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Compensation in addition

addition

Compensation in addition

Adjust one number to make a friendly sum, then compensate.

Quick answer

Compensation in addition means making one number easier to work with by adjusting it, then compensating for the change by adjusting the other number. This helps make addition easier and faster.

Learning outcome

By the end of this page, you will be able to use compensation to make addition problems easier to solve by adjusting one number to a friendly number and then compensating for the change. Success signs:

You can spot when a number is close to a friendly number like 10, 20, or 100
You can add a number by making it easier, then adjust the other number
You can solve addition problems more quickly using this strategy
You can explain how compensation makes maths easier

Why this matters

Compensation in addition is a powerful strategy that helps you solve problems faster and more confidently. It’s used in everyday life when you’re adding up shopping bills, counting scores in games, or working out how many toys you have. It’s also a helpful tool for mental maths, which is useful in school and in your daily life. Whether you’re playing a game, sharing snacks, or helping with the family budget, this skill makes maths feel less scary and more fun.

How it works

Compensation works by making one number easier to work with, then balancing the change by adjusting the other number. Here’s how:

Look at both numbers and see which one is close to a friendly number (like 10, 20, 50, or 100)
Adjust that number to make it a friendly number
Adjust the other number to keep the total the same
Add the new numbers together

Let’s take a simple example: 28 + 6. We can make 28 easier by adding 2 to make 30. But we must also take 2 away from 6 to keep the total the same. So we get 30 + 4 = 34.

Examples you can see

Let’s look at some examples you can imagine, draw, or act out. Example 1: 19 + 7

19 is close to 20, so we can add 1 to 19 to make 20
We must take 1 from 7 to keep the total the same, so 7 becomes 6
Now we have 20 + 6 = 26

Example 2: 48 + 5

48 is close to 50, so we add 2 to 48 to make 50
We take 2 from 5, so 5 becomes 3
Now we have 50 + 3 = 53

Example 3: 37 + 9

9 is close to 10, so we add 1 to 9 to make 10
We take 1 from 37, so 37 becomes 36
Now we have 36 + 10 = 46

These examples show how compensation makes addition easier by using friendly numbers.

Try it as a mini adventure

Adventure: The Treasure Hunt You and your friend are on a treasure hunt. You have to add up the clues to find the treasure. Here’s how the clues work:

Clue 1: 29 + 5
Clue 2: 47 + 6
Clue 3: 38 + 8

Can you solve each clue using compensation? Clue 1: 29 + 5

29 is close to 30, so we add 1 to 29 to make 30
We take 1 from 5, so 5 becomes 4
Now we have 30 + 4 = 34

Clue 2: 47 + 6

47 is close to 50, so we add 3 to 47 to make 50
We take 3 from 6, so 6 becomes 3
Now we have 50 + 3 = 53

Clue 3: 38 + 8

8 is close to 10, so we add 2 to 8 to make 10
We take 2 from 38, so 38 becomes 36
Now we have 36 + 10 = 46

You’ve solved all the clues and found the treasure! The numbers are 34, 53, and 46.

Common mistakes

Mistake: Adding to one number but forgetting to subtract from the other number.
Why it happens: Kids may focus only on making one number easier without thinking about balance.
Fix: Always remember to adjust the other number to keep the total the same.
Mistake: Making the wrong adjustment to make a number friendly.
Why it happens: Confusion about what numbers are close to 10, 20, 50, or 100.
Fix: Practice spotting numbers close to friendly numbers and use number lines or counting to check.
Mistake: Thinking that compensation changes the answer.
Why it happens: Not understanding that compensation keeps the total the same.
Fix: Use counters or draw pictures to show that the total stays the same.

Parent and carer guide

Parents and carers can support children by:

Practicing compensation with simple addition problems at home
Using everyday examples like shopping or cooking to show how this strategy works
Encouraging children to explain their thinking and how they adjusted the numbers
Using visual aids like counters, number lines, or drawing arrays to help children see the balance
Reassuring children that making mistakes is part of learning and that it’s okay to try different strategies

Try asking questions like:

“Can you think of a way to make this easier?”
“What number is close to 10?”
“How did you adjust the numbers to keep the same total?”

Practice questions

Use compensation to solve: 29 + 4 = ?
Use compensation to solve: 36 + 7 = ?
Use compensation to solve: 49 + 3 = ?
Use compensation to solve: 58 + 5 = ?
Use compensation to solve: 67 + 6 = ?

Answers:

29 + 4 = 30 + 3 = 33
36 + 7 = 37 + 6 = 43
49 + 3 = 50 + 2 = 52
58 + 5 = 60 + 3 = 63
67 + 6 = 68 + 5 = 73

FAQ

What is compensation in addition?

Compensation in addition is a strategy where you make one number easier to work with by adjusting it, then adjust the other number to keep the total the same.

Why is compensation useful?

It makes addition faster and easier by using friendly numbers, which are numbers that are easy to work with like 10, 20, or 100.

Can I use compensation with bigger numbers?

Yes! You can use compensation with any numbers. For example, 98 + 7 becomes 100 + 5 = 105.

How can I practice compensation at home?

Try adding numbers in your daily life, like when shopping or cooking. Ask: “Can I make one number easier to add?”

What if I get confused about which number to adjust?

Start by looking at both numbers and thinking: “Which one is close to 10, 20, 50, or 100?” That’s usually the one to adjust.