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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  1.    wt: 7:   13 Lessons on Limits and Continuity/
  2.    wt: 6:   11 Squares and Square Roots/
  3.    wt: 6:   12 Webvideo Lessons on Area and Volume Calculation/
  4.    wt: 6:   5 Lessons on Integration/
  5.    wt: 6:   4 Lessons on Using Derivatives/
  6.    wt: 5:   10 LCM GCD and Euclid GCD Algorithm/
  7.    wt: 5:   38 Lessons on Calculating Derivatives/
  8.    wt: 4:   14 Degrees to Radians and Radians to Degrees/
  9.    wt: 4:   11 Parallel Straight Lines and Transversals/
  10.    wt: 4:   10 Examples of Algebraic Reasoning/
  11.    wt: 4:   Step 4 Gaussian Elimination/
  12.    wt: 4:   Step 1 Stick diagram and fractions/
  13.    wt: 4:   1 Working With Sets/
  14.    wt: 4:   12 Comparison of Unsigned and Signed Numbers/
  15.    wt: 4:   4 Remainder Arithmetic and Divisibility/
  16.    wt: 4:   D Decimal Long Division Methods/
  17.    wt: 4:   A Decimal Counting and Adding Methods/
  18.    wt: 4:   1 Decimal Place Value/
  19.    wt: 4:   70 Calculus Starter Lessons/
  20.    wt: 3:   4 Lines and Slopes Take 1/
  21.    wt: 3:   4 Computation Rules and Function Notation/
  22.    wt: 3:   8 Arithmetic with Signed Numbers/
  23.    wt: 3:   7 Arithmetic and Fractions with Units/
  24.    wt: 3:   C Decimal Multiplication Methods/
  25.    wt: 3:   B Decimal Comparing and Subtracting Methods/
  26.    wt: 3:   2 Arithmetic with Decimals/
  27.    wt: 2:   Volume 1A Regles et modeles/
  28.    wt: 2:   4 Functions/
  29.    wt: 2:   1 Five Polynomial Operations/
  30.    wt: 2:   15 Arc or Inverse Trigonometric Function/
  31.    wt: 2:   13 Vectors/
  32.    wt: 2:   12 Function Translating and Rescaling/
  33.    wt: 2:   10 Intersecting Straight Lines and Transversals/
  34.    wt: 2:   1 Maps Plans Measurement/
  35.    wt: 2:   B Real Numbers Extrinsic Development/
  36.    wt: 2:   A Origins of Counting and Figuring Methods/
  37.    wt: 2:   9 Proportionality Backwards and Forwards/
  38.    wt: 2:   8 Unifying Theme For Algebra/
  39.    wt: 2:   7 Axioms Logic and Equivalent Equations/
  40.    wt: 2:   6 More Less Greater Than Inequalities and Comparison/
  41.    wt: 2:   5 Real Numbers/
  42.    wt: 2:   Step 3 Easy systems in 2 or more unknowns/
  43.    wt: 2:   Step 2 Algebraic solutions for one unknown/
  44.    wt: 2:   3 Solving Linear Equations/
  45.    wt: 2:   2 Formula Forward Use Evaluation/
  46.    wt: 2:   Algebra Starter Lessons/
  47.    wt: 2:   9 Combinatorics Trees Tables and Products/
  48.    wt: 2:   6 Fractions and Ratios/
  49.    wt: 2:   5 Integers/
  50.    wt: 2:   3 Prime Factorization Skills/
  51.    wt: 2:   Arithmetic and Number Theory Skills/
  52.    wt: 2:   Advanced Calculus Volume 3 Appendices/
  53.    wt: 2:   Volume 3 Why Slopes A Calculus Intro Etc/
  54.    wt: 2:   Volume 2 Three Skills For Algebra/
  55.    wt: 2:   Volume 1B Mathematics Curriculum Notes/
  56.    wt: 2:   Volume 1A Pattern Based Reason/
  57.    wt: 2:   Volume 1 Elements of Reason/
  58.    wt: 1:   Mathematics Education Essays/
  59.    wt: 1:   5 Factored Polynomial Sign Analysis Examples/
  60.    wt: 1:   9 Lines and Slopes Take 2 with tangent function/
  61.    wt: 1:   Time Date Matters/
  62.    wt: 1:   Skills with take home value/
  63.    wt: 1:   Mathematics 506 Lessons/
  64.    wt: 1:   Secondary Mathematics A Practical Approach/
  65.    wt: 1:   PreSchool and Primary Mathematics or Quantitative Skills/

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522 matches:

  1.    wt: 8:   10 Euclid Algorithm with 129 125 and with 45 14
  2.    wt: 4:   Ages 12 to 14 Skills with take home value
  3.    wt: 4:   14 GCD of 650 110 via Primes LCM via Product Rule
  4.    wt: 4:   1 Two cubic sketching exercises with 1st derivative
  5.    wt: 4:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  6.    wt: 3:   Ages 12 to 14 Geometry
  7.    wt: 3:   Ages 12 to 14 Arithmetic
  8.    wt: 3:   14 Adding and Subtracting with Like Denominators
  9.    wt: 3:   14 video Factors of 24 Take II
  10.    wt: 3:   4. How to add with decimals B with conversions
  11.    wt: 3:   014 Counting Days with Calendars
  12.    wt: 3:   Chapter 14 Limits and Continuity with and sans Decimals
  13.    wt: 2:   11 pure mathematics
  14.    wt: 2:   1 arithmetic with unsigned numbers
  15.    wt: 2:   Applied Maths Program14092009 POMME variant
  16.    wt: 2:   Postscript 2007 01 10
  17.    wt: 2:   chapitre 04 10 Etapes pour une meilleur raison
  18.    wt: 2:   chapitre 04 04 Parlons de la logique
  19.    wt: 2:   chapitre 04 01 Premiere enigme
  20.    wt: 2:   Quebec cahiers d apprentissage en mathematiques pour 4 16
  21.    wt: 2:   1 Conductance Resistance Duality01
  22.    wt: 2:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  23.    wt: 2:   14 Multiplication and Times Tables
  24.    wt: 2:   11 Help and Defend Your Child or Teens Education
  25.    wt: 2:   Ages 10 to 12 Geometry
  26.    wt: 2:   Ages 10 to 12 Arithmetic
  27.    wt: 2:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  28.    wt: 2:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  29.    wt: 2:   14 Surjections Injections Bijections
  30.    wt: 2:   11 Function Domain Range Source and Targets
  31.    wt: 2:   11 Growth and Decay in Biology
  32.    wt: 2:   1 Calculator Starter Exercises
  33.    wt: 2:   14 secant function Definition Graph and Inverse
  34.    wt: 2:   11 arctan left inverse of tangent Graph
  35.    wt: 2:   14 Why Scalar Multiplication Distributes Physical Argument
  36.    wt: 2:   11 Component Method
  37.    wt: 2:   14 Straight Lines Equations General Case
  38.    wt: 2:   11 Straight Lines Graphing y=mx
  39.    wt: 2:   34 sines and cosines of 2A 3A 4A 5A
  40.    wt: 2:   14 cosine even and sine and tangent are odd
  41.    wt: 2:   11 tangent function undefined when terminal side vertical
  42.    wt: 2:   4 sines and cosines for reference angle 45 degrees
  43.    wt: 2:   14 Law of cosines
  44.    wt: 2:   11 sine and cosine double triple angle formulas
  45.    wt: 2:   1 Angle Measurement with Degrees
  46.    wt: 2:   11 Triangle Similarity Missing Side Problem
  47.    wt: 2:   4 Similarity Definition with Coordinate
  48.    wt: 2:   12 Links Lessons elsewhere
  49.    wt: 2:   11 A Partial Summary
  50.    wt: 2:   11 Triangle Inequality
  51.    wt: 2:   18 Triangle Similarity Take 1
  52.    wt: 2:   15 Triangle Angle Sum is 180 degrees
  53.    wt: 2:   14 Parallel Lines Postulate
  54.    wt: 2:   11 Triangle Construction Fails
  55.    wt: 2:   17 Arrows Rotate to Reverse with Length Unchanged
  56.    wt: 2:   14 Vector Head to Tail Sums and Resultants
  57.    wt: 2:   11 Signed Number Addition and Addition Properties
  58.    wt: 2:   1 Fractions with Finite Decimal Expansions
  59.    wt: 2:   14 Real Number Multiplication
  60.    wt: 2:   11 Real Number Addition
  61.    wt: 2:   13 Naming Identifying Formulas with Words
  62.    wt: 2:   11 Volume of Sphere
  63.    wt: 2:   4 Square Roots with primes more
  64.    wt: 2:   11 GCD 2700 288 via Euclid Algorithm
  65.    wt: 2:   9 GCD of 360 110 via Primes and Euclid Algorithm
  66.    wt: 2:   4 LCM of 8 and 10 via Prime
  67.    wt: 2:   4 Counting with Trees Product Rule Take I
  68.    wt: 2:   11 What are real lengths and numbers
  69.    wt: 2:   4 Fractions with Units
  70.    wt: 2:   1 Addition and Subtraction with Units
  71.    wt: 2:   21 Working With Signs
  72.    wt: 2:   15 Adding and Subtracting with Unlike Denominators
  73.    wt: 2:   11 Simplification an Algebraic View
  74.    wt: 2:   D Remainders Modulo 11 Pair Rule
  75.    wt: 2:   C Divisibility by 11 Integer Recognition Method
  76.    wt: 2:   13 Subtraction with Additive Inverse
  77.    wt: 2:   11 Adding Integers Formulas and Examples
  78.    wt: 2:   24 Divisibility Tests for 2 3 5 9 10
  79.    wt: 2:   14 Remainder Arithmetic Modulo 9 Example
  80.    wt: 2:   12 Remainder Arithmetic Modulo 10 Example
  81.    wt: 2:   11 Remainder Arithmetic Long Division by 5 Quickly more
  82.    wt: 2:   4 Remainder Arithmetic Modulo 10 in general
  83.    wt: 2:   1 Remainder Arithmetic Modulo 10
  84.    wt: 2:   13 video Factors of 24 using prime
  85.    wt: 2:   11 Efficient Square Rule Use
  86.    wt: 2:   11 Another Single Digit Divisor Example
  87.    wt: 2:   4 Division with 2 Digit Divsors
  88.    wt: 2:   1 Why 3 times 5 gives 15
  89.    wt: 2:   6 Subtraction with Conversion Example with Exercises
  90.    wt: 2:   4 Subtraction with Conversions Borrows and Letter J
  91.    wt: 2:   Appendix 1 Counting Revisited 15 minute video
  92.    wt: 2:   11 Place Value SI Standard International way
  93.    wt: 2:   8 Review Lesson 1 2 4 and 6 All in One
  94.    wt: 2:   011 Division of Time Intervals By Numbers
  95.    wt: 2:   Example 4 with x function of y
  96.    wt: 2:   14 sine and cosine derivatives 2nd step
  97.    wt: 2:   13 sine and cosine derivatives 1st step
  98.    wt: 2:   11 Quotient rule
  99.    wt: 2:   1 Fall 1983 Why Slopes Appetizer
  100.    wt: 2:   13 Limits with Parameters and Derivatives Take II
  101.    wt: 2:   12 Limits with Parameters and Derivatives Take I
  102.    wt: 2:   11 Limits at infinity Three Examples
  103.    wt: 2:   10 Three one sided limits with infinite values
  104.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  105.    wt: 2:   Chapter 11. Graphing Slope versus Position
  106.    wt: 2:   Fall 1983 Calculus Appetizer
  107.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  108.    wt: 2:   Chapter 11. Why Shorthand
  109.    wt: 2:   Chapter 11 Elementary Instruction
  110.    wt: 2:   Chapter 19 What is in chapters 20 to 24
  111.    wt: 2:   Chapter 14 Deductive and Empirical Views of Mathematics
  112.    wt: 2:   Chapter 11 Accidental Patterns
  113.    wt: 2:   Chapter 9 What is in Chapters 10 to 18
  114.    wt: 2:   1 Links to Online Resources Elsewhere Take 1
  115.    wt: 2:   Appendix A Calculus with Proofs for Keen or Gifted
  116.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  117.    wt: 2:   Chapter 3 Algebra Starter Lessons
  118.    wt: 2:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  119.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  120.    wt: 2:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  121.    wt: 2:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  122.    wt: 1:   Appendix 2 primary school Arithmetic 01
  123.    wt: 1:   Appendix 1 primary and preschool mathematic
  124.    wt: 1:   Skills Chapter 5 Calculus
  125.    wt: 1:   Skills Chapter 4 Logic
  126.    wt: 1:   Skills Chapter 1 Arithmetic
  127.    wt: 1:   10 statistics
  128.    wt: 1:   4 algebra
  129.    wt: 1:   2 arithmetic with signed numbers
  130.    wt: 1:   the trouble with algebra
  131.    wt: 1:   05 13 OldSiteEntrancePage
  132.    wt: 1:   04 29 New Mathematics Curriculum
  133.    wt: 1:   04 25 when to stop or suspend mathemat
  134.    wt: 1:   02 21 words for teachers
  135.    wt: 1:   chapitre 12 00 les iles et division
  136.    wt: 1:   chapitre 07 01 principle D induction mathematique
