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Abacus lessons:
Introducing the Abacus
The Abax:
Introducing the Abax
Counting on the Abax:
Lesson 1
Lesson 2
Test
Addition on the Abax:
Lesson 1
lesson2
Lesson 3
Subtraction on the Abax:
Lesson 1
Lesson 2
Lesson 3

History of the Abacus
(not operational yet)

Related Lessons
Regrouping and Carrying
Tens Complements

Commutative Law of Addition
Order of columns in Subtraction

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Interesting Lessons and
Frequently Asked Questions about Math

New Lesson on:
Names of the Numbers in Basic Arithmetic Operations
(Posted Feb. 29, 2008)

There are some basic questions about math that get asked over and over again. It is amazing that so many people who have gone through, or are going through, the school system have no Idea about some of the basic laws of math, or why they work.

For instance, almost everyone has heard that, "You can't divide by zero." I am sure that there is at least one person in every single math class in American schools who doesn't know that, strictly speaking, that isn't true. You CAN divide by zero - you just won't get a useful answer when you do. Find out what answer you will get if you do, and why. Then you will understand (probably better then your teacher) why they say you can't divide by zero.

This is one of the basic problems of math education - you learn a bunch of "facts," but have no Idea of the deeper meanings behind them, or any Idea of how you might ever use them. This is failure to create any meaningful relationship to the material learned is rampant in our school systems, and nowhere more apparent than in math classes.

Here is a list of Frequently Asked Questions and assorted lessons that illustrate basic math concepts. Browse through them and find some that sound interesting to you, and to see if you are not clear on any of them. Then take those lessons to enhance your skills in that area.

 All of them are explained in plain english.

Lesson:
Concerns:
An Easier way to learn Long Division division
Multiplying and Dividing Fractions multiplication, division, fractions
prime factorization how numbers work
The "Pretty Good Guide" to prime factorization  
Why should we learn prime factorization? Mathematical philosophy, how numbers work, motivation to learn
products of odd or even integers how numbers work
squaring two 2-digit numbers which both end in 5 Speed-math
Triangular Numbers

Finding the sum of 1+2+3+4+5+6+7......+n, how numbers work

What's the Deal with the Laws in Mathematics? (A bit of "Legal Advice"), math philosophy
The Commutative Law of Addition Why it Doesn't Matter Which Column you Add First
Distributive law How numbers work
An Interactive Lesson about Infinity just weird
Can you create a 5-cell x 5-cell magic square whose sums are 130, using numbers between 2 and 50? Magic Squares, recreational math, problem solving
Can you make a 4-cell x 4-cell magic square, in which each of the numbers is a multiple of 5, using the numbers 5 - 80 (inclusive)? The sum of each of the columns, rows and diagonals must be 170. Magic Squares, recreational math, problem solving
Why does 2 + 2 = 4? Mathematical philosophy, how numbers work
Is 0.999... really equal to 1, and if so, why?
how numbers work
Why do we carry or regroup in math?
how numbers work
How do you do multiplication from left to right?
speed-math, arithmetic
2 to the power of x +x = 6   algebra
About our number-system
how numbers work
How do you find the area of a square?
geometry
I need help understanding how word problems work word problems
How do you remember which is the greater-than sign and which is the less-than sign?
Algebra, mnemonics
OK, so why can't you divide by zero? how numbers work
What is the origin of zero? Math History

What are tens complements and how do I use them?

Arithmetic, Speedmath, How numbers work
names of large and small numbers how numbers are named (-illions, -illionths, etc.), latin prefixes, scientific notation, how to pronounce numbers
left-to-right subtraction arithmetic, speedmath
How can you use the sense of sound to help you learn basic multiplication? multiplication, how to learn math
basic multiplication thoughts on how to learn multiplication
Why does any number to the 0 power equal 1, and not 0? exponents, how numbers work
Place values for Bases exponents, how numbers work
proof that 1 = 2 (?!?) how numbers work , mathematical fallacies
expanded notation How numbers work. Speedmath.
Introduction to Exponents (Powers) exponents, how numbers work
The Commutative Law of Multiplication multiplication, how numbers work
The Order of Operations

arithmetic, how numbers work

Negative Exponents arithmetic, exponents, how numbers work
How to Divide Exponents with the same Base arithmetic, exponents, division, how numbers work
Which is greater, x2*y2 or x2+y2?  
Simple Wording for Multiplication and Division
of Whole Numbers
arithmetic, multiplication, division, how numbers work
Names for the Division Symbol division, nomenclature
Making Math Meaningful for
Teachers and Students
  how to learn math
Insights Learned from a Silly Joke about Multiplication Math and Philosopy, Insights, Math and Meaning
Changing Fractions into Percent arithmetic, fractions, percents
Names of the Numbers in Basic Arithmetic Operations arithmetic, nomenclature, insights
   
   
   
   
   
   
   

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