Counting Forward to Subtract Up to 20

Counting forward to subtract, often called "counting on," is a strategy where you start at the smaller number in a subtraction problem and count forward, one number at a time, until you reach the larger number. The number of counts you make is the answer to the subtraction problem. This works because subtraction tells you the distance between two numbers, and counting forward measures that exact distance.

For example, in \( 15 - 12 \), instead of starting at 15 and counting backward, you start at 12 and count forward: 13, 14, 15. That is 3 counts, so \( 15 - 12 = 3 \).

Counting forward is most useful when the number you are subtracting (the smaller number) is close to the total (the larger number). When the gap between the two numbers is small, counting forward only takes a few steps and is much faster than counting backward from a large number. If the gap is large, it may be quicker to use a different method, such as recalling known facts directly. You can review those facts in the lesson on subtraction facts up to 20.

Follow these steps for any subtraction problem written as \( a - b \), where \( a \) is the larger number (the total) and \( b \) is the smaller number:

1. Start at \( b \), the smaller number.

2. Count forward one number at a time, saying each number out loud or tracking it on your fingers.

3. Stop counting as soon as you reach \( a \), the larger number.

4. Count how many numbers you said. That total is the answer to \( a - b \).

Start at 12, since it is the smaller number. Count forward until you reach 15.

You made 3 jumps to get from 12 to 15, so \( 15 - 12 = 3 \). Checking your jumps on a number line like this is a great way to confirm your answer; see more examples in the lesson on using a number line to subtract up to 20.

Start at 17, the smaller number, and count forward: 18, 19, 20. That is 3 counts, so \( 20 - 17 = 3 \). Notice how quick this is compared to counting backward all the way from 20, since the gap between 17 and 20 is small.

Counting back works by starting at the larger number and counting down, which is helpful when the number being subtracted is small. Counting forward works the opposite way, starting at the smaller number and counting up, which is helpful when the number being subtracted is close to the total. Practicing both strategies, alongside other methods shown in the lesson on subtracting with digits up to 20, helps you choose the fastest approach for each problem.

Before counting, take a quick look at the two numbers in your subtraction problem. If they are close together, counting forward from the smaller number will usually be the fastest way to find the answer. As you practice, try to count forward smoothly without stopping, and always double check by seeing if your final count lands exactly on the larger number.

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