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: 6:   3 Cartesian and Polar Coordinates/
  6.    wt: 5:   15 Arc or Inverse Trigonometric Function/
  7.    wt: 5:   14 Degrees to Radians and Radians to Degrees/
  8.    wt: 5:   12 Function Translating and Rescaling/
  9.    wt: 5:   11 Parallel Straight Lines and Transversals/
  10.    wt: 5:   10 Intersecting Straight Lines and Transversals/
  11.    wt: 5:   9 Lines and Slopes Take 2 with tangent function/
  12.    wt: 5:   7 Complex Numbers/
  13.    wt: 5:   5 What is Similarity/
  14.    wt: 5:   4 Lines and Slopes Take 1/
  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

65 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:   6 Vectors with Coordinates
  5.    wt: 2:   Euclidean Geometry Elsewhere LINKS
  6.    wt: 2:   Short Course on Euclidean Geometry
  7.    wt: 2:   4 Angles on Maps Plans drawn to scale
  8.    wt: 2:   3 Lengths and Areas on Maps and Plans
  9.    wt: 2:   8 Coordinates for Maps and Planes
  10.    wt: 2:   3 signed coordinates for maps and planes
  11.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  12.    wt: 1:   Ramblings Extrinsic numbers theory
  13.    wt: 1:   Skills Chapter 2 Geometry
  14.    wt: 1:   8 analytic geometry etc
  15.    wt: 1:   About site lesson plans
  16.    wt: 1:   Theory of Knowledge
  17.    wt: 1:   Ages 12 to 14 Geometry
  18.    wt: 1:   Ages 10 to 12 Geometry
  19.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  20.    wt: 1:   20 Interchanging coordinates a reflection
  21.    wt: 1:   9 Set theory term relation possible origins
  22.    wt: 1:   5 Swapping Coordinates is a reflection
  23.    wt: 1:   13 Velocity Vectors in Physics
  24.    wt: 1:   8 Parallel Vectors
  25.    wt: 1:   3 Navigation with Arrows or Vectors
  26.    wt: 1:   2 Signed Coordinates
  27.    wt: 1:   1 Unsigned Coordinates
  28.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  29.    wt: 1:   C Straight Lines Slope from Coordinates
  30.    wt: 1:   Unit Circle Development of Trigonometry
  31.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  32.    wt: 1:   8 Unit Circle Development of Trigonometry
  33.    wt: 1:   1 Rectangular Polar Coordinates Review
  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:   3 Similarity by Design with coordinates
  38.    wt: 1:   9 Midpoint Coordinates Half Endpoint Sum
  39.    wt: 1:   12 Spatial Coordinates
  40.    wt: 1:   4 Polar Coordinates to and from
  41.    wt: 1:   3 Rectangular Coordinates Review
  42.    wt: 1:   2 Cartesian Coordinates with signs
  43.    wt: 1:   1 Cartesian Coordinates sans signs
  44.    wt: 1:   PS E Multiplication with Polar Coordinates
  45.    wt: 1:   PS D Addition with Cartesian Coordinates
  46.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  47.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  48.    wt: 1:   6 Figuring with Maps Not to Scale
  49.    wt: 1:   19 Signed Multiples of Vectors
  50.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  51.    wt: 1:   13 Arrows and Vectors in a Plane
  52.    wt: 1:   12 Real Numbers Line Signed Coordinates
  53.    wt: 1:   9 Coordinates for Regions in Space
  54.    wt: 1:   8 GCD from Euclidean Algorithm
  55.    wt: 1:   4 signed coordinates for regions in space
  56.    wt: 1:   2 signed and unsigned numbers as coordinates
  57.    wt: 1:   1 Integers as Coordinates
  58.    wt: 1:   Chapter 23 Links To Trigonometry
  59.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  60.    wt: 1:   Chapter 7 Two Treatments of Geometry
  61.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  62.    wt: 1:   Chapter 6 More Algebra and Geometry
  63.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  64.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  65.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics

Extended Search

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