Napier’s bones are easier than slide rules,” my seven year old announced the other day. I had found extra-wide wooden craft sticks (popsicle sticks), shown him how to write the multiplication table on them, dividing the one’s digit from the ten’s digit with a diagonal line. Each stick contained the first ten multiples of one number. They could be arranged in various patterns and used to multiply.
For example, to multiply the numbers 524 by three a person would arrange three sticks in order: 5 2 and 4. Then you look down the list at the third multiples. Look at the two diagonal lines as creating triangles that join together into parallelograms. The numbers inside the parallelograms need to be added together to create the answer. In this case 1,572.
Reason #1. The process of making them allows a child to practice writing out the multiples of numbers.
Reason #2. By separating the ones and tens in the list of multiples, they help a child look for patterns. The stick for the multiples of nines will have the list 1 to 9 in one column of triangles and 9 to 1 on the other. Kids can look for patterns in the number of times a particular digit is repeated. How many times is each tens digit repeated in the multiples of 3? 4?
Reason #3. By making multi-digit multiplication quick and easy a child can practice it. I can hand my son the handful of sticks and assign him two questions to answer before we begin the rest of our math lesson.
Reason #4. It is a physical way to explore the place value system. If you think of the triangles as being “upper” and “lower” triangles. The lower triangle (on the right of a stick) represents whatever unit the stick itself is being used for, and the “upper” triangle represents groups of ten of those units. In the example I give here the four stick is representing ones, so the “upper” triangle with the one is going to be the extra passed up to be gathered with the six in the “lower” triangle of the two stick.
Reason #5. They lend themselves to games. Pick a stick, hide it and the rest and give off a few hints. “I have a stick that has only 0s and 5s in the lower triangles.” or “My stick has multiples of 8. Can you find another stick that contains the first four multiples of my stick?” or “The stick I’m holding has 24 on it but not 20 or 30. What is it?”