Solve Multi-Step Word Problems

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4th Grade Math › Solve Multi-Step Word Problems

Questions 1 - 10
1

A school has 157 students going to a museum. Each van holds 6 students. How many vans are needed to take all the students? Estimate first, then find the exact answer and decide what to do with any remainder.

27 vans

26 vans

26 vans with 1 student left out

25 vans

Explanation

This question tests 4th grade ability to solve multistep word problems with whole numbers using the four operations, including interpreting remainders, representing with equations using variables, and assessing reasonableness with estimation (CCSS.4.OA.3). Multi-step problems require performing two or more operations in the correct order to reach the answer. Students must identify what operations are needed (addition, subtraction, multiplication, or division) based on the problem context, perform them in logical sequence, and ensure each step builds toward the final answer. For problems with division, remainders must be interpreted based on context—sometimes round up (need whole vans), sometimes round down (complete groups only), sometimes the remainder is the answer (how many left over). This problem requires 1 main step with remainder interpretation: divide 157 by 6; the sequence is 157 ÷ 6 = 26 r1. The context requires rounding up because all students must go, so an extra van is needed for the 1 leftover student. Choice B is correct because following the steps: 157 ÷ 6 = 26 r1, rounding up to 27 vans to accommodate all; estimation check: 160 ÷ 6 ≈26.7, rounding up to 27, close to exact 27 vans. Choice A represents using only the quotient without interpreting the remainder, which happens when students don't consider the context for needing to include everyone. To help students: Read carefully and identify ALL steps needed before starting. Determine what to find first, then what to do with that result. Write out steps or use mental notes: Step 1 finds quotient and remainder, Step 2 interprets based on context. For remainder problems, consider context: 'How many vans NEEDED' means round UP (26 r1 → need 27 vans). Use variables to represent unknowns: Let v = number of vans, then v = ceil(157 ÷ 6) = 27. Check reasonableness: estimate by rounding (160 ÷ 6 ≈27), close to exact 27 ✓. Practice breaking complex problems into steps. Watch for: stopping after first step, wrong operation choice, computing in wrong order, misinterpreting remainders, and arithmetic errors.

2

Amir is setting up chairs for a show. He sets up 14 rows with 8 chairs in each row. Then 17 more chairs are brought in and added to the total. How many chairs are there altogether? Estimate first, then find the exact answer.

129 chairs

131 chairs

95 chairs

112 chairs

Explanation

This question tests 4th grade ability to solve multistep word problems with whole numbers using the four operations, including interpreting remainders, representing with equations using variables, and assessing reasonableness with estimation (CCSS.4.OA.3). Multi-step problems require performing two or more operations in the correct order to reach the answer. Students must identify what operations are needed (addition, subtraction, multiplication, or division) based on the problem context, perform them in logical sequence, and ensure each step builds toward the final answer. For problems with division, remainders must be interpreted based on context—sometimes round up (need whole vans), sometimes round down (complete groups only), sometimes the remainder is the answer (how many left over). This problem requires two steps: multiply rows by chairs per row, then add additional chairs. The sequence is: 14 × 8 = 112 initial, then 112 + 17 = 129 total. Choice A is correct because following the steps: Step 1: 14 × 8 = 112, Step 2: 112 + 17 = 129 chairs. Estimation check: 10 × 8 = 80, but 14 × 8 ≈112, +20 ≈132, close to exact 129. Choice B represents only the multiplication without adding, which happens when students don't continue through all steps. To help students: Read carefully and identify ALL steps needed before starting. Determine what to find first, then what to do with that result. Write out steps or use mental notes: Step 1 multiplies to 112, Step 2 adds 17 to find 129. Use variables to represent unknowns: Let c = chairs total, then c = (14 × 8) + 17. Check reasonableness: estimate by rounding (14 × 10 ≈140 +20 ≈160, but adjust for 8 to ≈112 +17=129 ✓). Practice breaking complex problems into steps. Watch for: stopping after first step, wrong operation choice, computing in wrong order, misinterpreting remainders, and arithmetic errors.

3

Carlos is making party bags. He has 95 pieces of candy. He puts 7 candies in each bag. How many complete bags can he make, and how many candies will be left over?