  137.    wt: 1:   chapitre 04 09 Regles accidentelles
  138.    wt: 1:   chapitre 04 08 Limitations et benefices
  139.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  140.    wt: 1:   chapitre 04 06 engagements
  141.    wt: 1:   chapitre 04 05 Implication versus suggestion
  142.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  143.    wt: 1:   chapitre 04 02 Deuxieme enigme
  144.    wt: 1:   chapitre 04 00 Les regles d implication
  145.    wt: 1:   chapitre 01 00 Introduction
  146.    wt: 1:   4 Energy Power Heat09
  147.    wt: 1:   1 Energy Power Heat06
  148.    wt: 1:   D Energy Power04
  149.    wt: 1:   A Energy Power01
  150.    wt: 1:   F Wire Resistance Calculation04
  151.    wt: 1:   C Wire Resistance Calculation01
  152.    wt: 1:   A Wire Resistance Qualitative01
  153.    wt: 1:   2 Unlike resistors in parallel01
  154.    wt: 1:   1 Like resistors in series
  155.    wt: 1:   G Series Circuit01
  156.    wt: 1:   B Electromotive force conventional current01
  157.    wt: 1:   24 Standards For Skill Develoment Take II
  158.    wt: 1:   24 Standards For Skill Develoment
  159.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  160.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  161.    wt: 1:   18 Primary School Mathematics
  162.    wt: 1:   17 Math Booklets for children and young teenagers
  163.    wt: 1:   16 Secondary Mathematics Tips
  164.    wt: 1:   15 Counting For Parents
  165.    wt: 1:   13 Addition and Addition Tables
  166.    wt: 1:   12 Goals and Objectives For Mathematics
  167.    wt: 1:   10 Ends values for work study instruction
  168.    wt: 1:   4 Learning Takes Time and Effort
  169.    wt: 1:   1 Speaking Skills
  170.    wt: 1:   Ages 9 to 10
  171.    wt: 1:   Ages 4 plus to 5 plus
  172.    wt: 1:   Ages 3 plus to 4 plus
  173.    wt: 1:   sign monoticity analysis example 4
  174.    wt: 1:   sign monoticity analysis example 1
  175.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  176.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  177.    wt: 1:   19 Horizontal line rule and method
  178.    wt: 1:   18 Vertical Line Rule and Method
  179.    wt: 1:   17 Function maxima minima and their location
  180.    wt: 1:   16 Increasing or decreasing on intervals
  181.    wt: 1:   15 Sign analysis of functions
  182.    wt: 1:   13 From one to one to many to one
  183.    wt: 1:   12 Function Domain Recognition Exercises
  184.    wt: 1:   10 Interval Notation
  185.    wt: 1:   7 Functions with finite domains
  186.    wt: 1:   4 Function notation in and beyond mathematics
  187.    wt: 1:   1 Geometric Introduction of Function Notation
  188.    wt: 1:   10 quadratic exercises
  189.    wt: 1:   4 quadratics difference of two squares
  190.    wt: 1:   1 quadratics graphing exercises
  191.    wt: 1:   Quadratics in 10 steps
  192.    wt: 1:   10 Exponential Growth and Decay Models
  193.    wt: 1:   9 Formulas for Real Exponents with Logarithms
  194.    wt: 1:   8 Formulas for Fractional Exponents with Logarithms
  195.    wt: 1:   7 Formulas for Roots with Logarithms Derivation
  196.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  197.    wt: 1:   7 Links Lessons Elsewhere
  198.    wt: 1:   4 Polynomials Long division linear divisor
  199.    wt: 1:   1 Polynomials Distributive Law
  200.    wt: 1:   16 cotangent function Definition Graph and Inverse
  201.    wt: 1:   15 cosecant function Definition Graph and Inverse
  202.    wt: 1:   13 cosecant function Definition Graph and Inverse
  203.    wt: 1:   12 motivation for term arctan
  204.    wt: 1:   10 arctan left inverse of tangent Definition
  205.    wt: 1:   4 possible motivation for term arccos
  206.    wt: 1:   1 cosine function properties
  207.    wt: 1:   4 Circle Sector Area proportional to Central Angle
  208.    wt: 1:   1 Degrees and Radians Introduction
  209.    wt: 1:   15 Dot and Cross Product
  210.    wt: 1:   13 Velocity Vectors in Physics
  211.    wt: 1:   12 From Applied To Pure Mathematics
  212.    wt: 1:   10 Parallelogram Addition Method
  213.    wt: 1:   6 Vectors with Coordinates
  214.    wt: 1:   4 Resultant of a Sum of Movements
  215.    wt: 1:   3 Navigation with Arrows or Vectors
  216.    wt: 1:   1 Unsigned Coordinates
  217.    wt: 1:   4 graphing y=Asin(x c)
  218.    wt: 1:   1 graphing y=f(x a)
  219.    wt: 1:   Triangle Angles Sum To 180 Degrees
  220.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  221.    wt: 1:   12 Straight Lines Graphing mx plus b
  222.    wt: 1:   10 Straight Lines through Origin Equations More
  223.    wt: 1:   4 Tangent Function Properties
  224.    wt: 1:   1 Straight Lines Slope Concept
  225.    wt: 1:   17 tangent function angle sum formulas
  226.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  227.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  228.    wt: 1:   31 basic secant cosecant cotangent trig identities
  229.    wt: 1:   24 tangent Angle Difference Formula
  230.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  231.    wt: 1:   21 sine and cosine Half Angle Formulas
  232.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  233.    wt: 1:   18 sum of sinusoidal waves as a single wave
  234.    wt: 1:   17G Pythagorean Theorem Converse
  235.    wt: 1:   17F Law of cosines
  236.    wt: 1:   17E Trig Formulas for dot and cross Products
  237.    wt: 1:   17D cis formulas for sine cosines and tangent
  238.    wt: 1:   17C sine and cosine double triple angle formulas
  239.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  240.    wt: 1:   17A The complex number valued trig function cis
  241.    wt: 1:   16 Right Triangle Complementary Angle Relations
  242.    wt: 1:   15 sine cosine Complementary Angle Relations
  243.    wt: 1:   13 Graph of tangent function many periods
  244.    wt: 1:   12 Graph of tangent function for one period
  245.    wt: 1:   10 Graphs of sines and cosines many periods
  246.    wt: 1:   1 Unit Points Reflections Rotations
  247.    wt: 1:   21 Logarithms Powers and Exponentials
  248.    wt: 1:   19 N th Roots of Unity
  249.    wt: 1:   18 Sixth Roots of Unity
  250.    wt: 1:   17 Cube Roots of unity
  251.    wt: 1:   16 References and Originality Question
  252.    wt: 1:   15 Pythagorean Theorem Converse
  253.    wt: 1:   13 Trig Formulas for dot and cross Products
  254.    wt: 1:   12 cis formulas for sine cosines and tangent
  255.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  256.    wt: 1:   4 Multiplication Properties
  257.    wt: 1:   1 Rectangular Polar Coordinates Review
  258.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  259.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  260.    wt: 1:   12 Triangles Similarity More Problems
  261.    wt: 1:   10 Similarity of Triangles Equivalent of Two Criteria
  262.    wt: 1:   3 Similarity by Design with coordinates
  263.    wt: 1:   1 Early Concept of Like or Similar Shapes
  264.    wt: 1:   10 Midpoint of [a b] and [b a]
  265.    wt: 1:   4 Equations for lines three forms
  266.    wt: 1:   1 Numerical view of lines and their equations
  267.    wt: 1:   13 Pythagorean spatial distance formulas
  268.    wt: 1:   12 Spatial Coordinates
  269.    wt: 1:   10 Pythagorean plane distance formula
  270.    wt: 1:   4 Polar Coordinates to and from
  271.    wt: 1:   2 Cartesian Coordinates with signs
  272.    wt: 1:   1 Cartesian Coordinates sans signs
  273.    wt: 1:   PS E Multiplication with Polar Coordinates
  274.    wt: 1:   PS D Addition with Cartesian Coordinates
  275.    wt: 1:   21 Parallelograms
  276.    wt: 1:   19 Right Triangle Similarity
  277.    wt: 1:   17 Right Bisectors of Triangle Sides
  278.    wt: 1:   16 Angles Subtended By Chords and Diameters
  279.    wt: 1:   13 Angle Side Angle Failure
  280.    wt: 1:   12 Side Angle Side Failure
  281.    wt: 1:   10 Dropping a perpendicular to line
  282.    wt: 1:   4 Side Side Side
  283.    wt: 1:   1 Initial Concepts and Terms
  284.    wt: 1:   A Measurement with Ruler Proper Use
  285.    wt: 1:   6 Figuring with Maps Not to Scale
  286.    wt: 1:   4 Angles on Maps Plans drawn to scale
  287.    wt: 1:   1 Length Measurement
  288.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  289.    wt: 1:   21 Addition of Multiples of a Single Vector
  290.    wt: 1:   19 Signed Multiples of Vectors
  291.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  292.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  293.    wt: 1:   15 Head to Tails in place Addition Associative
  294.    wt: 1:   13 Arrows and Vectors in a Plane
  295.    wt: 1:   12 Real Numbers Line Signed Coordinates
  296.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  297.    wt: 1:   9 Division with Digits after Decimal Point
  298.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  299.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  300.    wt: 1:   4 Location of Point in Decimal Addition
  301.    wt: 1:   4 Commutative Law Groups Counting Form
  302.    wt: 1:   1 The Counting Origins of Numbers
  303.    wt: 1:   4 Fraction Operations Axiomatic Development
  304.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  305.    wt: 1:   4 Rates Ratios and Proporitionality
  306.    wt: 1:   1 What is Proportionality
  307.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  308.    wt: 1:   1 Changing Calculations
  309.    wt: 1:   4 Subtraction and Division Axioms
  310.    wt: 1:   1 Equivalent Computation Rules
  311.    wt: 1:   4 Comparison of Negative Numbers
  312.    wt: 1:   3 More and Less Than with Unlike Signs
  313.    wt: 1:   1 Real Numbers Comparison
  314.    wt: 1:   16 Real Numbers Comparison
  315.    wt: 1:   15 Real Number Division
  316.    wt: 1:   13 Real Number Subtraction
  317.    wt: 1:   12 Real Number Additive Inverses or Negatives
  318.    wt: 1:   10 Real Number Lengths and Signs
  319.    wt: 1:   4 Rational Numbers
  320.    wt: 1:   1 Whole and Natural Numbers
  321.    wt: 1:   4 Changing Letters
  322.    wt: 1:   1 Formulas Dependence and Function Notation
  323.    wt: 1:   4 GE III Animated Examples
  324.    wt: 1:   1 GE Substitution four examples
  325.    wt: 1:   4 Solving a triangular system exercise
  326.    wt: 1:   2 Essentially one exercises three with solution
  327.    wt: 1:   1 Essentially One Unknown
  328.    wt: 1:   4 Four Examples Fractional Coefficients
  329.    wt: 1:   1 Proper Equal Sign Usage
  330.    wt: 1:   10 One Example
  331.    wt: 1:   4 Two Examples
  332.    wt: 1:   12 Cone Cylinder Sphere Lesson Idea
  333.    wt: 1:   10 Volume of Pyramid
  334.    wt: 1:   4 Circle Area Formula Example
  335.    wt: 1:   1 Written work formats for developing and showing skill
  336.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  337.    wt: 1:   4 Subset Builder Notation
  338.    wt: 1:   3 Counting with Sets etc
  339.    wt: 1:   1 Finite Sets
  340.    wt: 1:   4 A Brief Story of numbers and algebra
  341.    wt: 1:   1 Three Skills For Algebra
  342.    wt: 1:   4 Greater More Less Than Signs in General
  343.    wt: 1:   2 More and Less Than with Unlike Signs
