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

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

Ages 15+: Why study slopes Polynomials Quadratics Why factor polynomials Logarithms Functions
What is similarity Euclidean geometry leanly Coordinates + complex no.s Vectors DC Electric Circuits
Ages 12+: Prime factorization Written work formats Decimal place value Extend arithmetic skills orally
What is a variable 5. Fraction Operations by Raising Terms Solving Linear Equations: Take I Take II

Online Volumes: 1 - Elements of Reason, 2 - 3 Skills For Algebra, 3 - Why Slopes and
More Math, 1A - Pattern Based Reason, 1B - Skill Development Principles + Troubles

Welcome: Site content may develop critical thinking, improve reading and writing, and build mathematics skills. See online chapters on on logic and pattern based reason.

Teachers: This December 2011, 5-phase framework offers a context for mathematics & logic instruction. Phases 1 to 3 focus on skills with actual or potential value for adult & daily life. College-oriented phases 5 & 4 focus on calculus & preparation for it. Phases 1 to 4 may also serve trades & professions not dependent on calculus.

Site Review: Math resources ... span ... arithmetic, logic, algebra, calculus, complex numbers, and Euclidean geometry. Lessons and how-tos .... provide a good foundation for high school and college ... mathematics. Read more.

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24 matches:

  1.    wt: 8:   Step 3 Easy systems in 2 or more unknowns/
  2.    wt: 7:   Step 4 Gaussian Elimination/
  3.    wt: 7:   Step 2 Algebraic solutions for one unknown/
  4.    wt: 7:   Step 1 Stick diagram and fractions/
  5.    wt: 7:   3 Solving Linear Equations/
  6.    wt: 4:   7 Axioms Logic and Equivalent Equations/
  7.    wt: 3:   B Real Numbers Extrinsic Development/
  8.    wt: 3:   A Origins of Counting and Figuring Methods/
  9.    wt: 3:   10 Examples of Algebraic Reasoning/
  10.    wt: 3:   9 Proportionality Backwards and Forwards/
  11.    wt: 3:   8 Unifying Theme For Algebra/
  12.    wt: 3:   6 More Less Greater Than Inequalities and Comparison/
  13.    wt: 3:   5 Real Numbers/
  14.    wt: 3:   4 Computation Rules and Function Notation/
  15.    wt: 3:   2 Formula Forward Use Evaluation/
  16.    wt: 3:   1 Working With Sets/
  17.    wt: 3:   Algebra Starter Lessons/
  18.    wt: 3:   12 Webvideo Lessons on Area and Volume Calculation/
  19.    wt: 3:   5 Lessons on Integration/
  20.    wt: 3:   4 Lessons on Using Derivatives/
  21.    wt: 3:   38 Lessons on Calculating Derivatives/
  22.    wt: 3:   13 Lessons on Limits and Continuity/
  23.    wt: 2:   70 Calculus Starter Lessons/
  24.    wt: 1:   Mathematics 506 Lessons/

Web Page Search

30 matches:

  1.    wt: 3:   6 Intersection of lines by solving linear systems
  2.    wt: 3:   Chapter 15. Solving Linear Equations
  3.    wt: 2:   Straight Lines Instersection Solving Equations
  4.    wt: 2:   6 Equations and Systems Equivalent or Implied
  5.    wt: 2:   Chapter 3 Algebra Starter Lessons
  6.    wt: 1:   G LAMP Introduction Problem Solving Skills
  7.    wt: 1:   1 Calculator Starter Exercises
  8.    wt: 1:   7 Links Lessons Elsewhere
  9.    wt: 1:   5 Polynomials Long division Nonlinear divisor
  10.    wt: 1:   4 Polynomials Long division linear divisor
  11.    wt: 1:   14 Straight Lines Equations General Case
  12.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  13.    wt: 1:   10 Straight Lines through Origin Equations More
  14.    wt: 1:   9 Straight Lines through Origin Equations
  15.    wt: 1:   8 Triangles Cascade Problem Solving
  16.    wt: 1:   12 Links Lessons elsewhere
  17.    wt: 1:   4 Equations for lines three forms
  18.    wt: 1:   1 Numerical view of lines and their equations
  19.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  20.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  21.    wt: 1:   3 Linear Equation Literal Solution More
  22.    wt: 1:   2 Linear Equation Literal Solution
  23.    wt: 1:   4 Solving a triangular system exercise
  24.    wt: 1:   3 Solving triangular system example
  25.    wt: 1:   A Related lessons in Volume 3
  26.    wt: 1:   20 Chain Rule for Pulley Systems
  27.    wt: 1:   19 Chain Rule for linear functions
  28.    wt: 1:   H more Routine to non routine problem solving
  29.    wt: 1:   H Jigsaw puzzles and problem solving
  30.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

