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Solve Two-Step Multi-Operation Problems - 3rd Grade Math

  1. Zoe has 90 minutes to play. She spends 35 minutes reading, then splits the remaining time into 5 equal parts. How many minutes are in each part?
    Answer: 11 minutes After reading, Zoe has 90 minus 35, which is 55 minutes left, and splitting 55 minutes into 5 equal parts gives 11 minutes each, matching choice C. Choice A is the remaining time before it is split into parts. Choices B and D come from dividing the remaining time incorrectly.
  2. Emma collected 84 seashells at the beach. She gave 27 shells to her sister and then found 19 more shells. Which equation, using n for her final number of shells, correctly represents this situation?
    Answer: n=84−27+19n = 84 - 27 + 19 Emma starts with 84 shells, gives away 27 (subtract), then finds 19 more (add), so the equation is n=84−27+19n = 84 - 27 + 19, making Choice D correct. Choice A adds 27 instead of subtracting it, reversing what actually happened to those shells. Choice B subtracts both numbers instead of adding the 19 she found. Choice C multiplies instead of subtracting, which does not match giving shells away.
  3. Grace picks 64 apples. She gives 16 apples away. She packs the rest equally into 8 bags. How many apples per bag?
    Answer: 6 apples per bag 6 apples per bag is correct because 64 minus 16 equals 48 apples, and 48 divided by 8 equals 6. 48 apples per bag is incorrect because it stops after subtracting and skips dividing by the number of bags. 10 apples per bag is incorrect because it does not match dividing 48 by 8. 8 apples per bag is incorrect because it repeats the number of bags instead of giving the quotient.
  4. Liam has 7 red marbles and 5 blue marbles. He has 3 times as many green marbles as the number of red and blue marbles combined. How many green marbles does he have?
    Answer: 36 marbles The red and blue marbles combined total 7 plus 5, or 12, and 3 times 12 is 36 green marbles. Choice A is only the combined total of red and blue marbles, without multiplying by 3. Choice B comes from multiplying only the red marbles by 3. Choice C comes from an addition error.
  5. A store has 64 balloons. It sells 16 balloons, then shares the rest equally into 6 bags. How many balloons per bag?
    Answer: 8 balloons per bag After selling 16 of the 64 balloons, 48 remain, and sharing 48 balloons equally into 6 bags gives 8 balloons per bag. Choice A comes from a division error. Choice B is the number of balloons remaining before sharing, not the amount per bag. Choice C comes from dividing by the wrong number.
  6. A library has 72 books. 18 books are checked out. The rest are placed equally on 9 shelves. How many books per shelf?
    Answer: 6 books per shelf 72 minus 18 leaves 54 books, and 54 divided by 9 equals 6 books per shelf, so A is correct. Choice B (10) does not match dividing 54 by 9. Choice C (8) is close to but not equal to the correct quotient. Choice D (54) is the number of books remaining before dividing them among the shelves, not the final answer.
  7. There are 45 cookies shared equally into 9 bags. How many cookies are in each bag?
    Answer: 5 cookies per bag The 45 cookies are shared equally among 9 bags, so 45 divided by 9 equals 5 cookies per bag, making Choice C correct. Choice A (9 cookies per bag) mixes up the number of bags with the number of cookies in each bag. Choice B (36 cookies per bag) comes from subtracting 9 from 45 instead of dividing. Choice D (4 cookies per bag) is an off-by-one division error.
