## Adding and Subtracting Two-Digit Numbers and Money Amounts: Overview

In the following exercise, the numbers 35 and 22 are the addends. The number 57 is the sum. When adding two-digit numbers that are not multiples of ten, children can use visual aids, such as base-ten blocks, to model the addends and to find the sum. With the numbers represented by blocks, children can count the number of ones and the number of tens. They can also group the ones together to represent their addition and then count them. This method can be repeated for the tens. Blocks help children add, because the sum will always be the total number of blocks.

Some children may prefer simply to use paper and pencil for exercises rather than to use mental math or visual aids. Children can write the numbers and use basic facts to help them complete the exercises. For example, to add 53 and 25, children can be reminded that they should first add 5 and 3 in the ones column to get 8, and then add 2 and 5 in the tens column to get 7, giving the sum of 78.

As in addition, children can use mental math and their knowledge of basic facts to subtract two-digit numbers that are multiples of ten. For example, to subtract the number 30 from the number 70, children can use the basic fact 7 − 3 = 4. The basic facts will help children understand that 70 − 30 = 40.

As shown in the example below, children can also use visual aids to model subtraction, by using base-ten blocks, writing the numbers in a tens-and-ones frame, and then removing blocks from the model to represent the subtraction. To subtract 12 from 37, display 3 tens rods and 7 ones. Remove 2 blocks from the ones column and write 5 in the ones column of the tens-and-ones frame; then remove 1 ten and write 2 in the tens column of the tens-and-ones frame.

Some children prefer to use just paper and pencil to complete subtraction exercises. They can simply write the numbers and use basic facts to help them subtract. For example, in the exercise 48 − 17, children can write the numbers vertically. Then it's easy for them to see that they must first subtract 7 from 8 in the ones column and 1 from 4 in the tens column. They can thus see that the difference is 31.

Show children that they can use addition to check subtraction. When they subtract a smaller number from a larger number and get a difference, they can check the difference by adding the difference (31) and the subtrahend (17). Their answer should be the same as the minuend (48).

You can also show children that adding and subtracting money amounts less than one dollar is just like adding and subtracting two-digit numbers. Children should add or subtract the ones first and the tens next. Remind them to write the cents ¢ symbol (¢) along with their answer.