Appetizers and Lessons for Mathematics and Reason (www.whyslopes.com)
||Définition d'une variable || Algèbre || Arithmetique || Logique ||La raison basée sur les règles et modelés||

Online Volumes
1,  Elements of Reason.
1A. Pattern Based Reason 
1B. Math Curriculum Notes
2. Three Skills for Algebra
3. Why Slopes & More Math

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More Site Areas 
1. Help Your Child or Teen Learn 
2. Solving Linear Equations
3. Fractions Ratios Rates Proportions & Units
4. Euclidean Geometry
5. Analytic Geometry/Functions 
6. Number Theory
7. More Calculus
More Site Areas 
8. Complex Numbers 
9. Qc Maths  Education  
10. Secondary IV(?) maths
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15. Algebra, Odds & Ends, Etc
More Site Areas 
16. Math Education Essays
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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

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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.

2.1  Use of the Equal Sign

Here are a few words about the equal sign. The equal sign = is used to say or suggest the following.
  1. two different symbols (or expressions) are shorthand for the same number and quantity.
  2. two different calculations or expressions give the same result when done, or
  3. the value of a number or quantity can be computed using another expression.
The suggestion in question can be true or false depending on circumstances. Examples follow:
4+5
=
7+2
r2
=
r·r
3x+1
=
x+7
x+4
=
x+6

Here the first equation or equality holds (meaning is true) since both 4+5 and 7+2 are expressions giving the value 9. The second equation r2 = r·r always holds, no matter what value you give to r. It tells us how to compute the number or quantity described by the expression r2. The third equation 3x+1 = x+7 holds (is true) when and only when x = 2. When x has a value other than 2, the statement (suggestion or assertion) that 3x+1 gives the same result as x+7 is false. The fourth statement x+4 = x+6 is always false. No value given to (or substituted for) x will make this statement true. Adding 4 and adding 6 to the same number give different results, no matter what the number is.

Abuse of Equal Sign

The solution of the equation

3
4
x
3

is given x =3. But is an error, a mistake, a major misuse of the equal sign to insert an = 3 besides the x in the above equation to obtain 

3
4
x =3
3     

in place of writing x = 3. While a person who writes 

x  = 3
3         

may mean x = 3, the expression 

x  = 3
3         

actually means a third of x  is 3.  

M Ouch!

 

 

www.whyslopes.com
Solving Linear Equations 

|(Feb 14, 2005)

a secondary I to V reference  for  solving linear equations and for  recognizing word problems in essentially one variable whether you like it or not, skill in arithmetic with fractions is a must for algebra. .

Area Entrance
Proper Use of Equal Sign
A. Letters and Lengths
B.. Solving Linear Eq'ns.
C. Solving Linear Eq'ns
D.Almost One
E: 2D Systems - Sub Method.
E:  Continued
E: Still More
F. Larger Systems


Area Entrance
(i) x + 20 = 29
(ii) 2x + 5 = 20
(iii) 3x + 10 = 32
(iv) 5a + 16 = 3a+ 24
(v)  (½)x + 8 = 24½
(vI)  (¾)a + 16 = (¼)a+ 24
(vii) (¾)q + 17 = 32
(viii) 13 =[2/3]x +7 twice
(x) Animated Examples
(i) Integral Coefficients (A)
(ii) Integral Coefficients (B)
(iii) Fractional Coefficients
(iv) With parameters


Up
Proper Use of Equal Sign
A. Letters and Lengths
B.. Solving Linear Eq'ns.
C. Solving Linear Eq'ns
D.Almost One
E: 2D Systems - Sub Method.
E:  Continued
E: Still More
F. Larger Systems
 


Arithmetic Videos

Decimal Addition Methods
Decimal Subtraction Methods
Decimal Multiplication Methods
Decimal Division Methods


Fractions
Primes
Greatest Common Divisors

Least Common Multiples

Square Root Simplification

Site books and further webpages on learning and teaching mathematics and pattern based reason may develop critical thinking, improve reading and writing, and give a base for learning or teaching high school and college mathematics.

Great_Expectations: If you can learn to follow a multi-step methods in any subject precisely, you can do so in other subjects, as well.

Good news: Site pages  identify what you need to study.

Bad news: Site pages do not explain everything  

Worse news: Learning takes time, yours

Lesson Plans and Ideas for Teachers & Tutors:

Secondary I - fractions & allied concepts (decimals, percentages)

Secondary II - Algebra  (arithmetic versus algebraic methods, backward use of formulas and proportionality equations)

Secondary IV - Functions to Trig & Statistics

Calculus Intro 

Algebra Lesson Notes - All levels


 

 



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