Extended Search

246 matches:

  1.    wt: 9:   4 Solving a triangular system exercise
  2.    wt: 9:   3 Solving triangular system example
  3.    wt: 8:   2 Essentially one exercises three with solution
  4.    wt: 8:   1 Essentially One Unknown
  5.    wt: 7:   More Exercises
  6.    wt: 7:   Simple Exercises
  7.    wt: 7:   5 Gaussian Elimination for 3 unknowns 2nd example
  8.    wt: 7:   4 GE III Animated Examples
  9.    wt: 7:   3 Gaussian Elimination 3 unknowns first example
  10.    wt: 7:   3 GE III Equation Addition and Multiplication
  11.    wt: 7:   2 GE II Comparison
  12.    wt: 7:   1 GE Substitution four examples
  13.    wt: 7:   6 Algebraic Solution Example
  14.    wt: 7:   5 Algebraic Solutions Introduction
  15.    wt: 7:   4 Four Examples Fractional Coefficients
  16.    wt: 7:   3 Four Examples
  17.    wt: 7:   2 Three Examples
  18.    wt: 7:   1 Proper Equal Sign Usage
  19.    wt: 7:   Skill Development Notes
  20.    wt: 7:   10 One Example
  21.    wt: 7:   9 Three Examples
  22.    wt: 7:   8 One Example
  23.    wt: 7:   7 Two Examples
  24.    wt: 7:   6 Three Examples
  25.    wt: 7:   5 Three Examples
  26.    wt: 7:   4 Two Examples
  27.    wt: 7:   3 Two Examples
  28.    wt: 7:   2 Three Examples
  29.    wt: 7:   Using Letters for Physical Quantities
  30.    wt: 7:   Formula Usage Show Work Format
  31.    wt: 6:   6 Equations and Systems Equivalent or Implied
  32.    wt: 4:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  33.    wt: 4:   16 Collinear Horizontal Arrows Vectors
  34.    wt: 4:   3 Linear Equation Literal Solution More
  35.    wt: 4:   2 Linear Equation Literal Solution
  36.    wt: 4:   5 Equality in Algebra
  37.    wt: 4:   4 Subtraction and Division Axioms
  38.    wt: 4:   3 Product Axioms Two Forms
  39.    wt: 4:   2 Addition and Multiplication Axioms
  40.    wt: 4:   1 Equivalent Computation Rules
  41.    wt: 4:   A Related lessons in Volume 3
  42.    wt: 4:   20 Chain Rule for Pulley Systems
  43.    wt: 4:   19 Chain Rule for linear functions
  44.    wt: 3:   6 Intersection of lines by solving linear systems
  45.    wt: 3:   musings do not puiblish real numbers
  46.    wt: 3:   A Modular and Remainder Arithmetic
  47.    wt: 3:   A Signed Number Arithmetic Review
  48.    wt: 3:   26 More Less Greater Than Comparison
  49.    wt: 3:   25 Mid way Convergence to Axiomatic Approach
  50.    wt: 3:   24 Signed Numbers Arithmmetic Properties
  51.    wt: 3:   23 Distributive Law Two Derivations
  52.    wt: 3:   22 Multiplication of Signed Numbers
  53.    wt: 3:   21 Addition of Multiples of a Single Vector
  54.    wt: 3:   19 Signed Multiples of Vectors
  55.    wt: 3:   18 Geometrically Why Vector Addition Commutes
  56.    wt: 3:   17 Arrows Rotate to Reverse with Length Unchanged
  57.    wt: 3:   15 Head to Tails in place Addition Associative
  58.    wt: 3:   14 Vector Head to Tail Sums and Resultants
  59.    wt: 3:   13 Arrows and Vectors in a Plane
  60.    wt: 3:   12 Real Numbers Line Signed Coordinates
  61.    wt: 3:   11 Signed Number Addition and Addition Properties
  62.    wt: 3:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  63.    wt: 3:   9 Division with Digits after Decimal Point
