Compare Three-Digit Numbers - 2nd Grade Math

1. Which is less: 804 or 840?
   Answer: 804 Comparing the two numbers, both have $8$ hundreds, but $804$ has $0$ tens while $840$ has $4$ tens, so $804$ is less, making A correct. Choice B is wrong because it reverses the comparison and picks the greater number. Choice C is wrong because the two numbers are not equal. Choice D is wrong because both numbers are given, so the comparison can be made.
2. A librarian is organizing books by the number of pages. She has books with $328$, $283$, $238$, and $382$ pages. Which list shows the books arranged from greatest to least number of pages?
   Answer: $382, 328, 283, 238$ Arranged from greatest to least, the order is $382 > 328 > 283 > 238$. Choice B lists them from least to greatest instead. Choice C mixes up the order without a consistent pattern. Choice D swaps the second and third numbers (328 and 283).
3. Which of these numbers is the greatest: 368, 638, 386, or 683?
   Answer: 683 Comparing the hundreds digit first, 638 and 683 both start with a 6, which is more than the 3 in 368 and 386. Comparing the tens digit between 638 and 683, the 8 in 683 is greater than the 3 in 638, so 683 is the greatest. 368 and 386 both have only 3 hundreds, so they are smaller than either 638 or 683. Comparing place value digit by digit, starting with the largest place, is the key to ordering numbers like these.
4. Which is less: 719 or 791?
   Answer: 719 Comparing the tens place, 719 has 1 ten and 791 has 9 tens, so 719 is the smaller number. Choice A is wrong because the two numbers are not equal. Choice B is wrong because both numbers are given, so there is enough information. Choice D is the greater of the two numbers, not the lesser one.
5. Order from least to greatest: 318, 381, 331.
   Answer: 318, 331, 381 Comparing the tens digit of each number, since all three share the same hundreds digit (3), 318 is the smallest, 331 is in the middle, and 381 is the greatest. So from least to greatest, the order is 318, 331, 381. Any other order mixes up which number has the smaller tens or ones digit. Comparing the tens digit first (1 in 318, 3 in 331, 8 in 381) is the quickest way to put these three numbers in order.
6. Which number is the smallest: 726, 762, 627, or 672?
   Answer: 627 Comparing the hundreds digit first, 627 and 672 both start with a 6, which is less than the 7 in 726 and 762. Comparing the tens digit between 627 and 672, the 2 in 627 is less than the 7 in 672, so 627 is the smallest. 726 and 762 both have 7 hundreds, so they are both greater than either 627 or 672. Comparing place value digit by digit, starting with the largest place, is the key to ordering numbers like these.
7. Which number equals 6 hundreds?
   Answer: 600 6 hundreds means 6 groups of 100, which equals 600. A student might pick 60 by mixing up hundreds with tens. A student might pick 6,000 by adding an extra zero and mixing up hundreds with thousands. A student might pick 6 by only using the digit itself and forgetting what place value it represents.
8. Which is greater: $582$ or $528$?
   Answer: 582 582 is greater than 528 because although both numbers have 5 hundreds, 582 has 8 tens while 528 has only 2 tens. 528 is the smaller of the two numbers, not the greater one. The two numbers are not equal, since their tens digits are different.
9. Which statement correctly compares 639 and 636?
   Answer: 639 is greater than 636 639 is greater than 636 because 639 has more ones than 636 when the hundreds and tens digits match. Choice A is wrong because 639 is not less than 636. Choice B is wrong because the two numbers are not equal. Choice C reverses the comparison and states it backward.
10. Which is less: $714$ or $741$?
    Answer: 714 714 has 7 hundreds, 1 ten, and 4 ones; 741 has 7 hundreds, 4 tens, and 1 one. Comparing the tens place, 714 has fewer tens (1 vs 4), so 714 is less. Choice A picks the greater number. Choice C is not one of the two numbers being compared. Choice D is wrong because 714 and 741 are different numbers.
