Add and Subtract Within 1000 - 2nd Grade Math

Sofia has 346 stickers and gets 289 more. How many altogether?
Answer: 635 The correct answer is 635, because 346 + 289 = 635. Choice A (545) makes a regrouping error in the ones place. Choice B (655) makes a regrouping error in the tens place. Choice C (625) is close but still off by ten from the correct sum.
What number, minus $276$ , equals $419$ ?
Answer: 695 Since the missing number minus 276 equals 419, add back: $419+276=695$ . Choice A is ten less than the correct sum. Choice B is what you get if you subtract instead of add ( $419-276=143$ ). Choice C is ten more than the correct sum.
What is $500 - 137$ ?
Answer: 363 Subtracting 137 from 500 gives 363. Choice B, 373, is off by a regrouping error. Choice C, 343, is also off due to a regrouping error. Choice D, 463, is much too large for this subtraction.
School had 476 students. 238 more enrolled. How many now?
Answer: 714 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.
Maya has 438 stickers and gets 129 more. How many altogether?
Answer: 567 The correct answer is 567, because 438 + 129 = 567. Choice A (577) makes a regrouping error in the tens place. Choice B (667) makes a regrouping error in the hundreds place. Choice D (557) is close but still off by ten from the correct sum.
Solve: $357 + 289$ . Use the standard algorithm.
Answer: 646 Adding the ones, tens, and hundreds with regrouping gives $357 + 289 = 646$ , so A is correct. Choice B is ten less, which can happen when a carried digit is dropped while regrouping the tens. Choice C is one hundred too high, which can happen from an extra carry into the hundreds place. Choice D is far too low and would result from mixing up addition with subtraction.
What is $563 - 278$ ?
Answer: $285$ 563 - 278 = 285, so Choice C is correct. Choice A is wrong because it does not regroup the tens correctly. Choice B is wrong because it does not regroup the hundreds correctly. Choice D is wrong because it is too far from the correct answer to reflect a small subtraction error.
What is $700 - 358$ ?
Answer: 342 Subtracting 358 from 700 gives 342. Choice A comes from not regrouping across the hundreds place correctly. Choice B is off by 110 from a larger regrouping mistake. Choice C is off by 10 from a smaller regrouping error in the tens place.
Solve: $803 - 467$ .
Answer: 336 Subtracting 467 from 803 with regrouping gives 336. Choice B, 436, comes from a borrowing error in the hundreds place. Choice C, 346, comes from a borrowing error in the tens place. Choice D, 266, comes from compounding regrouping mistakes across multiple place values.
Use mental math: $650 - 298$ .
Answer: 352 Subtracting 298 from 650 gives 352. Choice A, 342, comes from a small subtraction slip in the tens place. Choice C, 452, comes from a regrouping error that adds instead of subtracts one hundred. Choice D, 358, comes from a small subtraction slip in the ones place.
What is $352 + 489$ ?
Answer: 841 Adding 352 and 489 gives 841. Choice A is off by 10 from a mistake carrying a regrouped ten. Choice C is off by 10 in the other direction. Choice D is off by 100 from a mistake regrouping the hundreds.
What is $392 + 185$ ?
Answer: 577 Adding 392 and 185 gives 577. Choice A is off by 10, a common error when regrouping the tens incorrectly. Choice B is off by 100, from a mistake regrouping the hundreds. Choice D is off by 10 in the other direction, from adding one extra ten.
What is $586 - 239$ ?
Answer: 347 Subtracting 239 from 586 gives 347. Choice A is off by 100 from a mistake regrouping the hundreds. Choice B is off by 10 in the other direction. Choice C is off by 10 from an error in the tens place.
What is $409 + 378$ ?
Answer: 787 The correct answer is 787, because $409 + 378 = 787$ (ones: $9+8=17$ , write 7 carry 1; tens: $0+7+1=8$ ; hundreds: $4+3=7$ ). Choice A (887) comes from an error in the hundreds place, adding one too many hundreds. Choice B (777) comes from an error in the tens place. Choice C (697) comes from an error carrying between the ones and tens places.
Calculate $709 - 465$ . Regroup if needed.
Answer: 244 244 is correct because subtracting 465 from 709 with proper regrouping gives 244. Choice A, 274, comes from a regrouping mistake in the tens place. Choice C, 254, comes from a small error in the ones place after regrouping. Choice D, 344, comes from failing to regroup the hundreds place correctly.
The library had 563 books. 278 were checked out. How many books are left?
Answer: 285 Subtracting the checked-out books from the total gives $563 - 278 = 285$ , so B is correct. Choice A comes from a regrouping slip while subtracting across place values. Choice C comes from adding the two numbers instead of subtracting them. Choice D is a different regrouping slip that overstates how many books remain.
What is $468 + 257$ ?
Answer: 725 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.
What is $704 - 268$ ?
Answer: 436 Subtracting 268 from 704 gives 436. Choice B, 442, is off by a small regrouping error. Choice C, 446, is also off due to a regrouping error. Choice D, 536, is much too large for this subtraction.
The library had 563 books. 278 were checked out. How many were left?
Answer: 285 There were 285 books left, because $563 - 278 = 285$ . Choice A (345) and Choice D (315) come from borrowing errors during subtraction. Choice C (841) comes from adding the two numbers instead of subtracting.
What number added to 347 equals 633?
Answer: 286 Since 347 plus 286 equals 633, 286 is the missing number. Choice A, 280, is close but does not make the equation true. Choice B, 633, is the total itself, not the missing addend. Choice C, 347, is the number already given in the problem.

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