  344.    wt: 1:   1 More and Less Than for Counts and Measures
  345.    wt: 1:   5 Square Roots with primes more still
  346.    wt: 1:   3 Properties of Square Roots with example
  347.    wt: 1:   2 Square Roots with Prime
  348.    wt: 1:   1 Squares and Square Roots Introduction
  349.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  350.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  351.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  352.    wt: 1:   13 GCD from given Prime Factorization
  353.    wt: 1:   5 Common Divisors 60 45 via Prime
  354.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  355.    wt: 1:   1 Least Common Multiples LCM Introduction
  356.    wt: 1:   12 GCD 2700 288 via Prime
  357.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  358.    wt: 1:   3 Counting with Tables and Trees II
  359.    wt: 1:   2 Counting with Tables and Trees I
  360.    wt: 1:   1 Counting and Counting Methods I
  361.    wt: 1:   10 dividing signed numbers
  362.    wt: 1:   4 signed coordinates for regions in space
  363.    wt: 1:   6 Simplification of Fractions with Units
  364.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  365.    wt: 1:   21 Reciprocals for Fractions and Wholes
  366.    wt: 1:   19 Dividing Fractions How TO
  367.    wt: 1:   18 Efficient Ways to Multiply
  368.    wt: 1:   17 Efficient Ways to Add and Subtract
  369.    wt: 1:   16 Addition Subtraction Comparision Compared
  370.    wt: 1:   13 Fraction Comparison Algebraic View
  371.    wt: 1:   12 Fraction Comparison
  372.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  373.    wt: 1:   4 Fraction Multiplication
  374.    wt: 1:   1 What is a fraction Take II
  375.    wt: 1:   1 What is a fraction
  376.    wt: 1:   12 Adding Integers More Examples
  377.    wt: 1:   10 Integer Multiplication Formulas
  378.    wt: 1:   4 Adding Movements wiht opposite directions
  379.    wt: 1:   3 Adding Movements with same direction
  380.    wt: 1:   1 Integers as Coordinates
  381.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  382.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  383.    wt: 1:   21 Remainder Arithmetic Modulo 3
  384.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  385.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  386.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  387.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  388.    wt: 1:   15 Remainder Arithmetic Modulo 9 Example
  389.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  390.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  391.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  392.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  393.    wt: 1:   19 video Prime Factorization Unique
  394.    wt: 1:   18 video Count Factors given Prime Factorization
  395.    wt: 1:   17 Identify and Count Factors using Primes
  396.    wt: 1:   16 video Factors of 980 using prime
  397.    wt: 1:   15 video Factors of 20 using Prime Factorization
  398.    wt: 1:   12 LCD GCD and LCM using Primes
  399.    wt: 1:   10 video Prime Factorization upto 23 squared
  400.    wt: 1:   9 video Prime Factorization upto 19 squared
  401.    wt: 1:   8 video Prime Factorization upto 19
  402.    wt: 1:   4 video Prime Factorization Introduction
  403.    wt: 1:   2 Prime and Composites less than 16
  404.    wt: 1:   1 video how Products are bigger than factor
  405.    wt: 1:   Division with Counts and Length
  406.    wt: 1:   Long Division forwards and backwards Example 1
  407.    wt: 1:   12 Why Long Division Works Take III
  408.    wt: 1:   10 Division by Five Long and Short Ways
  409.    wt: 1:   2 Division with Single Digit Divisors
  410.    wt: 1:   1 Divsion Physical Examples
  411.    wt: 1:   C Counting Areas with Powers of Ten
  412.    wt: 1:   4 Two and Three Digit Multipliers
  413.    wt: 1:   Appendix 1 Decimals Comparison Method Take II
  414.    wt: 1:   Subtraction with J Conversions Example
  415.    wt: 1:   8 Subtraction with Units of Measure
  416.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  417.    wt: 1:   1 Comparison and Subtraction Easy Direct Cases
  418.    wt: 1:   3. How to add with decimals A sans conversions
  419.    wt: 1:   1. Explaining Addition Table
  420.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  421.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  422.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  423.    wt: 1:   The 12 Times Table Visually
  424.    wt: 1:   016 Numbering Occidental Calendar Days
  425.    wt: 1:   015 School and work day counting tables
  426.    wt: 1:   013 Travel Time Tables
  427.    wt: 1:   012 Division of Time Intervals by Time Intervals
  428.    wt: 1:   010 Repeated Addition of Time Intervals
  429.    wt: 1:   4 Mixing and Changing Units of Time
  430.    wt: 1:   1 Intro of Kids To Time Date Skills
  431.    wt: 1:   Example 1 volume of a pyramid
  432.    wt: 1:   Example 1. Area Between x and x squared
  433.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  434.    wt: 1:   Example 1
  435.    wt: 1:   Area Between Curves Lesson Take 1
  436.    wt: 1:   4 Definite Integrals Evaluation Exercises
  437.    wt: 1:   1 Chain Rule in Reverse Integration Method
  438.    wt: 1:   A Related lessons in Volume 3
  439.    wt: 1:   4 Second derivative test exercise example
  440.    wt: 1:   34 Derivative of exponential function
  441.    wt: 1:   31 Derivatives of inverse functions
  442.    wt: 1:   24 Chain Rule Animated Examples
  443.    wt: 1:   21 Chain Rule for powers
  444.    wt: 1:   19 Chain Rule for linear functions
  445.    wt: 1:   18 Chain Rule Introduction
  446.    wt: 1:   17 Derivatives of quotients of sine and cosine
  447.    wt: 1:   16 Derivatives of reciprocals of sine and cosine
  448.    wt: 1:   15 sine and cosine derivatives 3rd step
  449.    wt: 1:   12 Quotient rule examples
  450.    wt: 1:   10 Power rule for negative integers
  451.    wt: 1:   4 Sum Rule
  452.    wt: 1:   2 Motivation for Limit Definition Take 1
  453.    wt: 1:   4 Numerical properties
  454.    wt: 1:   1 Numerical introduction
  455.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  456.    wt: 1:   G.5 Motions With Bounded Velocities
  457.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  458.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  459.    wt: 1:   F.4 Finite Covering Theorem
  460.    wt: 1:   F.1 What Functions are Continuous
  461.    wt: 1:   E1 Error Control Inequalities
  462.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  463.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  464.    wt: 1:   A1. Introduction
  465.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  466.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  467.    wt: 1:   Chapter 21 Arrow Addition
  468.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  469.    wt: 1:   Chapter 18. Slopes Areas Integration
  470.    wt: 1:   Chapter 17. Area Approximation
  471.    wt: 1:   Chapter 16. Velocity Approximation
  472.    wt: 1:   Chapter 15. Slope Approximation
  473.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  474.    wt: 1:   Chapter 13. Acceleration
  475.    wt: 1:   Chapter 12. Units and Slopes
  476.    wt: 1:   Chapter 10 Slopes and Units
  477.    wt: 1:   Chapter 9 About First Courses in Calculus
  478.    wt: 1:   Chapter 4. More Slope Sign Analysis
  479.    wt: 1:   Chapter 1.Introduction
  480.    wt: 1:   Chapter 31 Direct and Indirect Reason
  481.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  482.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  483.    wt: 1:   Chapter 21. Third Reading Guide
  484.    wt: 1:   Chapter 19. Functions and Sets
  485.    wt: 1:   Chapter 18. Rules for Algebra
  486.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  487.    wt: 1:   Chapter 16. Painless Theorem Proving
  488.    wt: 1:   Chapter 15. Solving Linear Equations
  489.    wt: 1:   Chapter 13. Second Reading Guide
  490.    wt: 1:   Chapter 12. Shorthand Usage Guide
  491.    wt: 1:   Chapter 10 Describing and Changing Calculations
  492.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  493.    wt: 1:   Chapter 4 Longer Chains of Reason
  494.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  495.    wt: 1:   Chapter 12 Four Phases
  496.    wt: 1:   Chapter 10 Transition
  497.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  498.    wt: 1:   Chapter 1 Introduction
  499.    wt: 1:   Chapter 24 Direct and Indirect Reason
  500.    wt: 1:   Chapter 21 Occurrence Tables
  501.    wt: 1:   Chapter 18 Sense and Knowledge
  502.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  503.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  504.    wt: 1:   Chapter 15 Objective Processes
  505.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  506.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  507.    wt: 1:   Chapter 10 Responsibility
  508.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  509.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  510.    wt: 1:   Chapter 1 Introduction
  511.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions
  512.    wt: 1:   L Skills with take home value
  513.    wt: 1:   D. Check work a must with a caution
  514.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  515.    wt: 1:   Chapter 1 Arithmetic
  516.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  517.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  518.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  519.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  520.    wt: 1:   More Algebra and Slope based Calculus Preview
  521.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  522.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

Extended Search

1043 matches:

  1.    wt: 9:   5 Square Roots with primes more still
  2.    wt: 9:   3 Properties of Square Roots with example
  3.    wt: 9:   2 Square Roots with Prime
  4.    wt: 9:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  5.    wt: 9:   Example 4 with x function of y
  6.    wt: 9:   Area Between Curves Lesson Take 2
  7.    wt: 9:   Area Between Curves Lesson Take 1
  8.    wt: 9:   1 Numerical introduction
  9.    wt: 8:   17 GCD LCM of 85 and 60 via Prime
  10.    wt: 8:   16 GCD and LCM of 650 225 via Prime
  11.    wt: 8:   11 GCD 2700 288 via Euclid Algorithm
  12.    wt: 8:   9 GCD of 360 110 via Primes and Euclid Algorithm
  13.    wt: 8:   4 LCM of 8 and 10 via Prime
  14.    wt: 8:   24 Divisibility Tests for 2 3 5 9 10
  15.    wt: 8:   11 Another Single Digit Divisor Example
  16.    wt: 8:   4. How to add with decimals B with conversions
  17.    wt: 8:   11 Place Value SI Standard International way
  18.    wt: 8:   Area Between Crossing Curves Lesson Take 2
  19.    wt: 8:   Area Between Crossing Curves Lesson Take 1
  20.    wt: 8:   14 sine and cosine derivatives 2nd step
  21.    wt: 8:   13 sine and cosine derivatives 1st step
  22.    wt: 8:   9 Limits Continuity and Composition
  23.    wt: 8:   4 Numerical properties
  24.    wt: 7:   11 A Partial Summary
  25.    wt: 7:   13 GCD from given Prime Factorization
