I was a math major in college and never heard of a method called lattice multiplication. Maybe because at that point we were all using calculators. Shabakh is a method of multiplication that uses a lattice, developed in India from the twelfth century onwards and seen in Hindu works. I apologize if you are already familiar with this method but I thought it was worth sharing especially for those with young children or if you are ever in a situation that you have to multiply two large numbers without a calculator. I just learned this method last week. Below are the steps but it will make more sense when I show you the example.
Step 1. Make a table the size of the numbers to be multiplied. For example, (22 x 45) would be a two by two table and (4,355 x 347) would be a four by three table.
Step 2. Draw diagonal line through each cell from the top right to the bottom left extending them below the bottom of the table.
Step 3. Write the numbers to be multiplied on the outside of the table
Step 4. Multiply each number that corresponds to its cell.
Step 5. Write the “tens” portion of the answer in the upper ½ of the cell and the “ones” portion in the lower ½ of the cell. If the number is less than 10 you can write “0” in the “tens” place or leave it blank.
Step 6. Repeat Step 5 for each cell
Step 7. Add the numbers within each diagonal and write answer below table within the extended diagonal lines. If the number is greater than 10 you have to carry it into the next set of diagonal lines to the left by writing the appropriate number 1 for 10, 2 for 20 etc…
Step 8. You answer is the numbers in diagonal written together.
Here is an example of: 278 x 24
This just demonstrates how cells are multiplied. Top right cell is 8×3=24. Notice where the 2 and 4 are written.
This last diagram has the full problem:
Let’s add the tens place value: 8+3+4=15. You write the 5 and carry the one.
Now let’s add the hundreds place value: 8+2+1+2 = 13, Then add the one that was carried to get 14 and again write 4 and carry the one again.
I hope you found this method as interesting as I did. One additional benefit of this method for young children is that parents can easily see where they made a multiplication mistake by looking within each cell. While this method probably goes against the grain of traditional teaching it is another tool at your or your children’s disposal. Additionally, it is a good method to go back and double-check your work.
