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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33 matches:

  1.    wt: 7:   1 Maps Plans Measurement/
  2.    wt: 6:   13 Vectors/
  3.    wt: 6:   8 Unit Circle Trigonometry/
  4.    wt: 6:   6 Trigonometry first steps/
  5.    wt: 5:   15 Arc or Inverse Trigonometric Function/
  6.    wt: 5:   14 Degrees to Radians and Radians to Degrees/
  7.    wt: 5:   12 Function Translating and Rescaling/
  8.    wt: 5:   11 Parallel Straight Lines and Transversals/
  9.    wt: 5:   10 Intersecting Straight Lines and Transversals/
  10.    wt: 5:   9 Lines and Slopes Take 2 with tangent function/
  11.    wt: 5:   7 Complex Numbers/
  12.    wt: 5:   5 What is Similarity/
  13.    wt: 5:   4 Lines and Slopes Take 1/
  14.    wt: 5:   3 Cartesian and Polar Coordinates/
  15.    wt: 5:   Geometry maps plans trigonometry vectors/
  16.    wt: 2:   D Decimal Long Division Methods/
  17.    wt: 2:   C Decimal Multiplication Methods/
  18.    wt: 2:   B Decimal Comparing and Subtracting Methods/
  19.    wt: 2:   A Decimal Counting and Adding Methods/
  20.    wt: 2:   2 Arithmetic with Decimals/
  21.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  22.    wt: 1:   11 Squares and Square Roots/
  23.    wt: 1:   10 LCM GCD and Euclid GCD Algorithm/
  24.    wt: 1:   9 Combinatorics Trees Tables and Products/
  25.    wt: 1:   8 Arithmetic with Signed Numbers/
  26.    wt: 1:   7 Arithmetic and Fractions with Units/
  27.    wt: 1:   6 Fractions and Ratios/
  28.    wt: 1:   5 Integers/
  29.    wt: 1:   4 Remainder Arithmetic and Divisibility/
  30.    wt: 1:   3 Prime Factorization Skills/
  31.    wt: 1:   1 Decimal Place Value/
  32.    wt: 1:   Arithmetic and Number Theory Skills/
  33.    wt: 11:   2 Euclidean Geometry Constructions Theory extras/

Web Page Search

56 matches:

  1.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  2.    wt: 2:   3 Euclidean Geometry Leanly
  3.    wt: 2:   Maps Plans Drawings
  4.    wt: 2:   1 Polynomials Distributive Law
  5.    wt: 2:   5 An Easy Proof of the Distributive Law
  6.    wt: 2:   Euclidean Geometry Elsewhere LINKS
  7.    wt: 2:   PS H Distributive Law For Complex Numbers
  8.    wt: 2:   Short Course on Euclidean Geometry
  9.    wt: 2:   4 Angles on Maps Plans drawn to scale
  10.    wt: 2:   3 Lengths and Areas on Maps and Plans
  11.    wt: 2:   23 Distributive Law Two Derivations
  12.    wt: 2:   5 Distributive Law for Whole Numbers
  13.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  14.    wt: 1:   Ramblings Extrinsic numbers theory
  15.    wt: 1:   Skills Chapter 2 Geometry
  16.    wt: 1:   8 analytic geometry etc
  17.    wt: 1:   About site lesson plans
  18.    wt: 1:   Theory of Knowledge
  19.    wt: 1:   E Kirchoffs Second Law
  20.    wt: 1:   D Kirchoff First Law
  21.    wt: 1:   Ages 12 to 14 Geometry
  22.    wt: 1:   Ages 10 to 12 Geometry
  23.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  24.    wt: 1:   9 Set theory term relation possible origins
  25.    wt: 1:   13 Velocity Vectors in Physics
  26.    wt: 1:   8 Parallel Vectors
  27.    wt: 1:   6 Vectors with Coordinates
  28.    wt: 1:   3 Navigation with Arrows or Vectors
  29.    wt: 1:   17F Law of cosines
  30.    wt: 1:   Unit Circle Development of Trigonometry
  31.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  32.    wt: 1:   14 Law of cosines
  33.    wt: 1:   8 Unit Circle Development of Trigonometry
  34.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  35.    wt: 1:   Why Trigonometry the whyslopes view
  36.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  37.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  38.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  39.    wt: 1:   6 Figuring with Maps Not to Scale
  40.    wt: 1:   19 Signed Multiples of Vectors
  41.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  42.    wt: 1:   13 Arrows and Vectors in a Plane
  43.    wt: 1:   4 Commutative Law Groups Counting Form
