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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9 matches:

  1.    wt: 3:   12 Comparison of Unsigned and Signed Numbers/
  2.    wt: 2:   Parent Center/
  3.    wt: 1:   5 Factored Polynomial Sign Analysis Examples/
  4.    wt: 1:   A Origins of Counting and Figuring Methods/
  5.    wt: 1:   10 Examples of Algebraic Reasoning/
  6.    wt: 1:   6 More Less Greater Than Inequalities and Comparison/
  7.    wt: 1:   2 Formula Forward Use Evaluation/
  8.    wt: 1:   8 Arithmetic with Signed Numbers/
  9.    wt: 1:   Volume 1 Elements of Reason/

Web Page Search

233 matches:

  1.    wt: 3:   27 Logarithmic use of products of sines and cosines
  2.    wt: 3:   1 Proper Equal Sign Usage
  3.    wt: 2:   15 Sign analysis of functions
  4.    wt: 2:   2 Algebraic use of function notation
  5.    wt: 2:   8 quadratics backward use of various formulas
  6.    wt: 2:   4 Resultant of a Sum of Movements
  7.    wt: 2:   6 Field Properties of Complex Number
  8.    wt: 2:   5 An Easy Proof of the Distributive Law
  9.    wt: 2:   2 Similar Triangles Equality of Corresponding Side Ratios
  10.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  11.    wt: 2:   A Measurement with Ruler Proper Use
  12.    wt: 2:   8 More Use of Maps Not Drawn to Scale
  13.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  14.    wt: 2:   22 Multiplication of Signed Numbers
  15.    wt: 2:   21 Addition of Multiples of a Single Vector
  16.    wt: 2:   19 Signed Multiples of Vectors
  17.    wt: 2:   11 Signed Number Addition and Addition Properties
  18.    wt: 2:   3 Properties of Square Roots with example
  19.    wt: 2:   5 lengths and signs of numbers
  20.    wt: 2:   2 signed and unsigned numbers as coordinates
  21.    wt: 2:   17 Derivatives of quotients of sine and cosine
  22.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  23.    wt: 2:   E2 Algebraic Properties of Limits
  24.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  25.    wt: 1:   2 arithmetic with signed numbers
  26.    wt: 1:   1 arithmetic with unsigned numbers
  27.    wt: 1:   Mathematics Education Professors
  28.    wt: 1:   Theory of Knowledge
  29.    wt: 1:   Different Kinds of Reasoning in maths
  30.    wt: 1:   three kinds of reason in mathematics
  31.    wt: 1:   E Kirchoffs Second Law
  32.    wt: 1:   D Kirchoff First Law
  33.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  34.    wt: 1:   22 Student Centered Highschool Mathematics
  35.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  36.    wt: 1:   8 The Effect of Negative Remarks
  37.    wt: 1:   sign monoticity analysis example 4
  38.    wt: 1:   sign monoticity analysis example 3
  39.    wt: 1:   sign monoticity analysis example 2
  40.    wt: 1:   sign monoticity analysis example 1
  41.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  42.    wt: 1:   8 Set view of relations and functions
  43.    wt: 1:   1 Geometric Introduction of Function Notation
  44.    wt: 1:   4 quadratics difference of two squares
  45.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  46.    wt: 1:   11 arctan left inverse of tangent Graph
  47.    wt: 1:   10 arctan left inverse of tangent Definition
  48.    wt: 1:   8 arcsin left inverse of sine Graph
  49.    wt: 1:   7 arcsin left inverse of sine Definition
  50.    wt: 1:   6 Graph of arccos function
  51.    wt: 1:   3 Left Inverse of cosine arccos definition
  52.    wt: 1:   2 cosine function more properties
  53.    wt: 1:   1 cosine function properties
  54.    wt: 1:   8 Radian Measures of Common Angles
  55.    wt: 1:   2 Radian Measure Numerical Value of one degree
  56.    wt: 1:   2 Signed Coordinates
  57.    wt: 1:   1 Unsigned Coordinates
  58.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  59.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  60.    wt: 1:   Straight Lines Intersection of
  61.    wt: 1:   B Straight Line Slope Scaling Properties More
  62.    wt: 1:   A Straight Line Slope Scaling Properties
  63.    wt: 1:   4 Tangent Function Properties
