Napier's Bones-Lattice Multiplication: A Viable Alternative

John Napier's Bones,  www.17centurymaths.com  

Way to go, blog!  You carried on valiantly without me!  And now I'm back, ready to take you off auto-pilot.

Hello friends!  It's good to be back.

Today, I'm sharing what I believe to be a lifesaver for your students who just don't understand the traditional multiplication algorithm.


Common Core states that all students must be able to multiply (at least) 2-digit numbers, using the traditional algorithm by the end of 5th grade. (5.NBT.5) I'm here to argue the case for a viable alternative, Lattice Multiplication.

Every year, I had 6th graders arrive in my class not understanding the traditional multiplication algorithm.  So every year, very close to the first day of school, I taught Napier’s Bones, Lattice Multiplication  to my entire class, whether they understood the regular algorithm or not.  It’s always good to have a choice.   

I did it for a couple reasons.  It was easier for students to spot mistakes, either in their multiplication or addition, because we were multiplying one-digit factors and simply adding the columns.  It empowered kids that felt like failures when they just couldn’t get the traditional way of multiplying multi-digit numbers. Spatial learners really picked it up quickly!  I actually had a student go home and teach lattice to her father.  He was excited because he told her he never understood the traditional algorithm. (I always cringed when parents, at conference time, would profess, "I was never good at math".)

Lattice in a nutshell.

During morning math warmups, I allowed them to use whichever method worked for them. Those formerly liking the traditional method made more mistakes and had a difficult time finding them.  Frequently, even those students chose "Napier's Bones".

  
While it's fun to try the actual "bones," using that type of manipulative wouldn't be allowed in a testing situation, so lattice is a logical alternative.  Place value  explanation looks a little different, but it’s there and I would expect students to be able to explain it.

The way I see it, the goal is to have all kids understanding how multiplication works.  We encourage them to work problems different ways, as long as they're able to explain it and the math is sound.  If they can explain this algorithm, and increase their accuracy, along with building their math confidence, it should be an acceptable alternative to the traditional algorithm.  As they move forward in their math careers, they’ll use calculators for the larger problems, as multiplying will only be part of the process and not necessarily the end product (no pun intended :) ).

How many of you have used Napier's Bones- Lattice Multiplication with your students?  Give it a try. I think you'll like the results!

"There is nothing so troublesome to mathematical practice ... than multiplications, divisions, square and cubical extractions of great numbers ... I began therefore to consider ... how I might remove those hinderances."  John Napier, scientist