Compare Three-Digit Numbers
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2nd Grade Math › Compare Three-Digit Numbers
Maya has 647 stickers. Chen has 674 stickers. Who has more?
Chen
Neither
Maya
They have the same
Explanation
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 compare Maya's 647 stickers and Chen's 674 stickers to see who has more. To solve, compare place by place: both have 6 hundreds (equal), compare tens: 4 tens < 7 tens, so 647 < 674, Chen has more. Choice B is correct because comparing 647 and 674 place by place shows 6 hundreds = 6 hundreds, then 4 tens < 7 tens, so 674 > 647, Chen has more. This correctly applies place value comparison. Choice A represents answering with the wrong person (said Maya has more when Chen has more—didn't compare tens correctly). This error typically happens when students compare wrong place value (looked at ones: 7 > 4, but should compare tens first: 4 < 7), work right to left instead of left to right, or context errors in identifying who has more. 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: 647 vs 674 (hundreds: 6 = 6, tens: 4 < 7, stop—647 < 674). 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' (674 > 647, mouth opens toward 674). Practice writing both: 674 > 647 and 647 < 674 (same comparison, two ways). Connect to real-world: 'Maya has 647, Chen has 674. Who has more? Compare 647 vs 674 (same hundreds, compare tens: 4 < 7), so 674 > 647, Chen has more.' Watch for: context errors, comparing wrong place values, working right to left.
Compare: 600 __ 6 hundreds. Use $<, >,$ or $=$.
not sure
=
<
Explanation
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 compare 600 and 6 hundreds to choose the correct symbol <, >, or =. To solve, recognize that 6 hundreds is 600 (same value), so 600 = 6 hundreds (symbol is =). Choice C is correct because 6 hundreds means 600, so 600 = 600 and the symbol is =. This correctly applies place value comparison. Choice A represents saying < when should be = (thinking 600 is less than 6 hundreds). 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: 600 vs 6 hundreds (both 600, so =). 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' but for =, no mouth needed. Practice writing both: 600 = 600. 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 600, Jamal has 6 hundreds. Who has more? They are equal.' Watch for: symbol reversal (> vs <), comparing wrong place values, working right to left, not stopping when difference found, ordering wrong direction, context errors.
Compare: “three hundred ninety-two” __ 329. Use $<$, $>$, or $=$.
$\ne$
<
=
Explanation
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 compare 'three hundred ninety-two' (which is 392) and 329 to choose the correct symbol. To solve, compare place by place: both have 3 hundreds (equal), compare tens: 9 tens > 2 tens, so 392 > 329 and the symbol is >. Choice C is correct because comparing 392 and 329 place by place shows 3 hundreds = 3 hundreds, then 9 tens > 2 tens, so 392 > 329 and the symbol is >. This correctly applies place value comparison. Choice A represents symbol reversal (said < when should be >, thinking 392 is less than 329). 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, or misread word form as number. 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: 392 vs 329 (hundreds: 3 = 3, tens: 9 > 2, stop—392 > 329). 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' (392 > 329, mouth opens toward 392). Practice writing both: 392 > 329 and 329 < 392 (same comparison, two ways). Practice converting word form to numerals before comparing.
Which symbol makes this true: $342\ __\ 300+40+2$?
$\ge$
=
<
Explanation
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 find the symbol that makes 342 __ 300+40+2 true. To solve, add 300+40+2=342 (same value), so 342 = 300+40+2 (symbol is =). Choice B is correct because 300+40+2 equals 342, so 342 = 342 and the symbol is =. This correctly applies place value comparison. Choice A represents saying < when should be = (thinking 342 is less than its expanded form). 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: 342 vs 300+40+2 (both 342, so =). 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' but for =, no mouth needed. Practice writing both: 342 = 342. 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 342, Jamal has 300+40+2. Who has more? They are equal.' Watch for: symbol reversal (> vs <), comparing wrong place values, working right to left, not stopping when difference found, ordering wrong direction, context errors.
Compare: $468\ __\ 486$. Use $<$, $>$, or $=$.
<
$\le$
=
Explanation
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 compare 468 and 486 to choose the correct symbol. To solve, compare place by place: both have 4 hundreds (equal), compare tens: 6 tens < 8 tens, so 468 < 486 and the symbol is <. Choice C is correct because comparing 468 and 486 place by place shows 4 hundreds = 4 hundreds, then 6 tens < 8 tens, so 468 < 486 and the symbol is <. This correctly applies place value comparison. Choice A represents symbol reversal (said > when should be <, thinking 468 is greater than 486). 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. 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: 468 vs 486 (hundreds: 4 = 4, tens: 6 < 8, stop—468 < 486). 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' (486 > 468, mouth opens toward 486). Practice writing both: 486 > 468 and 468 < 486 (same comparison, two ways).
