plans, and measure length, weight-mass and volume? Schools may promote your son or daughter without providing basic skills in reading, writing and arithmetic.

Arithmetic and Number Theory Skills

Algebra Starter Lessons

1 Working With Sets
2 Formula Forward Use - Evaluation
3 Solving Linear Equations - Skip first step with students able to solve 1 eqn in 1 unknown.
4 Computation Rules and Function Notation
5 Real Numbers
6 More Less Greater Than Inequalities and Comparison
7 Axioms Logic and Equivalent Equations
8 Unifying Theme For Algebra
9 Proportionality Backwards and Forwards
10 Examples of Algebraic Reasoning
A Origins of Counting and Figuring Methods
B Real Numbers Extrinsic Development


Site coverage of formuala evaluation format, of computation rules and axioms, and of the forward and backward use of formulas and proportionality relations lessens the amount of natural talent needed to understand and explain algebra.

Geometry - maps plans trigonometry vectors

1 Maps Plans Measurement
2 Euclidean Geometry - Constructions + extras
3 Cartesian and Polar Coordinates
4 Lines and Slopes Take 1
5 What is Similarity
6 Trigonometry first steps
7 Complex Numbers
8 Unit-Circle Trigonometry
9 Lines and Slopes Take 2 with tangent function
10 Intersecting Straight Lines and Transversals
11 Parallel Straight Lines and Transversals
12 Function Translating and Rescaling
13 Vectors
14 Degrees to Radians and Radians to Degrees
15 Arc or Inverse Trigonometric Function

Pre-Teen and young teen mastery of skills and practices which should be common with map-plans-diagrams drawn to scale, contour interpretation included, has actual or potential take-home value for daily- and adult-life in solving routine problems. Elevating some practices to principles, axioms or postualates, provides a base for analytic and Euclidean geometry, an analytic view of similarity, and an efficient mastery of trigonometry and complex numbers. Right triangle trigonometry provide an analytic alternative to solving geometric problems by drawing diagrams to scale.

More Algebra

Natural-Logarithms Exponentials Powers Roots
Five Polynomial Operations
Quadratics Geometrically
Functions
5 Factored Polynomial Sign Analysis Examples
Rewriting algebraic substitution as function substitutions

The first topic leads to a full high school level theory for the forward and backward mastery of growth and decay models and for definition, range and domains of radicals, roots and powers. The next two topics make quadratics and polynomials easier to learn and teach. Site coverage of functions turns vertical and horizontal line rules into computation methods for evaluating functions.

70 Calculus Starter Lessons

Calculus Lessons Elsewhere:

  1. How to Ace Calculus: Street Wise Guide - Mostly Text.

  2. Flash Video for Calculus Phobics

They cover basic topics in ways likely to complement your notes, your textbooks and site material. When Goldilocks trespassed in the house of the three bears, she found three bowls of porridge, two not to her liking, and one just right. Different bears have different tastes. As invited guest here and elsewhere, if one or more explanations is not to liking, try another. It may be better or just right.

Unsolicited Advice

Learning to do and high marks if it comes to easy is often deceptive - light rather than deep. For that reason, students with learning difficulties determined not to let it get in their way may go deeper and farther than those with none. High marks, if the come easy, may be deceptive - provide a too light and not a deep mastery. That could have been your problem in secondary school, one that leads to comprehension shock or difficulties in calculus and more generally in the first year of college. Bon Appetite.

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Logic-Reason for all
Careful Thinking
Chains of Reason
Mathematical Induction
Responsibility
Bodies-of-Knowledge

Arithmetic - Ages 10+
1. Deciml Place Value - fun
2. Decimals for Tutors
3. Prime Factors - quickly
4. Fractions + Ratios
5. Arith with units - science

Geometry
1 Maps + Plans Use
2 Euclidean Geometry
3 Rct +Polr Coordinates
4 Lines-Slopes [I]
5. What is Similarity 		Algebra Starters - the base
1. Better Work Format
2. Solve Linear Eqns
3. Computation Rules
4. Axioms, Item 3 Viewpnt
5. Formulas Backwards 		More Algebra
Logarithms-ax & m/nth roots
Five Polynomial Operations
Quadratics Geometrically
Functions || Vectors too
Arith. Skill Check+Answers 		Calculus Prep/Preview
What is a Variable
Why study slopes
Why factor polynomials
Complex Numbers
Limits + Continuity

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