  8. Read the problem. Liam has $60 and buys 7 notebooks for $6 each. How much money is left?
    Answer: $24 This question tests solving two-step word problems using multiple operations (CCSS.3.OA.8), specifically using multiplication and subtraction to solve a problem, representing it with an equation, and checking reasonableness. Two-step problems require two operations to solve—you can't find the answer in just one step. Strategy: (1) Read carefully and identify what you know and what you need to find. (2) Determine which operations are needed and in what order. (3) Do step 1, then use that result in step 2. (4) Write an equation using a letter for the unknown (like n, x, or s). (5) Check if answer is reasonable using estimation. Example: "Had 24 stickers, bought 3 packs of 8, how many now?" Step 1: Find stickers bought: 3×8=243 \times 8 = 24. Step 2: Add to original: 24+24=4824 + 24 = 48. Equation: 24+3×8=s24 + 3 \times 8 = s or s=24+3×8s = 24 + 3 \times 8. Check: About 20+30=50, so 48 is reasonable. In this problem, Liam starts with $60 and buys 7 notebooks at $6 each, asking how much money is left. This requires multiplication to find the total cost, then subtraction to find the remainder. Choice A is correct because Step 1: 7×6=427 \times 6 = 42 spent. Step 2: 60−42=1860 - 42 = 18 left. Equation: s=60−7×6=18s=60-7\times6=18. This answer is reasonable because 7 notebooks at about $5 each cost around $35, leaving about $25 from $60, but actual $42 spent leaves $18, which is close. Choice B is incorrect because it represents the total spent (7×6=427\times6=42) without subtracting from 60. This error occurs when students stop after one step. To help students solve two-step problems: Teach systematic approach: read, identify knowns/unknowns, plan operations, solve step-by-step, check. Model writing equations with unknowns (use letters students choose). Practice estimation BEFORE solving: "About 20+30=50" helps catch errors. Check reasonableness: "Does 847 stickers make sense from buying 3 packs? No!" Use bar models or diagrams to visualize steps. Emphasize order of operations: parentheses matter—(12+8)÷4≠12+8÷4(12+8) \div 4 \neq 12 + 8 \div 4. Connect to real life: students naturally solve two-step problems (saved $5 per week for 4 weeks, spent $12, how much left?). Watch for students who add all numbers regardless of context, or who stop after one step.
  9. At a soccer game, there are 88 rows of seats with 1515 seats in each row. If 3838 seats are empty, how many people are sitting in the seats?
    Answer: 8282 people are sitting in the seats There are 8 times 15, or 120, total seats. Subtracting the 38 empty seats gives 120 minus 38, which is 82 people sitting. Choice A, 77 people, comes from a subtraction error. Choice B, 158 people, comes from adding the empty seats instead of subtracting them. Choice C, 102 people, comes from an error in finding the total number of seats before subtracting.
  10. Jada collects 9 shells on Monday and 15 shells on Tuesday. She makes 4 equal groups of shells. How many shells are in each group?
    Answer: 6 shells per group Jada has 9 plus 15, which is 24 shells total, and dividing 24 by 4 equal groups gives 6 shells per group, matching choice B. Choice A is the total number of shells before dividing into groups. Choices C and D come from dividing the total incorrectly.
  11. 48 cookies are shared equally into 8 bags. How many cookies are in each bag?
    Answer: 6 cookies per bag 6 cookies per bag is correct because 48÷8=648 \div 8 = 6. 8 cookies per bag is incorrect; that's the number of bags, not the cookies in each one. 40 cookies per bag is incorrect because it comes from subtracting instead of dividing. 16 cookies per bag is incorrect; it doesn't result from dividing 48 by 8.
  12. Ben has 30 stickers. He gives 6 stickers to a friend. He shares the rest equally among 8 pages in a notebook. How many stickers are on each page?
    Answer: 3 stickers per page Ben has 30 stickers, gives away 6, leaving 24, then divides them evenly among 8 pages: 24 divided by 8 is 3 stickers per page, so Choice C is correct. Choice A (24 stickers per page) is the number of stickers left before dividing among the pages. Choice B (5 stickers per page) does not match dividing 24 by 8. Choice D (6 stickers per page) comes from dividing the original 30 stickers by 5 instead of solving the problem as given.
  13. Tia picked 15 apples and 9 more apples. She puts them equally into 6 bags. How many apples are in each bag?
    Answer: 4 apples per bag Tia has 15 plus 9, or 24 apples total, and 24 divided by 6 equals 4 apples per bag. Choice A (6) matches the number of bags instead of the answer. Choice B (24) is the total number of apples, not the amount per bag. Choice C (3) comes from dividing incorrectly.
  14. Ella has 9 pencils. Her teacher gives her 5 more packs with 4 pencils each. How many pencils does she have altogether?
    Answer: 29 pencils The 5 packs give 5 times 4, or 20 pencils. Adding those to her original 9 pencils gives 9 plus 20, which is 29 pencils altogether. Choice A, 14 pencils, comes from adding 9 and 5 and ignoring the pencils per pack. Choice C, 25 pencils, comes from a small error in adding the pencils from the packs to her original amount. Choice D, 20 pencils, only counts the new pencils and leaves out the 9 she started with.
