Teacher Exemplar
Solutions for Problems #5 through #8
Answer Key & Guide
Pedagogical Focus: Estimating 2-digit quotients and handling zeros in intermediate long division steps.
#5 Zero in Quotient 2,842 ÷ 14 = 203
203
14
2842
-28↓
04↓
-00
42
-42
0
Common Error:
Students record 23 instead of 203. Emphasize place value: 2 in hundreds, 0 in tens, 3 in ones.
203 × 14 = 2,842 ✓
Answer:
Quotient = 203 R = 0
#6 4,368 ÷ 24 = 182
182
24
4368
-24↓
196
-192↓
48
-48
0
Estimation Tip:
Round 24 to 20. How many 20s in 196? About 9 or 8. (24 × 8 = 192).
182 × 24 = 4,368 ✓
Answer:
Quotient = 182 R = 0
#7 With Remainder 5,876 ÷ 25 = 235 R 1
235 R 1
25
5876
-50↓
87
-75↓
126
-125
1
Remainder Rule:
Remainder 1 < Divisor 25. Check formula: (235 × 25) + 1 = 5,875 + 1 = 5,876.
5,875 + 1 = 5,876 ✓
Answer:
Quotient = 235 R = 1
#8 Challenge Solution Word Problem
Oak Elementary collected 1,728 cans of soup. If students pack exactly 16 cans into each box, how many boxes will they fill completely?
108
16
1728
-16↓
012↓
-000
128
-128
0
Context Note:
16 does not go into 12, so write 0 in the tens place! 108 × 16 = 1,728.
108 × 16 = 1,728 ✓
They will fill 108 boxes completely.
Teacher Exemplar • Grade 5 Division Page 2 of 3
KEY
Teacher Exemplar
Solutions for Problems #9 through #12
Answer Key & Guide
Advanced Practice: Multi-digit division with 2-digit divisors and context interpretation.
#9 966 ÷ 23 = 42
42
23
966
-92↓
46
-46
0
Check:
42 × 23 = 966 ✓
23 × 4 = 92; 23 × 2 = 46.
Answer:
Quotient = 42 R = 0
#10 4,257 ÷ 9 = 473
473
9
4257
-36↓
65
-63↓
27
-27
0
Check:
473 × 9 = 4,257 ✓
Divisibility rule: 4+2+5+7 = 18 (divisible by 9).
Answer:
Quotient = 473 R = 0
#11 3,825 ÷ 17 = 225
225
17
3825
-34↓
42
-34↓
85
-85
0
Check:
225 × 17 = 3,825 ✓
17 × 2 = 34; 17 × 5 = 85.
Answer:
Quotient = 225 R = 0
#12 Challenge Solution Word Problem
A school library received 2,496 books. The librarian places an equal number of books onto 32 empty shelves. How many books go on each shelf?
78
32
2496
-224↓
256
-256
0
Check:
78 × 32 = 2,496 ✓
32 × 7 = 224; 32 × 8 = 256.
Each shelf will hold 78 books.
Teacher Exemplar • Grade 5 Division Page 3 of 3
