Challenging Word Problems
4A · Chapter 5 · Lesson 5 · MATH-4A-C05-L06
Learning goal. Solve multistage division problems using labeled models, quotient checks and constraints.
Before you begin
Recall: Grade 3: single-digit division and remainder; 4A Ch4: multiplication estimates; Word Problems. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
381 pencils are packed 6 per box. How many full boxes can be filled, and how many pencils remain?
Show answer & reasoning
Group by 6: 381 = 63 full groups of 6, plus 3 left.
404 pencils are packed 4 per box. How many full boxes can be filled, and how many pencils remain?
Show answer & reasoning
Group by 4: 404 = 101 full groups of 4, plus 0 left.
2,154 pencils are packed 6 per box. How many full boxes can be filled, and how many pencils remain?
Show answer & reasoning
Group by 6: 2,154 = 359 full groups of 6, plus 0 left.
Key vocabulary
- dividend
- number being divided
- divisor
- number of equal groups or group size
- quotient
- result of division
- remainder
- amount left after complete groups
Understand the concept
A multistage division word problem contains more than one relationship. Draw a model, label intermediate quantities and calculate in order. For example, when additional tickets arrive before packaging, add the new tickets first and only then divide the total. Finally check the result against any grouping or capacity conditions.
Model it: before-and-after bars with group counts. Explain what every part of the model represents, then write a matching equation.
Fully worked examples
Read the problem first and predict the answer. Then study how each quantity is represented and calculated.
Worked example 1
A club has 894 tickets. After buying 40 more, they bundle tickets into packs of 8. How many full packs and tickets left?
Add first: 934. Divide by 8: 116 packs, with 6 tickets remaining.
Check your understanding 1
A club has 307 tickets. After buying 20 more, they bundle tickets into packs of 5. How many full packs and tickets left?
Show answer & reasoning
Add first: 327. Divide by 5: 65 packs, with 2 tickets remaining.
Worked example 2
A club has 2,604 tickets. After buying 30 more, they bundle tickets into packs of 6. How many full packs and tickets left?
Add first: 2,634. Divide by 6: 439 packs, with 0 tickets remaining.
Check your understanding 2
A club has 1,341 tickets. After buying 35 more, they bundle tickets into packs of 5. How many full packs and tickets left?
Show answer & reasoning
Add first: 1,376. Divide by 5: 275 packs, with 1 tickets remaining.
Worked example 3
A club has 1,296 tickets. After buying 32 more, they bundle tickets into packs of 4. How many full packs and tickets left?
Add first: 1,328. Divide by 4: 332 packs, with 0 tickets remaining.
Check your understanding 3
A club has 1,184 tickets. After buying 18 more, they bundle tickets into packs of 3. How many full packs and tickets left?
Show answer & reasoning
Add first: 1,202. Divide by 3: 400 packs, with 2 tickets remaining.
Guided practice
A club has 459 tickets. After buying 14 more, they bundle tickets into packs of 2. How many full packs and tickets left?
Show answer & reasoning
Add first: 473. Divide by 2: 236 packs, with 1 tickets remaining.
A club has 397 tickets. After buying 56 more, they bundle tickets into packs of 8. How many full packs and tickets left?
Show answer & reasoning
Add first: 453. Divide by 8: 56 packs, with 5 tickets remaining.
A club has 1,880 tickets. After buying 45 more, they bundle tickets into packs of 5. How many full packs and tickets left?
Show answer & reasoning
Add first: 1,925. Divide by 5: 385 packs, with 0 tickets remaining.
A club has 235 tickets. After buying 20 more, they bundle tickets into packs of 2. How many full packs and tickets left?
Show answer & reasoning
Add first: 255. Divide by 2: 127 packs, with 1 tickets remaining.
A club has 184 tickets. After buying 16 more, they bundle tickets into packs of 2. How many full packs and tickets left?
Show answer & reasoning
Add first: 200. Divide by 2: 100 packs, with 0 tickets remaining.
Independent practice
A club has 149 tickets. After buying 12 more, they bundle tickets into packs of 3. How many full packs and tickets left?
Show answer & reasoning
Add first: 161. Divide by 3: 53 packs, with 2 tickets remaining.
A club has 398 tickets. After buying 10 more, they bundle tickets into packs of 2. How many full packs and tickets left?
Show answer & reasoning
Add first: 408. Divide by 2: 204 packs, with 0 tickets remaining.
A club has 129 tickets. After buying 16 more, they bundle tickets into packs of 2. How many full packs and tickets left?
Show answer & reasoning
Add first: 145. Divide by 2: 72 packs, with 1 tickets remaining.
A club has 2,727 tickets. After buying 63 more, they bundle tickets into packs of 7. How many full packs and tickets left?
Show answer & reasoning
Add first: 2,790. Divide by 7: 398 packs, with 4 tickets remaining.
A club has 123 tickets. After buying 16 more, they bundle tickets into packs of 2. How many full packs and tickets left?
Show answer & reasoning
Add first: 139. Divide by 2: 69 packs, with 1 tickets remaining.
A club has 662 tickets. After buying 35 more, they bundle tickets into packs of 5. How many full packs and tickets left?
Show answer & reasoning
Add first: 697. Divide by 5: 139 packs, with 2 tickets remaining.
A club has 784 tickets. After buying 9 more, they bundle tickets into packs of 3. How many full packs and tickets left?
Show answer & reasoning
Add first: 793. Divide by 3: 264 packs, with 1 tickets remaining.
A club has 2,125 tickets. After buying 10 more, they bundle tickets into packs of 5. How many full packs and tickets left?
Show answer & reasoning
Add first: 2,135. Divide by 5: 427 packs, with 0 tickets remaining.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
1388 children ride vans seating 8 children each. A student says 173 vans are sufficient because the quotient is 173 remainder 4. Explain and find the necessary number of vans.
Show answer & reasoning
The 4 remaining children still need a van. The number of vans must be rounded up to 174.
A club has 116 tickets. After buying 20 more, they bundle tickets into packs of 4. How many full packs and tickets left?
Show answer & reasoning
Add first: 136. Divide by 4: 34 packs, with 0 tickets remaining.
Exit check
A club has 1,467 tickets. After buying 12 more, they bundle tickets into packs of 4. How many full packs and tickets left?
Show answer & reasoning
Add first: 1,479. Divide by 4: 369 packs, with 3 tickets remaining.
A club has 1,706 tickets. After buying 60 more, they bundle tickets into packs of 6. How many full packs and tickets left?
Show answer & reasoning
Add first: 1,766. Divide by 6: 294 packs, with 2 tickets remaining.
A club has 1,037 tickets. After buying 32 more, they bundle tickets into packs of 4. How many full packs and tickets left?
Show answer & reasoning
Add first: 1,069. Divide by 4: 267 packs, with 1 tickets remaining.