This question tests 2nd grade understanding of adding and subtracting within 1000 using strategies based on place value, properties of operations, and standard algorithms with regrouping (CCSS 2.NBT.B.7: Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones). When adding three-digit numbers like 347 + 286, use place value: add ones (7+6=13, write 3 carry 1), add tens (4+8+1=13, write 3 carry 1), add hundreds (3+2+1=6), result 633. When subtracting like 563 - 278, use regrouping: ones (can't do 3-8, regroup 6 tens 3 ones to 5 tens 13 ones, 13-8=5), tens (can't do 5-7, regroup 5 hundreds 5 tens to 4 hundreds 15 tens, 15-7=8), hundreds (4-2=2), result 285. Multiple regroupings often needed. Place value strategy: break into hundreds, tens, ones, add/subtract separately, combine. Mental math: use compensation (563-278 → 563-300+22 = 263+22=285). Number line: jump by hundreds, then tens, then ones. In this problem, the student must add 392 + 185 using place value strategy. To solve, break into place values: hundreds (300+100=400), tens (90+80=170), ones (2+5=7), combine 400+170=570, +7=577, or use standard algorithm with regrouping. Choice B is correct because adding 392+185 with place value or regrouping correctly—ones 2+5=7, tens 9+8=17 (write 7 carry 1), hundreds 3+1+1=5, giving 577. This accurately uses regrouping across multiple places. Choice A represents not carrying the tens correctly (added tens as 9+8=17 but wrote 7 without carry, got 567). This error typically happens when students don't carry correctly in addition, forget to regroup across multiple places, misunderstand place value, confuse operations, don't handle zeros correctly. To help students: Practice standard algorithm with clear alignment. Use vertical format, align by place value. For addition: 'Start with ones. 7+6=13. That's more than 10, so regroup: write 3 in ones, carry 1 ten to tens column. Now tens: 4+8=12, plus carried 1 = 13. Regroup: write 3 in tens, carry 1 hundred. Hundreds: 3+2=5, plus carried 1=6. Answer: 633.' For subtraction: 'Start with ones. Can we do 3-8? No, so regroup: borrow 1 ten from tens (6 tens becomes 5 tens), add 10 ones (3 ones becomes 13 ones). Now: 13-8=5. Tens: can we do 5-7? No, regroup: borrow 1 hundred (5 hundreds becomes 4), add 10 tens (5 tens becomes 15 tens). Now: 15-7=8. Hundreds: 4-2=2. Answer: 285.' Use base-ten blocks to show regrouping visually: trade 1 rod for 10 units, trade 1 flat for 10 rods. Practice regrouping with zeros: 400-137 requires regrouping from hundreds to tens to ones. Teach place value strategy: break apart, add/subtract by place. Use number line for mental math visualization. For word problems, identify operation (joining=add, separating/comparing=subtract). Watch for: not regrouping when needed, regrouping incorrectly, subtracting smaller from larger without borrowing, place value errors, handling zeros incorrectly, wrong operation.