  44.    wt: 1:   8 Coordinates for Maps and Planes
  45.    wt: 1:   8 GCD from Euclidean Algorithm
  46.    wt: 1:   3 signed coordinates for maps and planes
  47.    wt: 1:   A Associative Law Theorectical Note
  48.    wt: 1:   Chapter 23 Links To Trigonometry
  49.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  50.    wt: 1:   Chapter 7 Two Treatments of Geometry
  51.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  52.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  53.    wt: 1:   Chapter 6 More Algebra and Geometry
  54.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  55.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  56.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics

Extended Search

488 matches:

  1.    wt: 9:   4 Angles on Maps Plans drawn to scale
  2.    wt: 9:   3 Lengths and Areas on Maps and Plans
  3.    wt: 8:   8 More Use of Maps Not Drawn to Scale
  4.    wt: 8:   6 Figuring with Maps Not to Scale
  5.    wt: 7:   13 Velocity Vectors in Physics
  6.    wt: 7:   8 Parallel Vectors
  7.    wt: 7:   6 Vectors with Coordinates
  8.    wt: 7:   3 Navigation with Arrows or Vectors
  9.    wt: 7:   2 Signed Coordinates
  10.    wt: 7:   17F Law of cosines
  11.    wt: 7:   Unit Circle Development of Trigonometry
  12.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  13.    wt: 7:   5 An Easy Proof of the Distributive Law
  14.    wt: 7:   6 Trigonometry Sines of Supplementary Angles
  15.    wt: 7:   2 Similar Triangles Equality of Corresponding Side Ratios
  16.    wt: 7:   Why Trigonometry the whyslopes view
  17.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  18.    wt: 7:   A Measurement with Ruler Proper Use
  19.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  20.    wt: 7:   2 Measuring Area Directly
  21.    wt: 7:   1 Length Measurement
  22.    wt: 6:   A Global Time and Navigation
  23.    wt: 6:   15 Dot and Cross Product
  24.    wt: 6:   14 Why Scalar Multiplication Distributes Physical Argument
  25.    wt: 6:   12 From Applied To Pure Mathematics
  26.    wt: 6:   11 Component Method
  27.    wt: 6:   10 Parallelogram Addition Method
  28.    wt: 6:   9 Head to Tail Coordinate View
  29.    wt: 6:   7 Coordinate Addition and Scalar Multiplication
  30.    wt: 6:   5 Head To Tail Arrow Addition
  31.    wt: 6:   4 Resultant of a Sum of Movements
  32.    wt: 6:   1 Unsigned Coordinates
  33.    wt: 6:   Vector and Complex Number Applet
  34.    wt: 6:   17 tangent function angle sum formulas
  35.    wt: 6:   35 sines and cosines of 2A 3A 4A 5A
  36.    wt: 6:   34 sines and cosines of 2A 3A 4A 5A
  37.    wt: 6:   33 sines and cosines of 2A 3A 4A 5A
  38.    wt: 6:   32 seven rows of pascals triangle
  39.    wt: 6:   31 basic secant cosecant cotangent trig identities
  40.    wt: 6:   30 unit circle calculation of six trigonometric functions
  41.    wt: 6:   29 secant cosecant and cotangent for acute angles
  42.    wt: 6:   28 Expressing products of sines cosines as sums
  43.    wt: 6:   27 Logarithmic use of products of sines and cosines
  44.    wt: 6:   26 Formulas for products of sines and cosines
  45.    wt: 6:   25 tangent double angle formula Slope connection
  46.    wt: 6:   24 tangent Angle Difference Formula
  47.    wt: 6:   23 sine and cosine of 180 plus 22.5 degrees
  48.    wt: 6:   22 sine of 22.5 degrees via half angle formulas
  49.    wt: 6:   21 sine and cosine Half Angle Formulas
  50.    wt: 6:   20 sine and cosine Double Angle Formulas
  51.    wt: 6:   19 Pythagorean Identity For sine and cosine functions
  52.    wt: 6:   18 sum of sinusoidal waves as a single wave
  53.    wt: 6:   17G Pythagorean Theorem Converse
  54.    wt: 6:   17E Trig Formulas for dot and cross Products
  55.    wt: 6:   17D cis formulas for sine cosines and tangent
  56.    wt: 6:   17C sine and cosine double triple angle formulas
  57.    wt: 6:   17B sine cosine Angle Sum Formulas via cis
  58.    wt: 6:   17A The complex number valued trig function cis
