Monday, August 14, 2017

The Mayan Number Activity

While I was living in Guatemala this summer, I was introduced to Mayan numbers. Mayan numbers are interesting because they are base 20 and they are written vertically.

I knew I wanted to use Mayan numbers for an activity in my algebra classes, but wasn't sure where to go with it. A code-breaking activity seemed like a natural fit, but what would the motivation be for breaking the code? And how could this activity reinforce mathematical thinking?

As I started thinking about the first day of class, I realized it could be cool to "introduce myself" to the students using Mayan numbers. There are always a few things students REALLY want to know about me. What if I gave them the most common questions about myself AND gave them the answer in Mayan code? I thought this would be a great way to reinforce my belief that the answer is the least important part of the problem, while also giving students a chance to get to know me.

I put the activity together, and was pretty happy with the results. I wrote questions that were interesting (my age, the number of tattoos I have). I also used Mayan numbers that were 'easy' to figure out like 6 and 7 while also giving Mayan numbers that were challenging like 25 and 38. Basically creating a low floor, high ceiling task. In Mayan numbers, 25 looks just like the number 6, except the 'dot' in 25 is much higher--in Mayan numbers the height represents place-value. I liked what I had, but something was missing.

So, like I also do when I get stuck, I reached out to two colleagues for their advice. One colleague had recently gone to a workshop with Dan Meyer where he talked about a Goldilocks Guess (too high, too low, and a range of numbers that might make sense). I realized this was the missing piece for this activity!

Welcome to My Class

I've never been the type of teacher to read the syllabus on the first day. But I usually spend about 20 minutes on classroom routines and norms and then 20 minutes on a get-to-know-you, non-math activity like "stand up if...". [At my school the first day of class has 49 minute periods]

This year, I skipped all that! As students walked in, I let them sit where they wanted. (This was NOT a problem at all, but I will admit, I was scared about self-seating).

There were about 10 minutes of procedural stuff I wanted to go over. I did that. Then I showed the students this slide.

Then I asked students to take the following cards out of the group folder and to give one card to each group member. (students sit in groups of 4).

First, I asked students to think to themselves about their card for one minute. I showed students the following slide.

Then, I asked students to talk to their partner. The purpose was twofold: introduce themselves to their partner and also start to compare the different cards. I showed them this slide and let them talk for about two minutes.

Finally, I had the students stand up and huddle as a team of 4. I asked students to share their card with their group members and then try to order the cards from least to greatest. I also told groups they could ask me one question to help break the code. I would NOT answer a question about the code, but I would answer a question they had in code. For example, if they wanted me to write their age in code, I would do that. Groups worked for about 10 minutes. And they had AMAZING conversations.

As students worked, my student teacher and I circulated to look for interesting student work and interesting (but not necessarily correct) student thinking. I want to shout out Ms. D, my student teacher, for finding AMAZING examples of student thinking and for warmly inviting students to come up to the front of the class to share their thinking on the first day of school!

Ms. D did the following:

  1. She first called up a female student that figured out that the bar represented five and the dot represented one. The student talked about the question her group asked Ms. D (how to write the number 13 in code) and how she thought backwards to figure out what the bar and dot represented.
  2. Ms. D then called up a male student that built on the previous work. He knew that a bar was five and a dot was one, but couldn't figure out what that "floating dot" represented, but he knew that the floating dot was significant. I gave him a shout out for sharing a point of confusion. Something students are scared to do on the first day of class! For my age, he knew that the lower part of the number was 18, but he also recognized that I'm not 18. He just couldn't quite get the floating dot. 
We paused as a class to talk about the floating dot. I gave students time to talk to their partner. I asked them: What could the floating dot represent? Is it important? As I circulated, I heard one student share that he thought the floating dot was a 20, but couldn't quite explain why besides given the context of the questions, 20 made sense. My other class thought the floating dot was 15 for the same reason. Another student talked to his partner about an "invisible line". Basically the vertical division that gives the number a place value.  As I called on students to share their thinking with the class, I could see the light bulbs going off around the room. Wow!! I couldn't have been happier with this rich class discussion ON THE FIRST DAY OF SCHOOL!! 

Once they put it all together, I showed them the answers. The bell rang. Students left. And Ms. D and I were very, very happy about our first day of class! :) 

1 comment:

  1. Thanks so much for sharing this Rick! What a fun first day! It sounds like a super cool activity. I have a mayan numbers activity I got from someone, and I'll try to send it if I find it. So fun to read all the details of how someone does a class.


The Identity Project: Photo Essay

Students just finished presenting their photo essays. This was the first summative unit project for the year-long, PBL-based EL course I am...