  26.    wt: 7:   7 GCD and LCM from prime factorization
  27.    wt: 7:   LCM 60 45 Avoid List Method Use Prime
  28.    wt: 7:   1 Least Common Multiples LCM Introduction
  29.    wt: 7:   12 GCD 2700 288 via Prime
  30.    wt: 7:   11 What are real lengths and numbers
  31.    wt: 7:   25 Divisibility Tests for 2 3 5 9 10 Example
  32.    wt: 7:   17 Remainder Arithmetic Rule of 9 for checking sums I
  33.    wt: 7:   14 video Factors of 24 Take II
  34.    wt: 7:   Division with Counts and Length
  35.    wt: 7:   Long Division forwards and backwards Example 1
  36.    wt: 7:   4 Division with 2 Digit Divsors
  37.    wt: 7:   Appendix 1 Counting Revisited 15 minute video
  38.    wt: 7:   Example 2 volume of a cone
  39.    wt: 7:   Example 1 volume of a pyramid
  40.    wt: 7:   Example 1. Area Between x and x squared
  41.    wt: 7:   Example 2
  42.    wt: 7:   Example 1
  43.    wt: 7:   A Related Material in Volume 3
  44.    wt: 7:   4 Definite Integrals Evaluation Exercises
  45.    wt: 7:   2 Indefinite Integrals Exercises
  46.    wt: 7:   1 Chain Rule in Reverse Integration Method
  47.    wt: 7:   A Related lessons in Volume 3
  48.    wt: 7:   4 Second derivative test exercise example
  49.    wt: 7:   3 Second derivative test
  50.    wt: 7:   34 Derivative of exponential function
  51.    wt: 7:   24 Chain Rule Animated Examples
  52.    wt: 7:   19 Chain Rule for linear functions
  53.    wt: 7:   17 Derivatives of quotients of sine and cosine
  54.    wt: 7:   11 Quotient rule
  55.    wt: 7:   1 Fall 1983 Why Slopes Appetizer
  56.    wt: 7:   8 Four Animated Examples
  57.    wt: 7:   7 Evaluation by immediate or delayed substitution
  58.    wt: 7:   6 Continuity at a point
  59.    wt: 7:   5 Jumps and absence of unlimited error control
  60.    wt: 7:   3 Decimal insights for limits continuity convergence
  61.    wt: 7:   2 Algebraic codification
  62.    wt: 7:   Chapter 14 Limits and Continuity with and sans Decimals
  63.    wt: 6:   14 Surjections Injections Bijections
  64.    wt: 6:   11 Function Domain Range Source and Targets
  65.    wt: 6:   4 Circle Sector Area proportional to Central Angle
  66.    wt: 6:   14 Why Scalar Multiplication Distributes Physical Argument
  67.    wt: 6:   11 Component Method
  68.    wt: 6:   Triangle Angles Sum To 180 Degrees
  69.    wt: 6:   12 Links Lessons elsewhere
  70.    wt: 6:   4 GE III Animated Examples
  71.    wt: 6:   1 GE Substitution four examples
  72.    wt: 6:   Skill Development Notes
  73.    wt: 6:   10 One Example
  74.    wt: 6:   4 Two Examples
  75.    wt: 6:   10 Set View of Wordy Extensions To Arithmetic
  76.    wt: 6:   4 Greater More Less Than Signs in General
  77.    wt: 6:   1 More and Less Than for Counts and Measures
  78.    wt: 6:   8 GCD from Euclidean Algorithm
  79.    wt: 6:   6 GCD from Prime
  80.    wt: 6:   5 Common Divisors 60 45 via Prime
  81.    wt: 6:   4 Fractions with Units
  82.    wt: 6:   1 Addition and Subtraction with Units
  83.    wt: 6:   21 Working With Signs
  84.    wt: 6:   18 Efficient Ways to Multiply
  85.    wt: 6:   14 Adding and Subtracting with Like Denominators
  86.    wt: 6:   11 Adding Integers Formulas and Examples
  87.    wt: 6:   21 Remainder Arithmetic Modulo 3
  88.    wt: 6:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  89.    wt: 6:   19 Remainder Arithmetic Rule of 9 for checking sums III
  90.    wt: 6:   18 Remainder Arithmetic Rule of 9 for checking sums II
  91.    wt: 6:   16 Remainder Arithmetic Modulo 9 Example 2
  92.    wt: 6:   14 Remainder Arithmetic Modulo 9 Example
  93.    wt: 6:   12 Remainder Arithmetic Modulo 10 Example
  94.    wt: 6:   11 Remainder Arithmetic Long Division by 5 Quickly more
  95.    wt: 6:   10 Remainder Arithmetic Long Division by 5 Quickly
  96.    wt: 6:   4 Remainder Arithmetic Modulo 10 in general
  97.    wt: 6:   1 Remainder Arithmetic Modulo 10
  98.    wt: 6:   11 Efficient Square Rule Use
  99.    wt: 6:   Long Division forwards and backwards Example 3
  100.    wt: 6:   12 Why Long Division Works Take III
  101.    wt: 6:   10 Division by Five Long and Short Ways
  102.    wt: 6:   1 Divsion Physical Examples
  103.    wt: 6:   1 Why 3 times 5 gives 15
  104.    wt: 6:   Subtraction with J Conversions Example
  105.    wt: 6:   4 Subtraction with Conversions Borrows and Letter J
  106.    wt: 6:   1. Explaining Addition Table
  107.    wt: 6:   10 Names for Big Numbers and Powers of Ten Expansion
  108.    wt: 6:   8 Review Lesson 1 2 4 and 6 All in One
  109.    wt: 6:   4 Groups of 3 Place Value in Decimal Fractions
  110.    wt: 6:   1 Place Value in Three Digit Whole Numbers
  111.    wt: 6:   Volume of Solid by Cross Sections Lesson
  112.    wt: 6:   Example 3
  113.    wt: 6:   Summary
  114.    wt: 6:   5 Area Under Curve Exercise
  115.    wt: 6:   3 Two Chain Rule Method Exercises
  116.    wt: 6:   2 Second derivative test prequel
  117.    wt: 6:   38 Formulas and derivatives for powers and roots
  118.    wt: 6:   33 Chain Rule Real Player video examples
  119.    wt: 6:   31 Derivatives of inverse functions
  120.    wt: 6:   29 Chain Rule Optional Reading
  121.    wt: 6:   25 Chain Rule Animated Examples Continued
  122.    wt: 6:   23 Chain Rule in general
  123.    wt: 6:   21 Chain Rule for powers
  124.    wt: 6:   20 Chain Rule for Pulley Systems
  125.    wt: 6:   18 Chain Rule Introduction
  126.    wt: 6:   16 Derivatives of reciprocals of sine and cosine
  127.    wt: 6:   15 sine and cosine derivatives 3rd step
  128.    wt: 6:   12 Quotient rule examples
  129.    wt: 6:   10 Power rule for negative integers
  130.    wt: 6:   6 Power rule from product rule
  131.    wt: 6:   4 Sum Rule
  132.    wt: 6:   3 Motivation for Limit Definition Take 2
  133.    wt: 6:   2 Motivation for Limit Definition Take 1
  134.    wt: 6:   Chapter 11. Graphing Slope versus Position
  135.    wt: 6:   Chapter 14. Forward and Backward Use of a Formula
  136.    wt: 6:   Chapter 11. Why Shorthand
  137.    wt: 6:   Chapter 11 Elementary Instruction
  138.    wt: 6:   Chapter 14 Deductive and Empirical Views of Mathematics
  139.    wt: 6:   Chapter 11 Accidental Patterns
  140.    wt: 5:   Ages 12 to 14 Skills with take home value
  141.    wt: 5:   2 Radian Measure Numerical Value of one degree
  142.    wt: 5:   1 Degrees and Radians Introduction
  143.    wt: 5:   14 cosine even and sine and tangent are odd
  144.    wt: 5:   Four Simple Exercises
  145.    wt: 5:   10 Midpoint of [a b] and [b a]
  146.    wt: 5:   4 Equations for lines three forms
  147.    wt: 5:   1 Numerical view of lines and their equations
  148.    wt: 5:   1 Fractions with Finite Decimal Expansions
  149.    wt: 5:   4 Fraction Operations Axiomatic Development
  150.    wt: 5:   1 Decimals Modular and Remainder Arithmetic
  151.    wt: 5:   4 Changing Letters
  152.    wt: 5:   1 Formulas Dependence and Function Notation
  153.    wt: 5:   13 Naming Identifying Formulas with Words
  154.    wt: 5:   11 Volume of Sphere
  155.    wt: 5:   4 Subset Builder Notation
  156.    wt: 5:   3 Counting with Sets etc
  157.    wt: 5:   1 Finite Sets
  158.    wt: 5:   2 More and Less Than with Unlike Signs
  159.    wt: 5:   2 Least Common Multiple LCM intro via list method
  160.    wt: 5:   10 dividing signed numbers
  161.    wt: 5:   4 signed coordinates for regions in space
  162.    wt: 5:   6 Simplification of Fractions with Units
  163.    wt: 5:   5 Reciprocals and Division for Fractions with Units
  164.    wt: 5:   21 Reciprocals for Fractions and Wholes
  165.    wt: 5:   19 Dividing Fractions How TO
  166.    wt: 5:   17 Efficient Ways to Add and Subtract
  167.    wt: 5:   15 Adding and Subtracting with Unlike Denominators
  168.    wt: 5:   11 Simplification an Algebraic View
  169.    wt: 5:   4 Fraction Multiplication
  170.    wt: 5:   1 What is a fraction Take II
  171.    wt: 5:   1 What is a fraction
  172.    wt: 5:   D Remainders Modulo 11 Pair Rule
  173.    wt: 5:   C Divisibility by 11 Integer Recognition Method
  174.    wt: 5:   13 Subtraction with Additive Inverse
  175.    wt: 5:   27 Divisibility by 2 3 6 5 9 10 Example
  176.    wt: 5:   26 Divisibility by 2 3 5 Example
  177.    wt: 5:   23 Remainder Arithmetic Modulo 2
  178.    wt: 5:   22 Remainder Arithmetic Modulo 3 more
  179.    wt: 5:   15 Remainder Arithmetic Modulo 9 Example
  180.    wt: 5:   13 Remainder Arithmetic Modulo 5 Example
  181.    wt: 5:   7 Remainder Arithmetic Modulo 5 Examples I
  182.    wt: 5:   3 Remainder Arithmetic Modulos 10 more still
  183.    wt: 5:   2 Remainder Arithmetic Modulo 10 more
  184.    wt: 5:   13 video Factors of 24 using prime
  185.    wt: 5:   Long Division Backwards more
  186.    wt: 5:   Long Division forwards and backwards Example 2
  187.    wt: 5:   2 Division with Single Digit Divisors
  188.    wt: 5:   4 Two and Three Digit Multipliers
  189.    wt: 5:   Video Decimal Multiplication Geometric View Example 2
  190.    wt: 5:   6 Subtraction with Conversion Example with Exercises
  191.    wt: 5:   1 Comparison and Subtraction Easy Direct Cases
  192.    wt: 5:   3. How to add with decimals A sans conversions
  193.    wt: 5:   014 Counting Days with Calendars
  194.    wt: 5:   A Chain Rule Real Player video examples
  195.    wt: 5:   36 Cube root derivative animated
  196.    wt: 5:   30Chain Rule A Proof
  197.    wt: 5:   28 Chain Rule Preparation for a Proof
  198.    wt: 5:   27 Chain Rule sinusoidal outer inner functions EGS
  199.    wt: 5:   26 Chain Rule Recognising outer inner functions
  200.    wt: 5:   22 Chain Rule for polynomials
  201.    wt: 5:   9 Reciprocal rule
  202.    wt: 5:   8 Differentiation of polynomials
  203.    wt: 5:   7 Animated Differentiation Examples
  204.    wt: 5:   5 Product Rule
  205.    wt: 5:   G.1 First Fundamental Theorem of Calculus
  206.    wt: 5:   Chapter 19 What is in chapters 20 to 24
  207.    wt: 5:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  208.    wt: 4:   11 pure mathematics
  209.    wt: 4:   chapitre 04 10 Etapes pour une meilleur raison
  210.    wt: 4:   chapitre 04 04 Parlons de la logique
  211.    wt: 4:   chapitre 04 01 Premiere enigme
  212.    wt: 4:   14 Multiplication and Times Tables
  213.    wt: 4:   11 Help and Defend Your Child or Teens Education
  214.    wt: 4:   Ages 12 to 14 Geometry
  215.    wt: 4:   Ages 12 to 14 Arithmetic
  216.    wt: 4:   24 Monotoncity Injectivity and Inverse Functions
  217.    wt: 4:   21 Graphs of functions given by Horizontal Line Method
  218.    wt: 4:   19 Horizontal line rule and method
  219.    wt: 4:   18 Vertical Line Rule and Method
  220.    wt: 4:   17 Function maxima minima and their location
  221.    wt: 4:   16 Increasing or decreasing on intervals
  222.    wt: 4:   15 Sign analysis of functions
  223.    wt: 4:   13 From one to one to many to one
  224.    wt: 4:   12 Function Domain Recognition Exercises
  225.    wt: 4:   10 Interval Notation
  226.    wt: 4:   4 Function notation in and beyond mathematics
  227.    wt: 4:   1 Geometric Introduction of Function Notation
  228.    wt: 4:   11 Growth and Decay in Biology
