Using Addition to Solve Subtraction (Think-Addition) - First Grade Mathematics

Many students think addition and subtraction are completely separate topics, but secret masters of math know that subtraction is just addition in disguise! Whenever you face a tricky subtraction problem like 15 - 8 = ?, you do not have to count backward fifteen times. Instead, you can turn the problem around and ask an addition question: "8 plus WHAT number equals 15?" This technique is called the Think-Addition strategy. In this chapter, you will learn how to turn subtraction into a missing-addend mystery and solve subtraction within 20 with ease.

Turning Subtraction Around

Every subtraction problem is really an addition problem with a missing part.

The Think-Addition Flip:

Subtraction Problem:     14 - 9 = ?
                              |
                     Flip to Addition!
                              v
Addition Question:       9 + [ ? ] = 14

Why Think-Addition Is Faster

Our brains learn addition facts much faster and remember them more clearly than subtraction facts. When you ask "9 + ? = 14," your brain instantly searches its addition memories and finds: "9 + 5 = 14!" That means 14 - 9 MUST be 5!

Walking Through the Strategy Step by Step

Let us solve 13 - 7 using the Think-Addition strategy.

Solving 13 - 7 = ?
Step 1: Read the problem: 13 take away 7.
Step 2: Think addition: "7 plus how many makes 13?" (7 + ? = 13)
Step 3: Bridge to 10:
        Start at 7.
        7 + 3 gets you to 10.
        From 10, you need 3 more to reach 13.
        Combine the hops: 3 + 3 = 6!
Step 4: Answer: 7 + 6 = 13, so 13 - 7 = 6!

Bridging Through 10

When thinking addition across the teens, always stop at 10 on the way! From 8 up to 15: 8 needs 2 to get to 10. 10 needs 5 to get to 15. Add the two hops: 2 + 5 = 7. So 15 - 8 = 7!

Number Bonds Make the Connection Clear

Look at the number bond for 12, 8, and 4:

The Number Bond Connection:
            ( 12 )   <- Whole
           /      \
        ( 8 )    ( ? ) <- Missing Part

Addition Story:     8 + ? = 12  ->  8 + 4 = 12
Subtraction Story: 12 - 8 = ?   -> 12 - 8 = 4

Both Paths Lead to the Same Missing Part

Whether you write it as 8 + ? = 12 or 12 - 8 = ?, the missing piece of the puzzle is the exact same number: 4!

Practice Exercises

Exercise 1: Rewrite each subtraction problem as a "Think-Addition" question with a missing addend: 11 - 8 = ? 15 - 6 = ? 12 - 7 = ? 16 - 9 = ?

Exercise 2: Solve 14 - 8 using the Think-Addition strategy. Write down the addition fact you used to find the answer.

Exercise 3: Solve 12 - 9 by thinking addition. Describe how bridging to 10 helps you find the missing part.

Exercise 4: Explain why thinking addition is often easier than counting backward when solving problems like 17 - 9.

Solutions and Explanations

Solution to Exercise 1: 11 - 8 = ? becomes 8 + ? = 11 15 - 6 = ? becomes 6 + ? = 15 12 - 7 = ? becomes 7 + ? = 12 16 - 9 = ? becomes 9 + ? = 16

Solution to Exercise 2: To solve 14 - 8, think: "8 + ? = 14." Since 8 + 6 = 14, the answer is 6 (14 - 8 = 6).

Solution to Exercise 3: Think: "9 + ? = 12." Bridging to 10: starting at 9, it takes 1 hop to reach 10 (9 + 1 = 10). From 10, it takes 2 more hops to reach 12 (10 + 2 = 12). Add the hops: 1 + 2 = 3. Therefore, 9 + 3 = 12, and 12 - 9 = 3.

Solution to Exercise 4: Counting backward 9 times from 17 is slow and prone to errors. Thinking "9 + ? = 17" lets you immediately use your known fact 9 + 8 = 17 to find that 17 - 9 = 8 in a single mental step.