Has a math experience ever brought tears to your eyes in a good way? Have you ever felt goose-bumps while exploring a really great problem? Have you ever got caught up in the flow of problem solving with your peers or students?
Now, I am an emotional person, and people who know me won't be surprised, but this all happened to me again today!
Let's start at the beginning... Last year, I was in a math session in Vancouver lead by Jason To from Toronto. He is the most lovely person, by the way. He introduced us to a math task that would end up being my favourite, most authentic, engaging, learning experience... maybe even for all time, and forever and ever.
I'm not exaggerating! Here is a peek:
Already interested? Now, want to hear about what this is all about?
Here is the story, as shared by Jason and Michael Jacobs, and inspired by the students of Kaktovik:
In 1992, a group of middle-school students in Kaktovik, Alaska realized that the words they used in their language didn't match the Hindu Arabic number system that is commonly used around the world. So, they decided to create their own number system to go with their Inupiaq language.
Can you use the clues to determine the Kaktovik numbers from 1-20?
Now, I believe that any amazing math experience deserves to be done in a Thinking Classroom! Random groups of 2 or 3 at vertical non-permanent surfaces is just the key.
I have been so lucky to have had the chance to share this experience with hundreds of teachers and students; the excitement, flow, and joy gets me every time!
So, who can explore this problem? What grade do you think? What if I told you that the only grade I have yet to try it in is Kindergarten? I'm just waiting for an invite! Grades 1-12, and always an amazing experience. Plan for at least 45 minutes to an hour!
Here are some adults:
Here are some elementary and middle school students:
And, here is what happened with grade 1 students:
These grade 1s worked for 50 minutes straight, only to be interrupted for recess. There was so much engagement, excitement, and joy as they figured out the numbers. Some groups made it up to 16 and didn't want to stop. They are 5 and 6 years old. Note that I modified the clues.
It's amazing what kids can do when we give them opportunities to be challenged, to collaborate, to persevere!
Here are some hints (only if needed):
Make a list of numbers, then put the symbols beside them.
Show me the number with your fingers.
How do we make 6 if we know 5?
What could 10 be made of?
If we know 10, how could we make 11?
There is one clue that doesn't seem to work - ignore that one until the end.
Are there patterns that can be helpful to figure out the symbols that are missing?
They didn't just use their fingers, but also their toes.
It's not base 10!
Here are some extensions:
What other numbers can you figure out?
Can you go past 20?
How about 30? 39? 123? 444? 55.5?
Can you add with Kaktovik Numbers?
Can you subtract?
Multiply and divide?
This is only the beginning for this problem, because there are so many more beautiful pieces to explore. The number for 20 means "one complete person". The symbol for 0 is a person with their arms crossed over their head to signify that their is no counting happening. There is a video of students from Kaktovik explaining their symbols and their Inupiaq words for their numbers. There is an old newsletter explaining this beautiful creation. There is a converter site that will help you see how big of numbers you can build. There is even an article about Silicon Valley companies recognizing the Kaktovik Number System in some of their programs and software. Here is a link for a folder full of resources:
And, even more importantly, this is such a beautiful story of reclaiming pieces of language and culture, of creating belonging in a classroom, and of exploring something real and beautiful.
When was the last time math brought tears to your eyes in a good way?