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 Site Map || Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling; and for avid readers not in school

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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19 matches:

  1.    wt: 8:   13 Vectors/
  2.    wt: 7:   1 Maps Plans Measurement/
  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:   2 Euclidean Geometry Constructions Theory extras/
  16.    wt: 5:   Geometry maps plans trigonometry vectors/
  17.    wt: 1:   4 Functions/
  18.    wt: 1:   3 Prime Factorization Skills/
  19.    wt: 1:   13 Lessons on Limits and Continuity/

Web Page Search

95 matches:

  1.    wt: 2:   Maps Plans Drawings
  2.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take IV
  3.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take III
  4.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take II
  5.    wt: 2:   23 Modularized Skill Development Modularized Rigor
  6.    wt: 2:   21 Graphs of functions given by Horizontal Line Method
  7.    wt: 2:   13 Velocity Vectors in Physics
  8.    wt: 2:   PS C Similarity Use Recognize it in Trigonometry
  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:   16 Collinear Horizontal Arrows Vectors
  12.    wt: 2:   13 Arrows and Vectors in a Plane
  13.    wt: 2:   13 GCD from given Prime Factorization
  14.    wt: 2:   H Jigsaw puzzles and problem solving
  15.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  16.    wt: 1:   About site lesson plans
  17.    wt: 1:   05 13 OldSiteEntrancePage
  18.    wt: 1:   13 Addition and Addition Tables
  19.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  20.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  21.    wt: 1:   23 Inverse Functions
  22.    wt: 1:   19 Horizontal line rule and method
  23.    wt: 1:   15 Sign analysis of functions
  24.    wt: 1:   13 From one to one to many to one
  25.    wt: 1:   8 Set view of relations and functions
  26.    wt: 1:   7 Functions with finite domains
  27.    wt: 1:   13 cosecant function Definition Graph and Inverse
  28.    wt: 1:   8 Parallel Vectors
  29.    wt: 1:   6 Vectors with Coordinates
  30.    wt: 1:   3 Navigation with Arrows or Vectors
  31.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  32.    wt: 1:   30 unit circle calculation of six trigonometric functions
  33.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  34.    wt: 1:   13 Graph of tangent function many periods
  35.    wt: 1:   Unit Circle Development of Trigonometry
  36.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  37.    wt: 1:   13 Trig Formulas for dot and cross Products
  38.    wt: 1:   8 Unit Circle Development of Trigonometry
  39.    wt: 1:   Appetizer A Complex Number Applet
  40.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  41.    wt: 1:   Why Trigonometry the whyslopes view
  42.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  43.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  44.    wt: 1:   13 Pythagorean spatial distance formulas
  45.    wt: 1:   7 Complex Numbers Appetizer
  46.    wt: 1:   13 Angle Side Angle Failure
  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:   5 Areas of Rectangles Revisited
  51.    wt: 1:   13 Real Number Subtraction
  52.    wt: 1:   8 Coordinates for Maps and Planes
  53.    wt: 1:   13 Naming Identifying Formulas with Words
  54.    wt: 1:   7 GCD and LCM from prime factorization
  55.    wt: 1:   3 signed coordinates for maps and planes
  56.    wt: 1:   13 Fraction Comparison Algebraic View
  57.    wt: 1:   13 Subtraction with Additive Inverse
  58.    wt: 1:   5 Zero Movement and Additive Inverses
  59.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  60.    wt: 1:   20 Uniqueness of Prime Factorization
  61.    wt: 1:   19 video Prime Factorization Unique
  62.    wt: 1:   18 video Count Factors given Prime Factorization
  63.    wt: 1:   15 video Factors of 20 using Prime Factorization
  64.    wt: 1:   13 video Factors of 24 using prime
  65.    wt: 1:   10 video Prime Factorization upto 23 squared
