Teaching Models

Place Value/Addition and Subtraction

Whole Numbers and Numeration
The Hindu-Arabic system of enumeration is described as a base-ten positional number system or a decimal system. It begins with special symbols called digits to represent the first nine counting numbers—1, 2, 3, 4, 5, 6, 7, 8, 9. There is also a very important tenth digit, 0, that is used to represent an empty column. Hindus are credited with the development of this system, and Arabs with introducing it to Western Europe.

The importance and power of a positional numeration system cannot be understated. It is truly one of the most significant inventions of civilization. All standard computational algorithms for whole numbers and decimals that students learn in elementary school are based on and work because of the base-ten positional numeration system.

For whole numbers, the digit farthest to the right is in the ones place. Moving to the left, each digit has a place value equal to 10 times that of the digit to its right. This can be shown in a place-value chart. The number 347,052 can be understood by looking at the following place-value chart. The digit 7 is in the thousands place. Its value is 7 thousands. The digit 5 is in the tens place. Its value is 5 tens. When writing numbers in word form, hyphens are used for numbers between 21 and 99 (except those ending in 0).

Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones
10×10,000
or
105 therefore 100,000
10×1,000
or
104 therefore 10,000
10×100
or
103 therefore 1,000
10×10
or
102 therefore 100
10×1
or
101 therefore 10
1

100 therefore 1
3 4 7 0 5 2

Numerals are written symbols for numbers. For numerals greater than 999, the digits are grouped into periods of three that are set off by commas. The ones period consists of the digits in the hundreds, tens, and ones places. The thousands period consists of the three places to the left of the ones period. The millions period consists of the three places to the left of the thousands period. The numerals in each period are read as a three-digit number and the period name is then added (except for the ones period). Thus, for example, 6,526,041,375 is read as six billion, five hundred twenty-six million, forty-one thousand, three hundred seventy-five.


Teaching Model 1.2: Place Value and Powers of Ten


Houghton Mifflin Math Grade 6