Missing Addend Equations (e.g., 7 + ? = 15) - First Grade Mathematics

Imagine opening a treasure chest that is supposed to hold 15 gold coins, but when you count them, there are only 7 coins inside! You know immediately that some coins are missing. In mathematics, problems with a missing piece are called missing addend equations. An equation like 7 + ? = 15 is a mathematical mystery story where you are the detective. In this chapter, you will learn how to find the missing addend using number bonds, counting on, and subtraction.

What Is a Missing Addend?

In an addition equation, the numbers that are joined together are called addends: Addend + Addend = Sum. When one of those addends is replaced by a box, a question mark, or an empty blank, it is a missing addend.

Missing Addend Representations:
  7 + [ ? ] = 15
  7 +  ___  = 15
  7 +  [ ]  = 15
All three ask: "What number must be added to 7 to make 15?"

The Mystery Box

Think of the box [ ] as an empty box waiting to be filled. Your job is to find the exact number that makes both sides of the equal sign balance.

Strategy 1: Counting On to the Total

One of the most intuitive ways to solve a missing addend problem is to count on from the known addend until you reach the sum.

Solving 8 + [ ? ] = 13 by Counting On:
Step 1: Start at 8:   "EIGHT..."  (Lock 8 in your head!)
Step 2: Count forward until you reach 13:
        "Nine"       (1 finger)
        "Ten"        (2 fingers)
        "Eleven"     (3 fingers)
        "Twelve"     (4 fingers)
        "Thirteen!"  (5 fingers - STOP! You hit 13!)

Look at your hand: You are holding up 5 fingers!
Missing Addend = 5!
Equation: 8 + 5 = 13

Strategy 2: Using Subtraction (Think Part-Whole)

Look at the equation 7 + ? = 15 through a number bond lens: The whole is 15. One part is 7. The missing addend is the other part!

The Number Bond View:
            ( 15 )   <- Whole
           /      \
        ( 7 )    ( ? ) <- Missing Part

Subtraction Equation: 15 - 7 = 8
Therefore: 7 + 8 = 15!

The Subtraction Rule for Missing Addends

To find a missing addend, simply subtract the known addend from the total sum: Missing Addend = Sum - Known Addend! For 7 + ? = 15: 15 - 7 = 8!

Missing Addends in the First Position

The missing addend can also appear as the first number in the equation!

Solving [ ? ] + 6 = 14:
The problem asks: "What number plus 6 equals 14?"
Use subtraction: 14 - 6 = 8!
Check: 8 + 6 = 14! (True!)

Practice Exercises

Exercise 1: Find the missing addend in each equation: 8 + __ = 14 6 + __ = 11 __ + 5 = 13 9 + __ = 16

Exercise 2: Use the count-on strategy to solve 7 + [ ? ] = 12. Describe the numbers you say and how many fingers you hold up.

Exercise 3: Write a subtraction equation that can be used to solve [ ? ] + 8 = 17. What is the missing number?

Exercise 4: A jar needs 15 marbles to be full. It currently has 9 marbles inside. How many more marbles must you put into the jar to fill it? Write a missing addend equation and solve it.

Solutions and Explanations

Solution to Exercise 1: 8 + 6 = 14 6 + 5 = 11 8 + 5 = 13 9 + 7 = 16

Solution to Exercise 2: Start at 7 and say: "Seven..." Count forward to 12: "eight, nine, ten, eleven, twelve." You held up 5 fingers, so the missing addend is 5 (7 + 5 = 12).

Solution to Exercise 3: The subtraction equation is 17 - 8 = 9. The missing number is 9 (9 + 8 = 17).

Solution to Exercise 4: The missing addend equation is 9 + ? = 15. To solve, subtract 15 - 9 = 6 (or count on from 9 to 15: 6 steps). You must put 6 more marbles into the jar.