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Welcome! Today we'll learn how to compare multiples of 1000 using a place-value chart. A place-value chart organizes numbers by separating each digit into columns based on its place value. This makes it easy to compare large numbers systematically. Let's see how to compare two multiples of 1000 step by step. We'll compare 4,000 and 9,000. First, we write both numbers in our place-value chart. Then we start comparing from the leftmost column with non-zero digits. In the thousands column, we see 4 and 9. Since 9 is greater than 4, we know that 9,000 is greater than 4,000. Now let's try a more challenging example with larger numbers. We'll compare 23,000 and 17,000. When we place these numbers in our chart, we see digits in the ten thousands column. We start comparing from the leftmost column - the ten thousands place. Here we have 2 and 1. Since 2 is greater than 1, we immediately know that 23,000 is greater than 17,000. We don't even need to look at the thousands column! What happens when the first digits are the same? Let's compare 34,000 and 37,000. We start with the ten thousands column and see both numbers have 3. Since they're equal, we move to the next column - the thousands place. Here we compare 4 and 7. Since 7 is greater than 4, we conclude that 37,000 is greater than 34,000. This shows why we always start from the left and work our way right when comparing numbers. Let's summarize what we've learned about comparing multiples of 1000 using place-value charts. Remember these key steps: organize numbers in a place-value chart, start comparing from the leftmost column, and work your way right until you find different digits. The number with the larger digit in that position is the greater number. Let's try a quick practice: comparing 56,000 and 48,000. Looking at the ten thousands place, 5 is greater than 4, so 56,000 is greater than 48,000. You now have the tools to compare any multiples of 1000!