Add and Subtract Within 100 - 2nd Grade Math

1. What is $46 + 27$?
   Answer: 73 46 + 27 equals 73. A student might get 72 by making a small error when adding the ones. A student might get 83 by adding the tens incorrectly. A student might get 63 by forgetting to regroup the ones into a new ten. Adding the ones first, then the tens, and regrouping carefully leads to 73.
2. What number added to 47 equals 75?
   Answer: 28 Since 47 plus 28 equals 75, 28 is the missing number. Choice A, 75, is the total itself, not the missing addend. Choice B, 47, is the number already given in the problem. Choice C, 25, is close to the answer but does not make the equation true.
3. What is $67 - 19$?
   Answer: 48 67 − 19 = 48. One way: 67 − 20 = 47, then add 1 back to get 48. 38 takes away one ten too many. 58 subtracts only the 9 and forgets the ten. 49 is 1 too many.
4. Sofia has 90 points and loses 38. How many points does she have left?
   Answer: 52 Subtracting 38 from 90 gives 52. Choice A, 58, does not match this subtraction. Choice B, 62, is too large for this difference. Choice C, 48, is close but off by a regrouping error.
5. Maya has 39 stickers and gets 24 more. How many stickers does Maya have now?
   Answer: 63 Maya starts with 39 stickers and gets 24 more, so $39 + 24 = 63$. Choice B is one less than the correct total. Choice C mistakenly adds an extra ten. Choice D subtracts instead of adding.
6. What is $90 - 48$?
   Answer: 42 Subtracting, $90 - 48 = 42$, so D is correct. Choice A repeats one of the numbers from the problem instead of solving it. Choice B is ten less than the correct difference, likely from a regrouping slip in the tens place. Choice C is ten more than the correct difference for a similar reason.
7. Maya has 58 beads and gets 17 more. How many beads does Maya have now?
   Answer: 75 Maya starts with 58 beads and gets 17 more, so add 58 + 17 to get 75. Choice A, 65, is too small for this sum. Choice B, 85, is too large. Choice C, 74, is off by one from the correct total.
8. In Week 1, students read 42 books. In Week 2, students read 47 books. What is the total number of books read during both weeks?
   Answer: 89 books Adding the 42 books from Week 1 and the 47 books from Week 2 gives a total of 89 books read during both weeks. Getting 67 or 91 usually comes from a small addition mistake. Getting 47 only counts the books read in Week 2 and leaves out Week 1 entirely. Adding both weeks together, not just one, gives the correct combined total of 89.
9. Refer to the table below, which shows how many books each student read this month. How many more books did Rosa and Kim read together than Jack?
   Answer: $27$ Rosa + Kim = $28 + 17 = 45$. Then $45 - 18 = 27$. Choice B subtracts before adding correctly ($28-17+...$ common trap). Choice C adds all three: $28+17+18=63$. Choice D forgets to regroup in the final subtraction.
10. Ben scored $38$ points in his first game and $27$ points in his second game. Sarah scored $19$ more points than Ben's total. How many points did Sarah score?
    Answer: 84 Ben scored 38 + 27 = 65 points in total, and Sarah scored 19 more than that, so Sarah scored 65 + 19 = 84 points. Getting 57 comes from adding 19 only to Ben's first game instead of his total. Getting 65 is Ben's total, but it forgets to add the extra 19 points Sarah scored. Getting 46 comes from adding 19 only to Ben's second game instead of his total.
