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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2 matches:

  1.    wt: 2:   Parent Center/
  2.    wt: 1:   Time Date Matters/

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22 matches:

  1.    wt: 3:   learning takes time
  2.    wt: 3:   4 Learning Takes Time and Effort
  3.    wt: 2:   012 Division of Time Intervals by Time Intervals
  4.    wt: 1:   22 Student Centered Highschool Mathematics
  5.    wt: 1:   14 Multiplication and Times Tables
  6.    wt: 1:   A Global Time and Navigation
  7.    wt: 1:   3 video Primes and Composites from 9 times table
  8.    wt: 1:   1 Why 3 times 5 gives 15
  9.    wt: 1:   The 20 Times Table
  10.    wt: 1:   The 12 Times Table Visually
  11.    wt: 1:   013 Travel Time Tables
  12.    wt: 1:   011 Division of Time Intervals By Numbers
  13.    wt: 1:   010 Repeated Addition of Time Intervals
  14.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  15.    wt: 1:   8 Addition of Time Intervals via subtotaling
  16.    wt: 1:   7 Addition of Time Intervals
  17.    wt: 1:   4 Mixing and Changing Units of Time
  18.    wt: 1:   3 Units and Lengths of Time
  19.    wt: 1:   2 Time and Date Matters in School
  20.    wt: 1:   1 Intro of Kids To Time Date Skills
  21.    wt: 1:   O On Learning Mathematics and Science
  22.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense

Extended Search

55 matches:

  1.    wt: 5:   4 Learning Takes Time and Effort
  2.    wt: 3:   learning takes time
  3.    wt: 3:   22 Student Centered Highschool Mathematics
  4.    wt: 3:   14 Multiplication and Times Tables
  5.    wt: 3:   012 Division of Time Intervals by Time Intervals
  6.    wt: 2:   Home Tutoring and Home Schooling
  7.    wt: 2:   27 Graduated Correction and Penalties for Young Offenders
  8.    wt: 2:   25 Mathematics Education Leaving A Good Impression
  9.    wt: 2:   24 Standards For Skill Develoment Take II
  10.    wt: 2:   24 Standards For Skill Develoment
  11.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take IV
  12.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take III
  13.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take II
  14.    wt: 2:   23 Modularized Skill Development Modularized Rigor
  15.    wt: 2:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  16.    wt: 2:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  17.    wt: 2:   19 Extending the Oral Dimension of Mathematics
  18.    wt: 2:   18 Primary School Mathematics
  19.    wt: 2:   17 Math Booklets for children and young teenagers
  20.    wt: 2:   16 Secondary Mathematics Tips
  21.    wt: 2:   15 Counting For Parents
  22.    wt: 2:   13 Addition and Addition Tables
  23.    wt: 2:   12 Goals and Objectives For Mathematics
  24.    wt: 2:   11 Help and Defend Your Child or Teens Education
  25.    wt: 2:   10 Ends values for work study instruction
  26.    wt: 2:   9 Streaming by Student Cooperation
  27.    wt: 2:   8 The Effect of Negative Remarks
  28.    wt: 2:   7 Student Motivation
  29.    wt: 2:   6 Discipline Who is in Charge Conserving Authority
  30.    wt: 2:   5 Patience Please for Yourself and Your Charges
  31.    wt: 2:   3 Preparing for Science Studies
  32.    wt: 2:   2 Reading and Writing Skills
  33.    wt: 2:   1 Speaking Skills
  34.    wt: 2:   013 Travel Time Tables
  35.    wt: 2:   011 Division of Time Intervals By Numbers
  36.    wt: 2:   010 Repeated Addition of Time Intervals
  37.    wt: 2:   9 Comparison and Subtraction of Time Intervals
  38.    wt: 2:   8 Addition of Time Intervals via subtotaling
  39.    wt: 2:   7 Addition of Time Intervals
  40.    wt: 2:   4 Mixing and Changing Units of Time
  41.    wt: 2:   3 Units and Lengths of Time
  42.    wt: 2:   2 Time and Date Matters in School
  43.    wt: 2:   1 Intro of Kids To Time Date Skills
  44.    wt: 1:   A Global Time and Navigation
  45.    wt: 1:   3 video Primes and Composites from 9 times table
  46.    wt: 1:   1 Why 3 times 5 gives 15
  47.    wt: 1:   The 20 Times Table
  48.    wt: 1:   The 12 Times Table Visually
  49.    wt: 1:   016 Numbering Occidental Calendar Days
  50.    wt: 1:   015 School and work day counting tables
  51.    wt: 1:   014 Counting Days with Calendars
  52.    wt: 1:   6 How long is a million seconds
  53.    wt: 1:   5 Conversion Arithmetic
  54.    wt: 1:   O On Learning Mathematics and Science
  55.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense

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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The Rest © 1995-2011, by site author, Alan Selby, Ph. D., Montreal,
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