How modeling partial products can be used to find the products of greater numbers
To model partial products, we break down the multiplication of greater numbers into smaller, manageable steps. Here's a step-by-step guide on how to use this method to find the products of greater numbers:
Step 1: Break down the numbers
Take the two numbers you want to multiply and break them down into their place values. For example, if you want to multiply 345 and 67, you can break them down like this:
- 345 = 300 + 40 + 5
- 67 = 60 + 7
Step 2: Multiply each place value
Starting with the ones place, multiply each digit of the second number by each digit of the first number. Multiply 7 (ones place of 67) by each digit of 345:
- 7 x 5 = 35
- 7 x 4 = 28
- 7 x 3 = 21
Step 3: Write the partial products
Write each product you obtained in the previous step as a partial product. Align them vertically and add a zero to the right of each partial product based on its place value:
- 35
- 280 (28 with an additional zero)
- 210 (21 with an additional zero)
Step 4: Add the partial products
Add up the partial products:
- 35
- 280
- 210
--------
= 625
Step 5: Write the final product
The sum of the partial products gives you the final product of the two numbers. In our example, the product of 345 and 67 is 625.
This method of breaking down the numbers into their place values and multiplying them individually helps manage the multiplication of greater numbers and aids in avoiding errors.
Modeling partial products is a helpful strategy for finding the products of greater numbers. It involves breaking down the multiplication problem into smaller, more manageable parts. Here's an explanation of how to model the process:
Step 1: Break down the numbers
Consider the two numbers you want to multiply. For example, let's say you want to find the product of 345 and 27. Break down these numbers into their place values: 345 can be written as 300 + 40 + 5, and 27 can be written as 20 + 7.
Step 2: Create a grid or chart
Create a grid or chart with columns labeled for each place value: hundreds, tens, and ones. You can also create separate rows for each place value of the second number. In this case, create three rows for the tens, ones, and decimals place.
Step 3: Multiply each digit
Starting from the rightmost column, multiply each digit in the ones place of the second number with all the digits of the first number. Write the partial products in the corresponding rows and columns of the grid. For example, multiply the digit 7 of the ones place with each digit of the first number: 7 × 5 = 35 (write this in the ones column), 7 × 4 = 28 (write this in the tens column), and 7 × 3 = 21 (write this in the hundreds column).
Step 4: Add the partial products
Add up the partial products in each column. In our example, the ones column has only one partial product (35), the tens column has two partial products (28 and 40), and the hundreds column has one partial product (21). Add these up: 35 + 28 + 40 + 21 = 124.
Step 5: Combine the results
The final step is to combine the results from Step 4 to get the product of the two numbers. In our example, the product of 345 and 27 is 124.
Modeling partial products allows you to break down the process of multiplication, making it easier to focus on individual digits and maintain accuracy. It can be particularly helpful when multiplying larger numbers or when teaching multiplication conceptually.