11. Use the number line to add $34 + 27$.
    Answer: 61 This question tests 2nd grade understanding of adding and subtracting within 100, including using regrouping (carrying and borrowing) when necessary (CCSS 2.NBT.B.5: Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; CCSS 2.NBT.B.7: Add and subtract within 1000, using strategies and algorithms based on place value—focus here on within 100). When adding two-digit numbers, add ones first, then tens. If the ones sum is 10 or more, regroup: write the ones digit and carry 1 ten to the tens column (example: 47 + 28 → 7 + 8 = 15, write 5 and carry 1 → 4 + 2 + 1 = 7 → answer is 75). When subtracting, subtract ones first, then tens. If the ones digit in the top number is smaller than the ones digit in the bottom number, regroup (borrow): take 1 ten from the tens column and add 10 to the ones (example: 63 - 27 → can't do 3 - 7, so regroup 6 tens 3 ones into 5 tens 13 ones → 13 - 7 = 6, 5 - 2 = 3 → answer is 36). Place value strategy: Break numbers into tens and ones, add or subtract separately, combine (47 + 28 = 40 + 20 + 7 + 8 = 60 + 15 = 75). Number line: Start at first number, jump by tens then ones to add, or jump backward to subtract. In this problem, use the number line to add 34 + 27. To solve, on a number line start at 34, jump 20 to 54, then 7 to 61, or add ones: 4 + 7 = 11 (write 1, carry 1), tens: 3 + 2 + 1 = 6, answer 61. Choice C is correct because adding 34 + 27 using number line or algorithm—jump +20 to 54, +7 to 61, or with regrouping: 4 + 7 = 11 (write 1, carry 1), 3 + 2 + 1 = 6, giving 61. This correctly applies addition with regrouping. Choice A represents a basic fact error (perhaps 34 + 17 = 51 or misjumped on number line). This error typically happens when students make arithmetic mistakes, miscount jumps on the number line, or forget to carry. To help students: Teach regrouping explicitly with place value understanding. For addition: 'When ones add to 10 or more, we have too many ones. Group 10 ones into 1 ten. Write the remaining ones, carry the 1 ten.' Use base-ten blocks: 4 tens + 7 ones + 2 tens + 8 ones → combine ones (7 + 8 = 15 ones = 1 ten + 5 ones), combine tens (4 + 2 + 1 = 7 tens) → 75. For subtraction: 'If top ones < bottom ones, we need more ones. Borrow 1 ten (= 10 ones) from tens column.' Show with blocks: 6 tens 3 ones, need to subtract 7 ones (can't), so trade 1 ten for 10 ones (5 tens 13 ones), now can subtract. Practice standard algorithm vertically—align place values, work ones first then tens. Teach number line strategy: to add, jump forward; to subtract, jump backward. For word problems, identify operation: 'got more, combine, total' = add; 'gave away, left, how many more' = subtract. Practice mental math strategies: break apart by tens and ones, use friendly numbers. Watch for: not regrouping when needed, regrouping incorrectly (carrying/borrowing wrong amount), place value errors, wrong operation for context, basic arithmetic mistakes.
12. Use the number line to add $27 + 36$.
    Answer: 63 Start at 27 on the number line, jump 30 to 57, then jump 6 more to 63. So 27 + 36 = 63. The answer 53 misses the ten made by 7 + 6. The answer 62 uses 7 + 6 = 12, and 73 adds one ten too many.
13. Keisha had 64 stickers and gave away 29. How many stickers did Keisha have left?
    Answer: 35 64 minus 29 equals 35, so Keisha has 35 stickers left. 93 comes from adding instead of subtracting the two numbers. 45 comes from a regrouping mistake in the tens place. 43 comes from a smaller regrouping error in the ones place.
14. Use place value to solve $56 + 38$.
    Answer: 94 Using place value, 50 plus 30 is 80 and 6 plus 8 is 14, and 80 plus 14 gives 94. Choice B, 92, comes from a small addition slip in the ones place. Choice C, 84, comes from miscombining the tens and ones. Choice D, 104, comes from adding an extra ten.
15. Use a number line to add $56 + 18$. What is the sum?
    Answer: 74 Adding 56 and 18 on a number line gives 74. Choice A is 1 less than the correct sum, from a small counting error. Choice B is 10 more than the correct sum. Choice D is 10 less than the correct sum.
16. Start at 52, move 18 spaces to the left, then move 25 spaces to the right. Where do you end up?
    Answer: At 59 Starting at 52 and moving 18 to the left gives 34, then moving 25 to the right gives 59. Choice B, 61, does not match this two-step move. Choice C, 95, is much too large for these moves. Choice D, 34, only accounts for the first move and stops before the second one.
