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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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Advice for Secondary I Students
Mathematics Lift-Off Check-List
Primary school should give you whole number and fraction skills and sense.
You should know
- how to write whole numbers as decimals,
- the times and sums table
- how to recognize when a whole number is a multiple of 2, 3, 5 or 10.
- the place value of each position in a decimal, before and after the
decimal point.
- how to add, subtract and multiply whole numbers exactly, and how divide
whole numbers by long division to obtain a quotient and a remainder. Here
knowledge of the times and sum tables is useful.
- how to add, subtract and multiply whole numbers exactly, and how divide
whole numbers by long division to obtain a quotient and (?) a remainder when
the numbers are given by decimals with digits before and after the decimal
point.
- the meaning of unit fractions 1/2, 1/3, 1/4,1/5, .... 1/100 etc
These are adjectives describing how much of a quantity or object is present.
- the meaning of simple fractions m/n = m times 1/n = a whole
number multiple of a unit fraction. These are (compound) adjectives saying
or describing how many unit fractions of a quantity or object is present.
Simplification of Fractions - Unifying Theme
- how to simplify fractions or reduce them by canceling common factors from
numerators and denominators. Here knowledge of the times table and how to
recognize when a whole number is a multiple of 2, 3, 5 or 10. For improper
fractions is it better to simplify first or is it better to express as a
whole number plus a smaller fraction, and simplify the latter? What requires
less work?
- what does it mean for two fractions to be equivalent including (i) how a
unit fraction may be equivalent to a simple fraction, and how
multiples of the latter simple fraction are equivalent to multiples of a
unit fraction. Give some geometric examples.
- how to multiply fractions - how to calculate products efficiently. While
the product of fractions has denominators = the product of the denominator
of the product factors, and numerator = product of the numerator of the
factors in the product, simplifying of the product is done more efficiently
by canceling common factors of the factors. See examples for exact
meaning or how as the word factor appears to many times here.
- the meaning of a product - what does it describe.
- how to divide fractions - how to turn division by a fraction into a
multiplication by its reciprocal or multiplicative inverse
- the meaning of fraction divisions or quotient of fractions - what it
describes in terms of how many time one line segment goes into another line
segment when both segments are fractional multiples, improper or proper, of
a unit length.
- the existence of two ways to write the quotient of fractions, and how one
way gives what is called a compound fraction.
- how to add and subtract fractions with like denominators and
simplify the result.
- how to add and subtract fractions with unlike denominators using any
common denominators, and why smaller or least common denominators
usually leads to less work when simplifying the resulting sum or difference.
- how to calculate the least common denominator of two whole numbers via the
list method, and why the list method is awkward when the whole numbers are
not small?
Primes and their Use
-
Errors and Error Control in Measurements and in Calculations.
How to indicate accurarcy or maximum possible error using Scientific Notation
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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
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Complex No.s Intro.,.
Calculus Motivation
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Calculus. Guide-Long
Calculus Guide - Longest
Links - Many Subjects
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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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