Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Development with How-TOs Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling. Avid readers in school and out may like Site Volumes.

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

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:   8 Unit Circle Trigonometry/
  2.    wt: 7:   1 Maps Plans Measurement/
  3.    wt: 6:   13 Vectors/
  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:   8 Arithmetic with Signed Numbers/
  17.    wt: 2:   D Decimal Long Division Methods/
  18.    wt: 2:   C Decimal Multiplication Methods/
  19.    wt: 2:   B Decimal Comparing and Subtracting Methods/
  20.    wt: 2:   A Decimal Counting and Adding Methods/
  21.    wt: 2:   2 Arithmetic with Decimals/
  22.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  23.    wt: 1:   11 Squares and Square Roots/
  24.    wt: 1:   10 LCM GCD and Euclid GCD Algorithm/
  25.    wt: 1:   9 Combinatorics Trees Tables and Products/
  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

45 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:   Euclidean Geometry Elsewhere LINKS
  5.    wt: 2:   Short Course on Euclidean Geometry
  6.    wt: 2:   4 Angles on Maps Plans drawn to scale
  7.    wt: 2:   3 Lengths and Areas on Maps and Plans
  8.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  9.    wt: 1:   Ramblings Extrinsic numbers theory
  10.    wt: 1:   Skills Chapter 2 Geometry
  11.    wt: 1:   8 analytic geometry etc
  12.    wt: 1:   About site lesson plans
  13.    wt: 1:   Theory of Knowledge
  14.    wt: 1:   Ages 12 to 14 Geometry
  15.    wt: 1:   Ages 10 to 12 Geometry
  16.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  17.    wt: 1:   9 Set theory term relation possible origins
  18.    wt: 1:   13 Velocity Vectors in Physics
  19.    wt: 1:   8 Parallel Vectors
  20.    wt: 1:   6 Vectors with Coordinates
  21.    wt: 1:   3 Navigation with Arrows or Vectors
  22.    wt: 1:   Unit Circle Development of Trigonometry
  23.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  24.    wt: 1:   8 Unit Circle Development of Trigonometry
  25.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  26.    wt: 1:   Why Trigonometry the whyslopes view
  27.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  28.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  29.    wt: 1:   8 Isoceles Triangles
  30.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  31.    wt: 1:   6 Figuring with Maps Not to Scale
  32.    wt: 1:   19 Signed Multiples of Vectors
  33.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  34.    wt: 1:   13 Arrows and Vectors in a Plane
  35.    wt: 1:   8 Coordinates for Maps and Planes
  36.    wt: 1:   8 GCD from Euclidean Algorithm
  37.    wt: 1:   3 signed coordinates for maps and planes
  38.    wt: 1:   Chapter 23 Links To Trigonometry
  39.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  40.    wt: 1:   Chapter 7 Two Treatments of Geometry
  41.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  42.    wt: 1:   Chapter 6 More Algebra and Geometry
  43.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  44.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  45.    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:   8 Parallel Vectors
  4.    wt: 8:   Unit Circle Development of Trigonometry
  5.    wt: 8:   Right Triangle and Unit Circle Trigonometry
  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:   6 Vectors with Coordinates
  10.    wt: 7:   3 Navigation with Arrows or Vectors
  11.    wt: 7:   2 Signed Coordinates
  12.    wt: 7:   17 tangent function angle sum formulas
  13.    wt: 7:   35 sines and cosines of 2A 3A 4A 5A
  14.    wt: 7:   34 sines and cosines of 2A 3A 4A 5A
  15.    wt: 7:   33 sines and cosines of 2A 3A 4A 5A
  16.    wt: 7:   32 seven rows of pascals triangle
  17.    wt: 7:   31 basic secant cosecant cotangent trig identities