  64.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  65.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  66.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  67.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  68.    wt: 1:   32 seven rows of pascals triangle
  69.    wt: 1:   30 unit circle calculation of six trigonometric functions
  70.    wt: 1:   28 Expressing products of sines cosines as sums
  71.    wt: 1:   26 Formulas for products of sines and cosines
  72.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  73.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  74.    wt: 1:   18 sum of sinusoidal waves as a single wave
  75.    wt: 1:   17F Law of cosines
  76.    wt: 1:   13 Graph of tangent function many periods
  77.    wt: 1:   12 Graph of tangent function for one period
  78.    wt: 1:   10 Graphs of sines and cosines many periods
  79.    wt: 1:   9 Graphs of sine and cosine over one period
  80.    wt: 1:   8 period of tangent function
  81.    wt: 1:   7 period of sine and cosine
  82.    wt: 1:   Unit Circle Development of Trigonometry
  83.    wt: 1:   20 N th Roots of Complex Numbers
  84.    wt: 1:   19 N th Roots of Unity
  85.    wt: 1:   18 Sixth Roots of Unity
  86.    wt: 1:   17 Cube Roots of unity
  87.    wt: 1:   14 Law of cosines
  88.    wt: 1:   8 Unit Circle Development of Trigonometry
  89.    wt: 1:   4 Multiplication Properties
  90.    wt: 1:   3 Addition Properties
  91.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  92.    wt: 1:   9 Similarity of Triangles Usual Criteria
  93.    wt: 1:   8 Similarity of Triangles and Polygons
  94.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  95.    wt: 1:   3 Similarity by Design with coordinates
  96.    wt: 1:   2 Similarity By Design
  97.    wt: 1:   1 Early Concept of Like or Similar Shapes
  98.    wt: 1:   10 Midpoint of [a b] and [b a]
  99.    wt: 1:   6 Intersection of lines by solving linear systems
  100.    wt: 1:   5 Algebraic View of Slopes
  101.    wt: 1:   1 Numerical view of lines and their equations
  102.    wt: 1:   11 Triangle Inequality
  103.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  104.    wt: 1:   2 Cartesian Coordinates with signs
  105.    wt: 1:   1 Cartesian Coordinates sans signs
  106.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  107.    wt: 1:   17 Right Bisectors of Triangle Sides
  108.    wt: 1:   9 Construction of a right bisector
  109.    wt: 1:   3 Isometry of Triangles Congruence
  110.    wt: 1:   A Signed Number Arithmetic Review
  111.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  112.    wt: 1:   12 Real Numbers Line Signed Coordinates
  113.    wt: 1:   8 Division and Mulplication of Compound Fractions
  114.    wt: 1:   4 Location of Point in Decimal Addition
  115.    wt: 1:   3 Location of Point in Decimal Multiplication
  116.    wt: 1:   1 The Counting Origins of Numbers
  117.    wt: 1:   5 Areas of Rectangles Revisited
  118.    wt: 1:   3 Inequalities Algebraically
  119.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  120.    wt: 1:   5 Equality in Algebra
  121.    wt: 1:   5 Greater More Less Than Signs in General
  122.    wt: 1:   4 Comparison of Negative Numbers
  123.    wt: 1:   3 More and Less Than with Unlike Signs
  124.    wt: 1:   10 Real Number Lengths and Signs
  125.    wt: 1:   6 Unsigned Real Numbers
  126.    wt: 1:   11 Volume of Sphere
  127.    wt: 1:   10 Volume of Pyramid
  128.    wt: 1:   9 Volume of Cone
  129.    wt: 1:   6 Pythagorean Hypotenuse Calculation Example
  130.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  131.    wt: 1:   8 Sets of Numbers
  132.    wt: 1:   6 Three Notions of What is a Variable
  133.    wt: 1:   4 A Brief Story of numbers and algebra
  134.    wt: 1:   4 Greater More Less Than Signs in General
  135.    wt: 1:   3 Comparison of Negative Numbers
  136.    wt: 1:   2 More and Less Than with Unlike Signs
  137.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  138.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  139.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  140.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  141.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  142.    wt: 1:   4 LCM of 8 and 10 via Prime