This question tests 2nd grade understanding of adding and subtracting within 1000 using strategies based on place value, properties of operations, and standard algorithms with regrouping (CCSS 2.NBT.B.7: Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones). When adding three-digit numbers like 347 + 286, use place value: add ones (7+6=13, write 3 carry 1), add tens (4+8+1=13, write 3 carry 1), add hundreds (3+2+1=6), result 633. When subtracting like 563 - 278, use regrouping: ones (can't do 3-8, regroup 6 tens 3 ones to 5 tens 13 ones, 13-8=5), tens (can't do 5-7, regroup 5 hundreds 5 tens to 4 hundreds 15 tens, 15-7=8), hundreds (4-2=2), result 285. Multiple regroupings often needed. In this problem, student must add 392 + 408 using place value strategy. To solve, use place value strategy: break into hundreds, tens, ones, add separately (300+400=700, 90+0=90, 2+8=10), combine to 800. Choice C is correct because adding 392+408 with place value correctly—hundreds 300+400=700, tens 90+0=90, ones 2+8=10, total 800. This accurately uses regrouping across multiple places. Choice B represents place value error (misaligned digits, added wrong values like forgetting the 10 from ones, got 790 instead of 800). This error typically happens when students don't carry/borrow correctly, forget to regroup across multiple places, subtract in wrong direction when borrowing, misunderstand place value, confuse operations, don't handle zeros correctly. To help students: Practice standard algorithm with clear alignment. Use vertical format, align by place value. For addition: 'Start with ones. 7+6=13. That's more than 10, so regroup: write 3 in ones, carry 1 ten to tens column. Now tens: 4+8=12, plus carried 1 = 13. Regroup: write 3 in tens, carry 1 hundred. Hundreds: 3+2=5, plus carried 1=6. Answer: 633.' For subtraction: 'Start with ones. Can we do 3-8? No, so regroup: borrow 1 ten from tens (6 tens becomes 5 tens), add 10 ones (3 ones becomes 13 ones). Now: 13-8=5. Tens: can we do 5-7? No, regroup: borrow 1 hundred (5 hundreds becomes 4), add 10 tens (5 tens becomes 15 tens). Now: 15-7=8. Hundreds: 4-2=2. Answer: 285.' Use base-ten blocks to show regrouping visually: trade 1 rod for 10 units, trade 1 flat for 10 rods. Practice regrouping with zeros: 400-137 requires regrouping from hundreds to tens to ones. Teach place value strategy: break apart, add/subtract by place. Use number line for mental math visualization. For word problems, identify operation (joining=add, separating/comparing=subtract). Watch for: not regrouping when needed, regrouping incorrectly, subtracting smaller from larger without borrowing, place value errors, handling zeros incorrectly, wrong operation.

This question tests 2nd grade understanding of adding and subtracting within 1000 using strategies based on place value, properties of operations, and standard algorithms with regrouping (CCSS 2.NBT.B.7: Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones). When adding three-digit numbers like 347 + 286, use place value: add ones (7+6=13, write 3 carry 1), add tens (4+8+1=13, write 3 carry 1), add hundreds (3+2+1=6), result 633. When subtracting like 563 - 278, use regrouping: ones (can't do 3-8, regroup 6 tens 3 ones to 5 tens 13 ones, 13-8=5), tens (can't do 5-7, regroup 5 hundreds 5 tens to 4 hundreds 15 tens, 15-7=8), hundreds (4-2=2), result 285. Multiple regroupings often needed. In this problem, student must add 468 + 257, requiring regrouping in ones and tens. To solve, use standard algorithm—align by place value, add ones (8+7=15, carry 1), add tens (6+5+1=12, carry 1), add hundreds (4+2+1=7), answer 725. Choice B is correct because adding 468+257 with regrouping correctly—ones 8+7=15 (write 5 carry 1), tens 6+5+1=12 (write 2 carry 1), hundreds 4+2+1=7, giving 725. This accurately uses regrouping across multiple places. Choice A represents didn't carry correctly in addition (forgot to add carried 1 in hundreds, got 715 instead of 725). This error typically happens when students don't carry/borrow correctly, forget to regroup across multiple places, subtract in wrong direction when borrowing, misunderstand place value, confuse operations, don't handle zeros correctly. To help students: Practice standard algorithm with clear alignment. Use vertical format, align by place value. For addition: 'Start with ones. 7+6=13. That's more than 10, so regroup: write 3 in ones, carry 1 ten to tens column. Now tens: 4+8=12, plus carried 1 = 13. Regroup: write 3 in tens, carry 1 hundred. Hundreds: 3+2=5, plus carried 1=6. Answer: 633.' For subtraction: 'Start with ones. Can we do 3-8? No, so regroup: borrow 1 ten from tens (6 tens becomes 5 tens), add 10 ones (3 ones becomes 13 ones). Now: 13-8=5. Tens: can we do 5-7? No, regroup: borrow 1 hundred (5 hundreds becomes 4), add 10 tens (5 tens becomes 15 tens). Now: 15-7=8. Hundreds: 4-2=2. Answer: 285.' Use base-ten blocks to show regrouping visually: trade 1 rod for 10 units, trade 1 flat for 10 rods. Practice regrouping with zeros: 400-137 requires regrouping from hundreds to tens to ones. Teach place value strategy: break apart, add/subtract by place. Use number line for mental math visualization. For word problems, identify operation (joining=add, separating/comparing=subtract). Watch for: not regrouping when needed, regrouping incorrectly, subtracting smaller from larger without borrowing, place value errors, handling zeros incorrectly, wrong operation.