  59.    wt: 6:   16 Right Triangle Complementary Angle Relations
  60.    wt: 6:   15 sine cosine Complementary Angle Relations
  61.    wt: 6:   14 cosine even and sine and tangent are odd
  62.    wt: 6:   13 Graph of tangent function many periods
  63.    wt: 6:   12 Graph of tangent function for one period
  64.    wt: 6:   11 tangent function undefined when terminal side vertical
  65.    wt: 6:   10 Graphs of sines and cosines many periods
  66.    wt: 6:   9 Graphs of sine and cosine over one period
  67.    wt: 6:   8 period of tangent function
  68.    wt: 6:   7 period of sine and cosine
  69.    wt: 6:   6 sines and cosines for reference angle 30 degrees
  70.    wt: 6:   5 sines and cosines for reference angle 60 degrees
  71.    wt: 6:   4 sines and cosines for reference angle 45 degrees
  72.    wt: 6:   3 sines and cosines for reference angle 90 degrees
  73.    wt: 6:   2 Quadrant I reference Angles
  74.    wt: 6:   1 Unit Points Reflections Rotations
  75.    wt: 6:   14 Law of cosines
  76.    wt: 6:   8 Unit Circle Development of Trigonometry
  77.    wt: 6:   2 Complex Numbers made easier we hope
  78.    wt: 6:   8 Triangles Cascade Problem Solving
  79.    wt: 6:   7 Trignometric Ratios Unit Circle
  80.    wt: 6:   5 Trigonometric Ratios For Tangent and Special Triangles
  81.    wt: 6:   4 Trigonometric Ratios For Two Special Triangles
  82.    wt: 6:   3 Trigonometric Ratios sine and cosine
  83.    wt: 6:   1 Angle Measurement with Degrees
  84.    wt: 6:   2 point slope equation for a line
  85.    wt: 6:   2 Cartesian Coordinates with signs
  86.    wt: 5:   16 cotangent function Definition Graph and Inverse
  87.    wt: 5:   15 cosecant function Definition Graph and Inverse
  88.    wt: 5:   14 secant function Definition Graph and Inverse
  89.    wt: 5:   13 cosecant function Definition Graph and Inverse
  90.    wt: 5:   12 motivation for term arctan
  91.    wt: 5:   11 arctan left inverse of tangent Graph
  92.    wt: 5:   10 arctan left inverse of tangent Definition
  93.    wt: 5:   9 motivation for name arcsin
  94.    wt: 5:   8 arcsin left inverse of sine Graph
  95.    wt: 5:   7 arcsin left inverse of sine Definition
  96.    wt: 5:   6 Graph of arccos function
  97.    wt: 5:   5 Swapping Coordinates is a reflection
  98.    wt: 5:   4 possible motivation for term arccos
  99.    wt: 5:   3 Left Inverse of cosine arccos definition
  100.    wt: 5:   2 cosine function more properties
  101.    wt: 5:   1 cosine function properties
  102.    wt: 5:   9 Summary Degrees to Radians and back
  103.    wt: 5:   8 Radian Measures of Common Angles
  104.    wt: 5:   7 Radian Measures in special Triangles
  105.    wt: 5:   6 Radian Measure to Degrees
  106.    wt: 5:   5 Degrees to Radian Measure
  107.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  108.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  109.    wt: 5:   2 Radian Measure Numerical Value of one degree
  110.    wt: 5:   1 Degrees and Radians Introduction
  111.    wt: 5:   4 graphing y=Asin(x c)
  112.    wt: 5:   3 graphing y=f(x c) plus K
  113.    wt: 5:   2 Graphing y=Af(x) Vertical Scaling
  114.    wt: 5:   1 graphing y=f(x a)
  115.    wt: 5:   Parallel Lines and Parallel Transversals
  116.    wt: 5:   Proportionality of Line Segments From Parallel Transversals
  117.    wt: 5:   Triangle Angles Sum To 180 Degrees
  118.    wt: 5:   Parallel Lines and Alternating Corresponding Angles
  119.    wt: 5:   Parallel Lines and Interior Angles
  120.    wt: 5:   Construction Methods and Criteria for Isometric and Similar Triangles
  121.    wt: 5:   SAS Method For Isometric Or Proportional Triangle Construction
  122.    wt: 5:   Analytic View of Triangle Construction or Line Instersection More
  123.    wt: 5:   Straight Lines ASA Intersection Study More
  124.    wt: 5:   Straight Lines ASA Intersection Study
  125.    wt: 5:   Straight Lines Instersection Solving Equations
  126.    wt: 5:   Straight Lines Intersection of