  143.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  144.    wt: 1:   10 dividing signed numbers
  145.    wt: 1:   9 subtracting signed numbers
  146.    wt: 1:   8 multiplying signed numbers
  147.    wt: 1:   6 adding signed numbers
  148.    wt: 1:   4 signed coordinates for regions in space
  149.    wt: 1:   3 signed coordinates for maps and planes
  150.    wt: 1:   6 Simplification of Fractions with Units
  151.    wt: 1:   2 Equality and Units
  152.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  153.    wt: 1:   21 Working With Signs
  154.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  155.    wt: 1:   9 Improper Fractions and Mixed Numbers
  156.    wt: 1:   6 Multiplication of Mixed Numbers
  157.    wt: 1:   3 Unit fraction of a fraction
  158.    wt: 1:   8 Multiplication by Signed Numbers Integers
  159.    wt: 1:   7 Multiplication by Signs
  160.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  161.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  162.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  163.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  164.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  165.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  166.    wt: 1:   20 Uniqueness of Prime Factorization
  167.    wt: 1:   16 video Factors of 980 using prime
  168.    wt: 1:   15 video Factors of 20 using Prime Factorization
  169.    wt: 1:   14 video Factors of 24 Take II
  170.    wt: 1:   13 video Factors of 24 using prime
  171.    wt: 1:   11 Efficient Square Rule Use
  172.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  173.    wt: 1:   C Counting Areas with Powers of Ten
  174.    wt: 1:   B Powers of Ten
  175.    wt: 1:   8 Subtraction with Units of Measure
  176.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  177.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  178.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  179.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  180.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  181.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  182.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  183.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  184.    wt: 1:   Quick history of numbers and algebra
  185.    wt: 1:   012 Division of Time Intervals by Time Intervals
  186.    wt: 1:   011 Division of Time Intervals By Numbers
  187.    wt: 1:   010 Repeated Addition of Time Intervals
  188.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  189.    wt: 1:   8 Addition of Time Intervals via subtotaling
  190.    wt: 1:   7 Addition of Time Intervals
  191.    wt: 1:   4 Mixing and Changing Units of Time
  192.    wt: 1:   3 Units and Lengths of Time
  193.    wt: 1:   1 Intro of Kids To Time Date Skills
  194.    wt: 1:   Example 2 volume of a cone
  195.    wt: 1:   Example 1 volume of a pyramid
  196.    wt: 1:   Volume of Solid by Cross Sections Lesson
  197.    wt: 1:   Example 4 with x function of y
  198.    wt: 1:   34 Derivative of exponential function
  199.    wt: 1:   31 Derivatives of inverse functions
  200.    wt: 1:   30Chain Rule A Proof
  201.    wt: 1:   28 Chain Rule Preparation for a Proof
  202.    wt: 1:   8 Differentiation of polynomials
  203.    wt: 1:   5 Jumps and absence of unlimited error control
  204.    wt: 1:   4 Numerical properties
  205.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  206.    wt: 1:   G.3 Constant Difference Theorem Proof
  207.    wt: 1:   E1 Error Control Inequalities
  208.    wt: 1:   D2 Limits of Monotone Sequences
  209.    wt: 1:   C Triangle Inequalities
  210.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  211.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  212.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  213.    wt: 1:   Chapter 5. Slope Sign Tests
  214.    wt: 1:   Chapter 4. More Slope Sign Analysis
  215.    wt: 1:   Chapter 3. Slope Sign Analysis
  216.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  217.    wt: 1:   Chapter 6 Change of Language
  218.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  219.    wt: 1:   Chapter 4 Longer Chains of Reason
  220.    wt: 1:   Chapter 3 Chains of Reason