This question tests 2nd grade understanding of adding and subtracting within 1000 using strategies based on place value, properties of operations, and standard algorithms with regrouping (CCSS 2.NBT.B.7: Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones). When adding three-digit numbers like 347 + 286, use place value: add ones (7+6=13, write 3 carry 1), add tens (4+8+1=13, write 3 carry 1), add hundreds (3+2+1=6), result 633. When subtracting like 563 - 278, use regrouping: ones (can't do 3-8, regroup 6 tens 3 ones to 5 tens 13 ones, 13-8=5), tens (can't do 5-7, regroup 5 hundreds 5 tens to 4 hundreds 15 tens, 15-7=8), hundreds (4-2=2), result 285. Multiple regroupings often needed. Place value strategy: break into hundreds, tens, ones, add/subtract separately, combine. Mental math: use compensation (563-278 → 563-300+22 = 263+22=285). Number line: jump by hundreds, then tens, then ones. In this problem, the student must add 468 + 257 using regrouping; to solve, use the standard algorithm—align by place value, add ones (8+7=15, carry 1), add tens (6+5+1=12, carry 1), add hundreds (4+2+1=7), answer 725. Choice B is correct because adding 468+257 with regrouping correctly—ones 8+7=15 (write 5 carry 1), tens 6+5+1=12 (write 2 carry 1), hundreds 4+2+1=7, giving 725. This accurately uses regrouping across multiple places. Choice A represents not carrying correctly in addition (added without regrouping in tens, got 715 instead of 725). This error typically happens when students don't carry over the 1 from the tens place. To help students: Practice standard algorithm with clear alignment. Use vertical format, align by place value. For addition: 'Start with ones. 8+7=15. That's more than 10, so regroup: write 5 in ones, carry 1 ten to tens column. Now tens: 6+5=11, plus carried 1=12. Regroup: write 2 in tens, carry 1 hundred. Hundreds: 4+2=6, plus carried 1=7. Answer: 725.' For subtraction: 'Start with ones. Can we do 3-8? No, so regroup: borrow 1 ten from tens (6 tens becomes 5 tens), add 10 ones (3 ones becomes 13 ones). Now: 13-8=5. Tens: can we do 5-7? No, regroup: borrow 1 hundred (5 hundreds becomes 4), add 10 tens (5 tens becomes 15 tens). Now: 15-7=8. Hundreds: 4-2=2. Answer: 285.' Use base-ten blocks to show regrouping visually: trade 1 rod for 10 units, trade 1 flat for 10 rods. Practice regrouping with zeros: 400-137 requires regrouping from hundreds to tens to ones. Teach place value strategy: break apart, add/subtract by place. Use number line for mental math visualization. For word problems, identify operation (joining=add, separating/comparing=subtract). Watch for: not regrouping when needed, regrouping incorrectly, subtracting smaller from larger without borrowing, place value errors, handling zeros incorrectly, wrong operation.

