I was sent this You Tube clip recently explaining how the Chinese work out their multiplication problems, all through drawing and counting the number of line intersections. (There are a number of other similar clips) For some students they will enjoy exploring alternate ways of working out multiplication.
I regularly used and encouraged the "Lattice Method" method. This shows partial products but does need students to know their Basic Facts!
In response to the Chinese Drawing method of Multiplication. I have regularly encouraged a Lattice Method of multiplication that also shows the Place Value and can also be modelled by Place Value Blocks.
The difference here is that the students needs to know their ‘Basic Multiplication Facts’ but there are no rules such as “multiply, put down the ones and carry the tens OR just add a ‘Nought’ or Zero”
It is a schematic way of showing ‘Partial Products’
24 x 56 =
put 24 across the top two columns
Put the 56 on the right hand side of the two rows
Now multiply each pair of numbers and place the answer in the box, tens above the diagonal ones below
Add down the diagonals, carrying the an tens into the next diagonal to the left and above
The answer is 1344
The Lattice can be increased for all multiplication like 24 x 569, or 274 x 4590