  229.    wt: 4:   14 secant function Definition Graph and Inverse
  230.    wt: 4:   11 arctan left inverse of tangent Graph
  231.    wt: 4:   4 possible motivation for term arccos
  232.    wt: 4:   1 cosine function properties
  233.    wt: 4:   9 Summary Degrees to Radians and back
  234.    wt: 4:   8 Radian Measures of Common Angles
  235.    wt: 4:   7 Radian Measures in special Triangles
  236.    wt: 4:   6 Radian Measure to Degrees
  237.    wt: 4:   5 Degrees to Radian Measure
  238.    wt: 4:   3 Circle Arclengh Proportional to Central Angle
  239.    wt: 4:   15 Dot and Cross Product
  240.    wt: 4:   13 Velocity Vectors in Physics
  241.    wt: 4:   12 From Applied To Pure Mathematics
  242.    wt: 4:   10 Parallelogram Addition Method
  243.    wt: 4:   4 Resultant of a Sum of Movements
  244.    wt: 4:   1 Unsigned Coordinates
  245.    wt: 4:   Parallel Lines and Parallel Transversals
  246.    wt: 4:   Proportionality of Line Segments From Parallel Transversals
  247.    wt: 4:   Parallel Lines and Alternating Corresponding Angles
  248.    wt: 4:   Parallel Lines and Interior Angles
  249.    wt: 4:   Straight Lines ASA Intersection Study
  250.    wt: 4:   17 tangent function angle sum formulas
  251.    wt: 4:   16 Right Triangle Complementary Angle Relations
  252.    wt: 4:   4 sines and cosines for reference angle 45 degrees
  253.    wt: 4:   14 Law of cosines
  254.    wt: 4:   11 sine and cosine double triple angle formulas
  255.    wt: 4:   11 Triangle Similarity Missing Side Problem
  256.    wt: 4:   4 Similarity Definition with Coordinate
  257.    wt: 4:   11 Triangle Inequality
  258.    wt: 4:   14 Parallel Lines Postulate
  259.    wt: 4:   11 Triangle Construction Fails
  260.    wt: 4:   A Modular and Remainder Arithmetic
  261.    wt: 4:   17 Arrows Rotate to Reverse with Length Unchanged
  262.    wt: 4:   14 Vector Head to Tail Sums and Resultants
  263.    wt: 4:   11 Signed Number Addition and Addition Properties
  264.    wt: 4:   9 Division with Digits after Decimal Point
  265.    wt: 4:   7 Arithmetic with Infinite Decimal Expansions
  266.    wt: 4:   5 Fractions with Infinite Decimal Expansions
  267.    wt: 4:   4 Location of Point in Decimal Addition
  268.    wt: 4:   4 Commutative Law Groups Counting Form
  269.    wt: 4:   1 The Counting Origins of Numbers
  270.    wt: 4:   5 Areas of Rectangles Revisited
  271.    wt: 4:   3 Inequalities Algebraically
  272.    wt: 4:   2 Fraction Operations Physical Development
  273.    wt: 4:   4 Rates Ratios and Proporitionality
  274.    wt: 4:   1 What is Proportionality
  275.    wt: 4:   14 Real Number Multiplication
  276.    wt: 4:   11 Real Number Addition
  277.    wt: 4:   5 Independent versus Dependent Variables
  278.    wt: 4:   3 Geometric Formulas and Function Notation
  279.    wt: 4:   2 Computation Rules Evaluation
  280.    wt: 4:   5 Gaussian Elimination for 3 unknowns 2nd example
  281.    wt: 4:   3 Gaussian Elimination 3 unknowns first example
  282.    wt: 4:   3 GE III Equation Addition and Multiplication
  283.    wt: 4:   2 GE II Comparison
  284.    wt: 4:   4 Solving a triangular system exercise
  285.    wt: 4:   1 Essentially One Unknown
  286.    wt: 4:   4 Four Examples Fractional Coefficients
  287.    wt: 4:   1 Proper Equal Sign Usage
  288.    wt: 4:   9 Three Examples
  289.    wt: 4:   8 One Example
  290.    wt: 4:   7 Two Examples
  291.    wt: 4:   6 Three Examples
  292.    wt: 4:   5 Three Examples
  293.    wt: 4:   3 Two Examples
  294.    wt: 4:   2 Three Examples
  295.    wt: 4:   12 Cone Cylinder Sphere Lesson Idea
  296.    wt: 4:   10 Volume of Pyramid
  297.    wt: 4:   9 Sets in Probability and Statistics
  298.    wt: 4:   8 Sets of Numbers
  299.    wt: 4:   7 Cautious or Safe Set Construction
  300.    wt: 4:   6 Power Set Notation
  301.    wt: 4:   5 Product Builder Notation
  302.    wt: 4:   2 Venn Diagrams
  303.    wt: 4:   4 A Brief Story of numbers and algebra
  304.    wt: 4:   1 Three Skills For Algebra
  305.    wt: 4:   3 Comparison of Negative Numbers
  306.    wt: 4:   4 Counting with Trees Product Rule Take I
  307.    wt: 4:   7 Converting or Changing Units
  308.    wt: 4:   3 Multiplying Units and Numbers
  309.    wt: 4:   2 Equality and Units
  310.    wt: 4:   22 Complex Compound Fractions
  311.    wt: 4:   20 Dividing Fractions the Why
  312.    wt: 4:   16 Addition Subtraction Comparision Compared
  313.    wt: 4:   13 Fraction Comparison Algebraic View
  314.    wt: 4:   12 Fraction Comparison
  315.    wt: 4:   10 Simplification of Fractions and Mixed Numerals
  316.    wt: 4:   B Integer Long Division Multiple Choices
  317.    wt: 4:   12 Adding Integers More Examples
  318.    wt: 4:   10 Integer Multiplication Formulas
  319.    wt: 4:   4 Adding Movements wiht opposite directions
  320.    wt: 4:   1 Integers as Coordinates
  321.    wt: 4:   A Decimals Modular and Remainder Arithmetic
  322.    wt: 4:   9 Remainder Arithmetic Divisibility by 5
  323.    wt: 4:   8 Remainder Arithmetic Morulo 5 Examples II
  324.    wt: 4:   6 Remainder Arithmetic Modulo 5 Propertie
  325.    wt: 4:   5 Remainder Arithmetic Modulo 5
  326.    wt: 4:   19 video Prime Factorization Unique
  327.    wt: 4:   18 video Count Factors given Prime Factorization
  328.    wt: 4:   17 Identify and Count Factors using Primes
  329.    wt: 4:   16 video Factors of 980 using prime
  330.    wt: 4:   15 video Factors of 20 using Prime Factorization
  331.    wt: 4:   12 LCD GCD and LCM using Primes
  332.    wt: 4:   10 video Prime Factorization upto 23 squared
  333.    wt: 4:   4 video Prime Factorization Introduction
  334.    wt: 4:   1 video how Products are bigger than factor
  335.    wt: 4:   Long Division Backward
  336.    wt: 4:   9 Why Long Division Works Take II
  337.    wt: 4:   8 Correcting the Mistake
  338.    wt: 4:   7 Long Divison Mistake Catching
  339.    wt: 4:   6 Why Decimal Long Division Methods Works Take I
  340.    wt: 4:   5 Long Division Include Zeroes or not
  341.    wt: 4:   3 Division Single Digit Divisor Example
  342.    wt: 4:   D Decimal Multiplication Methods Derived
  343.    wt: 4:   C Counting Areas with Powers of Ten
  344.    wt: 4:   Video Decimal Multiplication Geometric View Example 2
  345.    wt: 4:   Video Power Notation in Decimal Expansion
  346.    wt: 4:   Appendix 1 Decimals Comparison Method Take II
  347.    wt: 4:   Subtraction Another Video Lesson
  348.    wt: 4:   8 Subtraction with Units of Measure
  349.    wt: 4:   7 Subtraction for Decimal Fractions with Exercises
  350.    wt: 4:   8 What skills and work habits to require
  351.    wt: 4:   7 Adding decimal fractions using decimal point
  352.    wt: 4:   6. Counting and adding units and mixed units
  353.    wt: 4:   5. How to add decimals C. Examples
  354.    wt: 4:   2 Decimal Counting Practices
  355.    wt: 4:   9 Place Value Review Decimal form of Avogrados number included
  356.    wt: 4:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  357.    wt: 4:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  358.    wt: 4:   5 More on Groups of 3 Place Value in Decimal Fractions
  359.    wt: 4:   3 More on Groups of 3 Multi Digit Place Value
  360.    wt: 4:   2 Groups of Three Place Value for Multidigit Decimals
  361.    wt: 4:   011 Division of Time Intervals By Numbers
  362.    wt: 4:   G.5 Motions With Bounded Velocities
  363.    wt: 4:   G.4 Lipschitz Continuity implies EquiContinuity
  364.    wt: 4:   G.1 Differentiable Functions Rolles Theorem
  365.    wt: 4:   F.5b Extreme Value Theorem
  366.    wt: 4:   F.4 Finite Covering Theorem
  367.    wt: 4:   F.3 Intermediate Value Theorem
  368.    wt: 4:   A1. Introduction
  369.    wt: 4:   Chapter 24 Logarithms Powers and Exponentials
  370.    wt: 4:   Chapter 21 Arrow Addition
  371.    wt: 4:   Chapter 19. Exponentials and Natural Logarithms
  372.    wt: 4:   Chapter 18. Slopes Areas Integration
  373.    wt: 4:   Chapter 17. Area Approximation
  374.    wt: 4:   Chapter 16. Velocity Approximation
  375.    wt: 4:   Chapter 15. Slope Approximation
  376.    wt: 4:   Chapter 15. Algebraic Evaluation of Limits
  377.    wt: 4:   Chapter 13. Acceleration
  378.    wt: 4:   Chapter 12. Units and Slopes
  379.    wt: 4:   Chapter 10 Slopes and Units
  380.    wt: 4:   Chapter 4. More Slope Sign Analysis
  381.    wt: 4:   Chapter 1.Introduction
  382.    wt: 4:   Fall 1983 Calculus Appetizer
  383.    wt: 4:   Appendix D. What to do in School and Why
  384.    wt: 4:   Appendix A. Reading Guide For Next Appendices
  385.    wt: 4:   Chapter 31 Direct and Indirect Reason
  386.    wt: 4:   Chapter 24. Personal Investment and Pension EGS
  387.    wt: 4:   Chapter 21. Third Reading Guide
  388.    wt: 4:   Chapter 19. Functions and Sets
  389.    wt: 4:   Chapter 18. Rules for Algebra
  390.    wt: 4:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  391.    wt: 4:   Chapter 16. Painless Theorem Proving
  392.    wt: 4:   Chapter 15. Solving Linear Equations
  393.    wt: 4:   Chapter 13. Second Reading Guide
  394.    wt: 4:   Chapter 12. Shorthand Usage Guide
  395.    wt: 4:   Chapter 10 Describing and Changing Calculations
  396.    wt: 4:   Chapter 4 Longer Chains of Reason
  397.    wt: 4:   Chapter 1 Introduction to Chapters 2 to 6
  398.    wt: 4:   Postscript B Mathematics Education References
  399.    wt: 4:   Chapter 12 Four Phases
  400.    wt: 4:   Chapter 10 Transition
  401.    wt: 4:   Chapter 4 Complex Numbers and Why Slopes
  402.    wt: 4:   Chapter 1 Introduction
  403.    wt: 4:   Chapter 24 Direct and Indirect Reason
  404.    wt: 4:   Chapter 21 Occurrence Tables
  405.    wt: 4:   Chapter 18 Sense and Knowledge
  406.    wt: 4:   Chapter 17 Objective Ways Trial and Error Discovery
  407.    wt: 4:   Chapter 16 Origins and Limitations of Rules and Patterns
  408.    wt: 4:   Chapter 15 Objective Processes
  409.    wt: 4:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  410.    wt: 4:   Chapter 12 Islands and Divisions of Knowledge
  411.    wt: 4:   Chapter 10 Responsibility
  412.    wt: 4:   Chapter 9 What is in Chapters 10 to 18
  413.    wt: 4:   Chapter 4 Implication Rules Forwards and Backwards
  414.    wt: 4:   Chapter 1 Introduction
  415.    wt: 4:   Appendix A Calculus with Proofs for Keen or Gifted
  416.    wt: 3:   Skills Chapter 4 Logic
  417.    wt: 3:   Skills Chapter 1 Arithmetic
  418.    wt: 3:   1 arithmetic with unsigned numbers
  419.    wt: 3:   Applied Maths Program14092009 POMME variant
  420.    wt: 3:   Mathematics Education Professors
  421.    wt: 3:   modern education
  422.    wt: 3:   grouping students according to ability
  423.    wt: 3:   Postscript 2007 01 10
  424.    wt: 3:   how letters appear
  425.    wt: 3:   Secondary Three Mathematics
  426.    wt: 3:   05 13 OldSiteEntrancePage
  427.    wt: 3:   04 29 New Mathematics Curriculum
  428.    wt: 3:   04 25 when to stop or suspend mathemat
  429.    wt: 3:   02 21 words for teachers
  430.    wt: 3:   Education in mathematics science and technology
  431.    wt: 3:   cultivating intelligence
  432.    wt: 3:   chapitre 12 00 les iles et division
