Multiply Using Partial Products Educational Resources

Learning how to multiply using partial products? The method is a mouthful, but we can make it a little bit easier. Our array of resources for multiplication help tackles multiplication from many approaches. Lattice, tables, or just some fun characters...chances are, we have a way to learn multiplication that works for you and your student.

Once your student is comfortable with the concept of single digit multiplication, they can move on to multi-digit multiplication. While Common Core has introduced new methods of performing these problems, the classic standard multiplication and partial product algorithms are still valid methods.

The partial product algorithm is by far the simpler method, allowing students to break the larger, multi-digit multiplication problems into multiple single digit multiplication facts with an a addition problem at the end. There are two basic steps to using the partial product algorithm:

First, multiply each digit in the multiplier by each digit in the multiplicand, writing each product in a new row beneath the original problem:
  63
× 9
 27
  63
× 9
 27
540
Then, add the products from the previous two steps to get the final product:
     63
×    9
     27
+ 540
   567
Depending on the number of digits in the factors involved, the number of steps will increase as well as the corresponding products that will be added in the final step.

When dealing with a multi-digit multiplier, it may be easier for younger students to use the lattice method of the partial product algorithm. This method involves drawing a grid with diagonal lines that bisect each row of cells in the grid, then writing the factors above and to the right side of the grid, each digit corresponding with a row or column of cells. The products of the digits are written in the cells, then added along the diagonals to get the final product.