Addition patterns over increasing place values

Key notes:

Understanding Place Values

First, let’s quickly review place values. Remember, each digit in a number has a value based on its position:

• Ones: The rightmost digit (e.g., in 23, the 3 is in the ones place).
• Tens: The next digit to the left (e.g., in 23, the 2 is in the tens place, representing 20).
• Hundreds: The next digit to the left (e.g., in 123, the 1 is in the hundreds place, representing 100).
• Thousands: And so on… (e.g., 1,000 represents one thousand).

Finding Addition Patterns

Now, let’s see how these place values create patterns when we add! We will look at some examples.

Example 1: Adding 5 to Increasing Place Values

Let’s add 5 to some numbers that are getting bigger by place value:

• 5 + 5 = 10
• 45 + 5 = 50
• 345 + 5 = 350
• 2,345 + 5 = 2,350

Notice the pattern? As we add 5 to a number with more place values, the ones place changes, and sometimes the tens place changes too!

Example 2: Adding 10 to Increasing Place Values

What happens when we add 10?

• 10 + 10 = 20
• 110 + 10 = 120
• 1,110 + 10 = 1,120
• 11,110 + 10 = 11,120

The tens place changes! Adding 10 increases the digit in the tens place by one.

Example 3: Adding 100 to Increasing Place Values

Let’s try adding 100:

• 100 + 100 = 200
• 1,100 + 100 = 1,200
• 11,100 + 100 = 11,200

The hundreds place changes! Adding 100 increases the digit in the hundreds place by one.

Why is This Useful?

Understanding these patterns can help you do math faster in your head! You can quickly add numbers by recognizing how the place values change.

Practice Time!

Try these on your own:

1. What is 6 + 4? What is 56 + 4? What is 456 + 4?
2. What is 20 + 10? What is 320 + 10? What is 5,320 + 10?
3. What is 300 + 100? What is 2,300 + 100? What is 12,300 + 100?

See if you can spot the patterns!

Summary

Today, we learned about addition patterns over increasing place values. We saw how adding the same number (like 5, 10, or 100) to numbers with different place values creates interesting patterns. Understanding these patterns can help you become math superstars!

Let’s practice!