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HIP,
HIP, HIP, Hooray
YOU are better than YOU think. Show yourself how:
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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
liinear2007 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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Our Neighbours
Logos Cafe -- more than arithmetic served here.
Appetizers -- eat on your feet
If one is not to your taste, try another. Gluttony is recommended.
- Arithmetic -- fare for
starters.
- English Lemons or French
Garlic-- flavoured algebra for two tongues. The lemon is larger, but not
bitter.
- What is a
Variable. Here a huge appetizer which shows how to talk about number and
quantities before algebra or the shorthand role of letters and symbols
begins.
- Skiing - A Visual
Interpretation of Slopes --- What can be visualized before priming
functions and starting calculus.
- Skiing - Visual Interpretation
of Slopes and a Calculus preview with the aid of factor polynomials
alone or in rational functions.
- Complex Numbers -- the second imaginary platter
(zero and negative numbers provided the first). Applet action
is available.
- Which founder of calculus never held an university post? Answer.
- Which founder of calculus thought more highly of proofs with geometry
before coordinates than algebraic proofs? Answer.
Why have times changed? Answer.
Just Desserts from Logic
There is more to mathematics than just doing arithmetic.
- Two Logic Puzzles
-- your egg and five questions twice over, lemon flavored. Available in Garlic
flavour too.
- Chains of Reason --
for sluggers.
- Longer Chains of
Reason -- for romantic types who like to climb ladders with accessible
steps.
- Islands and Divisions
of Pattern Based Thought --- an Euclidean model for thought, in separate
heaps, perhaps.
- Deception -
apart from white lies or diplomacy, not recommended all the time.
- Pedestrian Fare -- for future safe
returns.
Old Main Courses
take-out available.
New Main Courses
table-service only
- Students at all levels may learn algebra with the aid of a crutch: A
three column method for Solving
Linear Equations with proper and improper fractional operations on Stick
Diagrams. Fraction sense and skills are needed in calculus and
senior high school mathematics.
- Fractions,
Ratios, Rates, Proportions & Units - An assortment
of lessons that may clarify concepts for instructors if not students.
- Calculus Introduction
- Calculus Preparation for Page - 100 hours
- Euclidean Geometry Introduction
- Quebec Maths Education, Here are
three ways to ease or avoid this disaster: (i) to send your teen or
child out of the province, (ii) send your teen or child to an
international school which does not follow the Quebec Curriculum, or (iii)
get professional assistance from the site author.
- Number Theory Fresh baked ideas for
developing numbers from tally sticks and geometric principles in a way
accessible if not pure
- LaTeX2HotEqn - great idea, not yet used at this
site.
- Solving Linear Equations with Stick
Diagrams - a method for teachers, tutors and parents to introduce
algebra and point to the use of fraction after fractions
- fractions - more methods for teachers to
introduce fractions, ratios, proportionality, ratios and the role of units
in proportionality calculations.
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whyslopes.com
Entrance Level
Montreal Area Tutors
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
Site History/Content
Site Reviews
Vol 1. Elements of Reason
Maps Plans Drawings
Quantitative_Skills/index.html
Order Site Books
McGill-Quebec Nonsense & BS
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
25 hours per course
Site Areas by Age and Subject
Montreal Tutors
Entrance Continued
Still More Advice
Head Start Page
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
Logos Cafe
Logic Check List
Mathematics Cafe
Math CheckList
A Site Map
Advice for Secondary I Students
Three Ways to be a Better Student
Reason for HS Mathematics
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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