  433.    wt: 3:   chapitre 07 01 principle D induction mathematique
  434.    wt: 3:   chapitre 04 09 Regles accidentelles
  435.    wt: 3:   chapitre 04 08 Limitations et benefices
  436.    wt: 3:   chapitre 04 07 RepetablesEtReproductibles
  437.    wt: 3:   chapitre 04 06 engagements
  438.    wt: 3:   chapitre 04 05 Implication versus suggestion
  439.    wt: 3:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  440.    wt: 3:   chapitre 04 02 Deuxieme enigme
  441.    wt: 3:   chapitre 04 00 Les regles d implication
  442.    wt: 3:   chapitre 01 00 Introduction
  443.    wt: 3:   1 Conductance Resistance Duality01
  444.    wt: 3:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  445.    wt: 3:   Ages 10 to 12 Geometry
  446.    wt: 3:   Ages 10 to 12 Arithmetic
  447.    wt: 3:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  448.    wt: 3:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  449.    wt: 3:   sign monoticity analysis example 4
  450.    wt: 3:   sign monoticity analysis example 1
  451.    wt: 3:   7 Functions with finite domains
  452.    wt: 3:   10 quadratic exercises
  453.    wt: 3:   1 Calculator Starter Exercises
  454.    wt: 3:   7 Links Lessons Elsewhere
  455.    wt: 3:   4 Polynomials Long division linear divisor
  456.    wt: 3:   1 Polynomials Distributive Law
  457.    wt: 3:   16 cotangent function Definition Graph and Inverse
  458.    wt: 3:   15 cosecant function Definition Graph and Inverse
  459.    wt: 3:   13 cosecant function Definition Graph and Inverse
  460.    wt: 3:   12 motivation for term arctan
  461.    wt: 3:   10 arctan left inverse of tangent Definition
  462.    wt: 3:   9 motivation for name arcsin
  463.    wt: 3:   8 arcsin left inverse of sine Graph
  464.    wt: 3:   7 arcsin left inverse of sine Definition
  465.    wt: 3:   6 Graph of arccos function
  466.    wt: 3:   5 Swapping Coordinates is a reflection
  467.    wt: 3:   3 Left Inverse of cosine arccos definition
  468.    wt: 3:   2 cosine function more properties
  469.    wt: 3:   6 Vectors with Coordinates
  470.    wt: 3:   5 Head To Tail Arrow Addition
  471.    wt: 3:   3 Navigation with Arrows or Vectors
  472.    wt: 3:   4 graphing y=Asin(x c)
  473.    wt: 3:   1 graphing y=f(x a)
  474.    wt: 3:   SAS Method For Isometric Or Proportional Triangle Construction
  475.    wt: 3:   Analytic View of Triangle Construction or Line Instersection More
  476.    wt: 3:   Straight Lines ASA Intersection Study More
  477.    wt: 3:   Straight Lines Instersection Solving Equations
  478.    wt: 3:   14 Straight Lines Equations General Case
  479.    wt: 3:   13 Straight Lines Finding Equations from 2 points
  480.    wt: 3:   11 Straight Lines Graphing y=mx
  481.    wt: 3:   10 Straight Lines through Origin Equations More
  482.    wt: 3:   1 Straight Lines Slope Concept
  483.    wt: 3:   35 sines and cosines of 2A 3A 4A 5A
  484.    wt: 3:   34 sines and cosines of 2A 3A 4A 5A
  485.    wt: 3:   19 Pythagorean Identity For sine and cosine functions
  486.    wt: 3:   18 sum of sinusoidal waves as a single wave
  487.    wt: 3:   17G Pythagorean Theorem Converse
  488.    wt: 3:   17F Law of cosines
  489.    wt: 3:   17E Trig Formulas for dot and cross Products
  490.    wt: 3:   17D cis formulas for sine cosines and tangent
  491.    wt: 3:   17C sine and cosine double triple angle formulas
  492.    wt: 3:   17B sine cosine Angle Sum Formulas via cis
  493.    wt: 3:   17A The complex number valued trig function cis
  494.    wt: 3:   15 sine cosine Complementary Angle Relations
  495.    wt: 3:   13 Graph of tangent function many periods
  496.    wt: 3:   11 tangent function undefined when terminal side vertical
  497.    wt: 3:   1 Angle Measurement with Degrees
  498.    wt: 3:   10 Similarity of Triangles Equivalent of Two Criteria
  499.    wt: 3:   3 Similarity by Design with coordinates
  500.    wt: 3:   9 Midpoint Coordinates Half Endpoint Sum
  501.    wt: 3:   8 Mid Point Formula
  502.    wt: 3:   7 Exercises to test skill and concept mastery
  503.    wt: 3:   6 Intersection of lines by solving linear systems
  504.    wt: 3:   5 Algebraic View of Slopes
  505.    wt: 3:   3 Slope product for perpendicular lines
  506.    wt: 3:   2 point slope equation for a line
  507.    wt: 3:   What is and is not here
  508.    wt: 3:   18 Triangle Similarity Take 1
  509.    wt: 3:   15 Triangle Angle Sum is 180 degrees
  510.    wt: 3:   A Measurement with Ruler Proper Use
  511.    wt: 3:   6 Figuring with Maps Not to Scale
  512.    wt: 3:   4 Angles on Maps Plans drawn to scale
  513.    wt: 3:   1 Length Measurement
  514.    wt: 3:   24 Signed Numbers Arithmmetic Properties
  515.    wt: 3:   21 Addition of Multiples of a Single Vector
  516.    wt: 3:   19 Signed Multiples of Vectors
  517.    wt: 3:   18 Geometrically Why Vector Addition Commutes
  518.    wt: 3:   16 Collinear Horizontal Arrows Vectors
  519.    wt: 3:   15 Head to Tails in place Addition Associative
  520.    wt: 3:   13 Arrows and Vectors in a Plane
  521.    wt: 3:   12 Real Numbers Line Signed Coordinates
  522.    wt: 3:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  523.    wt: 3:   8 Division and Mulplication of Compound Fractions
  524.    wt: 3:   6 Infinite Decimals Ending in 9 repeating
  525.    wt: 3:   3 Location of Point in Decimal Multiplication
  526.    wt: 3:   2 Counting Digits in Decimal Multiplication
  527.    wt: 3:   4 Rectangle Area and Like Formulas Backwards
  528.    wt: 3:   1 Changing Calculations
  529.    wt: 3:   4 Subtraction and Division Axioms
  530.    wt: 3:   1 Equivalent Computation Rules
  531.    wt: 3:   4 Comparison of Negative Numbers
  532.    wt: 3:   3 More and Less Than with Unlike Signs
  533.    wt: 3:   1 Real Numbers Comparison
  534.    wt: 3:   16 Real Numbers Comparison
  535.    wt: 3:   15 Real Number Division
  536.    wt: 3:   13 Real Number Subtraction
  537.    wt: 3:   12 Real Number Additive Inverses or Negatives
  538.    wt: 3:   10 Real Number Lengths and Signs
  539.    wt: 3:   9 Coordinates for Regions in Space
  540.    wt: 3:   8 Coordinates for Maps and Planes
  541.    wt: 3:   7 Real Numbers as Line Cordinates
  542.    wt: 3:   6 Unsigned Real Numbers
  543.    wt: 3:   4 Rational Numbers
  544.    wt: 3:   1 Whole and Natural Numbers
  545.    wt: 3:   Simple Exercises
  546.    wt: 3:   2 Essentially one exercises three with solution
  547.    wt: 3:   Using Letters for Physical Quantities
  548.    wt: 3:   4 Circle Area Formula Example
  549.    wt: 3:   1 Written work formats for developing and showing skill
  550.    wt: 3:   6 Three Notions of What is a Variable
  551.    wt: 3:   5 Talking about Numbers and Quantities
  552.    wt: 3:   3 Adding Words To Arithmetic
  553.    wt: 3:   2 What is a Variable
  554.    wt: 3:   5 Counting with Tables Trees Product Rule Take II
  555.    wt: 3:   3 Counting with Tables and Trees II
  556.    wt: 3:   2 Counting with Tables and Trees I
  557.    wt: 3:   1 Counting and Counting Methods I
  558.    wt: 3:   9 subtracting signed numbers
  559.    wt: 3:   8 multiplying signed numbers
  560.    wt: 3:   7 negative and additive inverse
  561.    wt: 3:   6 adding signed numbers
  562.    wt: 3:   5 lengths and signs of numbers
  563.    wt: 3:   3 signed coordinates for maps and planes
  564.    wt: 3:   2 signed and unsigned numbers as coordinates
  565.    wt: 3:   9 Improper Fractions and Mixed Numbers
  566.    wt: 3:   8 Numerals Fractionals Quantals Take II
  567.    wt: 3:   7 Numerals Fractionals Quantals
  568.    wt: 3:   6 Multiplication of Mixed Numbers
  569.    wt: 3:   6 Multiplication Algebraically Take II
  570.    wt: 3:   5 Equivalent Fractions
  571.    wt: 3:   3 Unit fraction of a fraction
  572.    wt: 3:   2 Unit Fraction Multiplication
  573.    wt: 3:   A Associative Law Theorectical Note
  574.    wt: 3:   3 Adding Movements with same direction
  575.    wt: 3:   9 video Prime Factorization upto 19 squared
  576.    wt: 3:   8 video Prime Factorization upto 19
  577.    wt: 3:   2 Prime and Composites less than 16
  578.    wt: 3:   B Powers of Ten
  579.    wt: 3:   A Elementary Basis for Multiplication Methods
  580.    wt: 3:   6 Multiplication Commutes Order Not Important
  581.    wt: 3:   5 Decimal Fraction Multiplication
  582.    wt: 3:   3 More One Digit Multipliers
  583.    wt: 3:   2 One Digit Multipliers
  584.    wt: 3:   Appendix 2 Three Decimal Subtraction Methods
  585.    wt: 3:   9 22 Minute Subtraction Review Video
  586.    wt: 3:   5 A Tip for Efficent Subtraction
  587.    wt: 3:   3 Harder Cases Convert to Compare and Subtract
  588.    wt: 3:   2 Subtraction Easy Case Examples
  589.    wt: 3:   Formula Evaluation how to show work
  590.    wt: 3:   The 12 Times Table Visually
  591.    wt: 3:   016 Numbering Occidental Calendar Days
  592.    wt: 3:   015 School and work day counting tables
  593.    wt: 3:   013 Travel Time Tables
  594.    wt: 3:   012 Division of Time Intervals by Time Intervals
  595.    wt: 3:   010 Repeated Addition of Time Intervals
  596.    wt: 3:   G.2 Lipshitz Conditions Integration Calculus Reform
  597.    wt: 3:   G.3 Constant Difference Theorem Proof
  598.    wt: 3:   G.2 Differentiable Functions Mean Value Theorem
  599.    wt: 3:   F.5a Equicontinuity Theorems
  600.    wt: 3:   F.2 Closed Range Theorem
  601.    wt: 3:   F.1 What Functions are Continuous
  602.    wt: 3:   E1 Error Control Inequalities
  603.    wt: 3:   D1 Sets and Sequences GLBs and LGBs
  604.    wt: 3:   C Triangle Inequalities
  605.    wt: 3:   B1 Pigeon Hole Principles from combinatorics
  606.    wt: 3:   PostScript For and Against Decimal Perspectives
  607.    wt: 3:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  608.    wt: 3:   Chapter 9 About First Courses in Calculus
  609.    wt: 3:   Foreword
  610.    wt: 3:   Appendix E. How To Study Mathematics and Why
  611.    wt: 3:   Appendix C. How to Read
  612.    wt: 3:   Appendix B. How To Learn
  613.    wt: 3:   Chapter 26 What is in chapters 27 to 31
  614.    wt: 3:   Postscript Unifying Theme A Fourth Skill For Algebra
  615.    wt: 3:   Solutions For Arithmetic Exercises
  616.    wt: 3:   Chapter 7 Prep for Calculus Arithmetic Exercises
  617.    wt: 3:   Annotated Links to Material Elsehwere
  618.    wt: 3:   Postscript A Three Remarks
  619.    wt: 3:   Chapter 3 What is in chapters 4 to 8
  620.    wt: 3:   Chapter 7 Calculus Previews and Calculus Lightly
  621.    wt: 3:   Chapter 4 Logic for Reading Writing and Geometry etc
  622.    wt: 3:   Chapter 3 Algebra Starter Lessons
  623.    wt: 3:   Chapter 1 Arithmetic
  624.    wt: 3:   4 Money Matters Saving Earning Buying Selling and Budgets
  625.    wt: 3:   1 From Number Recognition and Counting to Arithmetic B
  626.    wt: 3:   1 From Number Recognition and Counting to Arithmetic A
  627.    wt: 3:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  628.    wt: 3:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  629.    wt: 2:   Skills Chapter 5 Calculus
  630.    wt: 2:   10 statistics
  631.    wt: 2:   4 algebra
  632.    wt: 2:   which way to go
  633.    wt: 2:   Teach the teachers plus goals