  221.    wt: 1:   Chapter 7 Two Treatments of Geometry
  222.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  223.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  224.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  225.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  226.    wt: 1:   Chapter 8 Change of Language
  227.    wt: 1:   Chapter 7 Longer Chains of Reason
  228.    wt: 1:   Chapter 6 Chains of Reason
  229.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  230.    wt: 1:   C. Domino effect of being careful
  231.    wt: 1:   B. Domino effect of errors
  232.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  233.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions

Extended Search

289 matches:

  1.    wt: 4:   4 Greater More Less Than Signs in General
  2.    wt: 4:   3 Comparison of Negative Numbers
  3.    wt: 4:   2 More and Less Than with Unlike Signs
  4.    wt: 3:   27 Graduated Correction and Penalties for Young Offenders
  5.    wt: 3:   22 Student Centered Highschool Mathematics
  6.    wt: 3:   19 Extending the Oral Dimension of Mathematics
  7.    wt: 3:   8 The Effect of Negative Remarks
  8.    wt: 3:   27 Logarithmic use of products of sines and cosines
  9.    wt: 3:   1 Proper Equal Sign Usage
  10.    wt: 3:   1 More and Less Than for Counts and Measures
  11.    wt: 3:   5 lengths and signs of numbers
  12.    wt: 3:   2 signed and unsigned numbers as coordinates
  13.    wt: 2:   Home Tutoring and Home Schooling
  14.    wt: 2:   25 Mathematics Education Leaving A Good Impression
  15.    wt: 2:   24 Standards For Skill Develoment Take II
  16.    wt: 2:   24 Standards For Skill Develoment
  17.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take IV
  18.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take III
  19.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take II
  20.    wt: 2:   23 Modularized Skill Development Modularized Rigor
  21.    wt: 2:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  22.    wt: 2:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  23.    wt: 2:   18 Primary School Mathematics
  24.    wt: 2:   17 Math Booklets for children and young teenagers
  25.    wt: 2:   16 Secondary Mathematics Tips
  26.    wt: 2:   15 Counting For Parents
  27.    wt: 2:   14 Multiplication and Times Tables
  28.    wt: 2:   13 Addition and Addition Tables
  29.    wt: 2:   12 Goals and Objectives For Mathematics
  30.    wt: 2:   11 Help and Defend Your Child or Teens Education
  31.    wt: 2:   10 Ends values for work study instruction
  32.    wt: 2:   9 Streaming by Student Cooperation
  33.    wt: 2:   7 Student Motivation
  34.    wt: 2:   6 Discipline Who is in Charge Conserving Authority
  35.    wt: 2:   5 Patience Please for Yourself and Your Charges
  36.    wt: 2:   4 Learning Takes Time and Effort
  37.    wt: 2:   3 Preparing for Science Studies
  38.    wt: 2:   2 Reading and Writing Skills
  39.    wt: 2:   1 Speaking Skills
  40.    wt: 2:   sign monoticity analysis example 4
  41.    wt: 2:   sign monoticity analysis example 3
  42.    wt: 2:   sign monoticity analysis example 2
  43.    wt: 2:   sign monoticity analysis example 1
  44.    wt: 2:   15 Sign analysis of functions
  45.    wt: 2:   2 Algebraic use of function notation
  46.    wt: 2:   8 quadratics backward use of various formulas
  47.    wt: 2:   4 Resultant of a Sum of Movements
  48.    wt: 2:   6 Field Properties of Complex Number
  49.    wt: 2:   5 An Easy Proof of the Distributive Law
  50.    wt: 2:   2 Similar Triangles Equality of Corresponding Side Ratios
  51.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  52.    wt: 2:   A Measurement with Ruler Proper Use
  53.    wt: 2:   8 More Use of Maps Not Drawn to Scale
  54.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  55.    wt: 2:   22 Multiplication of Signed Numbers
  56.    wt: 2:   21 Addition of Multiples of a Single Vector
  57.    wt: 2:   19 Signed Multiples of Vectors
  58.    wt: 2:   11 Signed Number Addition and Addition Properties
  59.    wt: 2:   1 The Counting Origins of Numbers
  60.    wt: 2:   5 Areas of Rectangles Revisited
  61.    wt: 2:   3 Inequalities Algebraically
