Napier's Bones and Lattice Multiplication

When my sons were in elementary school, they learned to multiply using the lattice method. It upset some of the parents because they did not understand what their children were doing.

As a math teacher, I was curious. I had my son show me and then I did a bit of research. Napier was a bit quirky but he did have a great way to teach/learn math. These rods, sticks, or bones--I have read all 3 names--were at one time made from actual bones. Creepy to me but little boys do not seem to mind.

The lattice method of multiplying is such a simple method to use that my sons still use it. I have used the method to teach multiplication of polynomials to kids who were having trouble. What amazed me was that my sons could multiply 2 and 3 digit numbers almost from the first day.

The parents still don't like it. I even had a parent come to me at a freshman football game. She asked me to tell her son that he was doing his math wrong. I looked at him and asked, "Lattice method?" He said, "Yep." I had them both do a multiplication problem using their own method. They both got the same answer. I told her she should trust him to do it his way since it obviously worked.

I have made several sets of these sticks to help certain kids who were having trouble with their times tables. It is best if you can have the child fill in all the numbers since he/she will get more out of the process.

Materials:

Tongue depressors--I used the foam ones (craft store) but wood works too

Pen or marker--permanent is best

College ruled sheet of paper

Marking the Sticks

You need to divide each stick into 9 spaces with an extra space at the top for the stick number. I found the easiest way was to use every other line on a sheet of college ruled notebook paper. Wide ruled paper doesn't allow you enough divisions.

Once you have the 9 spaces, you need to divide each space with a diagonal line.

Save one stick. Divide it into the 9 sections but don't mark the diagonals. Number this stick from 1 to 9.

Adding the Numbers

This is the part where I would have the child (or class) work with me.

At the top of each stick, write a single digit--zero through 9. I made multiple sticks for each number. You can also put a different number at the top of the back side of each stick. Using the backs too will increase the usefulness of each rod without having to buy twice as many sticks if you are working with a whole class of second graders.

On each rod, you or the child need to write the multiples of the number in the spaces. A two digit number is written with the first digit before the diagonal and the second digit after the diagonal. A single digit multiple is written with a zero before the diagonal.

This process can take a while if you are having the child do the work. Exercise patience and don't take over. It is a good opportunity for a child to practice their math.

Using the Rods: 2 Digits Times 1 Digit

In order to use Napier's rods, you find the rods that make up the longer number. Lay them out side by side. Lay down the row number rod (mine is green). I used a second green rod to underline the row I was going to use.

My sons were taught to make a grid on their paper. The numbers from the sticks fill in the grid. Then you just have to add each diagonal row. If the sum is a 2 digit number, you carry the second digit to the next column just like usual.

Using the Rods

I have a few examples to get you started using your new non-electronic calculator. With practice, the computations get faster and my children draw the grid but do not need the rods. It is as easy or easier (depending on who you ask) as the method of multiplication that most of us were taught in school.