  66.    wt: 1:   9 video Prime Factorization upto 19 squared
  67.    wt: 1:   8 video Prime Factorization upto 19
  68.    wt: 1:   5 Prime Factorization and a Square Rule
  69.    wt: 1:   4 video Prime Factorization Introduction
  70.    wt: 1:   5 Long Division Include Zeroes or not
  71.    wt: 1:   Appendix 1 Counting Revisited 15 minute video
  72.    wt: 1:   013 Travel Time Tables
  73.    wt: 1:   31 Derivatives of inverse functions
  74.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  75.    wt: 1:   26 Chain Rule Recognising outer inner functions
  76.    wt: 1:   19 Chain Rule for linear functions
  77.    wt: 1:   13 sine and cosine derivatives 1st step
  78.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  79.    wt: 1:   13 Limits with Parameters and Derivatives Take II
  80.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  81.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  82.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  83.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  84.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  85.    wt: 1:   F.1 What Functions are Continuous
  86.    wt: 1:   B3 Bolzano Weierstrass Theorem
  87.    wt: 1:   Chapter 23 Links To Trigonometry
  88.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  89.    wt: 1:   Chapter 13. Acceleration
  90.    wt: 1:   Fall 1983 Calculus Appetizer
  91.    wt: 1:   Chapter 19. Functions and Sets
  92.    wt: 1:   Chapter 13. Second Reading Guide
  93.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  94.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  95.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry

Extended Search

350 matches:

  1.    wt: 9:   8 Parallel Vectors
  2.    wt: 9:   6 Vectors with Coordinates
  3.    wt: 9:   3 Navigation with Arrows or Vectors
  4.    wt: 9:   4 Angles on Maps Plans drawn to scale
  5.    wt: 9:   3 Lengths and Areas on Maps and Plans
  6.    wt: 8:   A Global Time and Navigation
  7.    wt: 8:   15 Dot and Cross Product
  8.    wt: 8:   14 Why Scalar Multiplication Distributes Physical Argument
  9.    wt: 8:   12 From Applied To Pure Mathematics
  10.    wt: 8:   11 Component Method
  11.    wt: 8:   10 Parallelogram Addition Method
  12.    wt: 8:   9 Head to Tail Coordinate View
  13.    wt: 8:   7 Coordinate Addition and Scalar Multiplication
  14.    wt: 8:   5 Head To Tail Arrow Addition
  15.    wt: 8:   4 Resultant of a Sum of Movements
  16.    wt: 8:   2 Signed Coordinates
  17.    wt: 8:   1 Unsigned Coordinates
  18.    wt: 8:   Vector and Complex Number Applet
  19.    wt: 8:   32 seven rows of pascals triangle
  20.    wt: 8:   8 More Use of Maps Not Drawn to Scale
  21.    wt: 8:   6 Figuring with Maps Not to Scale
  22.    wt: 7:   35 sines and cosines of 2A 3A 4A 5A
  23.    wt: 7:   34 sines and cosines of 2A 3A 4A 5A
  24.    wt: 7:   33 sines and cosines of 2A 3A 4A 5A
  25.    wt: 7:   31 basic secant cosecant cotangent trig identities
  26.    wt: 7:   30 unit circle calculation of six trigonometric functions
  27.    wt: 7:   19 Pythagorean Identity For sine and cosine functions
  28.    wt: 7:   15 sine cosine Complementary Angle Relations
  29.    wt: 7:   13 Graph of tangent function many periods
  30.    wt: 7:   Unit Circle Development of Trigonometry
  31.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  32.    wt: 7:   13 Trig Formulas for dot and cross Products
  33.    wt: 7:   6 Trigonometry Sines of Supplementary Angles
  34.    wt: 7:   Why Trigonometry the whyslopes view
  35.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  36.    wt: 7:   13 Navigation Location from Angles to 2 Landmarks
  37.    wt: 7:   13 Pythagorean spatial distance formulas
  38.    wt: 7:   PS C Similarity Use Recognize it in Trigonometry
  39.    wt: 7:   13 Angle Side Angle Failure
  40.    wt: 7:   A Measurement with Ruler Proper Use
  41.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  42.    wt: 7:   2 Measuring Area Directly
  43.    wt: 7:   1 Length Measurement
  44.    wt: 6:   13 cosecant function Definition Graph and Inverse