  127.    wt: 5:   D Straight Lines Slope from Coordinates Examples
  128.    wt: 5:   C Straight Lines Slope from Coordinates
  129.    wt: 5:   B Straight Line Slope Scaling Properties More
  130.    wt: 5:   A Straight Line Slope Scaling Properties
  131.    wt: 5:   14 Straight Lines Equations General Case
  132.    wt: 5:   13 Straight Lines Finding Equations from 2 points
  133.    wt: 5:   12 Straight Lines Graphing mx plus b
  134.    wt: 5:   11 Straight Lines Graphing y=mx
  135.    wt: 5:   10 Straight Lines through Origin Equations More
  136.    wt: 5:   9 Straight Lines through Origin Equations
  137.    wt: 5:   8 Straight Lines Equation for vertical
  138.    wt: 5:   7 Tangent Function is odd on this domain
  139.    wt: 5:   6 Tangent Function Inclination Angle Take 2
  140.    wt: 5:   5 Tangent Function Graph
  141.    wt: 5:   4 Tangent Function Properties
  142.    wt: 5:   3 Straight Lines Slope as Tangent of Inclination Angle
  143.    wt: 5:   2 Straight Lines Slopes As Rise Over Run
  144.    wt: 5:   1 Straight Lines Slope Concept
  145.    wt: 5:   21 Logarithms Powers and Exponentials
  146.    wt: 5:   20 N th Roots of Complex Numbers
  147.    wt: 5:   19 N th Roots of Unity
  148.    wt: 5:   18 Sixth Roots of Unity
  149.    wt: 5:   17 Cube Roots of unity
  150.    wt: 5:   16 References and Originality Question
  151.    wt: 5:   15 Pythagorean Theorem Converse
  152.    wt: 5:   13 Trig Formulas for dot and cross Products
  153.    wt: 5:   12 cis formulas for sine cosines and tangent
  154.    wt: 5:   11 sine and cosine double triple angle formulas
  155.    wt: 5:   10 sine cosine Angle Sum Formulas via cis
  156.    wt: 5:   9 The complex number valued trig function cis
  157.    wt: 5:   7 Second Way to Calculate Products
  158.    wt: 5:   6 Field Properties of Complex Number
  159.    wt: 5:   4 Multiplication Properties
  160.    wt: 5:   3 Addition Properties
  161.    wt: 5:   1 Rectangular Polar Coordinates Review
  162.    wt: 5:   Appetizer A Complex Number Applet
  163.    wt: 5:   13 Navigation Location from Angles to 2 Landmarks
  164.    wt: 5:   12 Triangles Similarity More Problems
  165.    wt: 5:   11 Triangle Similarity Missing Side Problem
  166.    wt: 5:   10 Similarity of Triangles Equivalent of Two Criteria
  167.    wt: 5:   9 Similarity of Triangles Usual Criteria
  168.    wt: 5:   8 Similarity of Triangles and Polygons
  169.    wt: 5:   7 Translations Rotations Reflections Dilatations
  170.    wt: 5:   6 Geometric Diagrams in Class
  171.    wt: 5:   5 Similarity of Circles Squares and Rectangles
  172.    wt: 5:   4 Similarity Definition with Coordinate
  173.    wt: 5:   3 Similarity by Design with coordinates
  174.    wt: 5:   2 Similarity By Design
  175.    wt: 5:   1 Early Concept of Like or Similar Shapes
  176.    wt: 5:   Four Simple Exercises
  177.    wt: 5:   12 Links Lessons elsewhere
  178.    wt: 5:   11 A Partial Summary
  179.    wt: 5:   10 Midpoint of [a b] and [b a]
  180.    wt: 5:   9 Midpoint Coordinates Half Endpoint Sum
  181.    wt: 5:   8 Mid Point Formula
  182.    wt: 5:   7 Exercises to test skill and concept mastery
  183.    wt: 5:   6 Intersection of lines by solving linear systems
  184.    wt: 5:   5 Algebraic View of Slopes
  185.    wt: 5:   4 Equations for lines three forms
  186.    wt: 5:   3 Slope product for perpendicular lines
  187.    wt: 5:   1 Numerical view of lines and their equations
  188.    wt: 5:   What is and is not here
  189.    wt: 5:   13 Pythagorean spatial distance formulas
  190.    wt: 5:   12 Spatial Coordinates
  191.    wt: 5:   11 Triangle Inequality
  192.    wt: 5:   10 Pythagorean plane distance formula
  193.    wt: 5:   9 Pythagorean Theorem Chinese Square Proof
  194.    wt: 5:   8 Distance Between Points on a Line
  195.    wt: 5:   7 Complex Numbers Appetizer
  196.    wt: 5:   6 Polar Multiplication and Rotation
  197.    wt: 5:   5 Cartesian Addition and Translation
  198.    wt: 5:   4 Polar Coordinates to and from