  64.    wt: 3:   8 Division and Mulplication of Compound Fractions
  65.    wt: 3:   7 Arithmetic with Infinite Decimal Expansions
  66.    wt: 3:   6 Infinite Decimals Ending in 9 repeating
  67.    wt: 3:   5 Fractions with Infinite Decimal Expansions
  68.    wt: 3:   4 Location of Point in Decimal Addition
  69.    wt: 3:   3 Location of Point in Decimal Multiplication
  70.    wt: 3:   2 Counting Digits in Decimal Multiplication
  71.    wt: 3:   1 Fractions with Finite Decimal Expansions
  72.    wt: 3:   E Long Division Methods more
  73.    wt: 3:   D Long Division Methods
  74.    wt: 3:   C Three Decimal Subtraction Methods
  75.    wt: 3:   B Decimal Comparison and Subtraction
  76.    wt: 3:   A Decimal Addition Columm Methods
  77.    wt: 3:   8 Column Multiplication Methods in General
  78.    wt: 3:   7 Decimals Multiplication Methods Examples
  79.    wt: 3:   6 Column Methods for Decimal Multiplication
  80.    wt: 3:   5 Distributive Law for Whole Numbers
  81.    wt: 3:   4 Commutative Law Groups Counting Form
  82.    wt: 3:   3 Multiplicative Counting Skills Principles
  83.    wt: 3:   2 Combing Counts Addition Skills and Principles
  84.    wt: 3:   1 The Counting Origins of Numbers
  85.    wt: 3:   5 Areas of Rectangles Revisited
  86.    wt: 3:   4 Fraction Operations Axiomatic Development
  87.    wt: 3:   3 Inequalities Algebraically
  88.    wt: 3:   2 Fraction Operations Physical Development
  89.    wt: 3:   1 Decimals Modular and Remainder Arithmetic
  90.    wt: 3:   5 Proportionality in Equivalent Fractions
  91.    wt: 3:   4 Rates Ratios and Proporitionality
  92.    wt: 3:   3 Proportionality Examples
  93.    wt: 3:   2 Algebraic View
  94.    wt: 3:   1 What is Proportionality
  95.    wt: 3:   9 Circle Area and Perimeter Formula Backwards Forwards
  96.    wt: 3:   8 Pythagorean Relation Forwards Backwards
  97.    wt: 3:   7 Pythagorean Theorem Chinese Square Proof
  98.    wt: 3:   6 Compound Interest Forward and Backwards
  99.    wt: 3:   5 Triangle Area Formula Backwards
  100.    wt: 3:   4 Rectangle Area and Like Formulas Backwards
  101.    wt: 3:   1 Changing Calculations
  102.    wt: 3:   5 Greater More Less Than Signs in General
  103.    wt: 3:   4 Comparison of Negative Numbers
  104.    wt: 3:   3 More and Less Than with Unlike Signs
  105.    wt: 3:   2 More and Less Than for Counts and Measures
  106.    wt: 3:   1 Real Numbers Comparison
  107.    wt: 3:   16 Real Numbers Comparison
  108.    wt: 3:   15 Real Number Division
  109.    wt: 3:   14 Real Number Multiplication
  110.    wt: 3:   13 Real Number Subtraction
  111.    wt: 3:   12 Real Number Additive Inverses or Negatives
  112.    wt: 3:   11 Real Number Addition
  113.    wt: 3:   10 Real Number Lengths and Signs
  114.    wt: 3:   9 Coordinates for Regions in Space
  115.    wt: 3:   8 Coordinates for Maps and Planes
  116.    wt: 3:   7 Real Numbers as Line Cordinates
  117.    wt: 3:   6 Unsigned Real Numbers
  118.    wt: 3:   5 Rational Numbers More
  119.    wt: 3:   4 Rational Numbers
  120.    wt: 3:   3 Fractions
  121.    wt: 3:   2 Integers
  122.    wt: 3:   1 Whole and Natural Numbers
  123.    wt: 3:   5 Independent versus Dependent Variables
  124.    wt: 3:   4 Changing Letters