  45.    wt: 6:   3 Left Inverse of cosine arccos definition
  46.    wt: 6:   13 Straight Lines Finding Equations from 2 points
  47.    wt: 6:   17 tangent function angle sum formulas
  48.    wt: 6:   29 secant cosecant and cotangent for acute angles
  49.    wt: 6:   28 Expressing products of sines cosines as sums
  50.    wt: 6:   27 Logarithmic use of products of sines and cosines
  51.    wt: 6:   26 Formulas for products of sines and cosines
  52.    wt: 6:   25 tangent double angle formula Slope connection
  53.    wt: 6:   24 tangent Angle Difference Formula
  54.    wt: 6:   23 sine and cosine of 180 plus 22.5 degrees
  55.    wt: 6:   22 sine of 22.5 degrees via half angle formulas
  56.    wt: 6:   21 sine and cosine Half Angle Formulas
  57.    wt: 6:   20 sine and cosine Double Angle Formulas
  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:   14 cosine even and sine and tangent are odd
  68.    wt: 6:   12 Graph of tangent function for one period
  69.    wt: 6:   11 tangent function undefined when terminal side vertical
  70.    wt: 6:   10 Graphs of sines and cosines many periods
  71.    wt: 6:   9 Graphs of sine and cosine over one period
  72.    wt: 6:   8 period of tangent function
  73.    wt: 6:   7 period of sine and cosine
  74.    wt: 6:   6 sines and cosines for reference angle 30 degrees
  75.    wt: 6:   5 sines and cosines for reference angle 60 degrees
  76.    wt: 6:   4 sines and cosines for reference angle 45 degrees
  77.    wt: 6:   3 sines and cosines for reference angle 90 degrees
  78.    wt: 6:   2 Quadrant I reference Angles
  79.    wt: 6:   1 Unit Points Reflections Rotations
  80.    wt: 6:   8 Unit Circle Development of Trigonometry
  81.    wt: 6:   Appetizer A Complex Number Applet
  82.    wt: 6:   8 Triangles Cascade Problem Solving
  83.    wt: 6:   7 Trignometric Ratios Unit Circle
  84.    wt: 6:   5 Trigonometric Ratios For Tangent and Special Triangles
  85.    wt: 6:   4 Trigonometric Ratios For Two Special Triangles
  86.    wt: 6:   3 Trigonometric Ratios sine and cosine
  87.    wt: 6:   2 Similar Triangles Equality of Corresponding Side Ratios
  88.    wt: 6:   1 Angle Measurement with Degrees
  89.    wt: 6:   6 Geometric Diagrams in Class
  90.    wt: 6:   3 Similarity by Design with coordinates
  91.    wt: 6:   7 Complex Numbers Appetizer
  92.    wt: 5:   16 cotangent function Definition Graph and Inverse
  93.    wt: 5:   15 cosecant function Definition Graph and Inverse
  94.    wt: 5:   14 secant function Definition Graph and Inverse
  95.    wt: 5:   12 motivation for term arctan
  96.    wt: 5:   11 arctan left inverse of tangent Graph
  97.    wt: 5:   10 arctan left inverse of tangent Definition
  98.    wt: 5:   9 motivation for name arcsin
  99.    wt: 5:   8 arcsin left inverse of sine Graph
  100.    wt: 5:   7 arcsin left inverse of sine Definition
  101.    wt: 5:   6 Graph of arccos function
  102.    wt: 5:   5 Swapping Coordinates is a reflection
  103.    wt: 5:   4 possible motivation for term arccos
  104.    wt: 5:   2 cosine function more properties
  105.    wt: 5:   1 cosine function properties
  106.    wt: 5:   9 Summary Degrees to Radians and back
  107.    wt: 5:   8 Radian Measures of Common Angles
  108.    wt: 5:   7 Radian Measures in special Triangles
  109.    wt: 5:   6 Radian Measure to Degrees
  110.    wt: 5:   5 Degrees to Radian Measure
  111.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  112.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  113.    wt: 5:   2 Radian Measure Numerical Value of one degree
  114.    wt: 5:   1 Degrees and Radians Introduction
  115.    wt: 5:   4 graphing y=Asin(x c)
  116.    wt: 5:   3 graphing y=f(x c) plus K
  117.    wt: 5:   2 Graphing y=Af(x) Vertical Scaling
  118.    wt: 5:   1 graphing y=f(x a)
  119.    wt: 5:   Parallel Lines and Parallel Transversals
  120.    wt: 5:   Proportionality of Line Segments From Parallel Transversals
  121.    wt: 5:   Triangle Angles Sum To 180 Degrees
  122.    wt: 5:   Parallel Lines and Alternating Corresponding Angles