12 complete bags and 11 candies left

14 complete bags and 3 candies left

13 complete bags and 4 candies left

13 complete bags and 3 candies left

Explanation

This question tests 4th grade ability to solve multistep word problems with whole numbers using the four operations, including interpreting remainders, representing with equations using variables, and assessing reasonableness with estimation (CCSS.4.OA.3). Multi-step problems require performing two or more operations in the correct order to reach the answer. For problems with division, remainders must be interpreted based on context—sometimes round up (need whole vans), sometimes round down (complete groups only), sometimes the remainder is the answer (how many left over). This problem requires 1 step with remainder interpretation: divide total candies by candies per bag. The sequence is: 95 ÷ 7 = 13 remainder 4. The context asks for complete bags AND leftover candies. Choice A is correct because following the steps: Step 1: 95 ÷ 7 = 13 R4, meaning 13 complete bags can be made with 4 candies left over. This matches the context which asks for both complete bags (quotient = 13) and leftover candies (remainder = 4). Verification: 13 bags × 7 candies = 91 candies used, and 95 - 91 = 4 candies left over ✓. Choice C represents an arithmetic error in division, getting the wrong remainder. To help students: For remainder problems, understand what each part means - quotient is complete groups, remainder is what's left. Practice checking division: multiply quotient by divisor and add remainder to verify it equals the dividend (13 × 7 + 4 = 91 + 4 = 95 ✓). Watch for common errors in long division that lead to wrong remainders. Always verify your answer makes sense in the problem context.

4

Maya buys 4 notebooks that cost $7 each. She also buys a pencil case for $9. She pays with $50. Estimate first, then find the exact amount of change Maya should get back. How many dollars of change is that?

19 dollars

13 dollars

22 dollars

50 dollars

Explanation

This question tests 4th grade ability to solve multistep word problems with whole numbers using the four operations, including interpreting remainders, representing with equations using variables, and assessing reasonableness with estimation (CCSS.4.OA.3). Multi-step problems require performing two or more operations in the correct order to reach the answer. Students must identify what operations are needed (addition, subtraction, multiplication, or division) based on the problem context, perform them in logical sequence, and ensure each step builds toward the final answer. This problem requires 3 steps: multiply to find notebook cost, add the pencil case cost, then subtract from payment amount. The sequence is: 4 × $7 = $28, then $28 + $9 = $37, then $50 - $37 = $13. Choice A is correct because following the steps: Step 1: 4 notebooks × $7 = $28, Step 2: $28 + $9 = $37 total cost, Step 3: $50 - $37 = $13 change. Estimation check: rounding gives 4 × $7 ≈ $30, plus $10 ≈ $40 total, $50 - $40 ≈ $10, close to exact answer $13, confirming reasonableness. Choice C represents using only the payment amount without calculating costs, which happens when students don't complete all required steps. To help students: Read carefully and identify ALL steps needed before starting. Determine what to find first (total cost), then what to do with that result (subtract from payment). Write out steps: Step 1 finds notebook cost, Step 2 adds pencil case for total, Step 3 finds change. Use variables: Let c = change, then c = $50 - (4 × $7 + $9). Practice breaking complex problems into steps and always check reasonableness with estimation.

5

Chen is setting up chairs for a concert. There are 9 rows with 14 chairs in each row. Then 25 more chairs are added near the stage. Let $c$ be the total number of chairs. Write an equation with $c$ and solve. How many chairs are there altogether?

151 chairs

126 chairs

101 chairs

139 chairs

Explanation

This question tests 4th grade ability to solve multistep word problems with whole numbers using the four operations, including interpreting remainders, representing with equations using variables, and assessing reasonableness with estimation (CCSS.4.OA.3). Multi-step problems require performing two or more operations in the correct order to reach the answer. Students must identify what operations are needed (addition, subtraction, multiplication, or division) based on the problem context, perform them in logical sequence, and ensure each step builds toward the final answer. This problem requires 2 steps: multiply to find chairs in rows, then add extra chairs. The sequence is: 9 × 14 = 126, then 126 + 25 = 151. Choice A is correct because following the steps: Step 1: 9 rows × 14 chairs = 126 chairs in rows, Step 2: 126 + 25 = 151 total chairs. The equation is c = (9 × 14) + 25, which gives c = 151. Estimation check: 9 × 14 ≈ 10 × 15 = 150, plus 25 ≈ 175, or more precisely 9 × 14 ≈ 9 × 10 = 90 + 9 × 4 = 126, plus 25 = 151, confirming our exact answer. Choice B represents stopping after the multiplication (126), which happens when students forget to add the extra chairs. To help students: Read carefully for ALL chair sources - both in rows AND near stage. Write the equation: Let c = total chairs, then c = (9 × 14) + 25. Practice identifying when to combine results from different sources. Use parentheses to show order of operations clearly. Check by working backwards: 151 - 25 = 126, and 126 ÷ 9 = 14 ✓.

6

Amir reads 18 pages each day for 7 days. On the last day, he reads 6 extra pages. How many pages does Amir read in all? Estimate first, then find the exact answer.