  199.    wt: 5:   3 Rectangular Coordinates Review
  200.    wt: 5:   1 Cartesian Coordinates sans signs
  201.    wt: 5:   About Folder Contents
  202.    wt: 3:   2 Division with Single Digit Divisors
  203.    wt: 3:   2 One Digit Multipliers
  204.    wt: 3:   2 Subtraction Easy Case Examples
  205.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  206.    wt: 2:   3 Euclidean Geometry Leanly
  207.    wt: 2:   Maps Plans Drawings
  208.    wt: 2:   1 Polynomials Distributive Law
  209.    wt: 2:   23 Distributive Law Two Derivations
  210.    wt: 2:   5 Distributive Law for Whole Numbers
  211.    wt: 2:   2 More and Less Than with Unlike Signs
  212.    wt: 2:   8 GCD from Euclidean Algorithm
  213.    wt: 2:   3 signed coordinates for maps and planes
  214.    wt: 2:   A Associative Law Theorectical Note
  215.    wt: 2:   2 Integers Multiplies of a Unit Moverment
  216.    wt: 2:   2 Prime and Composites less than 16
  217.    wt: 2:   Long Division Backwards more
  218.    wt: 2:   Long Division Backward
  219.    wt: 2:   Division with Counts and Length
  220.    wt: 2:   Long Division forwards and backwards Example 3
  221.    wt: 2:   Long Division forwards and backwards Example 2
  222.    wt: 2:   Long Division forwards and backwards Example 1
  223.    wt: 2:   12 Why Long Division Works Take III
  224.    wt: 2:   11 Another Single Digit Divisor Example
  225.    wt: 2:   10 Division by Five Long and Short Ways
  226.    wt: 2:   9 Why Long Division Works Take II
  227.    wt: 2:   8 Correcting the Mistake
  228.    wt: 2:   7 Long Divison Mistake Catching
  229.    wt: 2:   6 Why Decimal Long Division Methods Works Take I
  230.    wt: 2:   5 Long Division Include Zeroes or not
  231.    wt: 2:   4 Division with 2 Digit Divsors
  232.    wt: 2:   3 Division Single Digit Divisor Example
  233.    wt: 2:   1 Divsion Physical Examples
  234.    wt: 2:   D Decimal Multiplication Methods Derived
  235.    wt: 2:   C Counting Areas with Powers of Ten
  236.    wt: 2:   B Powers of Ten
  237.    wt: 2:   A Elementary Basis for Multiplication Methods
  238.    wt: 2:   6 Multiplication Commutes Order Not Important
  239.    wt: 2:   5 Decimal Fraction Multiplication
  240.    wt: 2:   4 Two and Three Digit Multipliers
  241.    wt: 2:   3 More One Digit Multipliers
  242.    wt: 2:   Video Decimal Multiplication Geometric View Example 2
  243.    wt: 2:   Video Decimal Multiplication Geometric View Example 2
  244.    wt: 2:   Video Power Notation in Decimal Expansion
  245.    wt: 2:   1 Why 3 times 5 gives 15
  246.    wt: 2:   Appendix 2 Three Decimal Subtraction Methods
  247.    wt: 2:   Appendix 1 Decimals Comparison Method Take II
  248.    wt: 2:   Subtraction with J Conversions Example
  249.    wt: 2:   Subtraction Another Video Lesson
  250.    wt: 2:   9 22 Minute Subtraction Review Video
  251.    wt: 2:   8 Subtraction with Units of Measure
  252.    wt: 2:   7 Subtraction for Decimal Fractions with Exercises
  253.    wt: 2:   6 Subtraction with Conversion Example with Exercises
  254.    wt: 2:   5 A Tip for Efficent Subtraction
  255.    wt: 2:   4 Subtraction with Conversions Borrows and Letter J
  256.    wt: 2:   3 Harder Cases Convert to Compare and Subtract
  257.    wt: 2:   1 Comparison and Subtraction Easy Direct Cases
  258.    wt: 2:   Appendix 1 Counting Revisited 15 minute video
  259.    wt: 2:   8 What skills and work habits to require
  260.    wt: 2:   7 Adding decimal fractions using decimal point
  261.    wt: 2:   6. Counting and adding units and mixed units
  262.    wt: 2:   5. How to add decimals C. Examples
  263.    wt: 2:   4. How to add with decimals B with conversions
  264.    wt: 2:   3. How to add with decimals A sans conversions
  265.    wt: 2:   2 Decimal Counting Practices
  266.    wt: 2:   1. Explaining Addition Table
  267.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  268.    wt: 1:   Ramblings Extrinsic numbers theory
  269.    wt: 1:   Skills Chapter 2 Geometry
