What will Remain
A farmer packs 47 apples into boxes that hold 6 apples each. How many full boxes can he make, and what should he do with the leftover apples? Explain your reasoning.
Use partial quotients to divide 154 ÷ 7. Show the partial-quotient steps and the final quotient and remainder (if any).
Using place value sharing, divide 246 ÷ 3. Show how you break 246 into hundreds, tens, and ones for sharing.
Estimate the quotient of 842 ÷ 21 by rounding the divisor and dividend to friendly numbers. Explain your estimation steps and give the estimated quotient.
Compute 3,456 ÷ 8 using any one-digit division strategy (place-value or standard). Show the quotient and remainder (if any).
3,456 ÷ 8
A theater has 325 seats. Groups of 4 people buy tickets. After seating as many full groups of 4 as possible, how many people will not fit into full groups? For a real-world solution, explain two different ways the theater could handle the remainder and justify which is best.
Divide 938 ÷ 6 using partial quotients. Show each subtraction step and explain why partial quotients help check reasonableness of the result.
Explain and perform place-value sharing for 1,304 ÷ 4. Show how hundreds, tens, and ones are shared and how you handle borrowing between places.
Estimate 3,658 ÷ 34 to one-digit accuracy (i.e., find the closest whole-number estimate). Show how you used compatible numbers or rounding and check whether the estimate is too high or low using quick multiplication.
Solve 12,789 ÷ 9. Show your steps and explain how place-value thinking or the relationship to multiplication helped you.
12,789 ÷ 9
A teacher needs to place 82 students into teams of 5 for a project. She says, "I will leave the remainder as a smaller team." How many teams of 5 and what size is the smaller team? Then decide whether it might be better to redistribute students to make teams more balanced — show how and explain why.
A student used partial quotients to find 2,457 ÷ 9 but got an answer of 273 with remainder 0. Recreate a correct partial-quotients solution and explain where a likely error could have occurred in the student's method. Provide the correct quotient and remainder.
A student must divide 4,205 ÷ 5 using place-value sharing. Show the full place-value sharing steps and explain why the method guarantees the correct quotient and remainder.
A student estimated 9,401 ÷ 48 as 200. Determine whether the estimate is reasonable. Show multiplication to justify whether it's too high or too low and provide a better estimate with explanation.
A store has 5,432 identical boxes to pack equally onto 7 pallets. Use division to find how many boxes per pallet and explain how you would check your answer using multiplication.
5,432 ÷ 7
A bakery makes 1,234 muffins and packs them into boxes of 12. They must ship whole boxes only, but they want to advertise "packs of 12" with no loose muffins shown. Determine the number of full boxes and the leftover muffins. Then propose and justify one operational change (e.g., changing box size or making extra baked goods) that would minimize leftover muffins over time. Use calculations and reasoning to support your recommendation.
Design a partial-quotients strategy to divide 6,842 ÷ 13. Explain the choices of partial multiples you subtract (e.g., 13×100, 13×200) and how place-value thinking guided those choices. Show complete computation and check with multiplication.
Compare place-value sharing and standard long division for 7,218 ÷ 6. Solve the problem both ways, explain differences in thinking and steps, and argue which method helps students understand place value more deeply. Use calculations to support your comparison.
You must estimate the number of 28-seat buses needed to transport 12,345 students on field trips over the year, if each bus can carry 28 students per trip. Estimate the quotient quickly to guide budgeting, explain the rounding strategy, then refine the estimate to a near-exact whole-number answer and explain the difference between the two estimates.
Create a multi-step word problem that requires dividing a four-digit number by a one-digit divisor, then interpreting the remainder in context and using that interpretation to make a decision. Provide the problem, solve it, and explain your decision-making process.
(Example multi-step problem) — provide a solved example from the original prompt style:
A company produces 7,999 small gadgets and needs to pack them into crates holding 24 gadgets each. They want to minimize leftover gadgets each production run. Compute the number of full crates and remainder. Then analyze two different strategies (change crate size; combine runs) to reduce leftover waste and compare which strategy is more feasible mathematically and practically. Show all work and justify your conclusion.
A school orders 14,375 pencils to share evenly across 18 classrooms. Use partial-quotients to compute how many pencils each classroom receives and the remainder. Then create and justify a distribution plan for the remainder that is fair and uses classroom needs (e.g., some classrooms need 2 extra pencils each). Provide calculations showing reasonableness.
Create a word problem where a city must allocate 9,999 resources equally across 7 districts using place-value sharing. Solve it with place-value sharing, show the remainder, then evaluate whether changing allocation unit (grouping by 10s or 100s) would lead to a simpler plan. Support with numerical evidence.
Design an approach to estimate 78,942 ÷ 67 for use in a planning meeting where a quick but justifiable number is needed. Show at least two estimation strategies (e.g., round both numbers; use leading-digit division) and compare which gives a closer result. Explain your choice and compute the actual quotient (to nearest whole number) to measure estimation accuracy.
A charity received 24,997 food items to distribute equally to 11 community centers. Compute how many items each center receives and analyze the impact of the remainder. Then propose a fair redistribution or policy for leftover items, justify it with math, and consider operational constraints (e.g., keeping packages equal, storage limits).
24,997 ÷ 11