Missing addend problems

Quick answer

You can find the missing number in an addition problem by using a part-whole model or thinking about what number, when added to the known part, makes the whole.

Learning outcome

By the end of this page, you will be able to find the missing number in addition problems like 7 + □ = 12 using part-whole models or by counting on.

Success signs:

• You can draw a part-whole model to show what you know and what you need to find
• You can solve problems like 7 + □ = 12 by counting on from 7
• You can explain how you found the missing number to a friend
• You can use your knowledge to solve real-life problems with missing numbers

Why this matters

Missing addend problems are important because they help you think about addition in a new way. Instead of just adding two numbers together, you're trying to figure out what one of the numbers is. This is like being a detective in maths!

This skill is useful in everyday life. For example, if you have 7 sweets and need 12 sweets total, you can figure out how many more you need. You might also use this when sharing snacks, counting your pocket money, or solving puzzles.

In school, learning to solve missing addend problems helps you understand how numbers work together and prepares you for more advanced maths like subtraction and algebra.

How it works

Let's think about the problem 7 + □ = 12.

Step 1: Think about what you know.

• You have 7 apples
• You want to have 12 apples total

Step 2: Use a part-whole model.

A part-whole model is like a picture that shows how two parts make up a whole.

Step 3: Find the missing part.

You can think, "What number added to 7 makes 12?"

Step 4: Count on from 7.

Start at 7 and count on until you reach 12:

• 7, 8, 9, 10, 11, 12

You counted 5 numbers, so the missing number is 5.

Step 5: Check your answer.

7 + 5 = 12 ✓

Examples you can see

Let's look at some more examples using the part-whole model and counting on.

Example 1:

Problem: 4 + □ = 9

Part-whole model:

Count on from 4: 4, 5, 6, 7, 8, 9

You counted 5 numbers, so the missing number is 5.

Check: 4 + 5 = 9 ✓

Example 2:

Problem: □ + 6 = 11

Part-whole model:

Count on from 6: 6, 7, 8, 9, 10, 11

You counted 5 numbers, so the missing number is 5.

Check: 5 + 6 = 11 ✓

Example 3:

Problem: 8 + □ = 15

Part-whole model:

Count on from 8: 8, 9, 10, 11, 12, 13, 14, 15

You counted 7 numbers, so the missing number is 7.

Check: 8 + 7 = 15 ✓

Try it as a mini adventure

Imagine you are a treasure hunter on a quest to find the hidden treasure in a magical garden!

Step 1: You start with 5 golden coins.

Step 2: You find a note that says, "To reach the treasure, you need 12 coins in total."

Step 3: You need to figure out how many more coins you must collect.

Step 4: Draw your part-whole model:

Step 5: Count on from 5 to 12:

• 5, 6, 7, 8, 9, 10, 11, 12

You counted 7 numbers, so you need 7 more coins!

Step 6: Collect 7 more coins and continue your treasure hunt!

Common mistakes

Here are some mistakes children often make when solving missing addend problems and how to fix them:

Mistake 1: Thinking the missing number is the difference between the two numbers.

Incorrect answer: In 7 + □ = 12, some children think the answer is 12 - 7 = 5, but they forget to check if 7 + 5 = 12.

Why it happens: They may have learned subtraction as the way to find missing numbers but don't understand addition.

How to fix: Always check your answer by adding it back to the known part.

Mistake 2: Counting backwards instead of forwards.

Incorrect answer: In 7 + □ = 12, they might count backwards from 12 to 7 and say the answer is 5, but they may not know the difference.

Why it happens: They might be thinking of subtraction instead of addition.

How to fix: Start counting from the known part, not from the total.

Mistake 3: Not using a visual model.

Incorrect answer: They might guess the answer without thinking it through.

Why it happens: They are not used to visualising problems.

How to fix: Draw a part-whole model or use objects like counters or blocks to help see what they need.

Parent and carer guide

Helping your child with missing addend problems is easy and fun!

What to say:

• "Let's think about what we know and what we need to find."
• "Can you show me how you counted on?"
• "What does your part-whole model tell you?"

What to watch for:

• Do they draw part-whole models?
• Do they check their answers?
• Do they count on from the known number?

How to help:

1. Use everyday situations like sharing snacks or counting toys to create missing addend problems.
2. Encourage drawing part-whole models or using counters.
3. Practice counting on from different numbers to build confidence.
4. Be patient and celebrate their thinking, even if the answer is wrong at first.

Don't worry about:

• Getting the right answer immediately
• Being perfect at counting
• Speed – focus on understanding

Practice questions

1. 3 + □ = 8
2. □ + 4 = 10
3. 6 + □ = 14
4. □ + 9 = 15
5. 5 + □ = 13
6. □ + 7 = 12
7. 2 + □ = 9
8. □ + 3 = 11
9. 8 + □ = 16
10. □ + 6 = 13

Answers:

1. 5
2. 6
3. 8
4. 6
5. 8
6. 5
7. 7
8. 8
9. 8
10. 7

FAQ

What is a missing addend?

A missing addend is a number in an addition problem that we don't know yet. It's represented by a box or a question mark.

How do I know which number to count on from?

You always count on from the number you already know. For example, in 7 + □ = 12, you count on from 7.

Can I use a number line to solve missing addend problems?

Yes! A number line is a great way to see how many jumps you need to make to get to the total.

Why do I need to check my answer?

Checking helps you make sure your answer is correct and that you didn't make a mistake.

Are missing addend problems the same as subtraction?

They are related! You can think of missing addend problems as a kind of subtraction, but it's best to use addition to solve them.