Using the Lattice Method
The Lattice Method helps simplify the amount you have to remember when multiplying long numbers together, and provides you with more manageable magnitudes to multiply. To use the lattice method, first draw a lattice with as many columns as your multiplicand (the first number), and as many rows as your multiplier (the second number). For instance, if my problem were 12 times 47, I would draw two columns and two rows. Once you have drawn your rows and columns, write in the digits of your numbers and bisect (that means to split) your cells diagonally, from the top right to the bottom left. You will use each half of each cell for a specific purpose. The upper left half of each cell is used to hold the tens place of each multiplied number. The lower right half of each cell is used to hold the ones place of each multiplied number. To get your answer, multiply each digit on top (your multiplicand) by each digit in your multiplier (right side). Start by using the top rightmost digit of the multiplier. Remember that the tens values are placed in the upper left portion of each cell, and the ones values are placed in the lower right portion of each cell. Once you have multiplied all digits together, your lattice is full, and it is time to find your product. To find the product, add diagonally from the right to the left, and be sure to carry when necessary. Your product will be read from the left edge and bottom edge of the lattice. Give it a try! 

Here's a short video that explains how to use the Multiplication Tool to multiply using the partial products method. You may also view a schematic of how the tool works. 