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## Basics on the topicCompensation in Addition

Addition can quickly become confusing. Especially if the addends in the ones place add to a number higher than ten. But there is a strategy that you can follow to make complicated addition operations easier: It’s called compensation.

## Compensation Strategy – Definition

What is compensation? And, how do you use compensation in addition? Let’s look at the definition for the compensation strategy:

Compensation is something given in return for something. In maths, we use compensation with numbers. This can be a helpful strategy because it makes the numbers friendlier, or easier to add. However, when using addition compensation with manipulatives, always make sure that whatever you add or subtract to one side, you do the opposite to the other.

Step # What to do
1 Choose which addend to make friendlier,
or easier to add. You can do this by
looking for a zero or five in the ones place.
2 Make sure whatever you do to one addend,
you do the opposite to the other.
3 Create a new equation using the
4 Solve the equation!

## Compensation Method Maths – Example

In this example we are adding nuts and bolts to find out how many materials we have. How can we use the compensation strategy to add his thirty-two nuts and eight bolts?

nuts bolts
32 8

compensation 32 (+3) 8 (-3)
new equation 35 5

We can use compensation to make the new equation, thirty-five plus five which equals forty. Mr. Squeaks has forty materials to work with!

## Addition with Compensation – Summary

• Step one: choose which addend to make friendlier, or easier to add. You can do this by looking for a zero or five in the ones place.

• Step two: make sure whatever you do to one addend, you do the opposite to the other.

• Step three: create a new equation using the friendlier, or easier addends.

• Step four: solve the new equation!

Looking for extra practice with compensation in addition? After this video check out the interactive exercises and compensation addition worksheet.

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Compensation in Addition.
• ### How could we use compensation to solve 13 + 6?

Hints

Remember, whatever is done to one addend, the opposite must be done to the other.

For example, if we were solving 12 + 5, we could subtract 2 from 12 to make 10. We would then have to add 2 to 5 to make 7. We would create 10 + 7.

Solution

To solve 13 + 6, we could subtract 3 from 13 and then add 3 to 6.

We would create 10 + 9 which would be easier to solve. 10 + 9 = 19 therefore 13 + 6 = 19.

• ### How has Mr. Squeaks used compensation?

Hints

Remember, compensation in maths means something is given in return for something else.

If one number is added to a digit, the same number must be subtracted from the second digit.

Look at this example. When adding 25 + 6, we can make 25 easier to work with by adding 5 to make 30. This means we have to subtract 5 from the other addend, 6.

The new equation is 30 + 1.

• What do we add to 36 to make 40? This is the answer for the first box.
• What do we subtract from 4 to make 0? This is the answer for the second box.
Solution

Mr. Squeaks used compensation and added 4 to 36 to make 40. He then had to subtract 4 from 4 which equals 0.

• 36 + 4 = 40
• 4 - 4 = 0
The new equation is 40 + 0, which we can solve.

40 + 0 = 40

• ### How could we use compensation when adding 32 + 8?

Hints

Remember, when using compensation, whatever is added to one addend needs to be subtracted from the other.

For example, if we were solving 23 + 7, we would subtract 3 from 23 and add 3 to 7.

Solution

Since Imani is using compensation, they want to make friendlier numbers that are easier to work with.

They see 32, and subtract 2 to create 30. Since 2 was subtracted from one addend, it needs to be added to the other addend, 8. 8 plus 2 creates 10.

The new equation is : 30 + 10, which Imani can use to solve more easily. 30 + 10 = 40

• ### What are the steps taken when using compensation?

Hints

The first step for using compensation is to choose which number to make friendlier.

Once you have made one number easier to work with, you will need to do the opposite to the other.

For example, in 15 + 7, you could choose to add 5 to 15 to make it a friendly 20. From there, you would need to subtract 5 from 7 to even the equation.

Solution

These are the steps used in compensation.

For example, let's look at 25 + 8.

Step 1: Choose which number to make friendlier or easier to work with. Since 25 ends in a 5, you could add 5 to make it a friendlier 30.

Step 2: Add the amount chosen to one number, and subtract the amount chosen from the other. In this example, we add 5 to 25 to make 30 (25 + 5 = 30), and subtract 5 from 8 to make 3 (8 - 5 = 3).

Step 3: Create a new equation using the new addends. The new equation is: 30 + 3 =

Step 4: Solve the new equation: 30 + 3 = 33.

• ### Identify the equation using the new addends.

Hints

Remember, Imani is subtracting 2 from the number 22. They are then adding 2 to the number 5.

Think about the new equation. It will be (22 - 2) plus (5 + 2).

Solution

Now that Imani has used compensation, their new equation is 20 + 7.

They subtracted 2 from 22 to get 20, and added 2 to 5 to get 7.

Now they can add the numbers more easily to make 27!

• ### Can you answer the problems?

Hints

When using compensation, remember to make one number friendlier, or easier to work with, first.

Compensation means something is given in return for something else. For example:

24 + 7 = ?

We can make 24 easier to work with by adding 6 to make 30. Now, because we added 6 to one number, we must subtract 6 from the other. 7 - 6 makes 1.

The new equation is: 30 + 1.

30 + 1 = 31.

Solution

You may have solved these problems the same or differently, as there are multiple ways to use compensation.

45 + 7 = 52.

• We can add 3 to 7 to make 10 (3 + 7 = 10). Now, because we added 3 to one number, we must subtract 3 from the other number, 45. 45 - 3 makes 42.
• The new equation is: 42 + 10.
• We add this new equation more easily to solve the problem: 42 + 10 = 52.

12 + 8 = 20.

• We can subtract 2 from 12 to make 10 (12 - 2 = 10). Since we subtracted 2 from one number, we must add 2 to the other number (8 + 2 = 10).
• The new equation is: 10 + 10.
• We use this new equation to solve: 10 + 10 = 20.

7 + 6 = 13.

• We can add 3 to 7 to make 10 (3 + 7 = 10). Now, because we added 3 to one number, we must subtract 3 from the other number, 6. 6 - 3 makes 3.
• The new equation is 10 + 3.
• 10 + 3 = 13.