Multi-Digit Multiplication — Answer Key
Part A: Fill in the Blank
Write the missing word or number on each line.
1. For Grade 5 problem 36 times 24, the standard algorithm gives a final product of 864.
Standard algorithm: 36 times 4 is 144 and 36 times 20 is 720. Adding 144 and 720 produces 864, the same product all three Grade 5 methods must reach.
2. Using partial products for 36 times 24 in Grade 5, the four pieces are 600, 120, 120, and 24.
Partial products split the factors: 30 times 20 is 600, 30 times 4 is 120, 6 times 20 is 120, and 6 times 4 is 24. The four pieces sum to 864.
3. An area model for 36 times 24 has 4 rectangles; their areas total 864.
The area model shows the same four partial products as rectangles. Adding 600, 120, 120, and 24 totals 864, matching the standard algorithm and partial products.
4. In Grade 5 work, the area model and partial products show the same four partial products.
Both the area model and the partial products method break factors by place value into the same four partial products, just displayed as rectangles or as a vertical list.
5. For 47 times 13 using partial products, 40 times 10 equals 400.
When a Grade 5 student multiplies 40 by 10, the product is 400. This is one of four partial products, alongside 40 times 3, 7 times 10, and 7 times 3.
6. The standard algorithm regroups; the area model avoids regrouping by showing each rectangle separately.
Area models display each partial product as its own rectangle, so Grade 5 students do not need to regroup mid-step. Regrouping happens only when the four pieces are summed.
7. All three methods for the same Grade 5 problem must produce the same product.
Standard algorithm, partial products, and area model are different routes to the same destination. The final product is identical because they apply the same distributive property.
8. For 25 times 16, partial products 200, 50, 120, and 30 sum to 400.
Adding the four Grade 5 partial products 200, 50, 120, and 30 gives 400. This matches 25 times 16 from any of the three methods, confirming consistency.
9. When choosing a method, Grade 5 students may pick the area model to clearly see place value.
The area model labels each side by place value, so Grade 5 students see how tens and ones combine. This makes the connection between digits and magnitude visible.
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each item to its correct answer.
36 times 24 standard algorithm answer
→ 864
864
30 times 20 partial product
→ 600
600
Area model rectangle for 6 times 4
→ 24
24
Sum of all four partial products
→ Equal to standard answer
Equal to standard answer
Standard gives 864, partial product 30 times 20 is 600, the 6-by-4 rectangle has area 24, and summing partial products always equals the standard algorithm answer for Grade 5.