11. Which is greater: 583 or 538?
    Answer: 583 This question tests 2nd grade understanding of comparing three-digit numbers using place value and comparison symbols >, <, and = (CCSS 2.NBT.A.4: Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons). To compare three-digit numbers, use place value comparison working left to right: (1) Compare hundreds first—the number with more hundreds is greater (400 > 350 because 4 hundreds > 3 hundreds). (2) If hundreds are equal, compare tens—more tens means greater number (352 > 347 because both have 3 hundreds, but 5 tens > 4 tens). (3) If hundreds and tens are equal, compare ones—more ones means greater number (347 > 345 because both have 34 tens, but 7 ones > 5 ones). Stop comparing as soon as you find a difference. Greater than (>) has open side facing larger number (352 > 347). Less than (<) has open side facing larger number from other side (347 < 352). Equal to (=) means same value (347 = 347). Remember: mouth/open side 'eats' bigger number. In this problem, students must identify which is greater between 583 and 538. To solve, compare place by place: both have 5 hundreds (equal), compare tens: 8 tens > 3 tens, so 583 > 538 (583 is greater). Choice B is correct because comparing 583 and 538 place by place shows 5 hundreds = 5 hundreds, then 8 tens > 3 tens, so 583 is greater than 538 because it has more tens (8 tens vs 3 tens). This correctly applies place value comparison. Choice A represents identifying the wrong number as greater (said 538 is greater when 583 is greater—didn't compare tens correctly). This error typically happens when students reverse symbol meaning, don't use place value comparison systematically, compare wrong digits, work right to left instead of left to right, don't understand ordering terms, misidentify which number is greater in context. To help students: Teach place value comparison explicitly: 'Start at the left (hundreds). Compare hundreds. If different, done—larger hundreds = larger number. If same, move right to tens. Compare tens. If different, done—larger tens = larger number. If same, move right to ones. Compare ones. Larger ones = larger number.' Practice with examples: 583 vs 538 (hundreds: 5 = 5, tens: 8 > 3, stop—583 > 538). Use place value chart with numbers aligned vertically—visually compare each column left to right. Teach symbols with alligator analogy: 'Open mouth eats bigger number' (583 > 538, mouth opens toward 583). Practice writing both: 583 > 538 and 538 < 583 (same comparison, two ways). For ordering, compare all numbers systematically: find smallest first (lowest hundreds, then tens, then ones), then next smallest, continue. Use number line: plot numbers, see positions (further right = greater). Connect to real-world: 'Emma has 538, Jamal has 583. Who has more? Compare 538 vs 583 (same hundreds, compare tens: 3 < 8), so 583 > 538, Jamal has more.' Watch for: symbol reversal (> vs <), comparing wrong place values, working right to left, not stopping when difference found, ordering wrong direction, context errors.
12. Which symbol correctly compares 476 and 467?
    Answer: > The correct symbol is > because 476 is greater than 467. Comparing the tens digit, 7 is greater than 6, so 476 is the bigger number. The symbol = is wrong because the two numbers are not equal. The symbol < would mean 476 is smaller than 467, which is incorrect. The symbol ≠ only shows the numbers are different, but it does not show which one is greater.
13. Which expression equals 349?
    Answer: $300+40+9$ 300 + 40 + 9 equals 349, matching the number exactly by place value: 3 hundreds, 4 tens, and 9 ones. 300 + 4 + 9 only equals 313 because it treats the tens digit as if it were a 4 instead of a 40. 300 + 40 + 90 equals 430 because it treats the ones digit as if it were a 90 instead of a 9. 30 + 40 + 9 equals 79 because it treats the hundreds digit as if it were a 30 instead of a 300.
14. Order from least to greatest: 326, 362, 236.
    Answer: 236, 326, 362 Comparing the three numbers, 236 is the smallest, 326 is in the middle, and 362 is the largest, so the order from least to greatest is 236, 326, 362, making Choice D correct. Choice A is wrong because it starts with 326 instead of the smallest number. Choice B is wrong because it lists the numbers from greatest to least, not least to greatest. Choice C is wrong because it puts 236 first but then lists the other two out of order.
15. Which statement correctly compares 468 and 486?
    Answer: 468 is less than 486 468 is less than 486 because the tens digit 6 is smaller than the tens digit 8. Choice A is wrong because 468 is not greater than 486. Choice B is wrong because the two numbers are not equal. Choice D reverses the comparison and states it backward.
16. Which number is the greatest: 808, 818, 800, or 880?
    Answer: 880 880 is the greatest number because it has 8 tens, more than any of the other choices. 808, 818, and 800 all have fewer tens even though they share the same hundreds digit. Comparing the tens place after the hundreds place is the key to ordering these numbers. Looking only at the ones digit or the hundreds digit alone can lead to the wrong choice.
17. Roberto is thinking of a three-digit number. It is greater than 456 but less than 465. The tens digit is 6 and the ones digit is 2. What is Roberto's number?
    Answer: 462 462 is greater than 456 and less than 465, and it has 6 in the tens place and 2 in the ones place, so it fits all the clues. 456 does not have 6 in the tens place. 465 is not less than 465, so it does not fit the clue. 460 has 6 in the tens place but 0 in the ones place instead of 2.
18. Order from least to greatest: $615, 651, 516$.
    Answer: 516, 615, 651 Comparing digits shows 516 is smallest, then 615, then 651, so the order from least to greatest is 516, 615, 651. Choice A lists the numbers in the opposite order, from greatest to least. Choice B keeps 615 and 651 in the right order but puts 516 last instead of first. Choice D correctly starts with 516 but reverses the order of the last two numbers.
19. Use the table to answer the question. Which school has exactly $67$ more students than the school with the fewest students?
    Answer: Maple Elementary has $67$ more students than Oak Elementary First, find the school with fewest students by comparing: Oak (218), Maple (285), Pine (295). Since 218 < 285 < 295, Oak has the fewest. Now find which school has exactly 67 more than Oak (218): 285 - 218 = 67 and 295 - 218 = 77. Maple has exactly 67 more students than Oak. Choice A compares wrong schools. Choice C compares wrong schools (295 - 285 = 10). Choice D has the comparison backwards.
20. Which symbol correctly compares 342 and 300 + 40 + 2?
    Answer: #ERROR! The two expressions are equal because 300 + 40 + 2 equals 342, matching the number on the left. The symbol > would mean 342 is greater, which is not true since they are equal. The symbol < would mean 342 is smaller, which is also not true. The symbol ≠ says the two amounts are different, but they represent the exact same value.

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