The similarity to the old method is restricted only to the summation.
Step-by-step explanation:
The Partial Products Algorithm consists of
1) Drawing a square equally divided by four
2) Then place the tenths and units of decomposed 2 digit numbers
3) Multiply four products (these are the partial products) and then add it all up.
The similarity to the old method is restricted only to the summation. But in Partial Products, this addition is easier since the results are in rounded or in many addends.
Well the multiplication part is the same .Its in the ordering it has to be(ex: 42 times 35) but it has to be placed vertically .For the second number multiply to the right then the left .Repeat .Then you got your answer using 2 digits similar to regular multiplication partial products .Hope this helped !!