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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18 matches:

  1.    wt: 7:   1 Maps Plans Measurement/
  2.    wt: 6:   13 Vectors/
  3.    wt: 6:   8 Unit Circle Trigonometry/
  4.    wt: 6:   6 Trigonometry first steps/
  5.    wt: 5:   15 Arc or Inverse Trigonometric Function/
  6.    wt: 5:   14 Degrees to Radians and Radians to Degrees/
  7.    wt: 5:   12 Function Translating and Rescaling/
  8.    wt: 5:   11 Parallel Straight Lines and Transversals/
  9.    wt: 5:   10 Intersecting Straight Lines and Transversals/
  10.    wt: 5:   9 Lines and Slopes Take 2 with tangent function/
  11.    wt: 5:   7 Complex Numbers/
  12.    wt: 5:   5 What is Similarity/
  13.    wt: 5:   4 Lines and Slopes Take 1/
  14.    wt: 5:   3 Cartesian and Polar Coordinates/
  15.    wt: 5:   2 Euclidean Geometry Constructions Theory extras/
  16.    wt: 5:   Geometry maps plans trigonometry vectors/
  17.    wt: 1:   2 Natural Logarithms Exponentials Powers Roots/
  18.    wt: 1:   11 Squares and Square Roots/

Web Page Search

42 matches:

  1.    wt: 2:   Maps Plans Drawings
  2.    wt: 2:   4 Angles on Maps Plans drawn to scale
  3.    wt: 2:   3 Lengths and Areas on Maps and Plans
  4.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  5.    wt: 1:   About site lesson plans
  6.    wt: 1:   7 Formulas for Roots with Logarithms Derivation
  7.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  8.    wt: 1:   2 Square Root Simplification a prequel
  9.    wt: 1:   13 Velocity Vectors in Physics
  10.    wt: 1:   8 Parallel Vectors
  11.    wt: 1:   6 Vectors with Coordinates
  12.    wt: 1:   3 Navigation with Arrows or Vectors
  13.    wt: 1:   Unit Circle Development of Trigonometry
  14.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  15.    wt: 1:   20 N th Roots of Complex Numbers
  16.    wt: 1:   19 N th Roots of Unity
  17.    wt: 1:   18 Sixth Roots of Unity
  18.    wt: 1:   17 Cube Roots of unity
  19.    wt: 1:   8 Unit Circle Development of Trigonometry
  20.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  21.    wt: 1:   Why Trigonometry the whyslopes view
  22.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  23.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  24.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  25.    wt: 1:   6 Figuring with Maps Not to Scale
  26.    wt: 1:   19 Signed Multiples of Vectors
  27.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  28.    wt: 1:   13 Arrows and Vectors in a Plane
  29.    wt: 1:   8 Coordinates for Maps and Planes
  30.    wt: 1:   5 Square Roots with primes more still
  31.    wt: 1:   4 Square Roots with primes more
  32.    wt: 1:   3 Properties of Square Roots with example
  33.    wt: 1:   2 Square Roots with Prime
  34.    wt: 1:   1 Squares and Square Roots Introduction
  35.    wt: 1:   3 signed coordinates for maps and planes
  36.    wt: 1:   6 Simplification of Fractions with Units
  37.    wt: 1:   11 Simplification an Algebraic View
  38.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  39.    wt: 1:   38 Formulas and derivatives for powers and roots
  40.    wt: 1:   Chapter 23 Links To Trigonometry
  41.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  42.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry

