Teaching Models

Place Value to 100

Place Value
The Hindu-Arabic system of enumeration we use is described as a base-ten positional number 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. In future chapters the importance of this base-ten positional system will become apparent. 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 352 can be understood from the following place-value chart.

HUNDREDS TENS ONES
10 × 10
100
10 × 1
10
1
3 5 2

The digit 5 is in the tens place. Its value is 5 tens. The digit 3 is in the hundreds place. Its value is 3 hundreds.

Numerals are written symbols for numbers. When writing numbers in word form, hyphens are used for numbers between 21 and 99 (except for those ending in 0). There are three basic ways of showing a number. For the number 352 these are:

Standard Form
Expanded Form
Word Form
   352
   300 + 50 + 2
   three hundred fifty-two

At this grade level, a combination of expanded form and word form may also be given as 3 hundreds, 5 tens, 2 ones.

Because of the importance of ten to our number system, children need many experiences in grouping ones as tens, and then tens as hundreds.

Each number in our system, as mentioned before, has a word name. The numbers 0-12 all have unique word names. The fact that there are unique word names for 11 and 12 may indicate that at one time 11 and 12 were used as bases in a positional number system instead of 10. The numbers 13-19 are the teens and have names that are a combination of earlier names, with the ones place name first. For example, fourteen is a single word for “four ten” which means ten plus four. The numbers 20-99 are also combinations of earlier names, but reversed from the teens in that the tens place is named first. For example, the word name 57 is fifty-seven instead of seven fifty. The numbers 100-999 are a combination of the word hundred and previous names. For example, 327 is read three hundred twenty-seven. Notice that the word and does not appear in any of these names. The word and is reserved for separating the decimal part of the number from the whole-number part. For example, 1.2 is read one and two tenths.


Teaching Model 10.2: Tens and Ones


Houghton Mifflin Math Grade 1