This is an example of how I teach partial products.
75 x 64 = ?
Step 1: Recognize that 75 = 70 + 5 and 64 = 60 + 4.
Step 2: Multiply each part of 75 by each part of 64.
Step 3: Record all partial operations. Start in the ones place. This supports future success with the traditional algorithm that many of us use to perform mutlidigit multiplication. I have students write each partial product operation to the right of the problem. This allows them to understand exactly what they are doing and to take advantage of simple fact fluency and higher decade facts.
7 5
x 6 4
2 0 4 x 5 = 20 (The simple fact is 4 x 5 = 20.)
2 8 0 4 x 70 = 280 (The simple fact is 4 x 7 = 28.)
3 0 0 60 x 5 = 300 (The simple fact is 6 x 5 = 30.)
4,2 0 0 60 x 70 = 4,200 (The simple fact is 6 x 7 = 42.)
Step 4: Sum all numbers in each place column, starting in the ones column.
7 5
x 6 4
2 0
2 8 0
3 0 0
4,2 0 0
4,8 0 0
