Eric the Sheep


This week, the last week of instruction, my classes are completing portfolio and working on the Eric the Sheep problem.


I’m really enjoying another opportunity to run my class how I want to run it next year (all the time!). We started by brainstorming problem-solving methods. Then I asked if anyone knew anything about sheep shearing and showed an illustrative youtube video. I’m not sure how legit a use of technology that was, but it definitely helped hook students into the problem. We are 3 days away from the last day of classes and while a few students complained about doing work, zero (zero!) asked why they had to do this problem/what it had to do with real life. I think because it’s such a rich task (not because 100% of my students will one day be shearers/barbers). Here’s what students WERE saying …

“Ms. Langer, I need a way to figure out the answer without using chips!”
“We tried that rule too, like that exact rule, but it didn’t work for the first question, and any rule you make for a pattern has to work all the time.”
“She can’t watch this video; she’s vegetarian!”
“Why do you guys like goats and sheep so much!?”
“It’s not 18; it’s 16. Look!” (Actually, “it” was 17 … ;))
“You take all the time you need …” (A student who accurately answered the last step, which we had sloppily answered. Whoops/great!)
“I don’t want to draw 50 circles!”
“Wait, I didn’t understand what you just said about why I am wrong; can you say it again?”

AND I get to practice better discussions. Awesome. I tried to follow some of my discussion checklist for the discussion.  I had two goals: comparing representations of the pattern and generalizing. I had looked at the students’ work and had a trajectory/few ideas I wanted to surface (Why do you round up after dividing? What’s the connection between the groups who divided by 3 and the group that subtracted 3 repeatedly?). I didn’t choose a student to lead the discussion because that’s not a practice in my class this year, but I did have students present and they ended up taking over the conversation from me whenever I tried to direct things too much (sweetness).  Some questions I was left with included …

– How to deal with everyone writing up their math work but not everyone presenting. It seems much more authentic to write up your work neatly so that you are prepared to share your thinking with others (as opposed to writing it up b/c the teacher told you). And indeed, we did some really good talking and looking at each others’ work. But, I had everyone write up their thinking, and only some of the groups presented (some groups’ ideas overlapped/were incredibly similar). How did the students feel who wrote up their work but didn’t present, only participated in the discussion? (I guess I should ask them!) Would it work to have a norm of everyone writes up their math work so they’re ready to present/participate in discussion; not everyone will always “present,” but everyone will always participate?

– I HAVE TO worry less about content. I think worry less philosophically, but in the moment of class, I keep wanting to steer the discussion towards the generalized rule. I wanted to interrupt students who were inaccurately explaining why you round up. But really, the students were handling the discussion fine (and asking genuine questions), and I just needed to chill out!

Overall, super excited for next year, lots of problem-based learning, more discussions, more time on rich tasks, and less worry about content.



4 thoughts on “Eric the Sheep

  1. Love this problem set up. What age group/course level group was working on this? Did they ask for prompts about how long the line is? This reminds me a bit of the frog climbing up the wall of the well and sliding down some each night. I cannot decide whether the search for generalization is always a positive thing. I think it is, but I also think that I wish that this was not our instinct all the time.

    • This is 9th grade Algebra 1. At least in Algebra, I do feel committed to generalizing since if we didn’t generalize, we’d largely lose all the Algebra. But I don’t think I need to stress about it so much! And the problem included questions about different numbers of sheep in front of Eric before asking what if there were any number of sheep. It’d be cool to just give the prompt and see what happened sometime …

  2. Cool! I adapted this today for a multi-age math class (8 to 13 year-olds). I gave them some info about the sheep-shearing and asked them to write their own problems. They did some ingenious work. My favorite questions was this one.

    “If Shawn, who started at number 34, skips one sheep every time the shearer takes a sheep, who arrives to the front of the line first, Shawn or Eric?”

    See for the rest of the questions.

    • That’s awesome! You know, I’ve been wondering a lot how to get students re-used to asking questions after 9 years in public school. Next year, I’ll definitely try giving a prompt and asking students to write their own questions. Then maybe I can work from there towards more genuine questions from students. Thanks for the comment!

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