Partial-Product Multiplication

Partial-Products Multiplication (1-digit multipliers)

This blog post is intended to help explain how to use partial-product multiplication to solve multiplication problems. We teach many ways of multiplication in 4^th grade, and this is just another method. We like to provide the opportunity to let our students discover a method that works really well for them! I know this is not the way I learned when I was younger, but now as I teach, I really understand this method, and how it could be a method of choice for different students. If you would like more explanation surrounding this type of multiplication, I would love to explain further. J

~ In this method, multiplication is usually done from left to right. This ensures that the most important products, the largest ones, are calculated first, but it is not incorrect for a student to multiply from right to left.

~ Each part of the calculation, each partial product, is written on a separate line. Then the partial products are added. This is usually very simple and has the benefit of providing practice with column addition

How to:

1.)   As a class, we make estimations to help guide us, so we have an idea of what our answer should be around. For this problem, I would estimate 800 x 6 = 4,800

2.)   Line up your factors! It is very helpful to do this! It can be beneficial to draw a dotted line down to ensure that your numbers are being properly lined up. This will be very helpful in the last step.

3.)   For this next step, you can start from the left or the right of the larger number. I personally tend to start multiplying from the left to the right, even though this is very different from what I learned as a child. J I am going to start by multiplying 800 x 6. My answer is 4,800 and I write it down in its respective place value spots. Next, I multiply 60 x 9. My answer is 360 and I write it down in the respective spot. Finally, I multiply 6x9 and get 45. This number also goes into its respective spot.

4.)   The last step! This is where it pays off to have your products lined up correctly! Add all of your products together to find the answer. In this case, I added 4,800+360+54 and got 5, 214.

This method is difficult at first, and may take extra time to use, but I have seen it be a first choice for many students. Good luck using this method, and let me know if you have any questions!