  62.    wt: 2:   5 Greater More Less Than Signs in General
  63.    wt: 2:   4 Comparison of Negative Numbers
  64.    wt: 2:   3 More and Less Than with Unlike Signs
  65.    wt: 2:   11 Volume of Sphere
  66.    wt: 2:   10 Volume of Pyramid
  67.    wt: 2:   9 Volume of Cone
  68.    wt: 2:   6 Pythagorean Hypotenuse Calculation Example
  69.    wt: 2:   3 Properties of Square Roots with example
  70.    wt: 2:   10 dividing signed numbers
  71.    wt: 2:   9 subtracting signed numbers
  72.    wt: 2:   8 multiplying signed numbers
  73.    wt: 2:   6 adding signed numbers
  74.    wt: 2:   4 signed coordinates for regions in space
  75.    wt: 2:   3 signed coordinates for maps and planes
  76.    wt: 2:   17 Derivatives of quotients of sine and cosine
  77.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  78.    wt: 2:   E2 Algebraic Properties of Limits
  79.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  80.    wt: 1:   2 arithmetic with signed numbers
  81.    wt: 1:   1 arithmetic with unsigned numbers
  82.    wt: 1:   Mathematics Education Professors
  83.    wt: 1:   Theory of Knowledge
  84.    wt: 1:   Different Kinds of Reasoning in maths
  85.    wt: 1:   three kinds of reason in mathematics
  86.    wt: 1:   E Kirchoffs Second Law
  87.    wt: 1:   D Kirchoff First Law
  88.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  89.    wt: 1:   8 Set view of relations and functions
  90.    wt: 1:   1 Geometric Introduction of Function Notation
  91.    wt: 1:   4 quadratics difference of two squares
  92.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  93.    wt: 1:   11 arctan left inverse of tangent Graph
  94.    wt: 1:   10 arctan left inverse of tangent Definition
  95.    wt: 1:   8 arcsin left inverse of sine Graph
  96.    wt: 1:   7 arcsin left inverse of sine Definition
  97.    wt: 1:   6 Graph of arccos function
  98.    wt: 1:   3 Left Inverse of cosine arccos definition
  99.    wt: 1:   2 cosine function more properties
  100.    wt: 1:   1 cosine function properties
  101.    wt: 1:   8 Radian Measures of Common Angles
  102.    wt: 1:   2 Radian Measure Numerical Value of one degree
  103.    wt: 1:   2 Signed Coordinates
  104.    wt: 1:   1 Unsigned Coordinates
  105.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  106.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  107.    wt: 1:   Straight Lines Intersection of
  108.    wt: 1:   B Straight Line Slope Scaling Properties More
  109.    wt: 1:   A Straight Line Slope Scaling Properties
  110.    wt: 1:   4 Tangent Function Properties
  111.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  112.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  113.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  114.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  115.    wt: 1:   32 seven rows of pascals triangle
  116.    wt: 1:   30 unit circle calculation of six trigonometric functions
  117.    wt: 1:   28 Expressing products of sines cosines as sums
  118.    wt: 1:   26 Formulas for products of sines and cosines
  119.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  120.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  121.    wt: 1:   18 sum of sinusoidal waves as a single wave
  122.    wt: 1:   17F Law of cosines
  123.    wt: 1:   13 Graph of tangent function many periods
  124.    wt: 1:   12 Graph of tangent function for one period
  125.    wt: 1:   10 Graphs of sines and cosines many periods
  126.    wt: 1:   9 Graphs of sine and cosine over one period
  127.    wt: 1:   8 period of tangent function
  128.    wt: 1:   7 period of sine and cosine
  129.    wt: 1:   Unit Circle Development of Trigonometry
  130.    wt: 1:   20 N th Roots of Complex Numbers
  131.    wt: 1:   19 N th Roots of Unity
  132.    wt: 1:   18 Sixth Roots of Unity
  133.    wt: 1:   17 Cube Roots of unity
  134.    wt: 1:   14 Law of cosines
  135.    wt: 1:   8 Unit Circle Development of Trigonometry
  136.    wt: 1:   4 Multiplication Properties
  137.    wt: 1:   3 Addition Properties
  138.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  139.    wt: 1:   9 Similarity of Triangles Usual Criteria
