I have always been fascinated by languages. Being able to switch seamlessly between languages has always seemed like the coolest, most useful skill to me. Earlier this year I was thinking about the idea of counting in other languages, specifically counting in languages that are not base-10. Counting 1, 2, 3, … 8, 9, 10 and then starting again 11, 12, is something that we take for granted but several languages do this really differently. Super cool!
The task I assigned the students comes directly after some time spent on logarithms and logarithmic scale. I got the idea to do a linguistics, number-word task because they both have to do with bases. I also thought this would be a good, less-algebraic precursor to modular arithmetic.
I first gave the students a passage from The Crest of the Peacock, Non-European Roots of Mathematics that outlines four different types of number systems. This includes our base-10 system, and the illustrated body numbers I took a picture of out of the book:
As one of the students pointed out, if you wanted to say you were 17, you’d say “I’m neck years old,” which is totally how that worked.
Then they were asked to fill out a blank Pascal’s Triangle, where all the outside numbers are 1’s, and each number is the result of adding the two numbers above it:
So all the boxes on the outside are 1’s, and the box below the 1 and 2 would be 3, and so would the other one like that. What numbers come next?! ARE YOU HAVING FUN YET?!
Sidenote, I wrote a whole Pascal’s Triangle task for one of my other classes, and that was awesome too.
They compared their Pascal’s Triangle to an Ancient Chinese Pascal’s Triangle I found in order to understand Chinese numerals. There is a whole part of the book that’s about Ancient China that has the exact same graphic of the Pascal’s Triangle. I’m giving it to my one student who is way ahead and completely done to read tomorrow. The number 9 is nowhere on the Chinese triangle, but it does go all the way to 8, and 10’s on there, so I asked them to figure it out. These are the important pattern recognition skills that humans need in life! This is what the Common Core means by “look for and make use of structure”!
Then here’s the next part of the task. It’s a partially filled-in chart of number words in Ventureno, part of the now-extinct family of Native Chumashan languages spoken in present-day California. Students once again had to “look for and make use of structure”:
Can you figure it out? They had a pretty hard time with this because it’s not as strong a pattern as some of them.
I’m so excited about this task, and if there were an award for “activity you would have most wanted to do in high school,” I would totally nominate myself. I’ll be back with more dispatches soon, I’m trying to blog the most out the rest of the academic school year.