  18.    wt: 7:   30 unit circle calculation of six trigonometric functions
  19.    wt: 7:   29 secant cosecant and cotangent for acute angles
  20.    wt: 7:   28 Expressing products of sines cosines as sums
  21.    wt: 7:   27 Logarithmic use of products of sines and cosines
  22.    wt: 7:   26 Formulas for products of sines and cosines
  23.    wt: 7:   25 tangent double angle formula Slope connection
  24.    wt: 7:   24 tangent Angle Difference Formula
  25.    wt: 7:   23 sine and cosine of 180 plus 22.5 degrees
  26.    wt: 7:   22 sine of 22.5 degrees via half angle formulas
  27.    wt: 7:   21 sine and cosine Half Angle Formulas
  28.    wt: 7:   20 sine and cosine Double Angle Formulas
  29.    wt: 7:   19 Pythagorean Identity For sine and cosine functions
  30.    wt: 7:   18 sum of sinusoidal waves as a single wave
  31.    wt: 7:   17G Pythagorean Theorem Converse
  32.    wt: 7:   17F Law of cosines
  33.    wt: 7:   17E Trig Formulas for dot and cross Products
  34.    wt: 7:   17D cis formulas for sine cosines and tangent
  35.    wt: 7:   17C sine and cosine double triple angle formulas
  36.    wt: 7:   17B sine cosine Angle Sum Formulas via cis
  37.    wt: 7:   17A The complex number valued trig function cis
  38.    wt: 7:   16 Right Triangle Complementary Angle Relations
  39.    wt: 7:   15 sine cosine Complementary Angle Relations
  40.    wt: 7:   14 cosine even and sine and tangent are odd
  41.    wt: 7:   13 Graph of tangent function many periods
  42.    wt: 7:   12 Graph of tangent function for one period
  43.    wt: 7:   11 tangent function undefined when terminal side vertical
  44.    wt: 7:   10 Graphs of sines and cosines many periods
  45.    wt: 7:   9 Graphs of sine and cosine over one period
  46.    wt: 7:   8 period of tangent function
  47.    wt: 7:   7 period of sine and cosine
  48.    wt: 7:   6 sines and cosines for reference angle 30 degrees
  49.    wt: 7:   5 sines and cosines for reference angle 60 degrees
  50.    wt: 7:   4 sines and cosines for reference angle 45 degrees
  51.    wt: 7:   3 sines and cosines for reference angle 90 degrees
  52.    wt: 7:   2 Quadrant I reference Angles
  53.    wt: 7:   1 Unit Points Reflections Rotations
  54.    wt: 7:   8 Unit Circle Development of Trigonometry
  55.    wt: 7:   6 Trigonometry Sines of Supplementary Angles
  56.    wt: 7:   2 Similar Triangles Equality of Corresponding Side Ratios
  57.    wt: 7:   Why Trigonometry the whyslopes view
  58.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  59.    wt: 7:   A Measurement with Ruler Proper Use
  60.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  61.    wt: 7:   2 Measuring Area Directly
  62.    wt: 7:   1 Length Measurement
  63.    wt: 6:   A Global Time and Navigation
  64.    wt: 6:   15 Dot and Cross Product
  65.    wt: 6:   14 Why Scalar Multiplication Distributes Physical Argument
  66.    wt: 6:   12 From Applied To Pure Mathematics
  67.    wt: 6:   11 Component Method
  68.    wt: 6:   10 Parallelogram Addition Method
  69.    wt: 6:   9 Head to Tail Coordinate View
  70.    wt: 6:   7 Coordinate Addition and Scalar Multiplication
  71.    wt: 6:   5 Head To Tail Arrow Addition
  72.    wt: 6:   4 Resultant of a Sum of Movements
  73.    wt: 6:   1 Unsigned Coordinates
  74.    wt: 6:   Vector and Complex Number Applet
  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:   8 Mid Point Formula
  83.    wt: 6:   2 point slope equation for a line
  84.    wt: 6:   8 Distance Between Points on 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:   14 Law of cosines
  153.    wt: 5:   13 Trig Formulas for dot and cross Products
  154.    wt: 5:   12 cis formulas for sine cosines and tangent
  155.    wt: 5:   11 sine and cosine double triple angle formulas
  156.    wt: 5:   10 sine cosine Angle Sum Formulas via cis
  157.    wt: 5:   9 The complex number valued trig function cis