  270.    wt: 1:   8 analytic geometry etc
  271.    wt: 1:   About site lesson plans
  272.    wt: 1:   Theory of Knowledge
  273.    wt: 1:   2 Conductance Resistance Duality02
  274.    wt: 1:   E Kirchoffs Second Law
  275.    wt: 1:   D Kirchoff First Law
  276.    wt: 1:   2 Reading and Writing Skills
  277.    wt: 1:   Ages 12 to 14 Geometry
  278.    wt: 1:   Ages 10 to 12 Geometry
  279.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  280.    wt: 1:   20 Interchanging coordinates a reflection
  281.    wt: 1:   9 Set theory term relation possible origins
  282.    wt: 1:   19 Signed Multiples of Vectors
  283.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  284.    wt: 1:   13 Arrows and Vectors in a Plane
  285.    wt: 1:   4 Commutative Law Groups Counting Form
  286.    wt: 1:   2 Combing Counts Addition Skills and Principles
  287.    wt: 1:   2 Algebraic View
  288.    wt: 1:   8 Coordinates for Maps and Planes
  289.    wt: 1:   2 GE II Comparison
  290.    wt: 1:   2 Essentially one exercises three with solution
  291.    wt: 1:   2 Three Examples
  292.    wt: 1:   2 Three Examples
  293.    wt: 1:   arithmetic videos Real Player Format
  294.    wt: 1:   4 Greater More Less Than Signs in General
  295.    wt: 1:   3 Comparison of Negative Numbers
  296.    wt: 1:   1 More and Less Than for Counts and Measures
  297.    wt: 1:   5 Square Roots with primes more still
  298.    wt: 1:   4 Square Roots with primes more
  299.    wt: 1:   3 Properties of Square Roots with example
  300.    wt: 1:   2 Square Roots with Prime
  301.    wt: 1:   1 Squares and Square Roots Introduction
  302.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  303.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  304.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  305.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  306.    wt: 1:   13 GCD from given Prime Factorization
  307.    wt: 1:   11 GCD 2700 288 via Euclid Algorithm
  308.    wt: 1:   10 Euclid Algorithm with 129 125 and with 45 14
  309.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  310.    wt: 1:   7 GCD and LCM from prime factorization
  311.    wt: 1:   6 GCD from Prime
  312.    wt: 1:   5 Common Divisors 60 45 via Prime
  313.    wt: 1:   4 LCM of 8 and 10 via Prime
  314.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  315.    wt: 1:   2 Least Common Multiple LCM intro via list method
  316.    wt: 1:   1 Least Common Multiples LCM Introduction
  317.    wt: 1:   12 GCD 2700 288 via Prime
  318.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  319.    wt: 1:   4 Counting with Trees Product Rule Take I
  320.    wt: 1:   3 Counting with Tables and Trees II
  321.    wt: 1:   2 Counting with Tables and Trees I
  322.    wt: 1:   1 Counting and Counting Methods I
  323.    wt: 1:   11 What are real lengths and numbers
  324.    wt: 1:   10 dividing signed numbers
  325.    wt: 1:   9 subtracting signed numbers
  326.    wt: 1:   8 multiplying signed numbers
  327.    wt: 1:   7 negative and additive inverse
  328.    wt: 1:   6 adding signed numbers
  329.    wt: 1:   5 lengths and signs of numbers
  330.    wt: 1:   4 signed coordinates for regions in space
  331.    wt: 1:   2 signed and unsigned numbers as coordinates
  332.    wt: 1:   7 Converting or Changing Units
  333.    wt: 1:   6 Simplification of Fractions with Units
  334.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  335.    wt: 1:   4 Fractions with Units
  336.    wt: 1:   3 Multiplying Units and Numbers
  337.    wt: 1:   2 Equality and Units
  338.    wt: 1:   1 Addition and Subtraction with Units
  339.    wt: 1:   D Three Term Ratios
  340.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  341.    wt: 1:   B Fractions and Two Term Ratios
  342.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  343.    wt: 1:   22 Complex Compound Fractions
  344.    wt: 1:   21 Working With Signs
  345.    wt: 1:   21 Reciprocals for Fractions and Wholes
  346.    wt: 1:   20 Dividing Fractions the Why
