Video: Napier's Bones

You can create:

• Your own ways of multiplying large numbers
• A collection of favorite historic ways of multiplying

How?

This activity is heavily based on web searches, though you could probably run it in a large library. To find various ways people multiply, search for "multiplication algorithms," or "alternative algorithms" and "multiplication", or "historical algorithms." Two good starting sites to search, maybe just for "multiplication," are Wikipedia and YouTube. Here are a few neat algorithms I found so far. You can easily spend an afternoon exploring each one. Figuring out why and how these work leads to pattern exploration, a.k.a. algebra.

• Napier's bones, a manipulative for using the lattice method
• Multiplying on Chinese abacus, or suanpan - though it's a good idea to learn counting on it first!
• Russian peasant multiplication method, based on doubling and halving. It has very little to do with either Russia or peasants, historically.
• Trachtenberg's System. Also check out the story of Jacow Trachteberg using math to stay sane in a Nazi concentration camp.
• Mental math: multiplying from left to right. This is a story of a professional magician. "One advantage of doing it left to right is that you can start saying your answer while you are still working", the magician says. Most adults who can do math well in their heads, even non-magicians, multiply left to right.
• ___ your method here!

Kids are great developers of algorithms, if adults are there to help them organize thoughts and write things down coherently. Simply ask your kids who do not yet know how to multiply large numbers to figure out the problem using any way they can. Tell them you expect this to take a long time, maybe half an hour for one multiplication problem. Use objects to count, pictures, or manipulatives such as number blocks or graph paper if you ever get stuck. Out of all multiplication models, arrays are probably easiest to work with. I am yet to meet a kid who could not develop his or her own way of multiplying, say, 27 by 31, from scratch, using only the knowledge of how multiplication works, and adult support and encouragement.

Why? Because this activity offers all people support in developing multiplication algorithms fitting their thinking styles best.

As you go

• Think of what you like and dislike in each algorithm. What in your psyche makes it so?
• Consider making a poster or a collage out of all algorithms you create or find

Higher and deeper

• Always ask the "Why?" question - the most important in math! In this case, exploring why algorithms work leads to patterns and algebra
• History of mathematics is a fascinating subject. For wonderful math*history activites, head to the Living Math site.