Addition and Subtraction

Welcome to Addition and Subtraction!

Hi there! In Year 4, we are going to become masters of big numbers. We will learn how to add and subtract numbers with up to four digits (like \( 4,321 \) or \( 9,999 \)). Being good at this helps you with everything from managing your pocket money to building amazing things in games like Minecraft!

Don't worry if big numbers seem a bit scary at first. We are going to break them down into small, easy steps. By the end of these notes, you'll be a math superhero!

Step 1: Knowing Your Place Value

Before we start adding, we must remember where numbers live. In Year 4, we work with four "houses":
Thousands (Th), Hundreds (H), Tens (T), and Ones (O).

Example: In the number \( 3,526 \), we have:
• 3 Thousands (\( 3,000 \))
• 5 Hundreds (\( 500 \))
• 2 Tens (\( 20 \))
• 6 Ones (\( 6 \))

Top Tip: Always line up your numbers in the correct columns. If the columns are messy, the answer will be messy too!

Step 2: Column Addition (Up to 4 Digits)

When we add big numbers, we use Column Addition. We always start from the right side (the Ones column) and move to the left.

How to do it:

1. Write the numbers one on top of the other, lining up the columns.
2. Add the Ones. If the total is 10 or more, we "regroup" (carry) the ten to the next column.
3. Add the Tens (don't forget any numbers you carried!).
4. Add the Hundreds.
5. Add the Thousands.

Example: \( 2,456 + 1,327 \)
• Ones: \( 6 + 7 = 13 \). We write the 3 and carry the 1 ten to the Tens column.
• Tens: \( 5 + 2 + 1 \text{ (carried)} = 8 \).
• Hundreds: \( 4 + 3 = 7 \).
• Thousands: \( 2 + 1 = 3 \).
The answer is \( 3,783 \)!

Quick Review: When the sum of a column is more than 9, you must regroup it into the next column to the left.

Step 3: Column Subtraction (Up to 4 Digits)

Subtraction is like taking things away. Just like addition, we start from the right side (Ones).

The Trickiest Part: Exchanging (Borrowing)

Sometimes, the top number in a column is smaller than the bottom number. You can't take 8 away from 3! When this happens, we "exchange" (borrow) from the neighbor on the left.

Example: \( 5,432 - 2,151 \)
• Ones: \( 2 - 1 = 1 \).
• Tens: \( 3 - 5 \). We can't do this! We go to the Hundreds column. We take 1 hundred (leaving 3 behind) and give it to the Tens. Now we have \( 13 - 5 = 8 \).
• Hundreds: \( 3 - 1 = 2 \).
• Thousands: \( 5 - 2 = 3 \).
The answer is \( 3,281 \)!

Common Mistake to Avoid: Never just swap the numbers around! If you have \( 3 - 5 \), don't just do \( 5 - 3 \). You must exchange from the next column.

Did you know? Subtraction is also called "finding the difference." It's like measuring the gap between two numbers!

Step 4: Estimating Your Answer

Before you do the hard work, it's smart to estimate. This means taking a "good guess" so you know if your final answer makes sense.

To estimate, round the numbers to the nearest 10, 100, or 1,000.
Example: To estimate \( 3,995 + 2,010 \), you could round them to \( 4,000 + 2,000 \). Your estimate is \( 6,000 \). If your real answer is \( 9,500 \), you know something went wrong!

Key Takeaway: Estimating saves you from making big mistakes!

Step 5: Checking with Inverse Operations

Addition and Subtraction are best friends—they are inverses (opposites). You can use one to check the other.

• If \( 1,200 + 800 = 2,000 \), then \( 2,000 - 800 \) must be \( 1,200 \).
• If you think \( 500 - 200 = 300 \), check it by doing \( 300 + 200 \). If you get back to \( 500 \), you are correct!

Quick Review Box:
• Addition Check: Use Subtraction.
• Subtraction Check: Use Addition.

Step 6: Solving Two-Step Word Problems

In Year 4, some problems have two steps. This means you have to do two different calculations to find the answer.

Example Problem: "A shop has 500 apples. They sell 150 apples in the morning and 100 apples in the afternoon. How many are left?"
Step 1: Find out how many were sold in total: \( 150 + 100 = 250 \).
Step 2: Subtract the total sold from the starting amount: \( 500 - 250 = 250 \).
The answer is 250 apples.

Memory Aid (RUCSAC):
Read the question.
Understand (underline key info).
Choose the operation (+ or -).
Solve the problem.
Answer the question.
Check your work!

Summary of Key Terms

• Sum: The result of adding numbers together.
• Difference: The result of subtracting one number from another.
• Regrouping/Exchanging: Moving values between columns (carrying or borrowing).
• Inverse: The opposite operation.

Great job! You've covered the essentials of Year 4 Addition and Subtraction. Practice makes perfect, so keep trying those column methods and don't forget to check your answers!