Mentally Add/Subtract 10 or 100 - 2nd Grade Math

1. What number added to 468 equals 478?
   Answer: 10 Since 468 plus 10 equals 478, 10 is the missing number. Choice A, 1, is too small to bridge the gap between 468 and 478. Choice B, 100, is too large and would give a sum far greater than 478. Choice C, 468, is the original number, not the amount added to it.
2. What is $805 - 10$?
   Answer: 795 This question tests 2nd grade understanding of mentally adding and subtracting 10 or 100 to/from three-digit numbers using place value patterns (CCSS 2.NBT.B.8: Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900). To mentally add or subtract 10 or 100, understand which place value digit changes: (1) Adding 10 means adding 1 ten, so tens digit increases by 1 ($376 + 10$: $7$ tens becomes $8$ tens = $386$; ones and hundreds stay same). (2) Subtracting 10 means subtracting 1 ten, so tens digit decreases by 1 ($376 - 10$: $7$ tens becomes $6$ tens = $366$). (3) Adding 100 means adding 1 hundred, so hundreds digit increases by 1 ($376 + 100$: $3$ hundreds becomes $4$ hundreds = $476$; tens and ones stay same). (4) Subtracting 100 means subtracting 1 hundred, so hundreds digit decreases by 1 ($528 - 100$: $5$ hundreds becomes $4$ hundreds = $428$). Describe pattern: Look only at the digit that changes—just add or subtract 1 from that digit, leave other digits alone. This makes calculation easy to do mentally without writing. In this problem, student must subtract 10 from 805 mentally. To solve mentally, identify operation (-10), identify which digit changes (tens for -10), change that digit by 1 (decrease for subtraction), keep other digits same: $805 - 10$ → tens $0 \to 9$ (borrowing from hundreds), but since 0 tens, borrow: hundreds $8 \to 7$, tens $0 \to 9$ (actually $10-1=9$), ones 5 same, answer 795. Choice A is correct because subtracting 10 from 805 means subtracting 1 from tens digit, but with borrowing (0 tens can't subtract 1, so borrow from hundreds: 8 hundreds become 7, 0 tens become 10, then $10-1=9$ tens), keeping ones (5) same, giving 795. This correctly identifies and changes only the appropriate place value digit with borrowing. Choice B represents specific error: subtracted 100 instead of 10, giving 705 instead of 795. This error typically happens when students confuse subtracting 10 with subtracting 100 or don't understand which place value changes with -10 vs -100. To help students: Teach place value explicitly—'Subtracting 10 means subtracting 1 ten. Which place is tens? Middle digit. So middle digit goes down by 1. Hundreds and ones stay same.' Use place value chart: write 805, show subtracting 10 changes only tens, but borrow: 8 hundreds → 7 hundreds | 0 tens → 9 tens | 5 ones = 795. Practice with hundreds: 'Subtracting 100 means subtracting 1 hundred. Which place? Leftmost digit. So leftmost digit goes down by 1. Tens and ones stay same.' Show patterns visually: 825, 815, 805, 795—notice only tens digit changes ($2 \to 1 \to 0 \to 9$), with borrowing when needed. Use number line: jump by 10s backward, notice pattern. Connect to skip counting: counting backward by 10s ($820, 810, 800...$) uses same skill. Practice mental calculation: 'Don't write. Just change one digit in your head.' Teach exceptions: $398 + 10$ requires regrouping ($9$ tens + $1$ ten = $10$ tens = $1$ hundred $0$ tens), $302 - 10$ requires borrowing ($0$ tens, borrow from hundreds). Watch for: changing wrong digit, changing wrong amount, confusing ±10 with ±100, not understanding place value, changing multiple digits.
3. Calculate mentally: $430 + 100$.
   Answer: 530 Adding 100 increases the hundreds digit by 1: $430+100=530$. Choice A adds only 10 instead of 100. Choice C subtracts 100 instead of adding. Choice D adds only 1 instead of 100.
4. When you add 10 to 534, which digit changes?
   Answer: Tens digit Adding 10 to 534 only changes the tens digit, moving it from 3 to 4, giving 544. Choice A is wrong because the hundreds and ones digits do not change when you add 10. Choice B is wrong because adding 10 never affects the hundreds place. Choice C is wrong because the ones digit stays the same when you add a multiple of ten.