  634.    wt: 2:   activities for students
  635.    wt: 2:   site eurekas
  636.    wt: 2:   key notes and themes
  637.    wt: 2:   teacher certification
  638.    wt: 2:   learning takes time
  639.    wt: 2:   what should be learnt and When
  640.    wt: 2:   five decades make a difference
  641.    wt: 2:   Maps Plans Drawings
  642.    wt: 2:   Secondary Two Mathematics
  643.    wt: 2:   geometric implications for algebra
  644.    wt: 2:   the trouble with algebra
  645.    wt: 2:   02 20 mathematics education references
  646.    wt: 2:   three aims for mathematics students
  647.    wt: 2:   standards for course material
  648.    wt: 2:   Operational Viewpoint to Value
  649.    wt: 2:   formal or informal peer review
  650.    wt: 2:   Theory of Knowledge
  651.    wt: 2:   mathematics instruction in general
  652.    wt: 2:   Different Kinds of Reasoning in maths
  653.    wt: 2:   three kinds of reason in mathematics
  654.    wt: 2:   Four ways to improve education reform
  655.    wt: 2:   Leaner mathematics curriculum
  656.    wt: 2:   chapitre 07 00 Des chaines plus longues de la raison
  657.    wt: 2:   chapitre 06 00 Chaines de la raison
  658.    wt: 2:   chapitre 05 00 Deception
  659.    wt: 2:   chapitre 03 A Propos Des Prochains Chapitre
  660.    wt: 2:   chapitre 02 00 La Communication des idees
  661.    wt: 2:   Quebec cahiers d apprentissage en mathematiques pour 4 16
  662.    wt: 2:   problemes responses
  663.    wt: 2:   D Energy Power04
  664.    wt: 2:   A Energy Power01
  665.    wt: 2:   F Wire Resistance Calculation04
  666.    wt: 2:   C Wire Resistance Calculation01
  667.    wt: 2:   B Wire Resistance Qualitative02
  668.    wt: 2:   A Wire Resistance Qualitative01
  669.    wt: 2:   2 Unlike resistors in parallel01
  670.    wt: 2:   1 Like resistors in series
  671.    wt: 2:   24 Standards For Skill Develoment Take II
  672.    wt: 2:   24 Standards For Skill Develoment
  673.    wt: 2:   19 Extending the Oral Dimension of Mathematics
  674.    wt: 2:   18 Primary School Mathematics
  675.    wt: 2:   17 Math Booklets for children and young teenagers
  676.    wt: 2:   16 Secondary Mathematics Tips
  677.    wt: 2:   15 Counting For Parents
  678.    wt: 2:   13 Addition and Addition Tables
  679.    wt: 2:   12 Goals and Objectives For Mathematics
  680.    wt: 2:   10 Ends values for work study instruction
  681.    wt: 2:   4 Learning Takes Time and Effort
  682.    wt: 2:   1 Speaking Skills
  683.    wt: 2:   Ages 4 plus to 5 plus
  684.    wt: 2:   26 Function definitions done and coming
  685.    wt: 2:   25 Absolute Value greatest integer and saw tooth functions
  686.    wt: 2:   23 Inverse Functions
  687.    wt: 2:   22 Square Root function graphically
  688.    wt: 2:   20 Interchanging coordinates a reflection
  689.    wt: 2:   9 Set theory term relation possible origins
  690.    wt: 2:   8 Set view of relations and functions
  691.    wt: 2:   6 Set Existence Formation and Notation
  692.    wt: 2:   5 Function notation for geometric transformations
  693.    wt: 2:   3 Formula or function graphing exercise
  694.    wt: 2:   2 Algebraic use of function notation
  695.    wt: 2:   Introduction Reading Guide
  696.    wt: 2:   4 quadratics difference of two squares
  697.    wt: 2:   1 quadratics graphing exercises
  698.    wt: 2:   10 Exponential Growth and Decay Models
  699.    wt: 2:   8 Notes for instructors or tutors
  700.    wt: 2:   6 Polynomial Operations and Equivalent Computation Rules
  701.    wt: 2:   5 Polynomials Long division Nonlinear divisor
  702.    wt: 2:   3 Polynomials Multiplication Addition
  703.    wt: 2:   2 Column Multiplication Method
  704.    wt: 2:   A Global Time and Navigation
  705.    wt: 2:   9 Head to Tail Coordinate View
  706.    wt: 2:   8 Parallel Vectors
  707.    wt: 2:   7 Coordinate Addition and Scalar Multiplication
  708.    wt: 2:   2 Signed Coordinates
  709.    wt: 2:   Vector and Complex Number Applet
  710.    wt: 2:   3 graphing y=f(x c) plus K
  711.    wt: 2:   2 Graphing y=Af(x) Vertical Scaling
  712.    wt: 2:   Construction Methods and Criteria for Isometric and Similar Triangles
  713.    wt: 2:   Straight Lines Intersection of
  714.    wt: 2:   12 Straight Lines Graphing mx plus b
  715.    wt: 2:   4 Tangent Function Properties
  716.    wt: 2:   33 sines and cosines of 2A 3A 4A 5A
  717.    wt: 2:   32 seven rows of pascals triangle
  718.    wt: 2:   31 basic secant cosecant cotangent trig identities
  719.    wt: 2:   25 tangent double angle formula Slope connection
  720.    wt: 2:   24 tangent Angle Difference Formula
  721.    wt: 2:   23 sine and cosine of 180 plus 22.5 degrees
  722.    wt: 2:   22 sine of 22.5 degrees via half angle formulas
  723.    wt: 2:   21 sine and cosine Half Angle Formulas
  724.    wt: 2:   20 sine and cosine Double Angle Formulas
  725.    wt: 2:   12 Graph of tangent function for one period
  726.    wt: 2:   10 Graphs of sines and cosines many periods
  727.    wt: 2:   7 period of sine and cosine
  728.    wt: 2:   21 Logarithms Powers and Exponentials
  729.    wt: 2:   19 N th Roots of Unity
  730.    wt: 2:   18 Sixth Roots of Unity
  731.    wt: 2:   17 Cube Roots of unity
  732.    wt: 2:   16 References and Originality Question
  733.    wt: 2:   15 Pythagorean Theorem Converse
  734.    wt: 2:   13 Trig Formulas for dot and cross Products
  735.    wt: 2:   12 cis formulas for sine cosines and tangent
  736.    wt: 2:   10 sine cosine Angle Sum Formulas via cis
  737.    wt: 2:   4 Multiplication Properties
  738.    wt: 2:   1 Rectangular Polar Coordinates Review
  739.    wt: 2:   13 Navigation Location from Angles to 2 Landmarks
  740.    wt: 2:   12 Triangles Similarity More Problems
  741.    wt: 2:   8 Similarity of Triangles and Polygons
  742.    wt: 2:   1 Early Concept of Like or Similar Shapes
  743.    wt: 2:   13 Pythagorean spatial distance formulas
  744.    wt: 2:   12 Spatial Coordinates
  745.    wt: 2:   10 Pythagorean plane distance formula
  746.    wt: 2:   4 Polar Coordinates to and from
  747.    wt: 2:   1 Cartesian Coordinates sans signs
  748.    wt: 2:   PS D Addition with Cartesian Coordinates
  749.    wt: 2:   21 Parallelograms
  750.    wt: 2:   19 Right Triangle Similarity
  751.    wt: 2:   17 Right Bisectors of Triangle Sides
  752.    wt: 2:   16 Angles Subtended By Chords and Diameters
  753.    wt: 2:   13 Angle Side Angle Failure
  754.    wt: 2:   12 Side Angle Side Failure
  755.    wt: 2:   10 Dropping a perpendicular to line
  756.    wt: 2:   4 Side Side Side
  757.    wt: 2:   1 Initial Concepts and Terms
  758.    wt: 2:   8 More Use of Maps Not Drawn to Scale
  759.    wt: 2:   5 Drawing to Scale Avoids Angle Distortions
  760.    wt: 2:   3 Lengths and Areas on Maps and Plans
  761.    wt: 2:   2 Measuring Area Directly
  762.    wt: 2:   musings do not puiblish real numbers
  763.    wt: 2:   A Signed Number Arithmetic Review
  764.    wt: 2:   26 More Less Greater Than Comparison
  765.    wt: 2:   25 Mid way Convergence to Axiomatic Approach
  766.    wt: 2:   23 Distributive Law Two Derivations
  767.    wt: 2:   22 Multiplication of Signed Numbers
  768.    wt: 2:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  769.    wt: 2:   E Long Division Methods more
  770.    wt: 2:   D Long Division Methods
  771.    wt: 2:   C Three Decimal Subtraction Methods
  772.    wt: 2:   B Decimal Comparison and Subtraction
  773.    wt: 2:   A Decimal Addition Columm Methods
  774.    wt: 2:   8 Column Multiplication Methods in General
  775.    wt: 2:   7 Decimals Multiplication Methods Examples
  776.    wt: 2:   6 Column Methods for Decimal Multiplication
  777.    wt: 2:   5 Distributive Law for Whole Numbers
  778.    wt: 2:   3 Multiplicative Counting Skills Principles
  779.    wt: 2:   2 Combing Counts Addition Skills and Principles
  780.    wt: 2:   5 Proportionality in Equivalent Fractions
  781.    wt: 2:   3 Proportionality Examples
  782.    wt: 2:   2 Algebraic View
  783.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  784.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  785.    wt: 2:   7 Pythagorean Theorem Chinese Square Proof
  786.    wt: 2:   6 Compound Interest Forward and Backwards
  787.    wt: 2:   5 Triangle Area Formula Backwards
  788.    wt: 2:   3 Linear Equation Literal Solution More
  789.    wt: 2:   2 Linear Equation Literal Solution
  790.    wt: 2:   6 Equations and Systems Equivalent or Implied
  791.    wt: 2:   5 Equality in Algebra
  792.    wt: 2:   3 Product Axioms Two Forms
  793.    wt: 2:   2 Addition and Multiplication Axioms
  794.    wt: 2:   5 Greater More Less Than Signs in General
  795.    wt: 2:   2 More and Less Than for Counts and Measures
  796.    wt: 2:   5 Rational Numbers More
  797.    wt: 2:   3 Fractions
  798.    wt: 2:   2 Integers
  799.    wt: 2:   More Exercises
  800.    wt: 2:   3 Solving triangular system example
  801.    wt: 2:   6 Algebraic Solution Example
  802.    wt: 2:   5 Algebraic Solutions Introduction
  803.    wt: 2:   3 Four Examples
  804.    wt: 2:   2 Three Examples
  805.    wt: 2:   Formula Usage Show Work Format
  806.    wt: 2:   9 Volume of Cone
  807.    wt: 2:   8 Compound Interest Formula Evaluation
  808.    wt: 2:   7 Compound Interest Formula Introduction
  809.    wt: 2:   6 Pythagorean Hypotenuse Calculation Example
  810.    wt: 2:   5 Box Volume Formula Example
  811.    wt: 2:   3 Triangle Area Formula Example
  812.    wt: 2:   2 Another Rectangle Area Formula Example
  813.    wt: 2:   About Folder Contents
  814.    wt: 2:   arithmetic videos Real Player Format
  815.    wt: 2:   D Three Term Ratios
  816.    wt: 2:   C Equality for Fractions and Two Term Ratios and Fractions
  817.    wt: 2:   B Fractions and Two Term Ratios
  818.    wt: 2:   A Similarities between Fractions and Two Term Ratios
  819.    wt: 2:   Fraction Operations by Raising Terms A Simple Innovation
  820.    wt: 2:   9 Multiplying Integers
  821.    wt: 2:   8 Multiplication by Signed Numbers Integers
  822.    wt: 2:   7 Multiplication by Signs
  823.    wt: 2:   6 Multiplication by Natural Numbers
  824.    wt: 2:   5 Zero Movement and Additive Inverses
  825.    wt: 2:   2 Integers Multiplies of a Unit Moverment
  826.    wt: 2:   20 Uniqueness of Prime Factorization
  827.    wt: 2:   7 Calculator Usage Notes and Cautions
  828.    wt: 2:   6 Sieve of Eratosthenes and Square Rule
  829.    wt: 2:   5 Prime Factorization and a Square Rule
  830.    wt: 2:   3 video Primes and Composites from 9 times table
  831.    wt: 2:   Quick history of numbers and algebra
  832.    wt: 2:   Exact Arithmetic Wholes and Fractions
  833.    wt: 2:   Expression Evaluation how to show work
  834.    wt: 2:   The 20 Times Table
  835.    wt: 2:   Practical Methods Ends and Values for Arithmetic
  836.    wt: 2:   About folder contents
  837.    wt: 2:   4 Mixing and Changing Units of Time
  838.    wt: 2:   1 Intro of Kids To Time Date Skills
  839.    wt: 2:   Postscript One Sided and Intermediate Value Theorems
  840.    wt: 2:   G.6 Bounded Derivatives implies Lipshitz Continuity
