To compare multi-digit numbers, start from the leftmost digit (the highest place value) and work right. The number with a larger digit in the highest differing place is the greater number. For example, 4,382 > 4,291 because at the hundreds place, 3 > 2. Students should use the symbols >, <, and = and be able to order a set of numbers from least to greatest or greatest to least.
Connect to place value understanding explicitly: "Which place should we look at first? Why?" Use number lines to visualize relative position. Practice with numbers that differ in tricky ways (same leading digits, different lengths, zeros in the middle).
You already understand place value in whole numbers — that each digit's position tells you its worth, and that a digit in the hundreds place is worth ten times the same digit in the tens place. Comparing whole numbers is a direct application of that knowledge. The core principle is: the leftmost digit (the highest place value) is the most powerful. It dominates the comparison.
Start by counting digits. A 5-digit number is always greater than any 4-digit number — no matter what the individual digits are. 10,000 is larger than 9,999 because ten thousands beats thousands. If two numbers have the same number of digits, work left to right through the place values until you find a position where the digits differ. For example, comparing 4,382 and 4,291: both start with 4 (same), then 3 vs. 2 in the hundreds place — 3 > 2, so 4,382 > 4,291. You don't need to look at the tens or ones because the hundreds place already decided it.
The symbols >, <, and = are shorthand for this comparison. A helpful memory trick: the symbol opens toward the larger number (like a hungry mouth eating the bigger value). So 4,382 > 4,291 means 4,382 is greater than 4,291. Another way: > means "is greater than" and < means "is less than." Always read left to right.
Ordering a set of numbers from least to greatest (or greatest to least) just applies the comparison repeatedly. Start with the number of digits — any 3-digit numbers come before 4-digit numbers. Then sort within each group by comparing leading digits. A number line is a powerful visual tool here: numbers farther right are always greater. When you practice with tricky cases — numbers with zeros in the middle, like 50,002 vs. 50,020 — you're stress-testing your place-value intuition. In 50,002 vs. 50,020, the first three digits are the same (5, 0, 0), so you compare the tens place: 0 vs. 2, meaning 50,020 > 50,002.