120 pages

126 pages

132 pages

144 pages

Explanation

This question tests 4th grade ability to solve multistep word problems with whole numbers using the four operations, including interpreting remainders, representing with equations using variables, and assessing reasonableness with estimation (CCSS.4.OA.3). Multi-step problems require performing two or more operations in the correct order to reach the answer. Students must identify what operations are needed (addition, subtraction, multiplication, or division) based on the problem context, perform them in logical sequence, and ensure each step builds toward the final answer. For problems with division, remainders must be interpreted based on context—sometimes round up (need whole vans), sometimes round down (complete groups only), sometimes the remainder is the answer (how many left over). This problem requires 2 steps: multiply daily pages by days, then add extra on last day. The sequence is: 18 × 7 = 126, then 126 + 6 = 132. Choice B is correct because following the steps: Step 1: 18 × 7 = 126 for 7 days, Step 2: 126 + 6 = 132 total pages. Estimation check: 20 × 7 = 140, plus 6 ≈146, but adjusting for exact 18 gives close to 132, confirming reasonableness. Choice A represents forgetting to add the extra pages, just 18 × 7 = 126, which happens when students don't continue through all steps. To help students: Read carefully and identify ALL steps needed before starting. Determine what to find first, then what to do with that result. Write out steps or use mental notes: Step 1 finds base total, Step 2 adds extra. For remainder problems, consider context: 'How many vans NEEDED' means round UP (26 R1 → need 27 vans). 'How many COMPLETE groups' means quotient only (26 R1 → 26 complete groups). 'How many LEFT OVER' means just remainder (26 R1 → 1 left over). Use variables to represent unknowns: Let n = number of cookies left, then n = (5 × 12) - 8. Check reasonableness: estimate by rounding (5 boxes × 10 cookies ≈ 50, subtract 8 ≈ 42, close to exact 52 ✓). Practice breaking complex problems into steps. Watch for: stopping after first step, wrong operation choice, computing in wrong order, misinterpreting remainders, and arithmetic errors.

7

Jamal has 8 pencils. He gets 16 more pencils. He shares all the pencils equally among 4 friends. Let $p$ be the number of pencils each friend gets. Write an equation using $p$ and solve.

$p = (8 + 16) \times 4$, so $p = 96$

$p = (8 \div 4) + 16$, so $p = 18$

$p = 16 \div(8 + 4)$, so $p = 1$

$p = (8 + 16) \div 4$, so $p = 6$

Explanation

This question tests 4th grade ability to solve multistep word problems with whole numbers using the four operations, including interpreting remainders, representing with equations using variables, and assessing reasonableness with estimation (CCSS.4.OA.3). Multi-step problems require performing two or more operations in the correct order to reach the answer. Students must identify what operations are needed (addition, subtraction, multiplication, or division) based on the problem context, perform them in logical sequence, and ensure each step builds toward the final answer. For problems with division, remainders must be interpreted based on context—sometimes round up (need whole vans), sometimes round down (complete groups only), sometimes the remainder is the answer (how many left over). This problem requires 2 steps: add 8+16=24 total, divide 24÷4=6. The sequence is: 8+16=24, 24÷4=6. Choice B is correct because following the steps: Step 1: 8+16=24, Step 2: 24÷4=6 pencils each; estimation check: 10+15=25, 25÷4≈6, close to exact 6. Choice A represents wrong order like dividing first then adding wrong, which happens when students perform operations in illogical order. To help students: Read carefully and identify ALL steps needed before starting. Determine what to find first, then what to do with that result. Write out steps or use mental notes: Step 1 finds total pencils, Step 2 divides by friends. Use variables to represent unknowns: Let p = pencils each, then p=(8+16)÷4=6. Check reasonableness: estimate by rounding (8+16=24, 24÷4=6 ✓). Practice breaking complex problems into steps. Watch for: stopping after first step, wrong operation choice, computing in wrong order, misinterpreting remainders, and arithmetic errors.

8

Yuki’s class collected 96 cans for a food drive. They collected 48 more cans the next week. They put all the cans into boxes that hold 12 cans each. How many boxes do they need? What is the final number of boxes? Is your answer reasonable?

