Multi-Digit Multiplication — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. Grade 5 students need a 4-digit by 2-digit multiplication. Which problem fits?
A) 234 times 56
B) 1234 times 7
C) 1248 times 36
D) 12480 times 36
1248 has 4 digits and 36 has 2 digits, exactly the 4-digit by 2-digit format Grade 5 students need. The other choices have wrong digit counts.
2. A stadium seats 1248 fans per section with 36 sections. Total fans?
A) 44,928 fans
B) 4,928 fans
C) 44,488 fans
D) 44,288 fans
1248 times 36: 1248 times 30 is 37440 and 1248 times 6 is 7488. Adding gives 44928 fans. Grade 5 magnitude check: about 1250 times 36 is near 45000.
3. Estimating 1248 times 36, the Grade 5 magnitude is closest to which value?
A) About 4,000
B) About 45,000
C) About 450,000
D) About 4,500
Rounding 1248 to 1250 and 36 to 36 gives 1250 times 36, about 45000. This Grade 5 magnitude check confirms the exact product 44928 is reasonable.
4. Which step should Grade 5 students do FIRST when solving a 4-digit by 2-digit word problem?
A) Compute the exact product before reading
B) Identify what is asked and the factors
C) Round both numbers and stop
D) Subtract one factor from the other
Identifying the question and the factors comes first. Then Grade 5 students estimate magnitude, compute the product using a chosen method, and check the answer.
Part B: Fill in the Blank
Write the correct answer on each line.
1. A Grade 5 student writes: a warehouse stores 1248 boxes in each of 36 trucks. Total boxes equals 44928.
1248 times 36 equals 44928 boxes. Partial products: 1248 times 30 is 37440 and 1248 times 6 is 7488, summing to 44928 for Grade 5 verification.
2. Estimating 1248 times 36, Grade 5 students round to 1250 times 36, which equals 45000.
1250 times 36 equals 45000. This Grade 5 estimate is close to the exact 44928, confirming the magnitude is correct and the computation is reasonable.
3. Difference between exact 44928 and estimate 45000 is 72.
45000 minus 44928 equals 72. The small difference shows the Grade 5 estimate is very close to the actual product, validating the multiplication.
4. If the 36 trucks each gain 12 more boxes, the new total is 45360.
36 times 12 equals 432 extra boxes. Adding 432 to 44928 gives 45360 boxes. Grade 5 students confirm with partial products and magnitude reasoning.
5. A Grade 5 explanation must include the question, factors, method, computation, and magnitude check.
A complete Grade 5 explanation ends with a magnitude check, comparing the exact answer to a rounded estimate to confirm the product is reasonable and accurate.