  123.    wt: 5:   Parallel Lines and Interior Angles
  124.    wt: 5:   Construction Methods and Criteria for Isometric and Similar Triangles
  125.    wt: 5:   SAS Method For Isometric Or Proportional Triangle Construction
  126.    wt: 5:   Analytic View of Triangle Construction or Line Instersection More
  127.    wt: 5:   Straight Lines ASA Intersection Study More
  128.    wt: 5:   Straight Lines ASA Intersection Study
  129.    wt: 5:   Straight Lines Instersection Solving Equations
  130.    wt: 5:   Straight Lines Intersection of
  131.    wt: 5:   D Straight Lines Slope from Coordinates Examples
  132.    wt: 5:   C Straight Lines Slope from Coordinates
  133.    wt: 5:   B Straight Line Slope Scaling Properties More
  134.    wt: 5:   A Straight Line Slope Scaling Properties
  135.    wt: 5:   14 Straight Lines Equations General Case
  136.    wt: 5:   12 Straight Lines Graphing mx plus b
  137.    wt: 5:   11 Straight Lines Graphing y=mx
  138.    wt: 5:   10 Straight Lines through Origin Equations More
  139.    wt: 5:   9 Straight Lines through Origin Equations
  140.    wt: 5:   8 Straight Lines Equation for vertical
  141.    wt: 5:   7 Tangent Function is odd on this domain
  142.    wt: 5:   6 Tangent Function Inclination Angle Take 2
  143.    wt: 5:   5 Tangent Function Graph
  144.    wt: 5:   4 Tangent Function Properties
  145.    wt: 5:   3 Straight Lines Slope as Tangent of Inclination Angle
  146.    wt: 5:   2 Straight Lines Slopes As Rise Over Run
  147.    wt: 5:   1 Straight Lines Slope Concept
  148.    wt: 5:   21 Logarithms Powers and Exponentials
  149.    wt: 5:   20 N th Roots of Complex Numbers
  150.    wt: 5:   19 N th Roots of Unity
  151.    wt: 5:   18 Sixth Roots of Unity
  152.    wt: 5:   17 Cube Roots of unity
  153.    wt: 5:   16 References and Originality Question
  154.    wt: 5:   15 Pythagorean Theorem Converse
  155.    wt: 5:   14 Law of cosines
  156.    wt: 5:   12 cis formulas for sine cosines and tangent
  157.    wt: 5:   11 sine and cosine double triple angle formulas
  158.    wt: 5:   10 sine cosine Angle Sum Formulas via cis
  159.    wt: 5:   9 The complex number valued trig function cis
  160.    wt: 5:   7 Second Way to Calculate Products
  161.    wt: 5:   6 Field Properties of Complex Number
  162.    wt: 5:   5 An Easy Proof of the Distributive Law
  163.    wt: 5:   4 Multiplication Properties
  164.    wt: 5:   3 Addition Properties
  165.    wt: 5:   2 Complex Numbers made easier we hope
  166.    wt: 5:   1 Rectangular Polar Coordinates Review
  167.    wt: 5:   12 Triangles Similarity More Problems
  168.    wt: 5:   11 Triangle Similarity Missing Side Problem
  169.    wt: 5:   10 Similarity of Triangles Equivalent of Two Criteria
  170.    wt: 5:   9 Similarity of Triangles Usual Criteria
  171.    wt: 5:   8 Similarity of Triangles and Polygons
  172.    wt: 5:   7 Translations Rotations Reflections Dilatations
  173.    wt: 5:   5 Similarity of Circles Squares and Rectangles
  174.    wt: 5:   4 Similarity Definition with Coordinate
  175.    wt: 5:   2 Similarity By Design
  176.    wt: 5:   1 Early Concept of Like or Similar Shapes
  177.    wt: 5:   Four Simple Exercises
  178.    wt: 5:   12 Links Lessons elsewhere
  179.    wt: 5:   11 A Partial Summary
  180.    wt: 5:   10 Midpoint of [a b] and [b a]
  181.    wt: 5:   9 Midpoint Coordinates Half Endpoint Sum
  182.    wt: 5:   8 Mid Point Formula
  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:   2 point slope equation for a line
  189.    wt: 5:   1 Numerical view of lines and their equations
  190.    wt: 5:   What is and is not here
  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:   8 Distance Between Points on a Line
  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:   2 Cartesian Coordinates with signs
  201.    wt: 5:   1 Cartesian Coordinates sans signs
  202.    wt: 5:   Euclidean Geometry Elsewhere LINKS
  203.    wt: 5:   PS H Distributive Law For Complex Numbers
  204.    wt: 5:   PS G Rotation Distributes over Addition