  15. A class has 8 tables with 4 students at each table. Then 7 more students join the class. How many students are in the class now?
    Answer: 39 students 39 students is correct because 8 times 4 equals 32, and 32 plus 7 equals 39. 32 students is incorrect because it only counts the students at the tables and leaves out the 7 who joined. 47 students is incorrect because it does not match adding 7 to 32. 15 students is incorrect because it does not match the given numbers.
  16. Ella has 90 minutes to play. She spends 6 minutes on each of 8 levels. How many minutes does she have left?
    Answer: 42 minutes Ella spends 6 minutes on each of 8 levels, which is 6 times 8, or 48 minutes total. Subtracting 48 from 90 leaves 42 minutes, matching choice C. Choice A is the total time spent on levels, not the time left. Choices B and D come from incorrect subtraction.
  17. A teacher has 16 pencils. She buys 5 packs with 7 pencils in each pack. How many pencils does she have altogether?
    Answer: 51 pencils 51 pencils is correct because 5×7=355 \times 7 = 35 new pencils, and 35+16=5135 + 16 = 51 pencils total. 35 pencils is incorrect; it's only the pencils from the new packs, without adding the 16 she already had. 28 pencils is incorrect because it doesn't match 5×75 \times 7. 56 pencils is incorrect; it doesn't correspond to either step of the problem.
  18. There are 64 cookies shared equally into 8 bags. How many cookies are in each bag?
    Answer: 8 cookies per bag The 64 cookies are shared equally among 8 bags, so 64 divided by 8 equals 8 cookies per bag, making Choice A correct. Choice B (56 cookies per bag) comes from subtracting 8 from 64 instead of dividing. Choice C (72 cookies per bag) comes from adding 8 to 64 instead of dividing. Choice D (6 cookies per bag) would be correct only if there were 48 cookies instead of 64.
  19. Noah collects 15 cans on Monday and 21 cans on Tuesday. He puts them equally into 6 bags. How many cans per bag?
    Answer: 6 cans per bag This question tests solving two-step word problems using multiple operations (CCSS.3.OA.8), specifically using addition and division to solve a problem, representing it with an equation, and checking reasonableness. Two-step problems require two operations to solve—you can't find the answer in just one step. Strategy: (1) Read carefully and identify what you know and what you need to find. (2) Determine which operations are needed and in what order. (3) Do step 1, then use that result in step 2. (4) Write an equation using a letter for the unknown (like n, x, or s). (5) Check if answer is reasonable using estimation. In this problem, Noah collects 15 cans on Monday and 21 on Tuesday, then divides them equally into 6 bags. This requires addition to find the total cans, then division to find cans per bag. Choice B is correct because Step 1: 15+21=36 total cans. Step 2: 36÷6=6 cans per bag. Equation: c=(15+21)÷6=6. This answer is reasonable because about 36 cans divided into 6 bags gives 6 per bag. Choice A (9 cans) is incorrect because it appears to divide only the Tuesday cans (21÷6=3.5, rounded up or miscomputed as 9), ignoring Monday's collection. This error occurs when students don't add all quantities before dividing. To help students solve two-step problems: Teach systematic approach: read, identify knowns/unknowns, plan operations, solve step-by-step, check. Model writing equations with parentheses to show order: (15+21)÷6. Practice estimation: "About 40 cans in 6 bags is about 6-7 per bag." Use diagrams to show combining collections before dividing. Emphasize reading carefully: "equally into 6 bags" means divide the TOTAL, not just part.
  20. A farmer plants 99 rows of corn with 2828 seeds in each row. Birds eat 4545 of the seeds before they can grow. The farmer estimates that about 200200 seeds are left to grow. Which reasoning best evaluates this estimate?
    Answer: The estimate is too low because 10×30−50=25010 \times 30 - 50 = 250 seeds left Round 9 to 10, 28 to 30, and 45 to 50. Calculate: 10 × 30 - 50 = 300 - 50 = 250 seeds left. Since 250 > 200, the estimate is too low. Choice B doesn't round 9 to 10. Choice C rounds 28 down to 25, which is less accurate. Choice D has correct calculation but wrong conclusion about the estimate.

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