Arithmetic with
Decimals & Integers
(Flash Videos Lesson)
Section Entrance
Counting & Addition
Compare & Subtract
Multiplicaton
Long Division
Integers - Intro to Signed No.s
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Basic Arithmetic with Whole Numbers & Integers
This is a new site area - posted online November 14, 2007. Most lessons are based on flash videos -
access requires JavaScript and a flash viewer.
Most videos are two to six minutes long, usually one per lesson.
Subject: Counting, addition, comparison, subtraction, multiplication, long division
Four chapters with 40 lessons and more than 40 flash videos lessons follow.
- (8 lessons) counting and
adding whole numbers Counting and Addition of Decimals
- (9 lessons) comparing
and subtracting whole numbers and decimal fractions Comparing and
Subtracting with Decimals
- (11 lessons) multiplication
of whole numbers and decimal fractions - Multiplication Methods and Theory for Decimals
- (12 lessons) long division for
whole numbers - Long Division Methods and Theory for Decimals - Whole
numbers only,
Decimal notation and methods for counting, comparison and arithmetic are met
in primary school and should be reviewed and mastered in full by students 12 to
14 years of age in school.
Lessons on Integers and three
appendices include
exercises to consolidate and extend understanding - 15 plus flash videos.
Total viewing time for the webvideos will be about one hours - an hour per
chapter.
The lessons provide a
hands-on, thought based development. Lessons assign three geometric roles to integers
to develop and explain rules for integer arithmetic.
- Role I: Integer are first introduced as coordinates for points on a
line, where adjacent points are a unit distance apart.
- Role II. Integers then serve as multipliers in the definition of integer multiples
of a unit movement, integer multiples that can be added and multiplied by
whole numbers and then integers.
- Role III. Integers themselves may describe movements, how many steps to
the left or right, along a straight line, and so can be identified with
movement, integer multiples of a unit movement, now called a step. That
third role or identification leads allows integers to be added and
multiplied.
Exercises are included in most lessons.
Three appendices cover an
associative law, division quotient and remainder options for integers, and how
remainder arithmetic explains the alternating sum of digits test for
divisibility of decimals by 11.
Extension: This three role,
geometric development and explanation of integers starting with unsigned whole
numbers provides an example to follow for the development and
explanation of (i) rational numbers starting with unsigned fractions; and (ii)
real numbers starting from unsigned (positive) real numbers or their decimal
representation. The site exposition of complex numbers continues the geometric
development of number theory.
Decimals and Prime Number Decomposition
New webvideo lessons to be posted will replace or complement the current site
coverage of the following.
- Primes
& Composites
Composite numbers less than 101
Prime Numbers less than 101
- Primes
Factorization
Unique Prime Factorization Theorem (Cryptic Statement)
- Primes
& Composites
Calculation of Greatest Common Divisors and Least Common Multiples from
Prime Factorizations
- Prime
Factorization Aids & Prime
Factorization Examples (two pages) If a whole number N < 121 is
not divisible by each prime 2, 3, 5 and 7 < 121 = 112 then N
is prime. Alternatively, if N < 121 is composite then it will be a single
or repeat multiple at least one of the primes 2, 3, 5 and 7. Whence
recognizing whether or not a whole number N < 121 is divisible by 2, 3, 5
or 7 gives a quick test for primality and a quick method for prime
factorization. See examples.
- Counting
Whole No. Factors. How to count and generate all possible
factors of a whole number from its prime factorization. Introduces the
concept of proper and improper factors - For the latter, is there a more
standard terminology?
- Divisibility
Rules and Remainders for Division by 2, 3, 5, 9 and 11. There are many
rules for recognizing when whole numbers are multiples of 2, 3, 4, 5, 6, 7,
8, 9,10 and 11. Those rules are consequences of modulo or remainder
arithmetic
Again this is a new site area - posted online November
14. It complements and replace lessons in the Arithmetic
Reference Page. The latter page points to a 100 more site aids
for arithmetic
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Site
Entrance: www.whyslopes.com
(& entrance level pages)
Parents: Help
your Child/Teen Learn
Online
Volumes
1, Elements of
Reason. 1996
1A. Pattern
Based Reason 1995
1B. Math
Curriculum Notes 1996
2. Three
Skills for Algebra 1995
3 .Why.Slopes.&.More.Math.1995
Math
How-TOs & Notes 2008
1. Arithmetic
2. Algebra
3. More
Algebra
4. Geometry
5. More
Geometry
6. Calculus
Site
Description/Reviews
by 3rd parties
(many unsolicited)
Site
Math Folders
1. Arithmetic
Web Video Lessons- 11-2008
2. Algebra Videos (to appear)
3.-Fractions-Rates-Proportns-Units-2006
4. Algebra, Odds
& Ends, HS level-2001
5. Solving
Linear Equations 04-2005
6. Euclidean-Geometry
To Complex No.s
7. Analytic
Geometry/Functions 2006
8. Number
Theory. 2006-7
9. Complex
Numbers More 2001.
10 Exponents,
Radicals & logs. 2008
11. Calculus
2005
12.Real
Analysis 1995
13. Electric
Circuits Etc 2007
For Math
Professors/Instructors
Mathematics
education essays
K0-11Applied Math Program Outline
Lamp
- an earlier applied math program
Site
Content, technical description
Work Online With Others: Try the scriblink
java whiteboard. It works in IE8 and Firefox. It has text chat,
voice communication, print, save file, and share abilities.
Meet fellow students or tutors on it to share ideas. dabbleboard
(flash), twiddla, acrobat, and WiZiQ also provide
online meeting places. with math facilities.
Their whiteboards were very slow until I removed
background tasks on my PC.
Services For Hire:
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Private Instruction in
Montreal: Tutoring
plus non-credit Short courses for junior high school
students in Montreal (Math
Jobs)
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Online
Maths Help for
work, studies & instruction - whiteboard base. My
skills are for hire in tutoring, teaching; helping
people at work with simple formulas or with research projects
for profit or not; and helping math teachers learn the
maths they are suppose to teach.
For many subjects, not all the site author is available as a
tutor or instructor. Use your imagination.
email
contact form + text
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Books For Sale:
For offline reading or gifts,
paperback versions of site online Volumes 1,
2 and 3, are available
for $40 each. Site Volumes 1A and 1B are $26 each.
Quantities are limited. Shipping cost depends on where
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help, subtract $15 from the shipping cost.
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