Give and Take - Addition of 3-Digit Numbers

Understanding Place Value: Every 3-digit number consists of Hundreds ($H$), Tens ($T$), and Ones ($O$). Imagine these as vertical columns where $O$ is on the right, $T$ is in the middle, and $H$ is on the left. For example, in $452$, the digit $4$ is in the hundreds place, $5$ is in the tens place, and $2$ is in the ones place.

Addition without Regrouping: When the sum of digits in each column is less than $10$, we simply add them and write the result below. Visually, align the numbers one below the other: hundreds under hundreds, tens under tens, and ones under ones. For example, to add $123$ and $245$, add $3 + 5 = 8$, $2 + 4 = 6$, and $1 + 2 = 3$ to get $368$.

Addition with Regrouping (Carrying): If the sum of digits in a column is $10$ or more, we carry the tens digit to the next column on the left. Visually, this is represented by writing a small 'carry' digit (usually $1$) above the next column. For example, if adding $8 + 7 = 15$ in the ones column, write $5$ in the answer and carry $1$ over to the tens column.

The Order Property (Commutative): Changing the order of the numbers being added does NOT change the sum. For example, $200 + 300 = 500$ and $300 + 200 = 500$. You can visualize this by swapping two piles of blocks; the total number of blocks stays the same.

The Zero Property of Addition: When $0$ is added to any 3-digit number, the sum is the number itself. For example, $456 + 0 = 456$. This means the value in the place-value columns does not change when adding zero.

Mental Math - Breaking Numbers: To add numbers mentally, you can expand them into hundreds, tens, and ones. For $230 + 120$, think of it as $(200 + 100) + (30 + 20)$, which equals $300 + 50 = 350$. This is like looking at the H, T, and O parts of the number separately.

Addition Keywords in Word Problems: Look for specific words that mean you need to add. These include 'total', 'sum', 'altogether', 'in all', and 'plus'. Visually, word problems represent real-world scenarios where different groups are combined into one large group.