  347.    wt: 1:   19 Dividing Fractions How TO
  348.    wt: 1:   18 Efficient Ways to Multiply
  349.    wt: 1:   17 Efficient Ways to Add and Subtract
  350.    wt: 1:   16 Addition Subtraction Comparision Compared
  351.    wt: 1:   15 Adding and Subtracting with Unlike Denominators
  352.    wt: 1:   14 Adding and Subtracting with Like Denominators
  353.    wt: 1:   13 Fraction Comparison Algebraic View
  354.    wt: 1:   12 Fraction Comparison
  355.    wt: 1:   11 Simplification an Algebraic View
  356.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  357.    wt: 1:   9 Improper Fractions and Mixed Numbers
  358.    wt: 1:   8 Numerals Fractionals Quantals Take II
  359.    wt: 1:   7 Numerals Fractionals Quantals
  360.    wt: 1:   6 Multiplication of Mixed Numbers
  361.    wt: 1:   6 Multiplication Algebraically Take II
  362.    wt: 1:   5 Equivalent Fractions
  363.    wt: 1:   4 Fraction Multiplication
  364.    wt: 1:   3 Unit fraction of a fraction
  365.    wt: 1:   2 Unit Fraction Multiplication
  366.    wt: 1:   1 What is a fraction Take II
  367.    wt: 1:   1 What is a fraction
  368.    wt: 1:   Fraction Operations by Raising Terms A Simple Innovation
  369.    wt: 1:   D Remainders Modulo 11 Pair Rule
  370.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  371.    wt: 1:   B Integer Long Division Multiple Choices
  372.    wt: 1:   13 Subtraction with Additive Inverse
  373.    wt: 1:   12 Adding Integers More Examples
  374.    wt: 1:   11 Adding Integers Formulas and Examples
  375.    wt: 1:   10 Integer Multiplication Formulas
  376.    wt: 1:   9 Multiplying Integers
  377.    wt: 1:   8 Multiplication by Signed Numbers Integers
  378.    wt: 1:   7 Multiplication by Signs
  379.    wt: 1:   6 Multiplication by Natural Numbers
  380.    wt: 1:   5 Zero Movement and Additive Inverses
  381.    wt: 1:   4 Adding Movements wiht opposite directions
  382.    wt: 1:   3 Adding Movements with same direction
  383.    wt: 1:   1 Integers as Coordinates
  384.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  385.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  386.    wt: 1:   26 Divisibility by 2 3 5 Example
  387.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  388.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  389.    wt: 1:   23 Remainder Arithmetic Modulo 2
  390.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  391.    wt: 1:   21 Remainder Arithmetic Modulo 3
  392.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  393.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  394.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  395.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  396.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  397.    wt: 1:   15 Remainder Arithmetic Modulo 9 Example
  398.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  399.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  400.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  401.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  402.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  403.    wt: 1:   9 Remainder Arithmetic Divisibility by 5
  404.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  405.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  406.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  407.    wt: 1:   5 Remainder Arithmetic Modulo 5
  408.    wt: 1:   4 Remainder Arithmetic Modulo 10 in general
  409.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  410.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  411.    wt: 1:   1 Remainder Arithmetic Modulo 10
  412.    wt: 1:   20 Uniqueness of Prime Factorization
  413.    wt: 1:   19 video Prime Factorization Unique
  414.    wt: 1:   18 video Count Factors given Prime Factorization
  415.    wt: 1:   17 Identify and Count Factors using Primes
  416.    wt: 1:   16 video Factors of 980 using prime
  417.    wt: 1:   15 video Factors of 20 using Prime Factorization