5. Carlos counts $285$ jumping jacks. He wants to reach $385$ jumping jacks total. After doing $10$ more jumping jacks, how many more does he still need to do?
   Answer: $90$ more jumping jacks Carlos starts with 285, does 10 more to get 295 jumping jacks. He needs 385 total, so 385 - 295 = 90 more. Choice B forgets to add the 10 he already did. Choice C adds 10 to the difference instead of subtracting. Choice D makes an error in the final subtraction.
6. This pattern counts by 10s: 410, 420, 430. What comes next?
   Answer: 440 The correct answer is 440, because the pattern adds 10 each time, and 430 + 10 = 440. Choice A (431) adds only 1 instead of 10. Choice B (530) adds 100 instead of 10. Choice D (400) subtracts instead of adding.
7. What number comes next: 900, 800, 700, ___?
   Answer: 600 The pattern counts down by 100 each time, so after 700 comes 600. 701 mistakenly adds 1 instead of subtracting 100. 710 and 690 both subtract only 10 from 700 instead of subtracting the full 100.
8. Emma saves $164$ pennies in January. In February, she spends $10$ pennies on candy. In March, her grandmother gives her $100$ more pennies. What is the total number of pennies Emma has after March?
   Answer: $254$ pennies total Emma starts with 164 pennies, spends 10 to have 154, then receives 100 more: 154 + 100 = 254 pennies. Choice B adds all three numbers together. Choice C subtracts 100 instead of adding. Choice D makes an error by adding 10 instead of subtracting it initially.
9. What is $639 + 10$?
   Answer: 649 The correct answer is 649, because $639 + 10 = 649$. Choice B (739) adds 100 instead of 10. Choice C (629) subtracts 10 instead of adding it. Choice D (639) repeats the starting number without adding anything.
10. When you add 100 to 431, which digit changes?
    Answer: Hundreds digit Adding 100 changes only the hundreds digit: 431 becomes 531, since the hundreds digit goes from 4 to 5. Choice A is incorrect because the tens and ones digits stay the same. Choice C is incorrect because the ones digit isn't affected when adding a multiple of 100. Choice D is incorrect because the tens digit also stays the same.
11. Maya has 312 stickers and gets 10 more. How many stickers does she have now?
    Answer: 322 312 plus 10 equals 322, since adding 10 increases the tens digit by 1. 302 would result from subtracting 10 instead of adding it. 412 would result from adding 100 instead of 10. 313 would result from adding only 1 instead of 10.
12. What number completes the equation $672 + n = 682$?
    Answer: 10 The missing number is 10, because $672 + 10 = 682$ (the tens digit increases by 1, from 7 to 8). Choice A (100) adds a full hundred instead of a ten. Choice C (12) is close to 10 but doesn't produce the correct sum. Choice D (682) repeats the total instead of finding the missing addend.