  140.    wt: 1:   8 Similarity of Triangles and Polygons
  141.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  142.    wt: 1:   3 Similarity by Design with coordinates
  143.    wt: 1:   2 Similarity By Design
  144.    wt: 1:   1 Early Concept of Like or Similar Shapes
  145.    wt: 1:   10 Midpoint of [a b] and [b a]
  146.    wt: 1:   6 Intersection of lines by solving linear systems
  147.    wt: 1:   5 Algebraic View of Slopes
  148.    wt: 1:   1 Numerical view of lines and their equations
  149.    wt: 1:   11 Triangle Inequality
  150.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  151.    wt: 1:   2 Cartesian Coordinates with signs
  152.    wt: 1:   1 Cartesian Coordinates sans signs
  153.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  154.    wt: 1:   17 Right Bisectors of Triangle Sides
  155.    wt: 1:   9 Construction of a right bisector
  156.    wt: 1:   3 Isometry of Triangles Congruence
  157.    wt: 1:   A Signed Number Arithmetic Review
  158.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  159.    wt: 1:   12 Real Numbers Line Signed Coordinates
  160.    wt: 1:   8 Division and Mulplication of Compound Fractions
  161.    wt: 1:   4 Location of Point in Decimal Addition
  162.    wt: 1:   3 Location of Point in Decimal Multiplication
  163.    wt: 1:   E Long Division Methods more
  164.    wt: 1:   D Long Division Methods
  165.    wt: 1:   C Three Decimal Subtraction Methods
  166.    wt: 1:   B Decimal Comparison and Subtraction
  167.    wt: 1:   A Decimal Addition Columm Methods
  168.    wt: 1:   8 Column Multiplication Methods in General
  169.    wt: 1:   7 Decimals Multiplication Methods Examples
  170.    wt: 1:   6 Column Methods for Decimal Multiplication
  171.    wt: 1:   5 Distributive Law for Whole Numbers
  172.    wt: 1:   4 Commutative Law Groups Counting Form
  173.    wt: 1:   3 Multiplicative Counting Skills Principles
  174.    wt: 1:   2 Combing Counts Addition Skills and Principles
  175.    wt: 1:   4 Fraction Operations Axiomatic Development
  176.    wt: 1:   2 Fraction Operations Physical Development
  177.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  178.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  179.    wt: 1:   5 Equality in Algebra
  180.    wt: 1:   2 More and Less Than for Counts and Measures
  181.    wt: 1:   1 Real Numbers Comparison
  182.    wt: 1:   10 Real Number Lengths and Signs
  183.    wt: 1:   6 Unsigned Real Numbers
  184.    wt: 1:   13 Naming Identifying Formulas with Words
  185.    wt: 1:   12 Cone Cylinder Sphere Lesson Idea
  186.    wt: 1:   8 Compound Interest Formula Evaluation
  187.    wt: 1:   7 Compound Interest Formula Introduction
  188.    wt: 1:   5 Box Volume Formula Example
  189.    wt: 1:   4 Circle Area Formula Example
  190.    wt: 1:   3 Triangle Area Formula Example
  191.    wt: 1:   2 Another Rectangle Area Formula Example
  192.    wt: 1:   1 Written work formats for developing and showing skill
  193.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  194.    wt: 1:   8 Sets of Numbers
  195.    wt: 1:   6 Three Notions of What is a Variable
  196.    wt: 1:   4 A Brief Story of numbers and algebra
  197.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  198.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  199.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  200.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  201.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  202.    wt: 1:   4 LCM of 8 and 10 via Prime
  203.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  204.    wt: 1:   11 What are real lengths and numbers
  205.    wt: 1:   7 negative and additive inverse
  206.    wt: 1:   6 Simplification of Fractions with Units
  207.    wt: 1:   2 Equality and Units
  208.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  209.    wt: 1:   21 Working With Signs
  210.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  211.    wt: 1:   9 Improper Fractions and Mixed Numbers
  212.    wt: 1:   6 Multiplication of Mixed Numbers
  213.    wt: 1:   3 Unit fraction of a fraction
  214.    wt: 1:   8 Multiplication by Signed Numbers Integers