Extended Search

261 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 More Use of Maps Not Drawn to Scale
  4.    wt: 8:   6 Figuring with Maps Not to Scale
  5.    wt: 7:   13 Velocity Vectors in Physics
  6.    wt: 7:   8 Parallel Vectors
  7.    wt: 7:   6 Vectors with Coordinates
  8.    wt: 7:   3 Navigation with Arrows or Vectors
  9.    wt: 7:   Unit Circle Development of Trigonometry
  10.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  11.    wt: 7:   6 Trigonometry Sines of Supplementary Angles
  12.    wt: 7:   Why Trigonometry the whyslopes view
  13.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  14.    wt: 7:   A Measurement with Ruler Proper Use
  15.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  16.    wt: 7:   2 Measuring Area Directly
  17.    wt: 7:   1 Length Measurement
  18.    wt: 6:   A Global Time and Navigation
  19.    wt: 6:   15 Dot and Cross Product
  20.    wt: 6:   14 Why Scalar Multiplication Distributes Physical Argument
  21.    wt: 6:   12 From Applied To Pure Mathematics
  22.    wt: 6:   11 Component Method
  23.    wt: 6:   10 Parallelogram Addition Method
  24.    wt: 6:   9 Head to Tail Coordinate View
  25.    wt: 6:   7 Coordinate Addition and Scalar Multiplication
  26.    wt: 6:   5 Head To Tail Arrow Addition
  27.    wt: 6:   4 Resultant of a Sum of Movements
  28.    wt: 6:   2 Signed Coordinates
  29.    wt: 6:   1 Unsigned Coordinates
  30.    wt: 6:   Vector and Complex Number Applet
  31.    wt: 6:   17 tangent function angle sum formulas
  32.    wt: 6:   35 sines and cosines of 2A 3A 4A 5A
  33.    wt: 6:   34 sines and cosines of 2A 3A 4A 5A
  34.    wt: 6:   33 sines and cosines of 2A 3A 4A 5A
  35.    wt: 6:   32 seven rows of pascals triangle
  36.    wt: 6:   31 basic secant cosecant cotangent trig identities
  37.    wt: 6:   30 unit circle calculation of six trigonometric functions
  38.    wt: 6:   29 secant cosecant and cotangent for acute angles
  39.    wt: 6:   28 Expressing products of sines cosines as sums
  40.    wt: 6:   27 Logarithmic use of products of sines and cosines
  41.    wt: 6:   26 Formulas for products of sines and cosines
  42.    wt: 6:   25 tangent double angle formula Slope connection
  43.    wt: 6:   24 tangent Angle Difference Formula
  44.    wt: 6:   23 sine and cosine of 180 plus 22.5 degrees
  45.    wt: 6:   22 sine of 22.5 degrees via half angle formulas
  46.    wt: 6:   21 sine and cosine Half Angle Formulas
  47.    wt: 6:   20 sine and cosine Double Angle Formulas
  48.    wt: 6:   19 Pythagorean Identity For sine and cosine functions
  49.    wt: 6:   18 sum of sinusoidal waves as a single wave
  50.    wt: 6:   17G Pythagorean Theorem Converse
  51.    wt: 6:   17F Law of cosines
  52.    wt: 6:   17E Trig Formulas for dot and cross Products
  53.    wt: 6:   17D cis formulas for sine cosines and tangent
  54.    wt: 6:   17C sine and cosine double triple angle formulas
  55.    wt: 6:   17B sine cosine Angle Sum Formulas via cis
  56.    wt: 6:   17A The complex number valued trig function cis
  57.    wt: 6:   16 Right Triangle Complementary Angle Relations
  58.    wt: 6:   15 sine cosine Complementary Angle Relations
  59.    wt: 6:   14 cosine even and sine and tangent are odd
  60.    wt: 6:   13 Graph of tangent function many periods
  61.    wt: 6:   12 Graph of tangent function for one period
  62.    wt: 6:   11 tangent function undefined when terminal side vertical
  63.    wt: 6:   10 Graphs of sines and cosines many periods
  64.    wt: 6:   9 Graphs of sine and cosine over one period
  65.    wt: 6:   8 period of tangent function
  66.    wt: 6:   7 period of sine and cosine
  67.    wt: 6:   6 sines and cosines for reference angle 30 degrees
  68.    wt: 6:   5 sines and cosines for reference angle 60 degrees
  69.    wt: 6:   4 sines and cosines for reference angle 45 degrees
  70.    wt: 6:   3 sines and cosines for reference angle 90 degrees
  71.    wt: 6:   2 Quadrant I reference Angles
  72.    wt: 6:   1 Unit Points Reflections Rotations
  73.    wt: 6:   20 N th Roots of Complex Numbers
  74.    wt: 6:   19 N th Roots of Unity
  75.    wt: 6:   18 Sixth Roots of Unity
  76.    wt: 6:   17 Cube Roots of unity
  77.    wt: 6:   8 Unit Circle Development of Trigonometry
  78.    wt: 6:   8 Triangles Cascade Problem Solving
  79.    wt: 6:   7 Trignometric Ratios Unit Circle
  80.    wt: 6:   5 Trigonometric Ratios For Tangent and Special Triangles
  81.    wt: 6:   4 Trigonometric Ratios For Two Special Triangles
  82.    wt: 6:   3 Trigonometric Ratios sine and cosine
  83.    wt: 6:   2 Similar Triangles Equality of Corresponding Side Ratios
  84.    wt: 6:   1 Angle Measurement with Degrees
  85.    wt: 6:   PS C Similarity Use Recognize it in Trigonometry
  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:   16 References and Originality Question
  147.    wt: 5:   15 Pythagorean Theorem Converse
  148.    wt: 5:   14 Law of cosines
  149.    wt: 5:   13 Trig Formulas for dot and cross Products
  150.    wt: 5:   12 cis formulas for sine cosines and tangent
  151.    wt: 5:   11 sine and cosine double triple angle formulas
