Compensation in Addition
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Basics on the topic Compensation in Addition
Compensation 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.
In this learning text you can learn about compensation with addition. Take a look below to learn more about the compensation addition strategy.
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.
Using Compensation to Add
When using compensation in addition, you should follow these steps:
| 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 friendlier, or easier addends. |
| 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 |
| addend 1 (nuts) | addend 2 (bolts) | |
|---|---|---|
| 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
Remember, when using compensation in addition, you should follow these steps:
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.
Transcript Compensation in Addition
"I found it, the map to the giant waterfall!" "If we follow these directions and add all the steps, we can find it again." "We need to take twenty-five steps past the tree and six more to find the cave." Let's learn about compensation in addition to help Mr. Squeaks and Imani. There are many different strategies and tools to add. One is compensation, something given in return for something, in maths we use this with numbers. This can be a helpful strategy to add or subtract because it makes the numbers easier to work with. But, whatever is done to one addend, the opposite is done to the other. That means if we add to one addend, we must subtract the same amount from the other addend. Mr. Squeaks and Imani need to add twenty-five plus six. When using compensation, first choose which number to make friendlier, or easier to add. You might choose these numbers by looking for a zero or five in the ones place. Here we can add five to twenty-five to make it thirty. Since we added five to twenty-five, we must subtract it from six. What is six minus five? One. Next, create a new equation using the new addends. Our new equation is thirty plus one. Finally, solve the new equation now that it is easier to add. Here we can count on one in our heads to get our sum, or answer, thirty-one! That means that twenty-five plus six also equals thirty-one. "Ahh, I've missed this cave." "Next we need to skip thirty-two times and then eight more to find the secret tunnel inside the cave." How can we use compensation to help our friends find the secret tunnel? First choose which addend to make friendlier, or easier to add. We can add three to thirty-two to make it thirty-five. Since we added three to thirty-two, we must subtract three from eight. What is eight minus three? Five! Next, create a new equation using the new addends. Our new equation is thirty-five plus five. Finally, solve the new equation now that it is easier to add. What is thirty-five plus five? Forty! That means that thirty-two plus eight also equals forty. "It's a tighter squeeze this time!" "Oh, thanks, Imani!" "We're so close! We just need to run past forty-three rocks and then nine more to find the giant waterfall!" Let's use compensation one more time! First choose which addend to make friendlier. We can add one to the nine to make it ten. We added one to the nine, so we must subtract one from forty-three. Forty-three minus one is forty-two. Next, create a new equation with the new addends. Our new equation is forty-two plus ten. Finally, solve the new equation now that it is easier to add. What is forty-two plus ten? Fifty-two! Which means that forty-three plus nine is also fifty-two. Before we see the magical waterfall, remember! When using compensation in addition: first, choose which addend to make friendlier. You can do this by looking for a zero or five in the ones place. Whatever you do to one addend, the opposite must be done to the other. Next, create a new equation using the new addends. Finally, solve the new equation using mental maths now that it is easier to add. Now, let's see that waterfall! "We made it, Imani!" "Look at that, it's amazing!"
Compensation in Addition exercise
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How could we use compensation to solve 13 + 6?
HintsRemember, 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.
SolutionTo 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.
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How has Mr. Squeaks used compensation?
HintsRemember, 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.
SolutionMr. 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
40 + 0 = 40
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How could we use compensation when adding 32 + 8?
HintsRemember, 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.
SolutionSince 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
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What are the steps taken when using compensation?
HintsThe 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.
SolutionThese 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.
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Identify the equation using the new addends.
HintsRemember, 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).
SolutionNow 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!
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Can you answer the problems?
HintsWhen 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.
SolutionYou 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.