  158.    wt: 5:   7 Second Way to Calculate Products
  159.    wt: 5:   6 Field Properties of Complex Number
  160.    wt: 5:   5 An Easy Proof of the Distributive Law
  161.    wt: 5:   4 Multiplication Properties
  162.    wt: 5:   3 Addition Properties
  163.    wt: 5:   1 Rectangular Polar Coordinates Review
  164.    wt: 5:   Appetizer A Complex Number Applet
  165.    wt: 5:   13 Navigation Location from Angles to 2 Landmarks
  166.    wt: 5:   12 Triangles Similarity More Problems
  167.    wt: 5:   11 Triangle Similarity Missing Side Problem
  168.    wt: 5:   10 Similarity of Triangles Equivalent of Two Criteria
  169.    wt: 5:   9 Similarity of Triangles Usual Criteria
  170.    wt: 5:   8 Similarity of Triangles and Polygons
  171.    wt: 5:   7 Translations Rotations Reflections Dilatations
  172.    wt: 5:   6 Geometric Diagrams in Class
  173.    wt: 5:   5 Similarity of Circles Squares and Rectangles
  174.    wt: 5:   4 Similarity Definition with Coordinate
  175.    wt: 5:   3 Similarity by Design with coordinates
  176.    wt: 5:   2 Similarity By Design
  177.    wt: 5:   1 Early Concept of Like or Similar Shapes
  178.    wt: 5:   Four Simple Exercises
  179.    wt: 5:   12 Links Lessons elsewhere
  180.    wt: 5:   11 A Partial Summary
  181.    wt: 5:   10 Midpoint of [a b] and [b a]
  182.    wt: 5:   9 Midpoint Coordinates Half Endpoint Sum
  183.    wt: 5:   7 Exercises to test skill and concept mastery
  184.    wt: 5:   6 Intersection of lines by solving linear systems
  185.    wt: 5:   5 Algebraic View of Slopes
  186.    wt: 5:   4 Equations for lines three forms
  187.    wt: 5:   3 Slope product for perpendicular lines
  188.    wt: 5:   1 Numerical view of lines and their equations
  189.    wt: 5:   What is and is not here
  190.    wt: 5:   13 Pythagorean spatial distance formulas
  191.    wt: 5:   12 Spatial Coordinates
  192.    wt: 5:   11 Triangle Inequality
  193.    wt: 5:   10 Pythagorean plane distance formula
  194.    wt: 5:   9 Pythagorean Theorem Chinese Square Proof
  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:   3 signed coordinates for maps and planes
  203.    wt: 3:   8 Correcting the Mistake
  204.    wt: 3:   2 Division with Single Digit Divisors
  205.    wt: 3:   2 One Digit Multipliers
  206.    wt: 3:   8 Subtraction with Units of Measure
  207.    wt: 3:   2 Subtraction Easy Case Examples
  208.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  209.    wt: 2:   3 Euclidean Geometry Leanly
  210.    wt: 2:   Maps Plans Drawings
  211.    wt: 2:   2 More and Less Than with Unlike Signs
  212.    wt: 2:   8 GCD from Euclidean Algorithm
  213.    wt: 2:   11 What are real lengths and numbers
  214.    wt: 2:   10 dividing signed numbers
  215.    wt: 2:   9 subtracting signed numbers
  216.    wt: 2:   8 multiplying signed numbers
  217.    wt: 2:   7 negative and additive inverse
  218.    wt: 2:   6 adding signed numbers
  219.    wt: 2:   5 lengths and signs of numbers
  220.    wt: 2:   4 signed coordinates for regions in space
  221.    wt: 2:   2 signed and unsigned numbers as coordinates
  222.    wt: 2:   8 Multiplication by Signed Numbers Integers
  223.    wt: 2:   2 Integers Multiplies of a Unit Moverment
  224.    wt: 2:   8 video Prime Factorization upto 19
  225.    wt: 2:   2 Prime and Composites less than 16
  226.    wt: 2:   Long Division Backwards more
  227.    wt: 2:   Long Division Backward
  228.    wt: 2:   Division with Counts and Length
  229.    wt: 2:   Long Division forwards and backwards Example 3
  230.    wt: 2:   Long Division forwards and backwards Example 2
  231.    wt: 2:   Long Division forwards and backwards Example 1
  232.    wt: 2:   12 Why Long Division Works Take III
  233.    wt: 2:   11 Another Single Digit Divisor Example
  234.    wt: 2:   10 Division by Five Long and Short Ways
  235.    wt: 2:   9 Why Long Division Works Take II