  418.    wt: 1:   14 video Factors of 24 Take II
  419.    wt: 1:   13 video Factors of 24 using prime
  420.    wt: 1:   12 LCD GCD and LCM using Primes
  421.    wt: 1:   11 Efficient Square Rule Use
  422.    wt: 1:   10 video Prime Factorization upto 23 squared
  423.    wt: 1:   9 video Prime Factorization upto 19 squared
  424.    wt: 1:   8 video Prime Factorization upto 19
  425.    wt: 1:   7 Calculator Usage Notes and Cautions
  426.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  427.    wt: 1:   5 Prime Factorization and a Square Rule
  428.    wt: 1:   4 video Prime Factorization Introduction
  429.    wt: 1:   3 video Primes and Composites from 9 times table
  430.    wt: 1:   1 video how Products are bigger than factor
  431.    wt: 1:   11 Place Value SI Standard International way
  432.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  433.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  434.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  435.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  436.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  437.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  438.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  439.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  440.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  441.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  442.    wt: 1:   Quick history of numbers and algebra
  443.    wt: 1:   Exact Arithmetic Wholes and Fractions
  444.    wt: 1:   Formula Evaluation how to show work
  445.    wt: 1:   Expression Evaluation how to show work
  446.    wt: 1:   The 20 Times Table
  447.    wt: 1:   The 12 Times Table Visually
  448.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  449.    wt: 1:   About folder contents
  450.    wt: 1:   Chapter 23 Links To Trigonometry
  451.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  452.    wt: 1:   Chapter 7 Two Treatments of Geometry
  453.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  454.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  455.    wt: 1:   Chapter 6 More Algebra and Geometry
  456.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  457.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  458.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  459.    wt: 13:   Euclidean Geometry Elsewhere LINKS
  460.    wt: 13:   PS H Distributive Law For Complex Numbers
  461.    wt: 13:   Short Course on Euclidean Geometry
  462.    wt: 12:   PS C Similarity Use Recognize it in Trigonometry
  463.    wt: 12:   2 Correspondence between Triangles
  464.    wt: 11:   PS G Rotation Distributes over Addition
  465.    wt: 11:   PS F Scalar Multiplication Distributes over Addition
  466.    wt: 11:   PS E Multiplication with Polar Coordinates
  467.    wt: 11:   PS D Addition with Cartesian Coordinates
  468.    wt: 11:   PS B Parallelogram Construction Methods
  469.    wt: 11:   PS A Kite Construction Methods
  470.    wt: 11:   21 Parallelograms
  471.    wt: 11:   19 Right Triangle Similarity
  472.    wt: 11:   18 Triangle Similarity Take 1
  473.    wt: 11:   17 Right Bisectors of Triangle Sides
  474.    wt: 11:   16 Angles Subtended By Chords and Diameters
  475.    wt: 11:   15 Triangle Angle Sum is 180 degrees
  476.    wt: 11:   14 Parallel Lines Postulate
  477.    wt: 11:   13 Angle Side Angle Failure
  478.    wt: 11:   12 Side Angle Side Failure
  479.    wt: 11:   11 Triangle Construction Fails
  480.    wt: 11:   10 Dropping a perpendicular to line
  481.    wt: 11:   9 Construction of a right bisector
  482.    wt: 11:   8 Isoceles Triangles
  483.    wt: 11:   7 Angle Side Angle
  484.    wt: 11:   6 Ruler and compass Angle Bisection
  485.    wt: 11:   5 Side Angle Side
  486.    wt: 11:   4 Side Side Side
  487.    wt: 11:   3 Isometry of Triangles Congruence
  488.    wt: 11:   1 Initial Concepts and Terms

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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