Word Problems
4A · Chapter 5 · Lesson 4 · MATH-4A-C05-L05
Learning goal. Select fair-sharing or measurement interpretation and contextualize any remainder.
Before you begin
Recall: Grade 3: single-digit division and remainder; 4A Ch4: multiplication estimates; Dividing 4-Digit Numbers. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Divide 1,845 by 2. Give the quotient and remainder.
Show answer & reasoning
1,845 = 2 × 922 + 1; the remainder 1 is less than 2.
Divide 2,162 by 9. Give the quotient and remainder.
Show answer & reasoning
2,162 = 9 × 240 + 2; the remainder 2 is less than 9.
Divide 4,149 by 6. Give the quotient and remainder.
Show answer & reasoning
4,149 = 6 × 691 + 3; the remainder 3 is less than 6.
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
Division stories can ask for the size of a share or the number of groups. If 52 children ride eight-seat vans, 52÷8 is six full groups with four children left. You need seven vans, not six, because the remaining children still require transportation. The meaning of the remainder depends on the context.
Model it: equal-group bars and remainder interpretation. 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
492 pencils are packed 5 per box. How many full boxes can be filled, and how many pencils remain?
Group by 5: 492 = 98 full groups of 5, plus 2 left.
Check your understanding 1
1,677 pencils are packed 4 per box. How many full boxes can be filled, and how many pencils remain?
Show answer & reasoning
Group by 4: 1,677 = 419 full groups of 4, plus 1 left.
Worked example 2
110 pencils are packed 2 per box. How many full boxes can be filled, and how many pencils remain?
Group by 2: 110 = 55 full groups of 2, plus 0 left.
Check your understanding 2
1,117 pencils are packed 3 per box. How many full boxes can be filled, and how many pencils remain?
Show answer & reasoning
Group by 3: 1,117 = 372 full groups of 3, plus 1 left.
Worked example 3
3,031 pencils are packed 7 per box. How many full boxes can be filled, and how many pencils remain?
Group by 7: 3,031 = 433 full groups of 7, plus 0 left.
Check your understanding 3
2,212 pencils are packed 5 per box. How many full boxes can be filled, and how many pencils remain?
Show answer & reasoning
Group by 5: 2,212 = 442 full groups of 5, plus 2 left.
Guided practice
1,436 pencils are packed 5 per box. How many full boxes can be filled, and how many pencils remain?
Show answer & reasoning
Group by 5: 1,436 = 287 full groups of 5, plus 1 left.
536 pencils are packed 8 per box. How many full boxes can be filled, and how many pencils remain?
Show answer & reasoning
Group by 8: 536 = 67 full groups of 8, plus 0 left.
1,396 pencils are packed 5 per box. How many full boxes can be filled, and how many pencils remain?
Show answer & reasoning
Group by 5: 1,396 = 279 full groups of 5, plus 1 left.
739 pencils are packed 2 per box. How many full boxes can be filled, and how many pencils remain?
Show answer & reasoning
Group by 2: 739 = 369 full groups of 2, plus 1 left.
1,545 pencils are packed 5 per box. How many full boxes can be filled, and how many pencils remain?
Show answer & reasoning
Group by 5: 1,545 = 309 full groups of 5, plus 0 left.
Independent practice
692 pencils are packed 7 per box. How many full boxes can be filled, and how many pencils remain?
Show answer & reasoning
Group by 7: 692 = 98 full groups of 7, plus 6 left.
584 pencils are packed 7 per box. How many full boxes can be filled, and how many pencils remain?
Show answer & reasoning
Group by 7: 584 = 83 full groups of 7, plus 3 left.
223 pencils are packed 2 per box. How many full boxes can be filled, and how many pencils remain?
Show answer & reasoning
Group by 2: 223 = 111 full groups of 2, plus 1 left.
341 pencils are packed 2 per box. How many full boxes can be filled, and how many pencils remain?
Show answer & reasoning
Group by 2: 341 = 170 full groups of 2, plus 1 left.
745 pencils are packed 7 per box. How many full boxes can be filled, and how many pencils remain?
Show answer & reasoning
Group by 7: 745 = 106 full groups of 7, plus 3 left.
588 pencils are packed 3 per box. How many full boxes can be filled, and how many pencils remain?
Show answer & reasoning
Group by 3: 588 = 196 full groups of 3, plus 0 left.
180 pencils are packed 2 per box. How many full boxes can be filled, and how many pencils remain?
Show answer & reasoning
Group by 2: 180 = 90 full groups of 2, plus 0 left.
881 pencils are packed 2 per box. How many full boxes can be filled, and how many pencils remain?
Show answer & reasoning
Group by 2: 881 = 440 full groups of 2, plus 1 left.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
740 children ride vans seating 6 children each. A student says 123 vans are sufficient because the quotient is 123 remainder 2. Explain and find the necessary number of vans.
Show answer & reasoning
The 2 remaining children still need a van. The number of vans must be rounded up to 124.
1,092 pencils are packed 3 per box. How many full boxes can be filled, and how many pencils remain?
Show answer & reasoning
Group by 3: 1,092 = 364 full groups of 3, plus 0 left.
Exit check
1,148 pencils are packed 5 per box. How many full boxes can be filled, and how many pencils remain?
Show answer & reasoning
Group by 5: 1,148 = 229 full groups of 5, plus 3 left.
608 pencils are packed 3 per box. How many full boxes can be filled, and how many pencils remain?
Show answer & reasoning
Group by 3: 608 = 202 full groups of 3, plus 2 left.
929 pencils are packed 7 per box. How many full boxes can be filled, and how many pencils remain?
Show answer & reasoning
Group by 7: 929 = 132 full groups of 7, plus 5 left.