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

55 matches:

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