  125.    wt: 3:   3 Geometric Formulas and Function Notation
  126.    wt: 3:   2 Computation Rules Evaluation
  127.    wt: 3:   1 Formulas Dependence and Function Notation
  128.    wt: 3:   13 Naming Identifying Formulas with Words
  129.    wt: 3:   12 Cone Cylinder Sphere Lesson Idea
  130.    wt: 3:   11 Volume of Sphere
  131.    wt: 3:   10 Volume of Pyramid
  132.    wt: 3:   9 Volume of Cone
  133.    wt: 3:   8 Compound Interest Formula Evaluation
  134.    wt: 3:   7 Compound Interest Formula Introduction
  135.    wt: 3:   6 Pythagorean Hypotenuse Calculation Example
  136.    wt: 3:   5 Box Volume Formula Example
  137.    wt: 3:   4 Circle Area Formula Example
  138.    wt: 3:   3 Triangle Area Formula Example
  139.    wt: 3:   2 Another Rectangle Area Formula Example
  140.    wt: 3:   1 Written work formats for developing and showing skill
  141.    wt: 3:   10 Set View of Wordy Extensions To Arithmetic
  142.    wt: 3:   9 Sets in Probability and Statistics
  143.    wt: 3:   8 Sets of Numbers
  144.    wt: 3:   7 Cautious or Safe Set Construction
  145.    wt: 3:   6 Power Set Notation
  146.    wt: 3:   5 Product Builder Notation
  147.    wt: 3:   4 Subset Builder Notation
  148.    wt: 3:   3 Counting with Sets etc
  149.    wt: 3:   2 Venn Diagrams
  150.    wt: 3:   1 Finite Sets
  151.    wt: 3:   6 Three Notions of What is a Variable
  152.    wt: 3:   5 Talking about Numbers and Quantities
  153.    wt: 3:   4 A Brief Story of numbers and algebra
  154.    wt: 3:   3 Adding Words To Arithmetic
  155.    wt: 3:   2 What is a Variable
  156.    wt: 3:   1 Three Skills For Algebra
  157.    wt: 3:   About Folder Contents
  158.    wt: 3:   Example 2 volume of a cone
  159.    wt: 3:   Example 1 volume of a pyramid
  160.    wt: 3:   Volume of Solid by Cross Sections Lesson
  161.    wt: 3:   Example 1. Area Between x and x squared
  162.    wt: 3:   Area Between Crossing Curves Lesson Take 2
  163.    wt: 3:   Area Between Crossing Curves Lesson Take 1
  164.    wt: 3:   Example 4 with x function of y
  165.    wt: 3:   Example 3
  166.    wt: 3:   Example 2
  167.    wt: 3:   Example 1
  168.    wt: 3:   Area Between Curves Lesson Take 2
  169.    wt: 3:   Area Between Curves Lesson Take 1
  170.    wt: 3:   Summary
  171.    wt: 3:   A Related Material in Volume 3
  172.    wt: 3:   5 Area Under Curve Exercise
  173.    wt: 3:   4 Definite Integrals Evaluation Exercises
  174.    wt: 3:   3 Two Chain Rule Method Exercises
  175.    wt: 3:   2 Indefinite Integrals Exercises
  176.    wt: 3:   1 Chain Rule in Reverse Integration Method
  177.    wt: 3:   4 Second derivative test exercise example
  178.    wt: 3:   3 Second derivative test
  179.    wt: 3:   2 Second derivative test prequel
  180.    wt: 3:   1 Two cubic sketching exercises with 1st derivative
  181.    wt: 3:   A Chain Rule Real Player video examples
  182.    wt: 3:   38 Formulas and derivatives for powers and roots
  183.    wt: 3:   36 Cube root derivative animated
  184.    wt: 3:   34 Derivative of exponential function
  185.    wt: 3:   33 Chain Rule Real Player video examples
  186.    wt: 3:   31 Derivatives of inverse functions
  187.    wt: 3:   30Chain Rule A Proof