This question tests 2nd grade understanding of adding and subtracting within 1000 using strategies based on place value, properties of operations, and standard algorithms with regrouping (CCSS 2.NBT.B.7: Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones). When adding three-digit numbers like 347 + 286, use place value: add ones (7+6=13, write 3 carry 1), add tens (4+8+1=13, write 3 carry 1), add hundreds (3+2+1=6), result 633. When subtracting like 563 - 278, use regrouping: ones (can't do 3-8, regroup 6 tens 3 ones to 5 tens 13 ones, 13-8=5), tens (can't do 5-7, regroup 5 hundreds 5 tens to 4 hundreds 15 tens, 15-7=8), hundreds (4-2=2), result 285. Multiple regroupings often needed. In this problem, student must subtract 650 - 298 using mental math. To solve, use mental math with compensation (650-300=350, add back 2 since 298 is 2 less, 350+2=352). Choice B is correct because subtracting 650-298 with compensation correctly—650-300+2=352. This accurately uses regrouping across multiple places. Choice A represents wrong operation or compensation error (subtracted as 650-200 or misadded, got 452 instead of 352). This error typically happens when students don't carry/borrow correctly, forget to regroup across multiple places, subtract in wrong direction when borrowing, misunderstand place value, confuse operations, don't handle zeros correctly. To help students: Practice standard algorithm with clear alignment. Use vertical format, align by place value. For addition: 'Start with ones. 7+6=13. That's more than 10, so regroup: write 3 in ones, carry 1 ten to tens column. Now tens: 4+8=12, plus carried 1 = 13. Regroup: write 3 in tens, carry 1 hundred. Hundreds: 3+2=5, plus carried 1=6. Answer: 633.' For subtraction: 'Start with ones. Can we do 3-8? No, so regroup: borrow 1 ten from tens (6 tens becomes 5 tens), add 10 ones (3 ones becomes 13 ones). Now: 13-8=5. Tens: can we do 5-7? No, regroup: borrow 1 hundred (5 hundreds becomes 4), add 10 tens (5 tens becomes 15 tens). Now: 15-7=8. Hundreds: 4-2=2. Answer: 285.' Use base-ten blocks to show regrouping visually: trade 1 rod for 10 units, trade 1 flat for 10 rods. Practice regrouping with zeros: 400-137 requires regrouping from hundreds to tens to ones. Teach place value strategy: break apart, add/subtract by place. Use number line for mental math visualization. For word problems, identify operation (joining=add, separating/comparing=subtract). Watch for: not regrouping when needed, regrouping incorrectly, subtracting smaller from larger without borrowing, place value errors, handling zeros incorrectly, wrong operation.

This question tests 2nd grade understanding of adding and subtracting within 1000 using strategies based on place value, properties of operations, and standard algorithms with regrouping (CCSS 2.NBT.B.7: Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones). When adding three-digit numbers like 347 + 286, use place value: add ones (7+6=13, write 3 carry 1), add tens (4+8+1=13, write 3 carry 1), add hundreds (3+2+1=6), result 633. When subtracting like 563 - 278, use regrouping: ones (can't do 3-8, regroup 6 tens 3 ones to 5 tens 13 ones, 13-8=5), tens (can't do 5-7, regroup 5 hundreds 5 tens to 4 hundreds 15 tens, 15-7=8), hundreds (4-2=2), result 285. Multiple regroupings often needed. Place value strategy: break into hundreds, tens, ones, add/subtract separately, combine. Mental math: use compensation (563-278 → 563-300+22 = 263+22=285). Number line: jump by hundreds, then tens, then ones. In this problem, the student must subtract 709 - 465, regrouping if needed; to solve, use the standard algorithm—regroup as needed, ones (9-5=4), tens (0-6 can't, regroup from hundreds 7 to 6, tens 10, but 10-6=4), wait actually ones 9-5=4, tens 0-6 borrow making 10-6=4 but hundreds 6 (from 7-1), hundreds 6-4=2, answer 244. Choice A is correct because subtracting 709-465 with regrouping correctly—ones 9-5=4, tens 10-6=4 (after borrowing from hundreds), hundreds 6-4=2, giving 244. This accurately uses regrouping across multiple places. Choice B represents a regrouping error (added instead of subtracting or misborrowed, got 254 instead of 244). This error typically happens when students forget to adjust hundreds after borrowing. To help students: Practice standard algorithm with clear alignment. Use vertical format, align by place value. For addition: 'Start with ones. 7+6=13. That's more than 10, so regroup: write 3 in ones, carry 1 ten to tens column. Now tens: 4+8=12, plus carried 1=13. Regroup: write 3 in tens, carry 1 hundred. Hundreds: 3+2=5, plus carried 1=6. Answer: 633.' For subtraction: 'Start with ones. Can we do 3-8? No, so regroup: borrow 1 ten from tens (6 tens becomes 5 tens), add 10 ones (3 ones becomes 13 ones). Now: 13-8=5. Tens: can we do 5-7? No, regroup: borrow 1 hundred (5 hundreds becomes 4), add 10 tens (5 tens becomes 15 tens). Now: 15-7=8. Hundreds: 4-2=2. Answer: 285.' Use base-ten blocks to show regrouping visually: trade 1 rod for 10 units, trade 1 flat for 10 rods. Practice regrouping with zeros: 400-137 requires regrouping from hundreds to tens to ones. Teach place value strategy: break apart, add/subtract by place. Use number line for mental math visualization. For word problems, identify operation (joining=add, separating/comparing=subtract). Watch for: not regrouping when needed, regrouping incorrectly, subtracting smaller from larger without borrowing, place value errors, handling zeros incorrectly, wrong operation.

