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Completing Subtraction Statements Up to 20

This lesson teaches how to complete subtraction statements up to 20 when a number is missing from the minuend, subtrahend, or difference. Students learn to use fact families, related addition facts, and number lines to figure out the missing value and check their answer.

Introduction

A subtraction statement has three parts: the number you start with (the minuend), the number you take away (the subtrahend), and what is left (the difference). Completing a subtraction statement up to 20 means one of these three numbers is missing, and your job is to figure out what it must be.

This skill builds directly on knowing your subtraction facts up to 20 and on understanding what the minus sign in a subtraction sign is asking you to do. Once you can find any missing number in a statement like \( 15 - \square = 8 \), you can solve subtraction problems no matter where the blank appears.

The three places a number can be missing

A missing number can show up in any of the three spots in a subtraction statement:

Missing difference: \( 15 - 7 = \square \)
Missing subtrahend: \( 15 - \square = 8 \)
Missing minuend: \( \square - 7 = 8 \)

The first type is the easiest, since you just subtract like normal. The other two need a different strategy because the blank is not at the end of the statement.

The same three numbers, 15, 7, and 8, arranged with the missing number in a different position each time.

Using the addition and subtraction fact family

Every subtraction statement belongs to a fact family with a matching addition statement. If \( 15 - 7 = 8 \), then \( 8 + 7 = 15 \) is true too. This is the key idea for filling in a missing minuend or subtrahend, because turning the statement into addition often makes the missing number easier to see.

Example 1: missing subtrahend. Solve \( 15 - \square = 8 \). Think of the fact family: \( 8 + \square = 15 \). Since \( 8 + 7 = 15 \), the missing number is \( 7 \). Check it: \( 15 - 7 = 8 \). It works.

Example 2: missing minuend. Solve \( \square - 7 = 8 \). Rewrite it as an addition fact: \( 8 + 7 = \square \). Adding gives \( 15 \), so the missing minuend is \( 15 \). Check it: \( 15 - 7 = 8 \). It works.

If you are more comfortable subtracting than adding, you can also solve for a missing minuend directly, since the minuend is always the difference plus the subtrahend: \( \square = 8 + 7 = 15 \).

Using a number line to check your answer

A number line is a helpful way to see whether a missing number makes sense, especially while you are still getting comfortable with using a number line to subtract up to 20. To check \( 15 - \square = 8 \), start at \( 15 \) and count backward until you land on \( 8 \). Count how many jumps that takes, and that number of jumps is your missing subtrahend.

Starting at 15 and counting back 7 spaces lands on 8, confirming the missing subtrahend is 7.

Watching for zero and matching numbers

Some statements have a missing number of zero, which can look surprising at first. In \( 12 - \square = 12 \), the missing number is \( 0 \), because taking away nothing leaves the amount unchanged. This idea is covered in more depth in the lesson on subtracting with the number zero, which is worth reviewing if a zero shows up in your statement and the answer does not seem to match.

Step-by-step approach for any missing number

Read the statement and decide which part is missing: the minuend, the subtrahend, or the difference.
If the difference is missing, subtract the two known numbers as usual.
If the subtrahend or minuend is missing, rewrite the statement as its matching addition fact.
Solve the addition fact to find the missing number.
Substitute the number back into the original subtraction statement and check that both sides are equal.

Practice problem: Complete \( \square - 6 = 9 \). Using the fact family, \( 9 + 6 = \square \), so the missing minuend is \( 15 \). Checking: \( 15 - 6 = 9 \), which is correct.

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