  188.    wt: 3:   29 Chain Rule Optional Reading
  189.    wt: 3:   28 Chain Rule Preparation for a Proof
  190.    wt: 3:   27 Chain Rule sinusoidal outer inner functions EGS
  191.    wt: 3:   26 Chain Rule Recognising outer inner functions
  192.    wt: 3:   25 Chain Rule Animated Examples Continued
  193.    wt: 3:   24 Chain Rule Animated Examples
  194.    wt: 3:   23 Chain Rule in general
  195.    wt: 3:   22 Chain Rule for polynomials
  196.    wt: 3:   21 Chain Rule for powers
  197.    wt: 3:   18 Chain Rule Introduction
  198.    wt: 3:   17 Derivatives of quotients of sine and cosine
  199.    wt: 3:   16 Derivatives of reciprocals of sine and cosine
  200.    wt: 3:   15 sine and cosine derivatives 3rd step
  201.    wt: 3:   14 sine and cosine derivatives 2nd step
  202.    wt: 3:   13 sine and cosine derivatives 1st step
  203.    wt: 3:   12 Quotient rule examples
  204.    wt: 3:   11 Quotient rule
  205.    wt: 3:   10 Power rule for negative integers
  206.    wt: 3:   9 Reciprocal rule
  207.    wt: 3:   8 Differentiation of polynomials
  208.    wt: 3:   7 Animated Differentiation Examples
  209.    wt: 3:   6 Power rule from product rule
  210.    wt: 3:   5 Product Rule
  211.    wt: 3:   4 Sum Rule
  212.    wt: 3:   3 Motivation for Limit Definition Take 2
  213.    wt: 3:   2 Motivation for Limit Definition Take 1
  214.    wt: 3:   1 Fall 1983 Why Slopes Appetizer
  215.    wt: 3:   13 Limits with Parameters and Derivatives Take II
  216.    wt: 3:   12 Limits with Parameters and Derivatives Take I
  217.    wt: 3:   11 Limits at infinity Three Examples
  218.    wt: 3:   10 Three one sided limits with infinite values
  219.    wt: 3:   9 Limits Continuity and Composition
  220.    wt: 3:   8 Four Animated Examples
  221.    wt: 3:   7 Evaluation by immediate or delayed substitution
  222.    wt: 3:   6 Continuity at a point
  223.    wt: 3:   5 Jumps and absence of unlimited error control
  224.    wt: 3:   4 Numerical properties
  225.    wt: 3:   3 Decimal insights for limits continuity convergence
  226.    wt: 3:   2 Algebraic codification
  227.    wt: 3:   1 Numerical introduction
  228.    wt: 3:   Chapter 15. Solving Linear Equations
  229.    wt: 2:   Straight Lines Instersection Solving Equations
  230.    wt: 2:   Chapter 3 Algebra Starter Lessons
  231.    wt: 1:   G LAMP Introduction Problem Solving Skills
  232.    wt: 1:   1 Calculator Starter Exercises
  233.    wt: 1:   7 Links Lessons Elsewhere
  234.    wt: 1:   5 Polynomials Long division Nonlinear divisor
  235.    wt: 1:   4 Polynomials Long division linear divisor
  236.    wt: 1:   14 Straight Lines Equations General Case
  237.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  238.    wt: 1:   10 Straight Lines through Origin Equations More
  239.    wt: 1:   9 Straight Lines through Origin Equations
  240.    wt: 1:   8 Triangles Cascade Problem Solving
  241.    wt: 1:   12 Links Lessons elsewhere
  242.    wt: 1:   4 Equations for lines three forms
  243.    wt: 1:   1 Numerical view of lines and their equations
  244.    wt: 1:   H more Routine to non routine problem solving
  245.    wt: 1:   H Jigsaw puzzles and problem solving
  246.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

