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whyslopes.com
Entrance Level
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For Montreal Students: Head
Start Math Tutoring is available from the site author.
YOU are better than YOU think. Show yourself how:
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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
Do not leave here without it - 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
linear2007 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.
George Orwell: Is it
nonsense for arts and disciplines based on and respected for carefully
mastery of rules and methods, alone and combined, to face education reforms
based on the supposition that mastery of rules and methods is not a sign of
intelligence. Would you like to rewrite 1984 to include that angle?
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 twiddla.com
to set up whiteboards to work with the webpage of your choice.
Precalculus sites mathsisfun
& purplemath are
visually more appealling than this one. Do not go.
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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The first five steps below offer a solid base for high
school mathematics. The order can be changed.
Work a with friend or tutor to make your learning easier or more
social.
- Three Skills For Algebra (Chapters 1
to 14) & two postscripts What
is a Variable & Indirect
Reason. Chapters 1 to 5 on logic may improve learning abilities in all
subject, and lead to precision reading and writing. The postscript on Indirect
Reason may be postponed. In Chapter 14, look for the difference
between arithmetic and algebraic solutions. These chapters 1 to 14 give
a wordy introduction to logic and algebra. Do only the first
arithmetic review problems in Chapter 7.
- Solving Linear Equations with Stick
Diagrams If you have a tutor or teacher to help, I
would put step 2 first. Chapter 15 in Three
Skills for Algebra should be read along side this step. The
hope here is that Solving
Linear Equations with Stick Diagrams will strengthen fractions sense and
abilities. Work with another or with help if need-be.
(Hours: Stick diagrams 4½, Working
without Sticks 1½, Systems in essentially one variable 1½, Triangular
systems 1½)
Success in calculus requires fraction sense.
The hope here is that Solving Linear
Equations with Stick Diagrams will lead you to understand fractions -
what they are and how to work with them. If not, you will need to
learn or recall how to efficiently
add, efficiently
and efficient divide
fractions by hand. The Arithmetic
Videos (50+ in Realplayer format) may be viewed and Exercises on Mostly
Fractions (answers given) will also test and may develop
fraction know-how. More lessons, not needed we hope, appear
the site area Fractions, Ratios, Rates,
Proportions and Units
Time: 4 more hours
A Prerequisite for Arithmetic with Fractions: If
you do not instantly recall the sums and products of all pairs of whole
numbers from 1 to 10 or 12, you will need to learn. Using your head
or a calculator, fill-in the 10 or 12 times tables and the similar 10 or
12 sums table, and do so a few times until you can. These exercises can be
done when you have pencil and paper available, some spare time
(waiting for someone or for a course to begin). The skill here is a must
and it is quickly acquired.
- In Three Skills For Algebra See
two short chapters 16 and 17 for painless theorem proving and a simple
algebraic-geometric proof of the Pythagoras theorem.
- Leave this site, and explore the purple
math algebra modules to meet examples and more examples.
Then come back for the further steps below. There are many examples.
Look through the development or examples of fractions.
- Do not let these Mathematics Education
Perils harm your studies.
- Euclidean-Geometry
- Geometry before coordinates. See the application of implication rules
in mathematics. Meet coordinate free trigonometry.
- Analytic Geometry & Functions.
See how order pairs service as coordinates, may be used to
locate points in the plane, meet coordinate based trigonometry and
meet the ordered pair (set) view of functions and calculation rules. The
development of complex numbers here is optional. This site area covers
most of what you need and provides a solid base for the rest - may
complete explanations found elsewhere.
Go to the Kyrgyz-Turkish
High Schools Mathematics Pages (advanced material) for extra help or
examples.
- Do the remaining arithmetic
review problems with hints of algebra in the chapter 7 of the
online book Three Skills for Algebra. Could be started before or
during the previous step.
- The site calculus introduction
starts with a geometric
and algebraic preview of
calculus.
The previews are for reading during digressions from step 7
for rest and motivation. The first may be studied as soon as you
master slopes to straight lines . The second requires that you can
recognize a factored polynomial. The two previews, do not worry if all
is not understood, may provide a context for slopes, polynomials and
rational functions while developing and motivating algebraic thinking
skills.
The logical development in steps 1 to 7, its consequences and
connections are needed at full strength in calculus.
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whyslopes.com
Entrance Level
[ Back ] [ Site Entrance & Hub ] [ Next ]
Tutors - All Subjects
(use at your own risk)
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tutorfinder.com.au
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findatutor.ca
CDN: .i-tutor.ca
CDN:
Montreal Tutors
NZ: findatutor.co.nz
UK:
tutorhunt.com
USA: wiziq.com
USA: ziizoo.com
Pages For Teachers
Site Entrance & Hub
Permissions for Instructors
Lesson Plans - Sec I
Lesson Plan, Sec II
Lesson Plans - Sec III
Secondary Maths, Core Elements
About Site Books & Areas
Site History/Content
Site Reviews
Vol 1. Elements of Reason
Maps Plans Drawings
Quantitative_Skills/index.html
Order Site Books
HIP, HIP, HIP, Hooray for
site
content & history. Hype, Hype,
Hype, Hoorary, for deception.
Your IP Address & how to use
it
Pages for Students
Site Entrance & Hub
Head Start Page
25 hours per tear
More Advice & Directions
Aims to adopt to aid
Arithmetic Check List
Fraction Skill and Concept Check List
Site History and Content
Books to Read
Complex No.s Intro.,.
Calculus Motivation
Calculus. Guide Short
Calculus. Guide-Long
Calculus Guide - Longest
Links - Many Subjects
Links - Games/Activities
Long Site Intro
Still More Advice
Logos Cafe
Logic Check List
Mathematics Cafe
Math CheckList
Site Areas by Age and Subject
A Site Map
Advice for Secondary I Students
Three Ways to be a Better Student
Reason for HS Mathematics
Montreal Tutors
Three Links for Teachers:
(i) First
Year High School Math - Lesson Plans with Fraction Focus
(ii) Second
Year High School Math - Lesson Plans with an algebra focus
(iii) Algebra
Lesson Plans
Help U Learn/ Teach
- Algebra
words before symbols
- direct & indirect
use of formula, numerical versus algebraic solutions - what
is a variable (more words)
- Arithmetic
- exercises
- with fractions
-
videos on primes, lcm, gcm,lcd, square roots etc
- Calculus - geometric
preview, algebraic
preview,
3 study guides,
much more
- Complex numbers
-starter lesson with java applet - easy
consequences for trig & vectors in the plane
- Education
- Empirical Course Design
& Delivery
- Fractions
- alone
- by rote
- with
algebra
- videos
- Functions - introduction
hindsight
- composition aka
substitution -
- Geometry, Euclidean - Correspondence
of triangles, Triangle
construciton, duplication & Isometry - Failure
of ASA & the // line postulate - angle
sum in triangles -//
grams - Triangle
Similarity
- Geometry-
Analytic - functions, polynomials, complex numbers, unit circle
trigonometry
- Logic
- First Steps -
Symbols in Logic
-
Occurrence &
Truth Tables - Indirect
Reason -Indirect
Reason More
- Proportionality
- Definition -
Direct & Indirect Use - Numerical versus Algebraic Solutions
- Real Analysis
- Decimal View of concepts
and of proofs
- Rules &Patterns in Science, Technology & Society
- Pattern Based Reason
- Mathematical Reasoning, empirical, inductive or deductive
- Units
- in rates & slopes &
(?) derivatives
- in ratios
& proportions - slopes & rates included
- Complex Numbers & Vectors & Trig
- trig expression for dot
& cross - cosine law
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