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Investigate Head
Start Math Instruction for students in Montreal.
YOU are better than YOU think. Show yourself
how:
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Read logic
chapters 1 to 5 in online volume Three
Skills for Algebra for greater skills & confidence
in work
and study.
Learn to read notes and textbooks like a lawyer, so that no nuance, no
subtlety and no clause escapes your attention. |
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Logic
chapters 1 to 5 re- appear not in sequence, as is or longer,
in Volume 1A, Pattern Based
Reason, Bon Appetite.
Logic
Mastery
Amazing, Amusing, Amorous, Delicious, Delightful, Edifying,
Strengthening Elixir.
It eases work & learning difficulties Makes the hard easier. Opens eyes.
Leads to greater precision.
in reading and
writing
Logic
mastery makes the hard, easier. Logic
mastery leads to better, stronger and richer comprehension. Logic
mastery improves reading and writing. Logic
mastery ease learning difficulties. Logic
mastery gives a headstart. In sum, logic
mastery will develops critical thinking, improve reading and writing,
and give a firmer base for work and studies at many levels. Good luck.
After logic,
(a) continue reading Three
Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving
liinear Equations ; or (b) see this calculus
starter lesson and Volume 3, Why
Slopes & More Math, chapters 2 to 6;
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Caution: Site advice is approximately
correct, for some circumstances, not all. That leaves room for thought |
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What may be learnt and when depends on how skills
and concepts are developed. Making the hard easier and clearer will allow
earlier & richer development of skills and concepts.
Try the Twiddla
Whiteboard. In principle, it allows
to people to draw and chat together online on a copy of this webpage or a clean
sheet. The chat may be via text or audio. Visit www.twiddla.com
to set up whiteboards to work with the webpage of your choice.
For online automated help in senior high school maths & calculus,
visit quickmath.com For Automatic
Calculus and Algebra Help with derivatives, integrals, graphs, linear equations,
matrix algebra, visit calc101.com
With overlap, each site quickmath
& calc101offers a different range of
services, some free, some not, all based on webmathematica. Good luck.
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Logic
chapters 1 to 5 (Français)
in Volume 2, Three
Skills for Algebra introduce the Euclidean logic methods and questions in
mathematics free manner. See the last chapters and postscripts of Volume 1A,
Pattern Based Reason, for a further discussion of consistency questions and
indirect chains of reason in general, and not just in mathematics.
In the first part of your mathematics education, rules and
patterns may be accepted because they work in a repeatable, reproducible and
thus verifiable manner. What is right or wrong is thus clear, or can be checked.
The careful mastery of rules and patterns, one at a time and one after another,
with repeatable and reproducible results, is a sign of intelligence and
gives an operational viewpoint of mathematics and its mastery by rote or with
explanation. Explanation in mathematics may be based on giving examples to
suggest or illustrate and confirm a rule and pattern. Explanation in mathematics
may be based on combining rules and patterns to arrive at new ones. Explanation
in mathematics may also be based on logic - the direct and indirect use of
implication rules or patterns B IF A. Finally, with practice, mathematics
can be codified via logic:
In the Euclidean-style logical codification or development of
a mathematics or a body of knowledge, a few key patterns are assumed. A
further pattern is accepted as (judged to be) part of that body of
knowledge if its pass a test, namely, there is at least one chain of reason
employing the key patterns which implies the further The latter chains
of reason provides a proof and give a further reason for logic
mastery mastery - besides its development of precision writing
and reading, two must for work and study.
Most students will appreciate the use of logic in mathematics
when it gives new results or patterns. Students will see as redundant and
not necessary the explanation of what has worked before and been.. So
mathematics education may mix a previous operational command of earlier rules
and patterns with a proof-based command of new material. That may be
sufficient for many students - as the logical codification of mathematics take
time and effort, and interest too.
Remark: Along side the axioms for pure mathematics, there
should also be included in education for mathematics and quantitative
disciplines (accounting, physics, chemistry), extra applied mathematics
supporting axioms or assumptions that formally sanction for students, the
manipulation of units of measurement in calculations, and the geometric use of
coordinates. Just a thought: The full Euclidean style
axiomatic codification and derivation of pure mathematics and its applied
mathematics extension with units and coordinates might be left to after a mixed
mathematics mastery of calculus.
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www.whyslopes.com
Lesson & Lesson Plans for
Sec IV (Maths 436)
a reference for learning and teaching functions, polynomials, solving linear
systems,
powers + exponents + bases + radicals (roots) , quadratic formulas, equations
of straight lines
1A. Master Logic
1B. Problems Solving Method
2A Solve Linear Equations i
2B.Solve Linear Equation II
2C Use Equal Sign Properly
2D. Perfect Arithmetic Skills
3 Words & Symbols
3 Goals to Set for Students
4 Use Equations Backwardly
5. Master Functions & Relations
6. Exponents & Radicals I
7. Straight Lines
8. Polynomials (x,/,+/-)
9. Quadratics
10 Prove it
13 Similarity Scale Factors
12 Trig & Triangles
14 Statistics
MEQ Intermediate Objectives
Remarks for Teachers
Sit down and study - no one else can do that for you.
Advice and Directions
What to do in School & Why
How
to Study Maths & Why
Preparing
for Science
Good News: If you can learn to follow a multi-step
methods in any subject precisely, you should be able to do so in other
subjects, as well. Hint: Start with arithmetic
Words Before Symbols:
What is a Variable?
Level: Secondary II to VI, or Grades 7 to 12)
Introduction
Variation between Examples
Variation of Letters
A letter denotes a variable
Cases of Double Variation
Three Notions of a Variable
Constants, Parameters
& Variables
Talking about numbers
Dependent
or Independent
Variable, a Matter of Choice
Complex number starter lesson
Arithmetic Videos
Fractions
Primes
Greatest Common Divisors
Least Common Multiples
Square Root Simplification
Arithmetic Videos
Decimal Addition Methods
Decimal
Subtraction Methods
Decimal
Multiplication Methods
Decimal Division Methods
Fraction
Starter Lesson
(simplify, multiply, divide &
then add or subtract)
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