## Three-Digit Addition and Subtraction With Regrouping: Overview

In making the transition from adding and subtracting two-digit numbers to three-digit numbers, children will build on what they have already learned about place value and regrouping. It is important to remind children of the need for proper alignment of numbers when adding and subtracting numbers of more than one digit.

Begin with three-digit addition using basic facts and mental math. This will give children a chance to use what they already know. For example, to solve a basic three-digit addition problem, use numbers that involve basic addition facts, such as 200 + 400. Encourage children to use mental math (2 + 4 = 6), and then tell them to place 2 zeros after the 6 to make hundreds (600). Repeat this model for subtraction using the inverse operation: Since 6 − 4 = 2, 600 − 400 = 200.

Using base-ten blocks is a good way to help children visualize what they are doing when adding or subtracting three-digit numbers with regrouping. To solve an addition problem, regrouping ones, model the addends using base-ten blocks. The example below shows 125 + 137.

Remind children that to add or subtract, they should begin with the ones. In this case, group 5 ones and 7 ones to make 12 ones, regroup the ones as 1 ten, 2 ones, add the tens to make 6 tens, and add the hundreds to make 2 hundreds. The answer to the problem is 262.

The same process takes place when regrouping 10 tens, except regrouped tens become 1 hundred. The example below shows 153 + 172.

In this case, the ones do not need regrouping. Add to get 5 ones. Then group 5 tens and 7 tens to make 12 tens, and regroup the tens as 1 hundred, 2 tens. Add the hundreds. The answer to the problem is 325.

The same principles can be used in three-digit subtraction, except that regrouping works in reverse. One ten becomes 10 ones when regrouped. One hundred becomes 10 tens. Use the base-ten blocks to illustrate regrouping tens in three-digit subtraction for the problem 262 − 137. (Note that this is the inverse operation of the addition problem above.) Show how to regroup 6 tens as 5 tens, 10 ones, making 12 ones. Then subtract the ones: 12 ones − 7 ones = 5 ones. Remind children that they must then subtract tens using 5 tens, since they regrouped a ten as 10 ones to subtract the ones. Subtract the tens: 5 tens − 3 tens = 2 tens, or 20. Subtract the hundreds to solve the problem: 262 − 137 = 125.

Model this same method to illustrate regrouping hundreds to solve 325 - 153. Remind children that they can check their subtraction by using addition. Help them compare the subtraction to the addition problems you already did, making sure the numbers match.

Understanding these regrouping principles prepares children for learning horizontal addition and subtraction and for addition and subtraction of money. When teaching children to add and subtract horizontally, model how to rewrite the problem vertically. Make sure that children keep each digit in the correct place when rewriting numbers. Looking at the problem vertically makes it easier to see the hundreds, tens, and ones and to regroup if necessary. The example below illustrates how to rewrite a horizontal problem vertically in order to make it easier to solve.

Adding and subtracting with money is the same as regular three-digit addition and subtraction. Writing the amount $1.23 actually is the same as writing 123, except for the dollar sign and the decimal point. Children can think of dollars as hundreds, dimes as tens, and pennies as ones. You can regroup 1 dollar as 10 dimes and 1 dime as 10 pennies, and vice-versa.

Estimating is a good way to get a sense of the answer to an addition or subtraction exercise without actually computing. It also helps you see whether any answer you get is reasonable. To estimate a sum or difference, round numbers to the greatest place. The following example shows an estimate of 410 + 280.

Rounding each number to the nearest hundred, you find that the estimate of 410 + 280 is 700.