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What is the Compensation Strategy in Addition?
Grade Level:
Class 3
Maths, Computing
Definition
What is it?
The Compensation Strategy in Addition is a clever way to add numbers by making one number easier to work with. You 'borrow' some amount from one number and 'give' it to the other number to create a rounder, simpler number to add. This makes mental math much faster and easier.
Simple Example
Quick Example
Imagine you need to add the cost of a samosa (₹18) and a chai (₹15). Instead of adding 18 + 15 directly, you can take ₹2 from the chai's cost (making it ₹13) and give it to the samosa's cost (making it ₹20). Now you just add ₹20 + ₹13, which is ₹33. Much simpler!
Worked Example
Step-by-Step
Let's add 47 + 25 using the Compensation Strategy.
Step 1: Look at the numbers 47 and 25. We want to make one of them a 'round' number (ending in 0).
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Step 2: Let's make 47 into 50. To do this, we need to add 3 to 47. (47 + 3 = 50).
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Step 3: Since we added 3 to 47, we must subtract 3 from the other number, 25, to keep the sum the same. (25 - 3 = 22).
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Step 4: Now we have a new addition problem: 50 + 22.
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Step 5: Add these new numbers: 50 + 22 = 72.
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So, 47 + 25 = 72.
Why It Matters
This strategy is super useful for quick mental calculations, which is a key skill in daily life. It's used by shopkeepers to quickly calculate bills and by engineers to estimate measurements. Mastering this helps build a strong foundation for more complex math in computing and finance.
Common Mistakes
MISTAKE: Adding to one number but not subtracting from the other. For example, changing 38 + 14 to 40 + 14. | CORRECTION: Whatever you add to one number, you must subtract the same amount from the other number to keep the total the same. So, 38 + 14 becomes 40 + 12.
MISTAKE: Only trying to make the first number round. | CORRECTION: You can choose to make either number round! Pick the one that requires the smallest change to make it easier. For 23 + 59, it's easier to make 59 into 60 (add 1) than 23 into 20 (subtract 3).
MISTAKE: Confusing compensation with estimation. | CORRECTION: Compensation strategy gives the exact answer, not an estimate. The 'borrowing and giving' ensures the sum remains precisely the same as the original problem.
Practice Questions
Try It Yourself
QUESTION: Use the Compensation Strategy to solve 56 + 18. | ANSWER: 56 + 4 = 60, 18 - 4 = 14. So, 60 + 14 = 74.
QUESTION: A bus travelled 39 km in the morning and 23 km in the afternoon. How many total km did it travel? Use Compensation. | ANSWER: 39 + 1 = 40, 23 - 1 = 22. So, 40 + 22 = 62 km.
QUESTION: You have ₹77 and your friend has ₹46. How much money do you have together? Solve using Compensation, aiming to make ₹46 a round number. | ANSWER: 46 + 4 = 50, 77 - 4 = 73. So, 73 + 50 = 123. You have ₹123 together.
MCQ
Quick Quiz
Which of these shows the correct use of the Compensation Strategy for 63 + 29?
60 + 30
63 + 30 - 1
63 - 1 + 29 + 1
62 + 30
The Correct Answer Is:
D
To make 29 a round number, we add 1 to it (29 + 1 = 30). To compensate, we must subtract 1 from 63 (63 - 1 = 62). So, the new problem is 62 + 30. Option B adds 1 to 29 but only subtracts 1 from the *entire sum*, not the other number.
Real World Connection
In the Real World
When you're shopping at a local kirana store and the shopkeeper quickly adds up your bill in their head, they might be using this strategy! Or, if you're planning a trip and need to quickly add up travel times or distances, compensation helps you do it without a calculator, just like a smart travel agent or logistics manager would.
Key Vocabulary
Key Terms
COMPENSATION: Adjusting one part of a problem by making an opposite adjustment to another part to keep the total the same. | ROUND NUMBER: A number that ends in zero (e.g., 10, 20, 50, 100). | MENTAL MATH: Doing calculations in your head without writing them down or using a calculator. | STRATEGY: A plan or method used to achieve a goal.
What's Next
What to Learn Next
Great job learning the Compensation Strategy! Next, you can explore the 'Breaking Apart' or 'Decomposition' strategy for addition. This will show you another powerful way to simplify addition problems by breaking numbers into tens and ones, further boosting your mental math skills.
