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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.
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Caution: Site advice is
approximately correct, for some circumstances, not all. Site How-TOs
are logically developed, but not tried and tested. That leaves
room for thought and refinement.. |
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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;
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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Explore collaborative whiteboards from groupboard,
twiddla or
scriblink.
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Incomplete
5. Polynomials and Operations on them
Site Objective: Explain and introduce efficiently
polynomials and operation on them: Addition, subtraction, multiplication,
division by a linear factor, simplification of quotients.
Four Operations on Polynomials
For polynomials, site lessons present the following
- Area
Viewpoint of Multiplication
- Multiplication
Addition and Subtraction
- Long
Division with linear divisors
- Column
Methods for Mulitplication
Together they point to a different approach for understanding and explaining
four arithmetic operations on polynomials.
Mastery of long division and methods to check its results
implies mastery of the other three operations (addition, subtraction, and
multiplication).
Let mastery of long division with linear or nonlinear factors be your aim.
Explore the above lessons alone or with help. And for long division, do the
checks. Division with nonlinear factors is optional - not part of the 436
program.
Links
Visit www.purplemath.com
lessons
- Polynomials (definitions
& "like terms")
- Polynomials:
Adding & Subtracting
- Polynomials:
Multiplying
- Polynomials:
Dividing
- Polynomials,
simple factoring (2 lessons)
to met and master the definition, addition, subtraction, multiplication and
division of polynomials in a more traditional approach.
Two online perspectives are better than one.
Teachers 1. The area view of products - how
multiplication distributes over addition takes 20 minutes. Then you
can introduce multiplication of polynomials via the area approach. Then
introduce and shift to the column method for multiplication of polynomials in
general. That being said, the column method for addition is implicit or
very close to the surface in the column method for multiplication. So column
addition methods for adding polynomials comes next. Finally, the latter is
modified to imply a column method for subtraction. There-in goes two
lesson to cover addition, subtraction and multiplication. Long division
(with checks included) may take a few more lessons. The approach here might be
use in all or part in secondary III (314), secondary IV (416-426-436) and
secondary V (536) mathematics.
Teachers 2. Chapter 3, Slope
Sign Analysis, in Volume 3, Why
Slopes and More Math , shows how to do sign and zero analysis for
factored polynomials, alone or in rational functions. Those examples as is or
adapted would improve the algebraic thinking skills of your students - focus of
the sign analysis of the expressions in question and not on their role as slopes
or derivatives to functions.
Site lessons here
offer a different approach for understanding and explaining operations on
polynomials. which is still under-construction - present form is sufficient for
teachers, but not for students.
Teachers: Chapter 3, Slope
Sign Analysis, in Volume 3, Why
Slopes and More Math , shows how to do sign and zero analysis for
factored polynomials, alone or in rational functions. Those examples as is or
adapted would improve the algebraic thinking skills of your students - focus
of the sign analysis of the expressions in question and not on their role as
slopes or derivatives to functions.
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www.whyslopes.com
Lesson & Lesson Plans for
Secondary IV
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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