Teachers & Tutors: Site pages offer better or best practices for providing skills - simpler than expected & comprehensive but for exercises. For your charges, your duty is to study them alone or in groups and develop skill building exercises & activities to share. Start now. The effort here is the best I can do. Others are welcome to refine or exceed it. Please do.

Secondary Mathematics for Ages 11+, A Practical Approach for home-tutoring or -schooling, or for schools & colleges with local curriculum control. Study how to include site content - its skill development how-TOs and innovations into present or future lesson plans - some reading required.

Road Safety Messages and Questions: When and why should you face traffic when walking along a road or cycle path? Is it a good idea to hang limbs outside of cars etc? What gives more protection in a crash: a car, motorbike or bicycle? See too, the BBC-Belgium story Texting and Driving - texting & the impossible test - the article links to a gruesome utube video on the subject

The Logic of Injustice: How Texas sent an innocent man to his death - The wrong Carlos. Some judgments are irreversible. Procescution: Where and when prosectors play to win rather than for justice, guilt beyond a reasonable doubt goes unrespected due to prosecutors who putting winning first, those innocence before the law may be convicted. Some procescutors offices in continuing to accuse after a pardon due to reasonable doubt or innocent being shown, may sucessfully oppose compensaton for false convictions by asserting a pardon individual is still under suspicion. Then the pardoned individual or the latter's estate is not compensation for years or decade of improper or false imprisonment, or for execution. Site chapters on Logic
and some in Pattern Based Reason may slowly lead to greater precision in reading, applying and writing laws.

May 2012, Composition Starting: Pre-School and Primary Mathematics - Quantitative Skills, An Intellectual View, Feedback Welcome:

The 8 Most Popular Site Inlinks

20 Times Table - the most popular site page - popular pages - unexpected.
Fractions & Ratios - with lesson on raising terms to introduce & justify times, division & comparison as well addition & subtraction
Parent Center - See below
Volume 1, Elements of Reason - Intro to all site books.
What is a Variable - best for ages 13+
Written work formats for Arithmetic and Algebra - a skill method and standard!
Complex Numbers Visually - best for ages 13+
Natural Logs, Exponentials, Powers, Roots

Division of Labour: This site offers advice and directions with pointers to resources elsewhere, if known, when they help or lessen the need to write more.

Parent Center: Help your child or teen learn:

Parent-friendly Work Booklets for ages 3+ to 13 Use these or others to check or build skills. Other booklets are available but these booklets allow parents unsure of themselves in mathematics to help their children. The selection acquired in Canada is published in the USA. So it has a US orientation. In retrospect, the selection shows parents what to check with the booklets or by other ways, the choice is theirs. But in retrospect, the selection does not cover integral and fractions liquid weights and measures - ask the publishers to correct that! For ages 9 to 12 say, parents may compensate by showing boys and girls how to use weights or mass, and further measures in food preparation. Beyond that children may be shown how to measure and calculate angles, lengths and areas [proportional amounts too] directly or by using maps and plans drawns to scale. Learning how to gather and measure all the ingredients, pots and pans for a dish or a meal, along with cleaning up sets the stage for like activities or experiments in science courses, and in developing organizational skills, gives boys and girls a head start. Good luck. At the other extreme, more comprehensive than light, if your motto is McCainian: drill, drill, drill then Toronto mathematician and actor John Mighton's jump math organization has jump math workbooks for at least grades 3 to 8 for at-home and in-school use - training sessions for teachers available. Jump math has been expanding to cover older students. Jump Math Samples: plus Fractions for Grades 3-4 & Grades 5-6 [Read] Free Resources grades 1 to 8 [unread - likely to be good]. and

Mathematics Skills For Ages 3 to 14 - technical!

Skills with take home value - A few ideas

Basic skills include time-date-calendar Matters; money matters; map, plan and scale diagram matters;counting, measuring and figuring; decision making with logic and likelyhood; being careful and being aware of the domino effect of mistakes; reading and writing with precision.

Is your child able to add, subtract and multiply amounts of money, work with fractions, work with clocks and calendars, work with maps and plans, and measure length, weight-mass and volume? Schools may promote your son or daughter without providing basic skills in reading, writing and arithmetic.

