"Record the partial products in the area model" means to write down each of the individual multiplication results obtained when breaking down a larger multiplication problem into smaller, more manageable parts using the area model method. These partial products represent the area of each section within the area model rectangle, and their sum equals the total product of the original multiplication problem.
To elaborate:
The area model is a visual representation of multiplication, particularly useful for multiplying multi-digit numbers. Here's how recording partial products fits in:
- Breaking down the numbers: The numbers being multiplied are decomposed into their expanded form (e.g., 23 becomes 20 + 3).
- Creating the Area Model: A rectangle is drawn and divided into smaller sections based on the expanded forms of the numbers. Each section represents a smaller multiplication problem.
- Multiplying to find Partial Products: Each section's area is calculated by multiplying the corresponding parts of the expanded numbers. For example, if multiplying 23 x 14, one section might represent 20 x 10. The result (200 in this case) is a partial product.
- Recording: Writing down the result (e.g., 200) inside that section of the area model represents recording the partial product.
- Summing: After calculating all the partial products, they are added together to find the total product of the original multiplication problem.
Example:
Let's multiply 23 x 14 using the area model:
- 23 is broken down into 20 + 3
- 14 is broken down into 10 + 4
The area model would have four sections:
| 10 | 4 | |
|---|---|---|
| 20 | 200 | 80 |
| 3 | 30 | 12 |
Here, the recorded partial products are 200, 80, 30, and 12.
Adding these partial products gives us 200 + 80 + 30 + 12 = 322. Therefore, 23 x 14 = 322.
In conclusion, "recording the partial products" is a crucial step in using the area model for multiplication, as it provides a structured way to keep track of the intermediate results before summing them to find the final answer.