This question tests 2nd grade understanding of adding and subtracting within 1000 using strategies based on place value, properties of operations, and standard algorithms with regrouping (CCSS 2.NBT.B.7: Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones). When adding three-digit numbers like $347 + 286$, use place value: add ones ($7+6=13$, write 3 carry 1), add tens ($4+8+1=13$, write 3 carry 1), add hundreds ($3+2+1=6$), result 633. When subtracting like $563 - 278$, use regrouping: ones (can't do 3-8, regroup 6 tens 3 ones to 5 tens 13 ones, $13-8=5$), tens (can't do 5-7, regroup 5 hundreds 5 tens to 4 hundreds 15 tens, $15-7=8$), hundreds ($4-2=2$), result 285. Multiple regroupings often needed. Place value strategy: break into hundreds, tens, ones, add/subtract separately, combine. Mental math: use compensation ($563-278 \rightarrow 563-300+22 = 263+22=285$). Number line: jump by hundreds, then tens, then ones. In this problem, it's a word problem where the school had 476 students and 238 more enrolled, requiring addition to find total now; to solve, use standard algorithm—align by place value, add ones ($6+8=14$, carry 1), add tens ($7+3+1=11$, carry 1), add hundreds ($4+2+1=7$), answer 714. Choice B is correct because adding $476+238$ with regrouping correctly—ones $6+8=14$ (write 4 carry 1), tens $7+3+1=11$ (write 1 carry 1), hundreds $4+2+1=7$, giving 714. This accurately uses regrouping across multiple places. Choice A represents wrong operation (subtracted instead of adding, got 704 or similar error). This error typically happens when students confuse operations in word problems. To help students: Practice standard algorithm with clear alignment. Use vertical format, align by place value. For addition: 'Start with ones. $7+6=13$. That's more than 10, so regroup: write 3 in ones, carry 1 ten to tens column. Now tens: $4+8=12$, plus carried 1=$13$. Regroup: write 3 in tens, carry 1 hundred. Hundreds: $3+2=5$, plus carried 1=6. Answer: 633.' For subtraction: 'Start with ones. Can we do 3-8? No, so regroup: borrow 1 ten from tens (6 tens becomes 5 tens), add 10 ones (3 ones becomes 13 ones). Now: $13-8=5$. Tens: can we do 5-7? No, regroup: borrow 1 hundred (5 hundreds becomes 4), add 10 tens (5 tens becomes 15 tens). Now: $15-7=8$. Hundreds: $4-2=2$. Answer: 285.' Use base-ten blocks to show regrouping visually: trade 1 rod for 10 units, trade 1 flat for 10 rods. Practice regrouping with zeros: $400-137$ requires regrouping from hundreds to tens to ones. Teach place value strategy: break apart, add/subtract by place. Use number line for mental math visualization. For word problems, identify operation (joining=add, separating/comparing=subtract). Watch for: not regrouping when needed, regrouping incorrectly, subtracting smaller from larger without borrowing, place value errors, handling zeros incorrectly, wrong operation.

