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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.
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Counting in Groups
Distributive Law for Counting Units or Objects
Suppose each unit is a group of N elements. Then the initial distributive
law
A units + B units = (A+B) units (equal in the sense of bijective
tallies)
gives the distributive law.
A*N + B*N = (A+B)*N
due to the equality of two different ways count: We can tally the
elements in A units plus the elements in B units to count all, or we can tally
in the elements in (A+B) units.
Parallels in Daily Life
The above counting principle and the distributive law as is or extended
appears in many forms in daily life. For instance
12 apples + 14 apples = (12+ 14) apples = 26 apples.
Now if each apple correspond to or costs 5 cents, we say each apply
corresponds to set of 5 pennies. So we replace each apple by 5 pennies and conclude that
12 * (5 pennies) + 14*(5 pennies) = (12+ 14)*5 pennies
Hence 12*5+14* 5 tally marks (or ones) equals (12+14)*5 tally marks or ones
in the sense that tallying the pennies in two different ways will give the same
decimal number for their count.
The mathematics teacher who gets students to write
3 N + 4 N = 7 N
by apple analogies
3 apples + 4 apples = 7 apples
is unwittingly correct. There is a parallel.
Polynomials in Powers of Ten
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www.whyslopes.com
Number Theory
Start of Number Theory
Origins of Counting or Tallying
Adding Wholes
Multipling Wholes
Distributive Law Preamble
Distributive Law for Wholes
Consequences
More Consequences
What is a Fraction
Compound Fractions
Number Theory
Continued
Decimal Place Value
Place Value Reinforcement
Comparison Method
Addition Method
Subtraction Methods
Multiplication Methods
Division Methods
Remainder Arithmetic I
Primes & Composites
Primes Factorization Theorem
Primes & Composites
Prime Factorization Aids
Prime Factorization Examples
Counting Whole No. Factors
Arithmetic Videos
Square Roots & Primes
Long Division Continued
Fractions & Decimals
Fractions as Decimals
1 = 0.999 Recurring
Infinite Decimals Expansion Arithmetic
Ratio of Simple Fractions
Ratio of Decimal Fractions
Unsigned Reals Numbers
Signed Coordinates
Plane Vectors
Horizontal Vectors
Adding Vector Multiplies
Adding Signed Numbers
Multiplying Signed Numbers
Distributive Law for Reals
Real Numbers Axioms
Remainder Arithmetic II
Related Site Pages:
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
Food for thought: 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..
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