## Order and Compare Numbers

Numbers such as 1, 2, 3, and 4 are cardinal, or counting, numbers. Numbers such as first, second, third, and fourth are ordinal, or positional, numbers. Children need practice in identifying ordinal positions as well as the words (written and oral) associated with the positions. At this grade level, ordinal numbers through tenth are discussed. Development of ordinals beyond tenth is left to the discretion of the teacher.

Comparing and Ordering Numbers
An important application of place value arises in the comparison of numbers. In comparing 51 and 9, children note that the first number has two digits and the second number has one digit. They will conclude that 51 is greater than 9 (51 > 9). This method is justified by the fact that for whole numbers the least 2-digit number (10) is greater than the greatest 1-digit number (9), the least 3-digit number (100) is greater than the greatest 2-digit number (99), and so on.

To compare two whole numbers with the same number of digits, children begin by comparing the digits in each place, starting at the left. If the left-most digit is the same in both numbers, then children compare the digits in the next place to the right. When the two numbers have different digits in the same place, the number containing the greater of the two digits is the greater number. For example, 24 and 26 have the same digits in the tens place but different digits in the ones place. The fact that 6 > 4 implies that 26 > 24. Children should also notice that 6 > 4 can also be written as 4 < 6, which implies that 24 < 26. Remind children that the symbols < and > always points to the smaller number.

Use of a number line allows children to develop the sense of order of numbers. Indicating the position of a number relative to another number as before, after, or between enhances development of vocabulary.

Teaching Model 11.2: Ordinal Numbers