This question tests 2nd grade understanding of adding and subtracting within 1000 using strategies based on place value, properties of operations, and standard algorithms with regrouping (CCSS 2.NBT.B.7: Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones). When adding three-digit numbers like 347 + 286, use place value: add ones (7+6=13, write 3 carry 1), add tens (4+8+1=13, write 3 carry 1), add hundreds (3+2+1=6), result 633. When subtracting like 563 - 278, use regrouping: ones (can't do 3-8, regroup 6 tens 3 ones to 5 tens 13 ones, 13-8=5), tens (can't do 5-7, regroup 5 hundreds 5 tens to 4 hundreds 15 tens, 15-7=8), hundreds (4-2=2), result 285. Multiple regroupings often needed. In this problem, student must find missing addend in 347 + ___ = 633, which requires subtraction 633 - 347. To solve, use standard algorithm—align by place value, subtract with regrouping—regroup twice (tens and hundreds), calculate 286. Choice A is correct because subtracting 633-347 with regrouping correctly—regroup tens and hundreds as needed, 13-7=6, 12-4=8, 5-3=2, giving 286. This accurately uses regrouping across multiple places. Choice B represents didn't borrow correctly in subtraction (rounded or subtracted incorrectly without full regrouping, got 280 instead of 286). This error typically happens when students don't carry/borrow correctly, forget to regroup across multiple places, subtract in wrong direction when borrowing, misunderstand place value, confuse operations, don't handle zeros correctly. To help students: Practice standard algorithm with clear alignment. Use vertical format, align by place value. For addition: 'Start with ones. 7+6=13. That's more than 10, so regroup: write 3 in ones, carry 1 ten to tens column. Now tens: 4+8=12, plus carried 1 = 13. Regroup: write 3 in tens, carry 1 hundred. Hundreds: 3+2=5, plus carried 1=6. Answer: 633.' For subtraction: 'Start with ones. Can we do 3-8? No, so regroup: borrow 1 ten from tens (6 tens becomes 5 tens), add 10 ones (3 ones becomes 13 ones). Now: 13-8=5. Tens: can we do 5-7? No, regroup: borrow 1 hundred (5 hundreds becomes 4), add 10 tens (5 tens becomes 15 tens). Now: 15-7=8. Hundreds: 4-2=2. Answer: 285.' Use base-ten blocks to show regrouping visually: trade 1 rod for 10 units, trade 1 flat for 10 rods. Practice regrouping with zeros: 400-137 requires regrouping from hundreds to tens to ones. Teach place value strategy: break apart, add/subtract by place. Use number line for mental math visualization. For word problems, identify operation (joining=add, separating/comparing=subtract). Watch for: not regrouping when needed, regrouping incorrectly, subtracting smaller from larger without borrowing, place value errors, handling zeros incorrectly, wrong operation.

This question tests 2nd grade understanding of adding and subtracting within 1000 using strategies based on place value, properties of operations, and standard algorithms with regrouping (CCSS 2.NBT.B.7: Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones). When adding three-digit numbers like 347 + 286, use place value: add ones (7+6=13, write 3 carry 1), add tens (4+8+1=13, write 3 carry 1), add hundreds (3+2+1=6), result 633. When subtracting like 563 - 278, use regrouping: ones (can't do 3-8, regroup 6 tens 3 ones to 5 tens 13 ones, 13-8=5), tens (can't do 5-7, regroup 5 hundreds 5 tens to 4 hundreds 15 tens, 15-7=8), hundreds (4-2=2), result 285. Multiple regroupings often needed. Place value strategy: break into hundreds, tens, ones, add/subtract separately, combine. Mental math: use compensation (563-278 → 563-300+22 = 263+22=285). Number line: jump by hundreds, then tens, then ones. In this problem, use mental math to subtract 563 - 278. To solve, use mental math with compensation—563-278 → 563-300+22 = 263+22=285, or place value strategy. Choice C is correct because subtracting 563-278 with mental math compensation correctly—adjust 278 to 300 by adding 22, subtract 300 from 563 to get 263, add back 22 to get 285. This accurately uses regrouping across multiple places. Choice B represents subtracting without proper regrouping (subtracted smaller from larger in each place getting 315 instead of 285). This error typically