3/9 Napier’s Bone (or the calm before the storm)

I’ve delayed writing about last week’s Math Club session up as life in the form of the covid19 pandemic has disruptingly intruded.  By the end of last week we were basically in a locked down situation and I was scrambling to figure out how home school my own kids, work from home remotely and secure an adequate supply of toilet paper. At this point school won’t resume until at least April 24th and I suspect will in fact end up being cancelled for the year.  Several math related cancellations have occurred including the MathCounts State Tournament being cancelled, AIME I nearly being cancelled and the entire AMC competition series being put on hiatus.  In sum, most of my blog entries look to be more personal for the next few months.

So here’s a bittersweet recap of the last time I was able to meet. I had decided a few weeks earlier that I wanted to focus on Napier’s Bones   My initial inspiration was an upcoming MathJam   (Also moved online now)  focused on mechanical calculation. Napier’s Bones make for a neat arts and craft project on top of the mathematics involved and really only require pen, paper, a rulers, some tape to hold things still when creating them and a supply of tongue depressors.

Here’s my trial runs at home:

• Print out the template:  https://drive.google.com/file/d/1sBBL53RCmCOrL98Z7cSUFiLM6WC4dI0O/view

!

• Tape 10 Popsicle sticks or tongue depressors together and draw 9 equally spaced horizontal lines across them.
• Then carefully draw parallel slanted lines from the corners across the sticks as shown above.
• Finally fill in a regular multiplication table putting the 10’s digit in the upper triangle of each box and the one’s unit in the lower triangle.
• Untape the sticks so you can arrange them as you need.

You’re now good to go!   By combining the sticks in various combinations, you have a multiplication table at hand for arbitrary large numbers.  

I also brought several videos to show using them for more complicated operations: (complete with a charming Scottish youtuber)

This was a really easy  day to run. I basically projected the template set of bones on the document camera and slowly explained the construction process. Then I handed out Popsicle sticks and everyone became busy building. We had just enough time to try them out on a few problems and watch the videos on square roots. Overall, it was really enjoyable and a good demonstration of pre-calculator techniques. Perhaps also its something someone could do at home who’s stuck looking for something out of the ordinary to do.