## Regrouping With Addition

The addition algorithm consists of adding ones, then tens, then hundreds, and so on, regrouping any sum greater than 9 in each place. The reason the addition algorithm works can be illustrated by examining the numbers in their expanded form. For example, have children consider 58 + 36.

__+ 36__

__+ 30 + 6__

80 + 14 = 80 + (10 + 4)

= (80 + 10) + 4

= 90 + 4

= 94

The standard algorithm takes place in two stages and provides a shortcut for recording the renaming process.

When a vertical addition problem is presented to children, be sure to emphasize the need to correctly align the digits before completing the addition.

## Estimating Sums

When an exact answer is not necessary, an estimate can be used. The most common method of estimating sums is to round each addend to a specific place and then add the rounded numbers. In this chapter, children round numbers to the nearest ten with the help of a number line.

48 → 50

__+ 31 → + 30__Round each number to the nearest ten.

80 Add the rounded numbers.

Mental math can often be used to complete estimates. At this grade level, however, explain that errors can be more easily identified if children write down their work when estimating answers.

**Teaching Model 10.3:** Regroup Ones as Tens