17. There are 62 students. 27 go home. How many students are left?
    Answer: 35 Since 27 students go home, subtract: $62 - 27 = 35$. Choice B adds instead of subtracting. Choices C and D reflect small subtraction errors.
18. There were 78 students. 26 went home. How many are left?
    Answer: 54 This question tests 2nd grade understanding of adding and subtracting within 100, including using regrouping (carrying and borrowing) when necessary (CCSS 2.NBT.B.5: Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; CCSS 2.NBT.B.7: Add and subtract within 1000, using strategies and algorithms based on place value—focus here on within 100). When adding two-digit numbers, add ones first, then tens. If the ones sum is 10 or more, regroup: write the ones digit and carry 1 ten to the tens column (example: 47 + 28 → 7 + 8 = 15, write 5 and carry 1 → 4 + 2 + 1 = 7 → answer is 75). When subtracting, subtract ones first, then tens. If the ones digit in the top number is smaller than the ones digit in the bottom number, regroup (borrow): take 1 ten from the tens column and add 10 to the ones (example: 63 - 27 → can't do 3 - 7, so regroup 6 tens 3 ones into 5 tens 13 ones → 13 - 7 = 6, 5 - 2 = 3 → answer is 36). Place value strategy: Break numbers into tens and ones, add or subtract separately, combine (47 + 28 = 40 + 20 + 7 + 8 = 60 + 15 = 75). Number line: Start at first number, jump by tens then ones to add, or jump backward to subtract. In this problem, there were 78 students and 26 went home, a word problem requiring subtraction to find how many are left. To solve, subtract 78 - 26: ones 8 - 6 = 2 (no borrow needed), tens 7 - 2 = 5, answer 52, or use place value: 70 - 20 = 50, 8 - 6 = 2, total 52. Choice C is correct because subtracting 78 - 26 correctly—8 - 6 = 2, 7 - 2 = 5, giving 52, or in context: 78 total, 26 left, 52 remain. This correctly applies subtraction without regrouping to the word problem. Choice B represents a wrong operation (perhaps added 78 + 26 = 104 but that's not an option, or miscalculated as 62 by borrowing unnecessarily or arithmetic error). This error typically happens when students confuse operations (add instead of subtract), make arithmetic mistakes, or don't understand word problem keywords like 'left'. To help students: Teach regrouping explicitly with place value understanding. For addition: 'When ones add to 10 or more, we have too many ones. Group 10 ones into 1 ten. Write the remaining ones, carry the 1 ten.' Use base-ten blocks: 4 tens + 7 ones + 2 tens + 8 ones → combine ones (7 + 8 = 15 ones = 1 ten + 5 ones), combine tens (4 + 2 + 1 = 7 tens) → 75. For subtraction: 'If top ones < bottom ones, we need more ones. Borrow 1 ten (= 10 ones) from tens column.' Show with blocks: 6 tens 3 ones, need to subtract 7 ones (can't), so trade 1 ten for 10 ones (5 tens 13 ones), now can subtract. Practice standard algorithm vertically—align place values, work ones first then tens. Teach number line strategy: to add, jump forward; to subtract, jump backward. For word problems, identify operation: 'got more, combine, total' = add; 'gave away, left, how many more' = subtract. Practice mental math strategies: break apart by tens and ones, use friendly numbers. Watch for: not regrouping when needed, regrouping incorrectly (carrying/borrowing wrong amount), place value errors, wrong operation for context, basic arithmetic mistakes.
19. Solve $63 - 27$.
    Answer: 36 The difference between 63 and 27 is 36, found by regrouping a ten to subtract the ones. Choosing 34 or 44 comes from a small subtraction error somewhere in the regrouping steps. Choosing 46 suggests adding instead of subtracting the two numbers.
20. What is $36 + 29$?
    Answer: 65 36 plus 29 equals 65, which is the correct sum. Choosing 55 comes from a small addition error, ten less than the correct total. Choosing 75 comes from a small addition error, ten more than the correct total. Choosing 64 is just one less than the correct sum, a minor counting mistake.

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