  215.    wt: 1:   7 Multiplication by Signs
  216.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  217.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  218.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  219.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  220.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  221.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  222.    wt: 1:   20 Uniqueness of Prime Factorization
  223.    wt: 1:   16 video Factors of 980 using prime
  224.    wt: 1:   15 video Factors of 20 using Prime Factorization
  225.    wt: 1:   14 video Factors of 24 Take II
  226.    wt: 1:   13 video Factors of 24 using prime
  227.    wt: 1:   11 Efficient Square Rule Use
  228.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  229.    wt: 1:   C Counting Areas with Powers of Ten
  230.    wt: 1:   B Powers of Ten
  231.    wt: 1:   8 Subtraction with Units of Measure
  232.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  233.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  234.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  235.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  236.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  237.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  238.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  239.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  240.    wt: 1:   Quick history of numbers and algebra
  241.    wt: 1:   012 Division of Time Intervals by Time Intervals
  242.    wt: 1:   011 Division of Time Intervals By Numbers
  243.    wt: 1:   010 Repeated Addition of Time Intervals
  244.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  245.    wt: 1:   8 Addition of Time Intervals via subtotaling
  246.    wt: 1:   7 Addition of Time Intervals
  247.    wt: 1:   4 Mixing and Changing Units of Time
  248.    wt: 1:   3 Units and Lengths of Time
  249.    wt: 1:   1 Intro of Kids To Time Date Skills
  250.    wt: 1:   Example 2 volume of a cone
  251.    wt: 1:   Example 1 volume of a pyramid
  252.    wt: 1:   Volume of Solid by Cross Sections Lesson
  253.    wt: 1:   Example 4 with x function of y
  254.    wt: 1:   34 Derivative of exponential function
  255.    wt: 1:   31 Derivatives of inverse functions
  256.    wt: 1:   30Chain Rule A Proof
  257.    wt: 1:   28 Chain Rule Preparation for a Proof
  258.    wt: 1:   8 Differentiation of polynomials
  259.    wt: 1:   5 Jumps and absence of unlimited error control
  260.    wt: 1:   4 Numerical properties
  261.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  262.    wt: 1:   G.3 Constant Difference Theorem Proof
  263.    wt: 1:   E1 Error Control Inequalities
  264.    wt: 1:   D2 Limits of Monotone Sequences
  265.    wt: 1:   C Triangle Inequalities
  266.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  267.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  268.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  269.    wt: 1:   Chapter 5. Slope Sign Tests
  270.    wt: 1:   Chapter 4. More Slope Sign Analysis
  271.    wt: 1:   Chapter 3. Slope Sign Analysis
  272.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  273.    wt: 1:   Chapter 6 Change of Language
  274.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  275.    wt: 1:   Chapter 4 Longer Chains of Reason
  276.    wt: 1:   Chapter 3 Chains of Reason
  277.    wt: 1:   Chapter 7 Two Treatments of Geometry
  278.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  279.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  280.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  281.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  282.    wt: 1:   Chapter 8 Change of Language
  283.    wt: 1:   Chapter 7 Longer Chains of Reason
  284.    wt: 1:   Chapter 6 Chains of Reason
  285.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  286.    wt: 1:   C. Domino effect of being careful
  287.    wt: 1:   B. Domino effect of errors
  288.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  289.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions

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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