13. Continue the pattern: 780, 770, 760, $\underline{\hspace{2em}}$.
    Answer: 750 This question tests 2nd grade understanding of mentally adding and subtracting 10 or 100 to/from three-digit numbers using place value patterns (CCSS 2.NBT.B.8: Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900). To mentally add or subtract 10 or 100, understand which place value digit changes: (1) Adding 10 means adding 1 ten, so tens digit increases by 1 (376 + 10: 7 tens becomes 8 tens = 386; ones and hundreds stay same). (2) Subtracting 10 means subtracting 1 ten, so tens digit decreases by 1 (376 - 10: 7 tens becomes 6 tens = 366). (3) Adding 100 means adding 1 hundred, so hundreds digit increases by 1 (376 + 100: 3 hundreds becomes 4 hundreds = 476; tens and ones stay same). (4) Subtracting 100 means subtracting 1 hundred, so hundreds digit decreases by 1 (528 - 100: 5 hundreds becomes 4 hundreds = 428). Describe pattern: Look only at the digit that changes—just add or subtract 1 from that digit, leave other digits alone. This makes calculation easy to do mentally without writing. In this problem, student must continue pattern of subtracting 10: 780, 770, 760, ___. To solve mentally, identify operation (-10 each time), identify which digit changes (tens for -10), change that digit by 1 (decrease for subtraction), keep other digits same: 760 - 10 → tens 6→5, answer 750. Choice A is correct because pattern 780, 770, 760 decreases by 10 each time (tens digit down by 1), so next is 750. This correctly identifies and changes only the appropriate place value digit. Choice B represents specific error: subtracted 100 instead of 10, giving 660 instead of 750. This error typically happens when students confuse subtracting 10 with subtracting 100 or don't recognize the pattern of changing tens. To help students: Teach place value explicitly—'Subtracting 10 means subtracting 1 ten. Which place is tens? Middle digit. So middle digit goes down by 1. Hundreds and ones stay same.' Use place value chart: write 760, show subtracting 10 changes only tens: 7 hundreds | 6 tens → 5 tens | 0 ones = 750. Practice with hundreds: 'Subtracting 100 means subtracting 1 hundred. Which place? Leftmost digit. So leftmost digit goes down by 1. Tens and ones stay same.' Show patterns visually: 780, 770, 760, 750—notice only tens digit changes (8→7→6→5), everything else same. Use number line: jump by 10s backward, notice pattern. Connect to skip counting: counting backward by 10s (780, 770, 760...) uses same skill. Practice mental calculation: 'Don't write. Just change one digit in your head.' Teach exceptions: 398 + 10 requires regrouping (9 tens + 1 ten = 10 tens = 1 hundred 0 tens), 302 - 10 requires borrowing (0 tens, borrow from hundreds). Watch for: changing wrong digit, changing wrong amount, confusing ±10 with ±100, not understanding place value, changing multiple digits.
14. What is $476 - 100$?
    Answer: 376 Subtracting 100 from 476 lowers the hundreds digit by one, giving 376. Choice A, 366, comes from subtracting 110 instead of 100. Choice C, 486, comes from adding 10 rather than subtracting 100. Choice D, 476, is the original number, as if nothing were subtracted.
15. Maya has 326 stickers and gets 100 more. How many stickers does she have now?
    Answer: 426 326 plus 100 equals 426, since adding 100 increases the hundreds digit by 1. 336 would result from adding only 10 instead of 100. 326 is Maya's starting amount, before getting more stickers. 226 would result from subtracting 100 instead of adding it.
16. A toy store starts the day with $513$ toys. They sell $10$ toys in the morning. A delivery truck brings $100$ new toys at noon. How many toys does the store have at the end of the day?
    Answer: $603$ toys available Store starts with 513 toys, sells 10 to have 503, then receives 100 more: 503 + 100 = 603 toys. Choice A only adds 10 to the original. Choice B subtracts both 10 and 100. Choice D adds both 10 and 100 to the original.
17. What is $390 + 10$?
    Answer: 400 The correct answer is 400, because $390 + 10 = 400$. Choice A (391) adds the 10 to the ones place instead of the tens place. Choice C (490) adds 100 instead of 10. Choice D (380) subtracts 10 instead of adding it.
18. A farmer picks $394$ apples from his orchard. He gives $100$ apples to the market and $10$ apples to his neighbor. How many apples does the farmer have left for his family?
    Answer: $284$ apples remaining Farmer starts with 394 apples, gives away 100 + 10 = 110 apples total. He has 394 - 110 = 284 apples left. Choice A adds instead of subtracts. Choice C only subtracts 10. Choice D only subtracts 100.
19. What comes next in the pattern: 850, 750, 650?
    Answer: 550 The correct answer is 550, because the pattern goes down by 100 each time, so 650 - 100 = 550. Choice A (640) subtracts 10 instead of 100. Choice C (600) subtracts only 50 instead of 100. Choice D (750) repeats a number already given in the pattern instead of continuing forward.
20. What is $267 + 100$?
    Answer: 367 Adding 100 to 267 increases the hundreds digit by one, giving 367. Choice B, 267, is the original number left unchanged, as if nothing were added. Choice C, 277, comes from adding only 10 instead of 100. Choice D, 257, comes from subtracting 10 rather than adding 100.

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