happens when students don't borrow correctly, forget to regroup across multiple places, subtract in wrong direction when borrowing, misunderstand place value, confuse operations, don't handle zeros correctly. To help students: Practice standard algorithm with clear alignment. Use vertical format, align by place value. For addition: 'Start with ones. 7+6=13. That's more than 10, so regroup: write 3 in ones, carry 1 ten to tens column. Now tens: 4+8=12, plus carried 1 = 13. Regroup: write 3 in tens, carry 1 hundred. Hundreds: 3+2=5, plus carried 1=6. Answer: 633.' For subtraction: 'Start with ones. Can we do 3-8? No, so regroup: borrow 1 ten from tens (6 tens becomes 5 tens), add 10 ones (3 ones becomes 13 ones). Now: 13-8=5. Tens: can we do 5-7? No, regroup: borrow 1 hundred (5 hundreds becomes 4), add 10 tens (5 tens becomes 15 tens). Now: 15-7=8. Hundreds: 4-2=2. Answer: 285.' Use base-ten blocks to show regrouping visually: trade 1 rod for 10 units, trade 1 flat for 10 rods. Practice regrouping with zeros: 400-137 requires regrouping from hundreds to tens to ones. Teach place value strategy: break apart, add/subtract by place. Use number line for mental math visualization. For word problems, identify operation (joining=add, separating/comparing=subtract). Watch for: not regrouping when needed, regrouping incorrectly, subtracting smaller from larger without borrowing, place value errors, handling zeros incorrectly, wrong operation.

This question tests 2nd grade understanding of adding and subtracting within 1000 using strategies based on place value, properties of operations, and standard algorithms with regrouping (CCSS 2.NBT.B.7: Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones). When adding three-digit numbers like 347 + 286, use place value: add ones (7+6=13, write 3 carry 1), add tens (4+8+1=13, write 3 carry 1), add hundreds (3+2+1=6), result 633. When subtracting like 563 - 278, use regrouping: ones (can't do 3-8, regroup 6 tens 3 ones to 5 tens 13 ones, 13-8=5), tens (can't do 5-7, regroup 5 hundreds 5 tens to 4 hundreds 15 tens, 15-7=8), hundreds (4-2=2), result 285. Multiple regroupings often needed. In this problem, word problem requires subtracting 563 - 278 to find books left. To solve, use standard algorithm—align by place value, subtract with regrouping—regroup twice (tens and hundreds), calculate 285. Choice C is correct because subtracting 563-278 with regrouping correctly—regroup tens and hundreds as needed, 13-8=5, 15-7=8, 4-2=2, giving 285. This accurately uses regrouping across multiple places. Choice B represents didn't borrow correctly in subtraction (subtracted smaller from larger in each place getting 315 instead of 285, or subtracted top from bottom after borrowing). This error typically happens when students don't carry/borrow correctly, forget to regroup across multiple places, subtract in wrong direction when borrowing, misunderstand place value, confuse operations, don't handle zeros correctly. To help students: Practice standard algorithm with clear alignment. Use vertical format, align by place value. For addition: 'Start with ones. 7+6=13. That's more than 10, so regroup: write 3 in ones, carry 1 ten to tens column. Now tens: 4+8=12, plus carried 1 = 13. Regroup: write 3 in tens, carry 1 hundred. Hundreds: 3+2=5, plus carried 1=6. Answer: 633.' For subtraction: 'Start with ones. Can we do 3-8? No, so regroup: borrow 1 ten from tens (6 tens becomes 5 tens), add 10 ones (3 ones becomes 13 ones). Now: 13-8=5. Tens: can we do 5-7? No, regroup: borrow 1 hundred (5 hundreds becomes 4), add 10 tens (5 tens becomes 15 tens). Now: 15-7=8. Hundreds: 4-2=2. Answer: 285.' Use base-ten blocks to show regrouping visually: trade 1 rod for 10 units, trade 1 flat for 10 rods. Practice regrouping with zeros: 400-137 requires regrouping from hundreds to tens to ones. Teach place value strategy: break apart, add/subtract by place. Use number line for mental math visualization. For word problems, identify operation (joining=add, separating/comparing=subtract). Watch for: not regrouping when needed, regrouping incorrectly, subtracting smaller from larger without borrowing, place value errors, handling zeros incorrectly, wrong operation.