Today, I met the Yekttis.
While our intention today was to plan for the lesson after these crazy, fabled, Investigations characters, this activity quickly became the center of our conversation. It seemed the more we talked, the more tangled we got in our own thinking around the math itself, in addition to how to pose the activity to students and what questions to ask as they sorted. It felt like wording was a big deal here. How were we using the words: attribute, category, rule? Were they interchangeable? Would they make a difference in the way student thought about it? Do they make a difference in how we think about it? What is this mathematically and where is it going? While I was planning with three other teachers, only one of the teachers had taught this lesson before and she expressed how difficult it was for students once they were asked to sort based on two rules. We were ready to rethink the whole thing and kept asking ourselves if it was worth what the students would get out of it. But, because of all the questions and confusion in our own thinking, we were really intrigued to see how students would think about it.
Feeling a little like I jumped into the middle of a series of lessons, the teachers were great about filling me in on the students’ work prior to this activity. They had played a game called “Guess My Rule” which I was knew from 5th grade. In this activity, the teacher secretly chooses a rule, points out a few students who fit the rule, others who do not, and students try to guess the rule used to sort. They were really successful with this and enjoyed it.
Now, enter the Yekttis. They are a bunch of cards like the ones above. They have different shaped faces, eyes, and antennae. We decided to give them some time to play with the Yektti cards today and ask them how we could sort the Yekttis. I am hoping Tara, Lauren, and Kristin comment on here so they can go into depth about what the students did because I had to be 5th grade while they taught this lesson. When I caught up with Lauren toward the end of the day to recap, she noticed that the students, at first, looked at sorting as organizing the Yekttis in patterns rather than by attributes. They finally got to what attributes they could use, but when asked if they could sort based on a second rule, they were stumped. They could say “has this, but not this” type of sorts, but were seeing that as two rules because they were creating two groups…the haves and the have nots. As her and I talked, we realized how difficult it was to ask students to sort by two rules vs only one.
Since I left school, I have been thinking about this and have reread the lesson (I will post that at the bottom, after my questions). To me, it feels really difficult for students to sort by two rules and create a Venn diagram based on that sort. Choosing the categories is the stickies part because up until this point, they have experience only choosing categories that are mutually exclusive.
I find the really cool part of this whole thing is students realizing what categories will have an overlap versus those that will not. For this reason, I don’t want to walk students through this, but I feel there are some questions to ask in the process that could be pretty important. This is where I am struggling. What do I ask that does not put the answer right in from of them or become just another process of representing data. My thought for tomorrow is to play Guess My Rule with the Yektiis. Put a few Yektti cards inside and outside of the circle and ask students what the rule could be. Once they guess the rule, I will label the circle and place the rest of the cards accordingly. Next, and this is the question I don’t know is the right one, I will ask “Is there another rule we can use to sort the Yekttis in our circle?” For example, I could choose “Has a Square Face” as my rule, we sort by placing all of the square faces in the circle and the others out. Now, let’s say the students say our second rule could be, “Has two antennae.” How do we proceed from here? Do I draw in the second circle that overlaps? Do I ask if the circles will overlap? Why does it then feel weird to then pull cards that were once outside of the circle back into the new circle?
After coming up this idea, I looked at the book to realize they handle it quite differently:
I don’t know how I feel about this and need to re-read it in the morning when I am not also thinking about a 3rd and 5th grade lesson for tomorrow! I feel it takes a bit of the “sorting power” out of the students hands? I would love any thoughts on this!