To compare three-digit numbers, compare digits from left to right, starting with the hundreds place. If the hundreds digits differ, the number with the greater hundreds digit is larger — regardless of the tens and ones. If hundreds are equal, compare the tens digits; if those are equal too, compare ones. Record comparisons using the symbols >, <, and =.
Start by comparing numbers with very different hundreds digits (e.g., 721 vs. 389) before introducing cases where hundreds are the same. Use base-ten blocks to make the comparison concrete. Have students justify their comparisons verbally: 'I know 721 > 389 because 7 hundreds is more than 3 hundreds.'
When you learned to compare two-digit numbers, you discovered that the tens place is the most important digit — 73 is greater than 58 because 7 tens beats 5 tens, no matter what the ones digits say. Three-digit numbers work exactly the same way, just with one extra place added at the front: the hundreds place. And hundreds beat everything. A number with more hundreds is bigger, period — you do not even need to look at the tens or ones.
Compare 741 and 389. How many hundreds does each have? 741 has 7 hundreds; 389 has 3 hundreds. Seven hundreds is more than three hundreds, so 741 > 389. You are done — the tens and ones digits are irrelevant. This is why place value is so powerful: it lets you make decisions quickly by looking at the most significant digit first.
Now suppose the hundreds are the same. Compare 456 and 431. Both have 4 hundreds, so move to the tens place: 5 tens versus 3 tens. Five is more, so 456 > 431. If the tens are also equal — compare 527 and 524 — then finally look at the ones place: 7 versus 4, so 527 > 524. The rule is always "compare left to right, and stop as soon as you find a difference."
A helpful way to remember the < and > symbols is that the symbol is an arrow that opens toward the bigger number. 741 > 389 means "741 is greater than 389," and the open mouth of > faces the 741. Alternatively, think of the symbol as a hungry mouth that always eats the bigger number. Use base-ten blocks if you want a concrete check: build both numbers and see which pile of hundreds blocks is taller.