Adding numbers:

When adding numbers within 1,000, students can use strategies such as place value, properties of operations (like commutative and associative properties), and the relationship between addition and subtraction. These strategies make it easier to break numbers down into manageable parts, solve problems efficiently, and build confidence in working with larger numbers.

Strategies for Addition:

1. Place Value: Breaking numbers into hundreds, tens, and ones.
2. Properties of Operations:
   • Commutative Property: The order in which you add numbers doesn’t change the sum. (e.g., 347 + 120 = 120 + 347)
   • Associative Property: When adding three or more numbers, the grouping of the numbers doesn’t change the sum. (e.g., (300 + 100) + 45 = 300 + (100 + 45))
3. Relationship Between Addition and Subtraction: Understanding that addition undoes subtraction and vice versa.

Example 1:

Adding 425 + 389 Using Place Value

Step-by-Step:

1. Break the numbers into hundreds, tens, and ones:
   • 425: 4 hundreds, 2 tens, 5 ones.
   • 389: 3 hundreds, 8 tens, 9 ones.
2. Add the ones:
   • 5 + 9 = 14. Write 4 in the ones place, and carry over 1 to the tens place.
3. Add the tens:
   • 2 + 8 = 10. Don’t forget the 1 from the ones! So, 10 + 1 = 11. Write 1 in the tens place and carry over 1 to the hundreds place.
4. Add the hundreds:
   • 4 + 3 = 7, and add the carry-over 1 from the tens place. So, 7 + 1 = 8.

Ans: 425 + 389 = 814

Example 2:

Adding 748 + 156 Using the Associative Property

The associative property allows you to group the numbers in a way that makes the addition easier.

1. Break the numbers into place values:
   • 748: 7 hundreds, 4 tens, 8 ones.
   • 156: 1 hundred, 5 tens, 6 ones.
2. Add the ones:
   • 8 + 6 = 14. Write 4 in the ones place and carry over 1 to the tens place.
3. Add the tens:
   • 4 + 5 = 9, plus the 1 carried over from the ones place makes 9 + 1 = 10. Write 0 in the tens place and carry over 1 to the hundreds place.
4. Add the hundreds:
   • 7 + 1 = 8, plus the 1 carried over from the tens place gives us 8 + 1 = 9.

 Ans: 748 + 156 = 904

Example 3:

Adding 283 + 672 Using Place Value and Mental Math

Here’s how you can break down the addition into chunks that are easy to solve mentally.

1. Break numbers into hundreds, tens, and ones:
   • 283: 2 hundreds, 8 tens, 3 ones.
   • 672: 6 hundreds, 7 tens, 2 ones.
2. Add the hundreds:
   • 200 + 600 = 800.
3. Add the tens:
   • 80 + 70 = 150.
4. Add the ones:
   • 3 + 2 = 5.
5. Combine everything:
   • 800 + 150 + 5 = 955.

Ans: 283 + 672 = 955

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