  205.    wt: 5:   PS F Scalar Multiplication Distributes over Addition
  206.    wt: 5:   PS E Multiplication with Polar Coordinates
  207.    wt: 5:   PS D Addition with Cartesian Coordinates
  208.    wt: 5:   PS B Parallelogram Construction Methods
  209.    wt: 5:   PS A Kite Construction Methods
  210.    wt: 5:   21 Parallelograms
  211.    wt: 5:   19 Right Triangle Similarity
  212.    wt: 5:   18 Triangle Similarity Take 1
  213.    wt: 5:   17 Right Bisectors of Triangle Sides
  214.    wt: 5:   16 Angles Subtended By Chords and Diameters
  215.    wt: 5:   15 Triangle Angle Sum is 180 degrees
  216.    wt: 5:   14 Parallel Lines Postulate
  217.    wt: 5:   12 Side Angle Side Failure
  218.    wt: 5:   11 Triangle Construction Fails
  219.    wt: 5:   10 Dropping a perpendicular to line
  220.    wt: 5:   9 Construction of a right bisector
  221.    wt: 5:   8 Isoceles Triangles
  222.    wt: 5:   7 Angle Side Angle
  223.    wt: 5:   6 Ruler and compass Angle Bisection
  224.    wt: 5:   5 Side Angle Side
  225.    wt: 5:   4 Side Side Side
  226.    wt: 5:   3 Isometry of Triangles Congruence
  227.    wt: 5:   2 Correspondence between Triangles
  228.    wt: 5:   1 Initial Concepts and Terms
  229.    wt: 5:   Short Course on Euclidean Geometry
  230.    wt: 5:   About Folder Contents
  231.    wt: 3:   21 Graphs of functions given by Horizontal Line Method
  232.    wt: 3:   13 From one to one to many to one
  233.    wt: 3:   13 video Factors of 24 using prime
  234.    wt: 2:   Maps Plans Drawings
  235.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take IV
  236.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take III
  237.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take II
  238.    wt: 2:   23 Modularized Skill Development Modularized Rigor
  239.    wt: 2:   13 Addition and Addition Tables
  240.    wt: 2:   25 Absolute Value greatest integer and saw tooth functions
  241.    wt: 2:   24 Monotoncity Injectivity and Inverse Functions
  242.    wt: 2:   23 Inverse Functions
  243.    wt: 2:   19 Horizontal line rule and method
  244.    wt: 2:   15 Sign analysis of functions
  245.    wt: 2:   8 Set view of relations and functions
  246.    wt: 2:   7 Functions with finite domains
  247.    wt: 2:   16 Collinear Horizontal Arrows Vectors
  248.    wt: 2:   13 Arrows and Vectors in a Plane
  249.    wt: 2:   13 GCD from given Prime Factorization
  250.    wt: 2:   20 Uniqueness of Prime Factorization
  251.    wt: 2:   19 video Prime Factorization Unique
  252.    wt: 2:   18 video Count Factors given Prime Factorization
  253.    wt: 2:   15 video Factors of 20 using Prime Factorization
  254.    wt: 2:   10 video Prime Factorization upto 23 squared
  255.    wt: 2:   9 video Prime Factorization upto 19 squared
  256.    wt: 2:   8 video Prime Factorization upto 19
  257.    wt: 2:   5 Prime Factorization and a Square Rule
  258.    wt: 2:   4 video Prime Factorization Introduction
  259.    wt: 2:   13 Limits with Parameters and Derivatives Take II
  260.    wt: 2:   Chapter 13. Acceleration
  261.    wt: 2:   Chapter 13. Second Reading Guide
  262.    wt: 2:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  263.    wt: 2:   H Jigsaw puzzles and problem solving
  264.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  265.    wt: 1:   Ramblings Extrinsic numbers theory
  266.    wt: 1:   Ramblings Introduction Algebra Essay
  267.    wt: 1:   Skills Chapter 3 Algebra
  268.    wt: 1:   About site lesson plans
  269.    wt: 1:   05 13 OldSiteEntrancePage
  270.    wt: 1:   A Wire Resistance Qualitative01
  271.    wt: 1:   26 Function definitions done and coming
  272.    wt: 1:   22 Square Root function graphically
  273.    wt: 1:   20 Interchanging coordinates a reflection
  274.    wt: 1:   18 Vertical Line Rule and Method
  275.    wt: 1:   17 Function maxima minima and their location
  276.    wt: 1:   16 Increasing or decreasing on intervals
  277.    wt: 1:   14 Surjections Injections Bijections
  278.    wt: 1:   12 Function Domain Recognition Exercises
  279.    wt: 1:   11 Function Domain Range Source and Targets
