Using Counting to Add Digits up to 100

When you add two numbers, you do not always need to count every single item from the very beginning. The counting on strategy lets you start at the larger number and count forward, one step at a time, by the amount of the smaller number. This is much faster than counting everything from 1, and it works well for adding digits up to 100.

For example, to solve \( 6 + 2 \), you do not need to count 1, 2, 3, 4, 5, 6, 7, 8. Instead you start at 6 (the bigger number) and count on 2 more: 7, 8. The answer is 8. As numbers get bigger, closer to 100, this same idea still works, you just count on further or use bigger jumps.

Follow these steps whenever you use counting to add two numbers:

• Look at both numbers and find the larger one.
• Start your count at that larger number.
• Count on, one number at a time, using the smaller number as how many times you count.
• The last number you say is the sum.

This works no matter which order the numbers are written in, since \( 4 + 34 \) gives the same sum as \( 34 + 4 \). Starting from the bigger number, 34, and counting on 4 is much quicker than starting from 4 and counting on 34.

Add \( 47 + 5 \).

The larger number is 47, so start there and count on 5 more: 48, 49, 50, 51, 52. So \( 47 + 5 = 52 \).

Counting one at a time gets slow once the smaller number is bigger than about 5. For a problem like \( 47 + 32 \), it is faster to count on by tens first, then finish with ones.

Break 32 into 3 tens and 2 ones. Starting at 47, count on by tens: 57, 67, 77. Then count on by ones: 78, 79. So \( 47 + 32 = 79 \).

This mix of counting by tens and then by ones is a natural bridge toward the more formal column methods used in adding digits up to 100, and it connects to a visual model in using a number line to add up to 100, where the same jumps are drawn as hops along a line.

Counting on is most useful when one of the two numbers is small, such as adding 2, 3, 4, or 5 to a bigger number. If both numbers are large, other approaches, like recognizing doubles or breaking numbers into tens and ones, can be quicker. You can compare counting on with these other options in addition strategies to decide which method fits a given problem best.

Say the numbers out loud as you count on, and touch or point to each one, whether it is a finger, a tally mark, or a spot on a number line. This keeps you from skipping a number or repeating one by accident, which is the most common mistake with the counting on strategy.

Related lessons

• Math 2