  236.    wt: 2:   7 Long Divison Mistake Catching
  237.    wt: 2:   6 Why Decimal Long Division Methods Works Take I
  238.    wt: 2:   5 Long Division Include Zeroes or not
  239.    wt: 2:   4 Division with 2 Digit Divsors
  240.    wt: 2:   3 Division Single Digit Divisor Example
  241.    wt: 2:   1 Divsion Physical Examples
  242.    wt: 2:   D Decimal Multiplication Methods Derived
  243.    wt: 2:   C Counting Areas with Powers of Ten
  244.    wt: 2:   B Powers of Ten
  245.    wt: 2:   A Elementary Basis for Multiplication Methods
  246.    wt: 2:   6 Multiplication Commutes Order Not Important
  247.    wt: 2:   5 Decimal Fraction Multiplication
  248.    wt: 2:   4 Two and Three Digit Multipliers
  249.    wt: 2:   3 More One Digit Multipliers
  250.    wt: 2:   Video Decimal Multiplication Geometric View Example 2
  251.    wt: 2:   Video Decimal Multiplication Geometric View Example 2
  252.    wt: 2:   Video Power Notation in Decimal Expansion
  253.    wt: 2:   1 Why 3 times 5 gives 15
  254.    wt: 2:   Appendix 2 Three Decimal Subtraction Methods
  255.    wt: 2:   Appendix 1 Decimals Comparison Method Take II
  256.    wt: 2:   Subtraction with J Conversions Example
  257.    wt: 2:   Subtraction Another Video Lesson
  258.    wt: 2:   9 22 Minute Subtraction Review Video
  259.    wt: 2:   7 Subtraction for Decimal Fractions with Exercises
  260.    wt: 2:   6 Subtraction with Conversion Example with Exercises
  261.    wt: 2:   5 A Tip for Efficent Subtraction
  262.    wt: 2:   4 Subtraction with Conversions Borrows and Letter J
  263.    wt: 2:   3 Harder Cases Convert to Compare and Subtract
  264.    wt: 2:   1 Comparison and Subtraction Easy Direct Cases
  265.    wt: 2:   Appendix 1 Counting Revisited 15 minute video
  266.    wt: 2:   8 What skills and work habits to require
  267.    wt: 2:   7 Adding decimal fractions using decimal point
  268.    wt: 2:   6. Counting and adding units and mixed units
  269.    wt: 2:   5. How to add decimals C. Examples
  270.    wt: 2:   4. How to add with decimals B with conversions
  271.    wt: 2:   3. How to add with decimals A sans conversions
  272.    wt: 2:   2 Decimal Counting Practices
  273.    wt: 2:   1. Explaining Addition Table
  274.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  275.    wt: 1:   Ramblings Extrinsic numbers theory
  276.    wt: 1:   Skills Chapter 2 Geometry
  277.    wt: 1:   8 analytic geometry etc
  278.    wt: 1:   About site lesson plans
  279.    wt: 1:   Theory of Knowledge
  280.    wt: 1:   2 Conductance Resistance Duality02
  281.    wt: 1:   8 The Effect of Negative Remarks
  282.    wt: 1:   2 Reading and Writing Skills
  283.    wt: 1:   Ages 12 to 14 Geometry
  284.    wt: 1:   Ages 10 to 12 Geometry
  285.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  286.    wt: 1:   20 Interchanging coordinates a reflection
  287.    wt: 1:   9 Set theory term relation possible origins
  288.    wt: 1:   19 Signed Multiples of Vectors
  289.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  290.    wt: 1:   13 Arrows and Vectors in a Plane
  291.    wt: 1:   2 Combing Counts Addition Skills and Principles
  292.    wt: 1:   2 Algebraic View
  293.    wt: 1:   8 Coordinates for Maps and Planes
  294.    wt: 1:   2 GE II Comparison
  295.    wt: 1:   2 Essentially one exercises three with solution
  296.    wt: 1:   2 Three Examples
  297.    wt: 1:   8 One Example
  298.    wt: 1:   2 Three Examples
  299.    wt: 1:   arithmetic videos Real Player Format
  300.    wt: 1:   4 Greater More Less Than Signs in General
  301.    wt: 1:   3 Comparison of Negative Numbers
  302.    wt: 1:   1 More and Less Than for Counts and Measures
  303.    wt: 1:   5 Square Roots with primes more still
  304.    wt: 1:   4 Square Roots with primes more
  305.    wt: 1:   3 Properties of Square Roots with example
  306.    wt: 1:   2 Square Roots with Prime
  307.    wt: 1:   1 Squares and Square Roots Introduction