  841.    wt: 2:   E2 Algebraic Properties of Limits
  842.    wt: 2:   D2 Limits of Monotone Sequences
  843.    wt: 2:   B3 Bolzano Weierstrass Theorem
  844.    wt: 2:   Postscript Pythagorean Theorem yet another proof
  845.    wt: 2:   Chapter 23 Links To Trigonometry
  846.    wt: 2:   Chapter 22 Complex Numbers
  847.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  848.    wt: 2:   Chapter 8. Slope Interpretation
  849.    wt: 2:   Chapter 7 Slopes and Velocity
  850.    wt: 2:   Chapter 6. Slopes and Vertical Shifts
  851.    wt: 2:   Chapter 5. Slope Sign Tests
  852.    wt: 2:   Chapter 3. Slope Sign Analysis
  853.    wt: 2:   Chapter 2. Slopes and Ski Trails
  854.    wt: 2:   Postscript More on Better Performance
  855.    wt: 2:   Postscript For Better Performance
  856.    wt: 2:   Chapter 30 Truth Tables
  857.    wt: 2:   Chapter 29 Contrapositive and Vacuously True Implications
  858.    wt: 2:   Chapter 28 Occurrence Tables
  859.    wt: 2:   Chapter 27 Shorthand Symbols as Pronouns
  860.    wt: 2:   Chapter 25. Mathematical Induction Examples
  861.    wt: 2:   Chapter 23. Notation For Sums
  862.    wt: 2:   Chapter 22. Geometric Sums and Sequences
  863.    wt: 2:   Chapter 20. Degrees and Radians
  864.    wt: 2:   Postscript What is a Variable
  865.    wt: 2:   Chapter 9 Talking about Numbers or Quantities
  866.    wt: 2:   Chapter 8 Three Skills For Algebra
  867.    wt: 2:   Chapter 6 Change of Language
  868.    wt: 2:   Chapter 5 Islands and Divisions of Knowledge
  869.    wt: 2:   Chapter 3 Chains of Reason
  870.    wt: 2:   Chapter 2 Implication Rules Forwards and Backwards
  871.    wt: 2:   Foreword
  872.    wt: 2:   Chapter 9 The Two Ends
  873.    wt: 2:   Chapter 8 Modern Instruction
  874.    wt: 2:   Chapter 7 Two Treatments of Geometry
  875.    wt: 2:   Chapter 6 Rule Based Reason in Mathematics
  876.    wt: 2:   Chapter 5 Four References
  877.    wt: 2:   Chapter 3 Algebra Difficulties
  878.    wt: 2:   Chapter 2 For and Against Mathematics
  879.    wt: 2:   Foreword
  880.    wt: 2:   Postscript D Reflections on Law of the Excluded Middle
  881.    wt: 2:   Postscript C Consistency as a Tool for Reason
  882.    wt: 2:   Postscript B More on Story Telling and Reason
  883.    wt: 2:   Postscript A Story Telling
  884.    wt: 2:   Chapter 23 Truth Tables
  885.    wt: 2:   Chapter 22 Contrapositive and Vacuously True Implications
  886.    wt: 2:   Chapter 20 Shorthand Symbols as Pronouns
  887.    wt: 2:   Chapter 8 Change of Language
  888.    wt: 2:   Chapter 7 Longer Chains of Reason
  889.    wt: 2:   Chapter 6 Chains of Reason
  890.    wt: 2:   Chapter 5 Deception
  891.    wt: 2:   Chapter 2 Skill Development
  892.    wt: 2:   Three Remarks
  893.    wt: 2:   Foreword
  894.    wt: 2:   1 Links to Online Resources Elsewhere Take 1
  895.    wt: 2:   P Exact Arithmetic With Whole Numbers and Fractions
  896.    wt: 2:   N Mathematics Prepare for College Studies
  897.    wt: 2:   L Skills with take home value
  898.    wt: 2:   N Improving Marks on Tests and Finals
  899.    wt: 2:   D. Check work a must with a caution
  900.    wt: 2:   Primary and Secondary Skills and Practices with Take Home Value
  901.    wt: 2:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  902.    wt: 2:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  903.    wt: 2:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  904.    wt: 1:   Appendix 2 primary school Arithmetic 01
  905.    wt: 1:   Appendix 1 primary and preschool mathematic
  906.    wt: 1:   K LAMP Musings Science Education
  907.    wt: 1:   J LAMP Introduction Extrinsic Origins
  908.    wt: 1:   I LAMP Introduction Study Habits
  909.    wt: 1:   H LAMP Introduction Instructional Concepts
  910.    wt: 1:   G LAMP Introduction Problem Solving Skills
  911.    wt: 1:   F LAMP Introduction Prerequisites
  912.    wt: 1:   E LAMP Introduction Modern Mathematics
  913.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  914.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  915.    wt: 1:   A Introduction Objectives
  916.    wt: 1:   Ramblings Extrinsic numbers theory
  917.    wt: 1:   Ramblings Introduction Algebra Essay
  918.    wt: 1:   Skills Chapter 3 Algebra
  919.    wt: 1:   Skills Chapter 2 Geometry
  920.    wt: 1:   Skills Chapter 0 Introduction
  921.    wt: 1:   2 arithmetic with signed numbers
  922.    wt: 1:   why bother
  923.    wt: 1:   website reviews
  924.    wt: 1:   three goals to set for students
  925.    wt: 1:   permissions for teachers
  926.    wt: 1:   Math Ed if it must be short make it lean effective
  927.    wt: 1:   links Education Resources online
  928.    wt: 1:   site origins
  929.    wt: 1:   About site lesson plans
  930.    wt: 1:   mathematics in context
  931.    wt: 1:   Education Reform Inconsistencies
  932.    wt: 1:   Secondary One Mathematics
  933.    wt: 1:   talk the algebra talk
  934.    wt: 1:   three difficulties
  935.    wt: 1:   teaching tips
  936.    wt: 1:   What to Tell Students
  937.    wt: 1:   mathematics curriculum shifts
  938.    wt: 1:   teaching tutoring algebraic reason
  939.    wt: 1:   Lessening Algebra Difficulties
  940.    wt: 1:   three goals for Mathematics Education
  941.    wt: 1:   How to be a better instructor
  942.    wt: 1:   Motivation and Context Problem
  943.    wt: 1:   need for a mixed mathematics curriculum
  944.    wt: 1:   Prequel In For A Penny In For A Pound
  945.    wt: 1:   education an empirical art
  946.    wt: 1:   fairness and inductive principles for instruction
  947.    wt: 1:   words for mathematics instructor
  948.    wt: 1:   problemes algebre et arithmetique
  949.    wt: 1:   4 Energy Power Heat09
  950.    wt: 1:   1 Energy Power Heat06
  951.    wt: 1:   E Wire Resistance Calculation03
  952.    wt: 1:   D Wire Resistance Calculation02
  953.    wt: 1:   3 Like resistors in parallel
  954.    wt: 1:   G Series Circuit01
  955.    wt: 1:   C Electromotive force conventional current02
  956.    wt: 1:   B Electromotive force conventional current01
  957.    wt: 1:   A Circuit Elements
  958.    wt: 1:   Home Tutoring and Home Schooling
  959.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  960.    wt: 1:   Ages 9 to 10
  961.    wt: 1:   Ages 3 plus to 4 plus
  962.    wt: 1:   sign monoticity analysis example 3
  963.    wt: 1:   sign monoticity analysis example 2
  964.    wt: 1:   9 quadratics physical and further context
  965.    wt: 1:   8 quadratics backward use of various formulas
  966.    wt: 1:   7 quadratic formulla derivation
  967.    wt: 1:   6 quadratics numerical approach
  968.    wt: 1:   5 quadratics completing the square
  969.    wt: 1:   3 quadratics factoring by inspection
  970.    wt: 1:   2 quadratics graphing in general
  971.    wt: 1:   Quadratics in 10 steps
  972.    wt: 1:   9 Formulas for Real Exponents with Logarithms
  973.    wt: 1:   8 Formulas for Fractional Exponents with Logarithms
  974.    wt: 1:   7 Formulas for Roots with Logarithms Derivation
  975.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  976.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  977.    wt: 1:   C Straight Lines Slope from Coordinates
  978.    wt: 1:   B Straight Line Slope Scaling Properties More
  979.    wt: 1:   A Straight Line Slope Scaling Properties
  980.    wt: 1:   9 Straight Lines through Origin Equations
  981.    wt: 1:   8 Straight Lines Equation for vertical
  982.    wt: 1:   7 Tangent Function is odd on this domain
  983.    wt: 1:   6 Tangent Function Inclination Angle Take 2
  984.    wt: 1:   5 Tangent Function Graph
  985.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  986.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  987.    wt: 1:   30 unit circle calculation of six trigonometric functions
  988.    wt: 1:   29 secant cosecant and cotangent for acute angles
  989.    wt: 1:   28 Expressing products of sines cosines as sums
  990.    wt: 1:   27 Logarithmic use of products of sines and cosines
  991.    wt: 1:   26 Formulas for products of sines and cosines
  992.    wt: 1:   9 Graphs of sine and cosine over one period
  993.    wt: 1:   8 period of tangent function
  994.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  995.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  996.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  997.    wt: 1:   1 Unit Points Reflections Rotations
  998.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  999.    wt: 1:   7 Translations Rotations Reflections Dilatations
  1000.    wt: 1:   6 Geometric Diagrams in Class
  1001.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  1002.    wt: 1:   2 Similarity By Design
  1003.    wt: 1:   2 Cartesian Coordinates with signs
  1004.    wt: 1:   PS E Multiplication with Polar Coordinates
  1005.    wt: 1:   PS A Kite Construction Methods
  1006.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  1007.    wt: 1:   8 Addition of Time Intervals via subtotaling
  1008.    wt: 1:   7 Addition of Time Intervals
  1009.    wt: 1:   6 How long is a million seconds
  1010.    wt: 1:   5 Conversion Arithmetic
  1011.    wt: 1:   3 Units and Lengths of Time
  1012.    wt: 1:   2 Time and Date Matters in School
  1013.    wt: 1:   S Adding words to algebra
  1014.    wt: 1:   R Why Learn Mathematics Skills
  1015.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  1016.    wt: 1:   O On Learning Mathematics and Science
  1017.    wt: 1:   M Words to extend arithmetic
  1018.    wt: 1:   J. More on written work and showing skill
  1019.    wt: 1:   A. Skill has to be seen to believed
  1020.    wt: 1:   Chapter 8 Skipped Topics and Why
  1021.    wt: 1:   Chapter 6 More Algebra and Geometry
  1022.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  1023.    wt: 1:   Chapter 2 Why Sets
  1024.    wt: 1:   7 Games and Activities for Instruction
  1025.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  1026.    wt: 1:   5 Interpreting and Drawing Maps and Plans.
  1027.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  1028.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  1029.    wt: 1:   Mathematics Education References
  1030.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  1031.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  1032.    wt: 1:   More Algebra and Slope based Calculus Preview
  1033.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  1034.    wt: 1:   The Math Forum and Site Content
  1035.    wt: 15:   10 Euclid Algorithm with 129 125 and with 45 14
  1036.    wt: 11:   14 GCD of 650 110 via Primes LCM via Product Rule
  1037.    wt: 11:   12 Limits with Parameters and Derivatives Take I
  1038.    wt: 11:   10 Three one sided limits with infinite values
  1039.    wt: 10:   4 Square Roots with primes more
  1040.    wt: 10:   1 Squares and Square Roots Introduction
  1041.    wt: 10:   1 Two cubic sketching exercises with 1st derivative
  1042.    wt: 10:   13 Limits with Parameters and Derivatives Take II
  1043.    wt: 10:   11 Limits at infinity Three Examples

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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