2nd Grade Math: Mastering Vertical Addition and Subtraction!

Hello everyone! Welcome to the world of "Vertical Calculation" (Hissan), a super important skill in 2nd-grade math.
Up until now, you've solved problems like "12 + 5" by writing them out in a line, but as numbers get bigger, that can get a bit tricky. That’s where vertical calculation comes in! Once you master this method, you’ll be able to solve calculations with even the largest numbers as easily as putting together a puzzle!
It might feel a bit difficult at first, but the rules are very simple. Let's take it one step at a time together.

1. The Basics of Vertical Calculation: "Aligning the Place Values" is Key

There is one rule you must always follow when setting up a vertical calculation: line up the "ones place" and the "tens place" perfectly in columns.

【Pro-Tip】
・Use the grid lines in your notebook to keep your numbers in straight columns.
・The far right column is the "ones place," and the column to its left is the "tens place."
・If you get the "place value alignment" right, you’ll avoid more than half of all calculation mistakes!

Did you know? Why is it called "Hissan"?

The name "Hissan" comes from using a "brush" (hitsu) to write out calculations. Long ago, people used brushes to write down their math. Today, we’ll use our pencils to do the same!

2. Vertical Addition (Without Regrouping)

Let’s start with a simple practice problem.
Example: \( 24 + 13 \)

【Steps】
1. Calculate the ones place: \( 4 + 3 = 7 \)
2. Calculate the tens place: \( 2 + 1 = 3 \)
3. The answer is 37.

The golden rule is: "Always start from the right (the ones place)!"

3. Vertical Addition (With Regrouping)

When you add and the ones place exceeds 10, you need to use "regrouping" (carrying over).
Example: \( 38 + 25 \)

【Steps】
1. Ones place: \( 8 + 5 = 13 \). Write the "3" in the ones place, and write a small "1" above the tens place. This is "carrying over."
2. Tens place: Add the "1" you carried over to the "3" and "2". \( 1 + 3 + 2 = 6 \)
3. The answer is 63.

【Common Mistake】
Sometimes, when calculating the tens place, you might forget to add the "1" you carried over. Don’t forget to include that little note in your total!

4. Vertical Subtraction (Without Borrowing)

Just like addition, subtraction starts from the ones place on the right.
Example: \( 48 - 15 \)

【Steps】
1. Ones place: \( 8 - 5 = 3 \)
2. Tens place: \( 4 - 1 = 3 \)
3. The answer is 33.

5. Vertical Subtraction (With Borrowing)

When you find a number in the ones place that you can't subtract, you need to "borrow" from the tens place. This is the biggest hurdle in 2nd-grade math!
Example: \( 52 - 18 \)

【Steps】
1. Ones place: You can't do \( 2 - 8 \). Oh no, we're stuck!
2. Borrow from the neighbor: Borrow "1 (which is 10)" from the "5" in the tens place. The "5" becomes a "4," and the "2" becomes "12."
3. Ones place: Calculate \( 12 - 8 = 4 \).
4. Tens place: Subtract 1 from the "4" that is left after borrowing. \( 4 - 1 = 3 \)
5. The answer is 34.

【Pro-Tip: The Magic Phrase】
Remember: "When you can't subtract, borrow 10 from your neighbor!" Crossing out the digit in the tens place and writing the new, smaller number (like 4 in the example above) will help you avoid mistakes.

Common Mistakes and How to Fix Them

1. The columns get crooked
Fix: Be mindful of your notebook's vertical lines to separate the ones and tens places. It’s okay to draw a guide line at first!

2. Forgetting to write notes for carrying or borrowing
Fix: Don't try to do it all in your head—always write down your notes. Those notes are your "roadmap" to the right answer.

3. Adding when you should be subtracting
Fix: Get into the habit of pointing your finger at the "+" or "-" sign next to your vertical calculation before you start.

Summary: Things to Remember!

・Always line up your columns (vertically)!
・Always start calculating from the ones place (on the right)!
・Always write down your "carrying" or "borrowing" notes!

It's perfectly okay if it takes time at first. As you practice more, your hands will start doing it automatically. Once you realize how magically useful vertical calculation is, you'll be a math master! Let's do our best together!