144 boxes

8 boxes

12 boxes

10 boxes

Explanation

This question tests 4th grade ability to solve multistep word problems with whole numbers using the four operations, including interpreting remainders, representing with equations using variables, and assessing reasonableness with estimation (CCSS.4.OA.3). Multi-step problems require performing two or more operations in the correct order to reach the answer. Students must identify what operations are needed (addition, subtraction, multiplication, or division) based on the problem context, perform them in logical sequence, and ensure each step builds toward the final answer. For problems with division, remainders must be interpreted based on context—sometimes round up (need whole vans), sometimes round down (complete groups only), sometimes the remainder is the answer (how many left over). This problem requires 2 steps: add collections, then divide by box capacity. The sequence is: 96 + 48 = 144, then 144 ÷ 12 = 12. The context requires the exact quotient since it divides evenly, no remainder interpretation needed. Choice A is correct because following the steps: Step 1: 96 + 48 = 144 total cans, Step 2: 144 ÷ 12 = 12 boxes. Estimation check: 100 + 50 = 150, 150 ÷ 10 = 15, adjusting for exact gives close to 12, confirming reasonableness. Choice B represents possibly dividing one collection only, like 96 ÷ 12 = 8, which happens when students don't add both amounts. To help students: Read carefully and identify ALL steps needed before starting. Determine what to find first, then what to do with that result. Write out steps or use mental notes: Step 1 finds total cans, Step 2 divides by box size. For remainder problems, consider context: 'How many vans NEEDED' means round UP (26 R1 → need 27 vans). 'How many COMPLETE groups' means quotient only (26 R1 → 26 complete groups). 'How many LEFT OVER' means just remainder (26 R1 → 1 left over). Use variables to represent unknowns: Let n = number of cookies left, then n = (5 × 12) - 8. Check reasonableness: estimate by rounding (5 boxes × 10 cookies ≈ 50, subtract 8 ≈ 42, close to exact 52 ✓). Practice breaking complex problems into steps. Watch for: stopping after first step, wrong operation choice, computing in wrong order, misinterpreting remainders, and arithmetic errors.

9

Sofia has 9 boxes of pencils with 12 pencils in each box. She gives 37 pencils to the office. How many pencils does she have left? Solve and check your answer.

108 pencils

85 pencils

71 pencils

145 pencils

Explanation

This question tests 4th grade ability to solve multistep word problems with whole numbers using the four operations, including interpreting remainders, representing with equations using variables, and assessing reasonableness with estimation (CCSS.4.OA.3). Multi-step problems require performing two or more operations in the correct order to reach the answer. Students must identify what operations are needed (addition, subtraction, multiplication, or division) based on the problem context, perform them in logical sequence, and ensure each step builds toward the final answer. For problems with division, remainders must be interpreted based on context—sometimes round up (need whole vans), sometimes round down (complete groups only), sometimes the remainder is the answer (how many left over). This problem requires two steps: multiply boxes by pencils per box, then subtract given away. The sequence is: 9 × 12 = 108 total, then 108 - 37 = 71 left. Choice A is correct because following the steps: Step 1: 9 × 12 = 108, Step 2: 108 - 37 = 71 pencils. Estimation check: 10 × 12 = 120, -40 ≈ 80, close to exact 71. Choice B represents adding instead of subtracting, like 108 + 37 =145, which happens when students misidentify operation needed. To help students: Read carefully and identify ALL steps needed before starting. Determine what to find first, then what to do with that result. Write out steps or use mental notes: Step 1 multiplies to 108, Step 2 subtracts 37 to find 71. Use variables to represent unknowns: Let p = pencils left, then p = (9 × 12) - 37. Check reasonableness: estimate by rounding (9 × 10 ≈ 90 - 40 ≈ 50, but adjust to 120 - 40 ≈80, close to 71 ✓). Practice breaking complex problems into steps. Watch for: stopping after first step, wrong operation choice, computing in wrong order, misinterpreting remainders, and arithmetic errors.

10

Jamal reads 18 pages each day for 7 days. Then he rereads 25 pages. How many pages does he read in all? Estimate first, then find the exact answer.

151 pages

126 pages

101 pages

143 pages

Explanation

This question tests 4th grade ability to solve multistep word problems with whole numbers using the four operations, including interpreting remainders, representing with equations using variables, and assessing reasonableness with estimation (CCSS.4.OA.3). Multi-step problems require performing two or more operations in the correct order to reach the answer. Students must identify what operations are needed (addition, subtraction, multiplication, or division) based on the problem context, perform them in logical sequence, and ensure each step builds toward the final answer. For problems with division, remainders must be interpreted based on context—sometimes round up (need whole vans), sometimes round down (complete groups only), sometimes the remainder is the answer (how many left over). This problem requires two steps: multiply daily pages by days, then add reread pages. The sequence is: 18 × 7 = 126 pages in 7 days, then 126 + 25 = 151 total pages. Choice A is correct because following the steps: Step 1: 18 × 7 = 126, Step 2: 126 + 25 = 151 pages. Estimation check: 20 × 7 = 140, +25 ≈ 165, close to exact 151. Choice B represents only the multiplication step without adding, which happens when students don't continue through all steps or stop after first operation. To help students: Read carefully and identify ALL steps needed before starting. Determine what to find first, then what to do with that result. Write out steps or use mental notes: Step 1 multiplies to 126, Step 2 adds 25 to find 151. Use variables to represent unknowns: Let p = pages total, then p = (18 × 7) + 25. Check reasonableness: estimate by rounding (20 × 7 ≈ 140 + 25 ≈ 165, close to exact 151 ✓). Practice breaking complex problems into steps. Watch for: stopping after first step, wrong operation choice, computing in wrong order, misinterpreting remainders, and arithmetic errors.

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