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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Problems Solving Method
Problem solving is like putting together a jigsaw puzzle. In the
case of textbook problems, all the pieces are present. Most just need to be
fitted together following the clues. In the case of real world problems, there
may be missing pieces or extra pieces, and no guarantee that the solution can be
done.
In solving a jigsaw puzzle, you fit the pieces
together, one at a time, one after another, in some order. The solution
follows an opportunistic path with pieces tried here and there, until done
or not. In solving a mathematics problem, the pieces to fit together are
collectively given by all the rules, methods & tricks you have met in
previous lessons and courses. A solution follows an opportunistic path
with pieces tried here and there, one at a time and one after another, until all
is done or not. Some pieces may be left-over. Each example or solution and each
proof or chain of reason met in mathematics may include a piece of
information, a trick, that you may recycle in further solutions. Once you know
the jigsaw approach or method for solving mathematics problems, rest is routine
and opportunistic. There is nothing more to problem solving than watching for
and collecting ideas or methods for opportunistic use. Can you do that?
First Hint: Master Logic
Problem solving is like putting together a jigsaw puzzle. In the case of
textbook problems, all the pieces are present and just need to be fitted
together following the clues, and an possible a picture showing the desired
result. In the case of real world problems, there may be missing pieces or
extra pieces, and no guarantee that the solution can be done.
Novice problem solvers should examine the following chapters in Volume 2, Three
Skills for Algebra.
- Two
Logic Puzzles
- Chains
of Reason
- Longer
Chains of Reason
- Islands
and Division of Knowledge
- Painless
Theorem Proving.
These appetizers and lessons show how rules and patterns may fit together to
arrive at conclusions or solve SOME problems. Problem Solving requires
precision reading and writing. Logic Mastery helps with that as well.
Second Hint: Master Fractions
Many applied mathematics problems involving chopping and combining lengths,
areas and volumes. So you need to know how to take a proper or improper
fraction of a length, area or volume. You need to understand that one
length may be 2.5 times or 2½ times or (5/2) times another. Any if you do
calculation, you need to do it with care or at least do it with the knowledge
that an error in one step makes all that follows wrong. The ability to figure
well and precisely, so that you answer is correct, shows or suggests the ability
to follow methods, one step at a time and one step after another in any subject,
and in problem solving as well.
Algebra Word Problems
one or more variables, that is the question.
If your interest is in solving algebra word problems at the high school
level, I would recommend learning how to solve linear equations in one to
several unknowns efficiently. The starting point for that could be the site area
Solving Linear
Equations with Stick Diagrams and chapters 8 to 15 in Three Skills for
Algebra.
High school students who can solve linear equations in one unknown are often
given word problems where extra variables have to be eliminated to formulate a
single equation in one unknown quantity to solve. The trick here is to draw or
extract a single equation from the given information. But in most such words
problems, it is easier to extract or draw from the given information several
linear equations in several unknowns to solve. Each sentence in the word problem
gives an equation in one or more unknowns or quantities. Now the algebraic way
of writing and thinking can be used to eliminate variables and to solve for the
one or more quantities of interest in an effortless fashion.
The algebraic solution of linear equations involves the elimination of
variables to obtain say one equation in one unknown. This elimination process
may be better done and recorded with algebraic notation. Going directly to one
equation in one unknown to solve a problem requires more work to be done with
words.
To learn more and to go further, see Solving
Linear Equations with Stick Diagrams and chapters
8 to 15 in Three Skills for Algebra.
PS. Being good in algebra and beyond requires an efficient command of
fractions, what they represent and how to work with them.
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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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