Grade 2: Two-Digit Addition: The Compensation Method Explained

Understanding Two-Digit Addition with Compensation ➕

The compensation method is a clever strategy to make addition easier by adjusting numbers to create friendlier values. It involves borrowing from one number and giving to another to simplify the calculation. Here’s how it works for two-digit addition:

Steps for Compensation Method 🪜

1. Identify Numbers: Start with the two numbers you want to add.
2. Find a Friendly Number: Look for a number close to a multiple of 10 (like 10, 20, 30, etc.).
3. Compensate: Borrow from one number to make the other a multiple of 10.
4. Add: Perform the simplified addition.
5. Adjust: Make sure to account for the borrowed amount.

Example 1: 27 + 18 💡

• Numbers: 27 and 18
• Friendly Number: 18 is close to 20.
• Compensate: Borrow 2 from 27 to give to 18. So, 27 becomes 25, and 18 becomes 20.
• Add: 25 + 20 = 45

Therefore, 27 + 18 = 45

Example 2: 36 + 19 🧮

• Numbers: 36 and 19
• Friendly Number: 19 is close to 20.
• Compensate: Borrow 1 from 36 to give to 19. So, 36 becomes 35, and 19 becomes 20.
• Add: 35 + 20 = 55

Therefore, 36 + 19 = 55

Example 3: 45 + 26 🤔

• Numbers: 45 and 26
• Friendly Number: 26 is close to 30.
• Compensate: Borrow 4 from 45 to give to 26. So, 45 becomes 41, and 26 becomes 30.
• Add: 41 + 30 = 71

Therefore, 45 + 26 = 71

Why Does This Work? 🧐

The compensation method works because you're essentially shifting values between the numbers without changing the total sum. It's based on the principle that $a + b = (a - x) + (b + x)$.

Practice Makes Perfect! 🎯

Encourage your child to practice with various two-digit addition problems using the compensation method. The more they practice, the more comfortable they'll become with it!