  152.    wt: 5:   10 sine cosine Angle Sum Formulas via cis
  153.    wt: 5:   9 The complex number valued trig function cis
  154.    wt: 5:   7 Second Way to Calculate Products
  155.    wt: 5:   6 Field Properties of Complex Number
  156.    wt: 5:   5 An Easy Proof of the Distributive Law
  157.    wt: 5:   4 Multiplication Properties
  158.    wt: 5:   3 Addition Properties
  159.    wt: 5:   2 Complex Numbers made easier we hope
  160.    wt: 5:   1 Rectangular Polar Coordinates Review
  161.    wt: 5:   Appetizer A Complex Number Applet
  162.    wt: 5:   13 Navigation Location from Angles to 2 Landmarks
  163.    wt: 5:   12 Triangles Similarity More Problems
  164.    wt: 5:   11 Triangle Similarity Missing Side Problem
  165.    wt: 5:   10 Similarity of Triangles Equivalent of Two Criteria
  166.    wt: 5:   9 Similarity of Triangles Usual Criteria
  167.    wt: 5:   8 Similarity of Triangles and Polygons
  168.    wt: 5:   7 Translations Rotations Reflections Dilatations
  169.    wt: 5:   6 Geometric Diagrams in Class
  170.    wt: 5:   5 Similarity of Circles Squares and Rectangles
  171.    wt: 5:   4 Similarity Definition with Coordinate
  172.    wt: 5:   3 Similarity by Design with coordinates
  173.    wt: 5:   2 Similarity By Design
  174.    wt: 5:   1 Early Concept of Like or Similar Shapes
  175.    wt: 5:   Four Simple Exercises
  176.    wt: 5:   12 Links Lessons elsewhere
  177.    wt: 5:   11 A Partial Summary
  178.    wt: 5:   10 Midpoint of [a b] and [b a]
  179.    wt: 5:   9 Midpoint Coordinates Half Endpoint Sum
  180.    wt: 5:   8 Mid Point Formula
  181.    wt: 5:   7 Exercises to test skill and concept mastery
  182.    wt: 5:   6 Intersection of lines by solving linear systems
  183.    wt: 5:   5 Algebraic View of Slopes
  184.    wt: 5:   4 Equations for lines three forms
  185.    wt: 5:   3 Slope product for perpendicular lines
  186.    wt: 5:   2 point slope equation for a line
  187.    wt: 5:   1 Numerical view of lines and their equations
  188.    wt: 5:   What is and is not here
  189.    wt: 5:   13 Pythagorean spatial distance formulas
  190.    wt: 5:   12 Spatial Coordinates
  191.    wt: 5:   11 Triangle Inequality
  192.    wt: 5:   10 Pythagorean plane distance formula
  193.    wt: 5:   9 Pythagorean Theorem Chinese Square Proof
  194.    wt: 5:   8 Distance Between Points on a Line
  195.    wt: 5:   7 Complex Numbers Appetizer
  196.    wt: 5:   6 Polar Multiplication and Rotation
  197.    wt: 5:   5 Cartesian Addition and Translation
  198.    wt: 5:   4 Polar Coordinates to and from
  199.    wt: 5:   3 Rectangular Coordinates Review
  200.    wt: 5:   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:   13 Angle Side Angle Failure
  218.    wt: 5:   12 Side Angle Side Failure
  219.    wt: 5:   11 Triangle Construction Fails
  220.    wt: 5:   10 Dropping a perpendicular to line
  221.    wt: 5:   9 Construction of a right bisector
  222.    wt: 5:   8 Isoceles Triangles
  223.    wt: 5:   7 Angle Side Angle
  224.    wt: 5:   6 Ruler and compass Angle Bisection
  225.    wt: 5:   5 Side Angle Side
  226.    wt: 5:   4 Side Side Side
  227.    wt: 5:   3 Isometry of Triangles Congruence
  228.    wt: 5:   2 Correspondence between Triangles
  229.    wt: 5:   1 Initial Concepts and Terms
  230.    wt: 5:   Short Course on Euclidean Geometry
  231.    wt: 5:   About Folder Contents
  232.    wt: 2:   Maps Plans Drawings
  233.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  234.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  235.    wt: 2:   2 Square Root Simplification a prequel
  236.    wt: 2:   5 Square Roots with primes more still
  237.    wt: 2:   4 Square Roots with primes more
  238.    wt: 2:   3 Properties of Square Roots with example
  239.    wt: 2:   2 Square Roots with Prime
  240.    wt: 2:   1 Squares and Square Roots Introduction
  241.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  242.    wt: 1:   About site lesson plans
  243.    wt: 1:   11 Growth and Decay in Biology
  244.    wt: 1:   10 Exponential Growth and Decay Models
  245.    wt: 1:   9 Formulas for Real Exponents with Logarithms
  246.    wt: 1:   8 Formulas for Fractional Exponents with Logarithms
  247.    wt: 1:   5 Natural Logarithm Calculator Exercises
  248.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  249.    wt: 1:   1 Calculator Starter Exercises
  250.    wt: 1:   19 Signed Multiples of Vectors
  251.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  252.    wt: 1:   13 Arrows and Vectors in a Plane
  253.    wt: 1:   8 Coordinates for Maps and Planes
  254.    wt: 1:   3 signed coordinates for maps and planes
  255.    wt: 1:   6 Simplification of Fractions with Units
  256.    wt: 1:   11 Simplification an Algebraic View
  257.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  258.    wt: 1:   38 Formulas and derivatives for powers and roots
  259.    wt: 1:   Chapter 23 Links To Trigonometry
  260.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  261.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
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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