We use a variant of Steve Stephenson's counting board, which we call "button arithmetic" as an activity. Stephenson (since deceased) was a retired engineer turned high school teacher who got very interested in counting boards in the 2000s. He made some YouTube videos here:
Some of Stephenson's historical speculations are somewhat implausible, but it's fun to think about, or try to invent your own alternative ideas, and overall I think ancient calculation methods are underestimated by many modern scholars.
With my kids (now 9 and 6), we haven't bothered with Stephenson's floating-point-with-exponents system, but we do base ten arithmetic using horizontal lines for powers of ten and a vertical line to separate positive/negative. The space between two lines represents (as in medieval Europe) five times the previous power of ten.
I went to a fabric store and examined every type of button they had in bulk, then bought a bunch of my favorite type: some round metal ones, somewhat smaller than pennies, symmetrical on top/bottom, with a slightly domed shape that makes them much easier to pick up than coins. But pennies also work okay, as do carefully chosen beach pebbles.
I think counting boards are quite helpful for kids, a powerful and flexible tool that they can grow into. They can get started with it at age 3–4, before having the manual dexterity to write numerals.
https://www.youtube.com/playlist?list=PL545ABCC6BA8D6F44
and some web pages:
https://ethw.org/Ancient_Computers
https://web.archive.org/web/20170903104702/http://sks23cu.ne...
Some of Stephenson's historical speculations are somewhat implausible, but it's fun to think about, or try to invent your own alternative ideas, and overall I think ancient calculation methods are underestimated by many modern scholars.
With my kids (now 9 and 6), we haven't bothered with Stephenson's floating-point-with-exponents system, but we do base ten arithmetic using horizontal lines for powers of ten and a vertical line to separate positive/negative. The space between two lines represents (as in medieval Europe) five times the previous power of ten.
I went to a fabric store and examined every type of button they had in bulk, then bought a bunch of my favorite type: some round metal ones, somewhat smaller than pennies, symmetrical on top/bottom, with a slightly domed shape that makes them much easier to pick up than coins. But pennies also work okay, as do carefully chosen beach pebbles.
I think counting boards are quite helpful for kids, a powerful and flexible tool that they can grow into. They can get started with it at age 3–4, before having the manual dexterity to write numerals.