Using the State Curriculum: Mathematics, Grade 3

To compare numbers, determine how their values differ—which is greater, which is less, which is the least. Then, in some instances, the numbers can be put in order from the greatest to the least, or from the least to the greatest. To compare numbers, look at the digits in each of the places within the number (thousands, hundreds, tens and ones) and take note of how those in the same place differ.

Comparing numbers can be done in several ways:

Using a place value model, compare 113 and 125.

This model gives a concrete representation of each place within a number and allows students to visually compare the values of specific places between numbers. There is the same number of 100's blocks for both numbers. However, there are 2 ten's rods in 125 and only 1 ten rod in 113. Therefore, 125>113.

Using a number line, compare 61 and 72. Again we focus on the place value within numbers. In this case, we compare the value in the tens place of each number and find that since 7 tens is greater than 6 tens, 72 is therefore greater than 61. As students compare various numbers using the number line, they will realize that the number furthest to the left on the number line is least in value and that the number furthest to the right is greater based again on place value.

Using place value, compare 4,568 and 4,666. Line up the place values beginning with one's place. Begin at the greatest place value and compare the value of the digits in that place. If the digits are the same, move to the next place value until there are different digits in the same place. A digit is any one of the ten symbols ( 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9).

Thousands	Hundreds	Tens	Ones
4	5	6	8
4	6	6	6

Since, the hundreds place is the first place value with different digits, this is the place value for comparison. 4,666 is greater than 4,565 because 600 is greater than 500 in the hundreds place. 4,666 > 4,565.

Use the same procedure in ordering the whole numbers.

Order the following set of numbers from least to greatest:

2,124   2,572   2,433   2,462   2,500

Place each number in the place value chart, beginning with one's place.

Thousands	Hundreds	Tens	Ones
2	1	2	4
2	5	7	2
2	4	3	3
2	5	0	0

Each number has a 2 in thousands place. In hundreds place the smallest digit is 1. So, 2,124 is the smallest number. The next smallest digit in hundreds place is 4. 2,433 is the next smallest number. So far: 2,124, 2,433,____, ____
The other two numbers both have 5 in hundreds place. In tens place, 2,572 has a 7 and 2,500 has a 0. Since 7 > 0, 2,572 > 2,500. Complete the ordering of the numbers from least to greatest: 2,124, 2,433, 2,500, 2,572.

The same procedure can be followed using the place value model for those students who still need to rely on a concrete/visual model.