  280.    wt: 1:   10 Interval Notation
  281.    wt: 1:   9 Set theory term relation possible origins
  282.    wt: 1:   6 Set Existence Formation and Notation
  283.    wt: 1:   5 Function notation for geometric transformations
  284.    wt: 1:   4 Function notation in and beyond mathematics
  285.    wt: 1:   3 Formula or function graphing exercise
  286.    wt: 1:   2 Algebraic use of function notation
  287.    wt: 1:   1 Geometric Introduction of Function Notation
  288.    wt: 1:   Introduction Reading Guide
  289.    wt: 1:   19 Signed Multiples of Vectors
  290.    wt: 1:   5 Areas of Rectangles Revisited
  291.    wt: 1:   13 Real Number Subtraction
  292.    wt: 1:   8 Coordinates for Maps and Planes
  293.    wt: 1:   13 Naming Identifying Formulas with Words
  294.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  295.    wt: 1:   7 GCD and LCM from prime factorization
  296.    wt: 1:   3 signed coordinates for maps and planes
  297.    wt: 1:   13 Fraction Comparison Algebraic View
  298.    wt: 1:   A Associative Law Theorectical Note
  299.    wt: 1:   13 Subtraction with Additive Inverse
  300.    wt: 1:   5 Zero Movement and Additive Inverses
  301.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  302.    wt: 1:   17 Identify and Count Factors using Primes
  303.    wt: 1:   16 video Factors of 980 using prime
  304.    wt: 1:   14 video Factors of 24 Take II
  305.    wt: 1:   12 LCD GCD and LCM using Primes
  306.    wt: 1:   11 Efficient Square Rule Use
  307.    wt: 1:   7 Calculator Usage Notes and Cautions
  308.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  309.    wt: 1:   3 video Primes and Composites from 9 times table
  310.    wt: 1:   2 Prime and Composites less than 16
  311.    wt: 1:   1 video how Products are bigger than factor
  312.    wt: 1:   5 Long Division Include Zeroes or not
  313.    wt: 1:   Appendix 1 Counting Revisited 15 minute video
  314.    wt: 1:   013 Travel Time Tables
  315.    wt: 1:   31 Derivatives of inverse functions
  316.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  317.    wt: 1:   26 Chain Rule Recognising outer inner functions
  318.    wt: 1:   19 Chain Rule for linear functions
  319.    wt: 1:   13 sine and cosine derivatives 1st step
  320.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  321.    wt: 1:   12 Limits with Parameters and Derivatives Take I
  322.    wt: 1:   11 Limits at infinity Three Examples
  323.    wt: 1:   10 Three one sided limits with infinite values
  324.    wt: 1:   9 Limits Continuity and Composition
  325.    wt: 1:   8 Four Animated Examples
  326.    wt: 1:   7 Evaluation by immediate or delayed substitution
  327.    wt: 1:   6 Continuity at a point
  328.    wt: 1:   5 Jumps and absence of unlimited error control
  329.    wt: 1:   4 Numerical properties
  330.    wt: 1:   3 Decimal insights for limits continuity convergence
  331.    wt: 1:   2 Algebraic codification
  332.    wt: 1:   1 Numerical introduction
  333.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  334.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  335.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  336.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  337.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  338.    wt: 1:   F.5a Equicontinuity Theorems
  339.    wt: 1:   F.1 What Functions are Continuous
  340.    wt: 1:   B3 Bolzano Weierstrass Theorem
  341.    wt: 1:   Chapter 23 Links To Trigonometry
  342.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  343.    wt: 1:   Fall 1983 Calculus Appetizer
  344.    wt: 1:   Chapter 19. Functions and Sets
  345.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  346.    wt: 1:   Postscript A Three Remarks
  347.    wt: 1:   M Words to extend arithmetic
  348.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  349.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  350.    wt: 11:   13 Velocity Vectors in Physics
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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