  308.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  309.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  310.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  311.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  312.    wt: 1:   13 GCD from given Prime Factorization
  313.    wt: 1:   11 GCD 2700 288 via Euclid Algorithm
  314.    wt: 1:   10 Euclid Algorithm with 129 125 and with 45 14
  315.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  316.    wt: 1:   7 GCD and LCM from prime factorization
  317.    wt: 1:   6 GCD from Prime
  318.    wt: 1:   5 Common Divisors 60 45 via Prime
  319.    wt: 1:   4 LCM of 8 and 10 via Prime
  320.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  321.    wt: 1:   2 Least Common Multiple LCM intro via list method
  322.    wt: 1:   1 Least Common Multiples LCM Introduction
  323.    wt: 1:   12 GCD 2700 288 via Prime
  324.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  325.    wt: 1:   4 Counting with Trees Product Rule Take I
  326.    wt: 1:   3 Counting with Tables and Trees II
  327.    wt: 1:   2 Counting with Tables and Trees I
  328.    wt: 1:   1 Counting and Counting Methods I
  329.    wt: 1:   7 Converting or Changing Units
  330.    wt: 1:   6 Simplification of Fractions with Units
  331.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  332.    wt: 1:   4 Fractions with Units
  333.    wt: 1:   3 Multiplying Units and Numbers
  334.    wt: 1:   2 Equality and Units
  335.    wt: 1:   1 Addition and Subtraction with Units
  336.    wt: 1:   D Three Term Ratios
  337.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  338.    wt: 1:   B Fractions and Two Term Ratios
  339.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  340.    wt: 1:   22 Complex Compound Fractions
  341.    wt: 1:   21 Working With Signs
  342.    wt: 1:   21 Reciprocals for Fractions and Wholes
  343.    wt: 1:   20 Dividing Fractions the Why
  344.    wt: 1:   19 Dividing Fractions How TO
  345.    wt: 1:   18 Efficient Ways to Multiply
  346.    wt: 1:   17 Efficient Ways to Add and Subtract
  347.    wt: 1:   16 Addition Subtraction Comparision Compared
  348.    wt: 1:   15 Adding and Subtracting with Unlike Denominators
  349.    wt: 1:   14 Adding and Subtracting with Like Denominators
  350.    wt: 1:   13 Fraction Comparison Algebraic View
  351.    wt: 1:   12 Fraction Comparison
  352.    wt: 1:   11 Simplification an Algebraic View
  353.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  354.    wt: 1:   9 Improper Fractions and Mixed Numbers
  355.    wt: 1:   8 Numerals Fractionals Quantals Take II
  356.    wt: 1:   7 Numerals Fractionals Quantals
  357.    wt: 1:   6 Multiplication of Mixed Numbers
  358.    wt: 1:   6 Multiplication Algebraically Take II
  359.    wt: 1:   5 Equivalent Fractions
  360.    wt: 1:   4 Fraction Multiplication
  361.    wt: 1:   3 Unit fraction of a fraction
  362.    wt: 1:   2 Unit Fraction Multiplication
  363.    wt: 1:   1 What is a fraction Take II
  364.    wt: 1:   1 What is a fraction
  365.    wt: 1:   Fraction Operations by Raising Terms A Simple Innovation
  366.    wt: 1:   D Remainders Modulo 11 Pair Rule
  367.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  368.    wt: 1:   B Integer Long Division Multiple Choices
  369.    wt: 1:   A Associative Law Theorectical Note
  370.    wt: 1:   13 Subtraction with Additive Inverse
  371.    wt: 1:   12 Adding Integers More Examples
  372.    wt: 1:   11 Adding Integers Formulas and Examples
  373.    wt: 1:   10 Integer Multiplication Formulas
  374.    wt: 1:   9 Multiplying 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:   1 Integers as Coordinates
  381.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  382.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  383.    wt: 1:   26 Divisibility by 2 3 5 Example