Arithmetic and Number Theory Skills

Algebra Starter Lessons

1 Working With Sets
2 Formula Forward Use - Evaluation
3 Solving Linear Equations - Skip first step with students able to solve 1 eqn in 1 unknown.
4 Computation Rules and Function Notation
5 Real Numbers
6 More Less Greater Than Inequalities and Comparison
7 Axioms Logic and Equivalent Equations
8 Unifying Theme For Algebra
9 Proportionality Backwards and Forwards
10 Examples of Algebraic Reasoning
A Origins of Counting and Figuring Methods
B Real Numbers Extrinsic Development


Site coverage of formuala evaluation format, of computation rules and axioms, and of the forward and backward use of formulas and proportionality relations lessens the amount of natural talent needed to understand and explain algebra.

Geometry - maps plans trigonometry vectors

1 Maps Plans Measurement
2 Euclidean Geometry - Constructions + extras
3 Cartesian and Polar Coordinates
4 Lines and Slopes Take 1
5 What is Similarity
6 Trigonometry first steps
7 Complex Numbers
8 Unit-Circle Trigonometry
9 Lines and Slopes Take 2 with tangent function
10 Intersecting Straight Lines and Transversals
11 Parallel Straight Lines and Transversals
12 Function Translating and Rescaling
13 Vectors
14 Degrees to Radians and Radians to Degrees
15 Arc or Inverse Trigonometric Function

Pre-Teen and young teen mastery of skills and practices which should be common with map-plans-diagrams drawn to scale, contour interpretation included, has actual or potential take-home value for daily- and adult-life in solving routine problems. Elevating some practices to principles, axioms or postualates, provides a base for analytic and Euclidean geometry, an analytic view of similarity, and an efficient mastery of trigonometry and complex numbers. Right triangle trigonometry provide an analytic alternative to solving geometric problems by drawing diagrams to scale.

More Algebra

Natural-Logarithms Exponentials Powers Roots
Five Polynomial Operations
Quadratics Geometrically
Functions
5 Factored Polynomial Sign Analysis Examples
Rewriting algebraic substitution as function substitutions

The first topic leads to a full high school level theory for the forward and backward mastery of growth and decay models and for definition, range and domains of radicals, roots and powers. The next two topics make quadratics and polynomials easier to learn and teach. Site coverage of functions turns vertical and horizontal line rules into computation methods for evaluating functions.

70 Calculus Starter Lessons

Calculus Lessons Elsewhere:

  1. How to Ace Calculus: Street Wise Guide - Mostly Text.

  2. Flash Video for Calculus Phobics

They cover basic topics in ways likely to complement your notes, your textbooks and site material. When Goldilocks trespassed in the house of the three bears, she found three bowls of porridge, two not to her liking, and one just right. Different bears have different tastes. As invited guest here and elsewhere, if one or more explanations is not to liking, try another. It may be better or just right.

Unsolicited Advice

Learning to do and high marks if it comes to easy is often deceptive - light rather than deep. For that reason, students with learning difficulties determined not to let it get in their way may go deeper and farther than those with none. High marks, if the come easy, may be deceptive - provide a too light and not a deep mastery. That could have been your problem in secondary school, one that leads to comprehension shock or difficulties in calculus and more generally in the first year of college. Bon Appetite.

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Logic-Reason for all
Careful Thinking
Chains of Reason
Mathematical Induction
Responsibility
Bodies-of-Knowledge

Arithmetic - Ages 10+
1. Deciml Place Value - fun
2. Decimals for Tutors
3. Prime Factors - quickly
4. Fractions + Ratios
5. Arith with units - science

Geometry
1 Maps + Plans Use
2 Euclidean Geometry
3 Rct +Polr Coordinates
4 Lines-Slopes [I]
5. What is Similarity 		Algebra Starters - the base
1. Better Work Format
2. Solve Linear Eqns
3. Computation Rules
4. Axioms, Item 3 Viewpnt
5. Formulas Backwards 		More Algebra
Logarithms-ax & m/nth roots
Five Polynomial Operations
Quadratics Geometrically
Functions || Vectors too
Arith. Skill Check+Answers 		Calculus Prep/Preview
What is a Variable
Why study slopes
Why factor polynomials
Complex Numbers
Limits + Continuity

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