Order from least to greatest: 318, 381, 331.
318, 331, 381
381, 331, 318
331, 318, 381
318, 381, 331
Explanation
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 order 318, 381, 331 from least to greatest. To solve, compare all numbers systematically: all have 3 hundreds, compare tens: 318 has 1 ten, 331 has 3 tens, 381 has 8 tens, so 1 < 3 < 8, order is 318, 331, 381. Choice B is correct because the correct order from smallest to largest is 318 (3 hundreds, 1 ten), then 331 (3 hundreds, 3 tens), then 381 (3 hundreds, 8 tens). This correctly applies place value comparison. Choice A represents ordering wrong (greatest to least instead of least to greatest). This error typically happens when students don't understand ordering terms, ordered wrong direction, or didn't compare tens correctly. 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: Order 318, 331, 381 (all 3 hundreds, tens: 1 < 3 < 8, so 318 < 331 < 381). Use place value chart with numbers aligned vertically—visually compare each column left to right. 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). Watch for: ordering wrong direction.
Compare: $300+40+9$ __ $349$. Use $ < $, $ > $, or $ = $.
=
cannot tell
<
Explanation
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, the student must compare $300+40+9$ and 349 and choose the correct symbol $ > $, $ < $, or $ = $. To solve, first expand $300+40+9$ to 349, then compare: both are 349, so they are equal (symbol is $ = $). Choice B is correct because $300+40+9$ equals 349, so the symbol is $ = $ as they have the same value. This correctly applies place value comparison. Choice A represents saying $ > $ when should be $ = $ (thinking the expanded form is greater). This error typically happens when students don't evaluate the expanded form correctly or misadd the place values. 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: $300+40+9$ vs 349 (both 349, so $ = $). 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' but for $ = $, no mouth needed. Practice writing both directions for inequalities. 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 $300+40+9$ stickers, which is 349, Jamal has 349. Who has more? They have the same.' Watch for: symbol reversal ($>$ vs $<$), comparing wrong place values, working right to left, not stopping when difference found, ordering wrong direction, context errors.
A librarian is organizing books by the number of pages. She has books with $$328$$ pages, $$283$$ pages, $$238$$ pages, and $$382$$ pages. If she arranges them from greatest to least number of pages, which book comes second?
The book with $$238$$ pages comes second in the arrangement
The book with $$382$$ pages comes second in the arrangement
The book with $$328$$ pages comes second in the arrangement
The book with $$283$$ pages comes second in the arrangement
Explanation
First, arrange from greatest to least by comparing hundreds digits: 382 and 328 both have 3 hundreds, while 283 and 238 have 2 hundreds. So 382 and 328 are the two largest. Comparing 382 and 328: both have 3 hundreds, but 8 > 2 in tens place, so 382 > 328. For the others: 283 > 238 (8 > 3 in tens). Order is: 382, 328, 283, 238. The second book has 328 pages.
Which statement correctly compares the numbers $$428$$ and $$482$$?
$$428 < 482$$ because $$2 < 8$$ in the tens place
$$428 < 482$$ because $$4 < 8$$ in the tens place
$$428 = 482$$ because both numbers have the same digits
$$428 > 482$$ because $$4 > 4$$ in the hundreds place
Explanation
Both numbers have 4 in the hundreds place, so we compare the tens place. In 428, the tens digit is 2. In 482, the tens digit is 8. Since 2 < 8, we have 428 < 482. Choice A incorrectly compares the ones place instead of tens. Choice B incorrectly claims 428 > 482 and that 4 > 4. Choice D incorrectly states the numbers are equal just because they use the same digits.
Three friends collected cans for recycling. Alex collected $$316$$ cans, Sam collected $$361$$ cans, and Jordan collected $$613$$ cans. If they want to arrange themselves in order from least to greatest number of cans, what is the correct order?
Alex, Sam, Jordan with $$316 < 361 < 613$$
Sam, Alex, Jordan with $$361 < 316 < 613$$
Alex, Jordan, Sam with $$316 < 613 < 361$$
Jordan, Sam, Alex with $$613 < 361 < 316$$
Explanation
Comparing the hundreds place: 316 has 3 hundreds, 361 has 3 hundreds, and 613 has 6 hundreds. Since 613 has the most hundreds, it's the largest. For 316 and 361, both have 3 hundreds, so we compare tens: 316 has 1 ten and 361 has 6 tens. Since 1 < 6, we have 316 < 361. Therefore: 316 < 361 < 613. Choice B incorrectly places 613 between the other numbers. Choices C and D have incorrect orderings.