## Number Concepts Through 50

One important application of place value arises in the comparison of numbers. For example, when comparing 51 and 29, children should note that five groups of ten are more than two groups of ten, so 51 is greater than 29. Symbolically, 5 > 2, so 51 > 29. Point out that the number of ones is not important when the number of tens is different. However, if two numbers have the same number of tens, then it is necessary to compare the ones. For example, in comparing 32 and 36, the digits in the tens place are the same, so just the digits in the ones place need to be compared. Since 2 < 6, it follows that 32 < 36. Students should also note that a two-digit number is always greater than a one-digit number because the smallest two-digit number (10) is greater than the greatest one-digit number (9).

The concept of place value is also central to rounding. In rounding a number to the nearest ten, we need to determine the closest multiple of tens or the closest number with a zero in the ones place. For example, 37 rounded to the nearest ten will be either 30 or 40. Since children are not yet proficient at subtraction involving two-digit numbers, a number line is best used to show how to round numbers to the nearest ten. Since 37 is closer to 40, 37 rounds to 40. If a number is the same distance from two multiples of ten, it is rounded to the next greater multiple of ten. So, 35 rounds to 40.

**Teaching Model 1.3:** Comparing Numbers