  384.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  385.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  386.    wt: 1:   23 Remainder Arithmetic Modulo 2
  387.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  388.    wt: 1:   21 Remainder Arithmetic Modulo 3
  389.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  390.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  391.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  392.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  393.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  394.    wt: 1:   15 Remainder Arithmetic Modulo 9 Example
  395.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  396.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  397.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  398.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  399.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  400.    wt: 1:   9 Remainder Arithmetic Divisibility by 5
  401.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  402.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  403.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  404.    wt: 1:   5 Remainder Arithmetic Modulo 5
  405.    wt: 1:   4 Remainder Arithmetic Modulo 10 in general
  406.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  407.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  408.    wt: 1:   1 Remainder Arithmetic Modulo 10
  409.    wt: 1:   20 Uniqueness of Prime Factorization
  410.    wt: 1:   19 video Prime Factorization Unique
  411.    wt: 1:   18 video Count Factors given Prime Factorization
  412.    wt: 1:   17 Identify and Count Factors using Primes
  413.    wt: 1:   16 video Factors of 980 using prime
  414.    wt: 1:   15 video Factors of 20 using Prime Factorization
  415.    wt: 1:   14 video Factors of 24 Take II
  416.    wt: 1:   13 video Factors of 24 using prime
  417.    wt: 1:   12 LCD GCD and LCM using Primes
  418.    wt: 1:   11 Efficient Square Rule Use
  419.    wt: 1:   10 video Prime Factorization upto 23 squared
  420.    wt: 1:   9 video Prime Factorization upto 19 squared
  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:   8 Isoceles Triangles
  456.    wt: 13:   Short Course on Euclidean Geometry
  457.    wt: 12:   PS C Similarity Use Recognize it in Trigonometry
  458.    wt: 12:   2 Correspondence between Triangles
  459.    wt: 11:   PS H Distributive Law For Complex Numbers
  460.    wt: 11:   PS G Rotation Distributes over Addition
  461.    wt: 11:   PS F Scalar Multiplication Distributes over Addition
  462.    wt: 11:   PS E Multiplication with Polar Coordinates
  463.    wt: 11:   PS D Addition with Cartesian Coordinates
  464.    wt: 11:   PS B Parallelogram Construction Methods
  465.    wt: 11:   PS A Kite Construction Methods
  466.    wt: 11:   21 Parallelograms
  467.    wt: 11:   19 Right Triangle Similarity
  468.    wt: 11:   18 Triangle Similarity Take 1
  469.    wt: 11:   17 Right Bisectors of Triangle Sides
  470.    wt: 11:   16 Angles Subtended By Chords and Diameters
  471.    wt: 11:   15 Triangle Angle Sum is 180 degrees
  472.    wt: 11:   14 Parallel Lines Postulate
  473.    wt: 11:   13 Angle Side Angle Failure
  474.    wt: 11:   12 Side Angle Side Failure
  475.    wt: 11:   11 Triangle Construction Fails
  476.    wt: 11:   10 Dropping a perpendicular to line
  477.    wt: 11:   9 Construction of a right bisector
  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: Site pages offer better or best practices for providing skills - simpler than expected & comprehensive but for exercises. For your charges, your duty is to study them alone or in groups and develop skill building exercises & activities to share. Start now. The effort here is the best I can do. Others are welcome to refine or exceed it. Please do.

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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