The following is a reflection on a 3-Act task I modeled for an 8th grade teacher last week. The 3-Act is In-N-Out Burger from Robert Kaplinsky and the plan I followed I completely stole from the amazing @approx_normal ‘s blog post on her work with the same 3-Act with administrators last year.
This past Thursday was the day we agreed on to model the lesson. So, this group of 8th grade students, who have never even seen me before, are wondering who this guy is that’s about to teach their class. And, just as planned, they were giving me weird looks when I showed them the first cheeseburger picture and asked them what they noticed. I believe one of them even asked, “Are you a teacher?”
Fast forward through to the “What do you wonder?” piece and the questions were amazingly well thought:
- “How much weight would you gain if you at that whole thing (100×100 burger?)”
- “How much do the ingredients cost for it (100×100 burger)?”
- How much does it (100×100 burger) cost?
- “Why would someone order that (100×100 burger)?”
- “Did someone really order that (100×100 burger)?”
- “How long did it take to make the (100×100 burger?)”
There were just a couple more, and they all came up very quickly. The students were curious from the moment we started the lesson. They are still working on precision of language. The parentheses in their questions above denote that this phrase was not used in the question, but was implied by the students. We had to ask what “it” or “that” was periodically throughout the lesson as they worked and as time went on, they did become more consistent.
The focus question chosen was:
- How much does it (the 100×100 burger) cost?
Students made estimates that ranged from $20 to $150. We discussed this briefly and decided that the cost of the 100 x 100 burger would be somewhere between $20 and $150, and many said it would be closer to $150 because “Cheeseburgers cost like $1.00, and double cheeseburgers cost like $1.50, so it’s got to be close to $150.” That’s some pretty sound reasoning for an estimate by a “low” student.
As students began Act 2, they struggled a bit. They weren’t used to seeking out information needed, but they persevered and decided that they needed to know how much a regular In-N-Out cheeseburger would cost, so I showed them the menu and they got to work.
I sat down with one group consisting of 2 boys (who were tossing ideas back and forth) and 1 girl (Angel) who was staring at the menu projected at the front of the room. She wasn’t lost. She had that look that says “I think I’ve got something.” So, I opened the door for her and asked her to share whatever idea she had that was in her head. She said, “Well, I think we need to find out how much just one beef patty and one slice of cheese costs, because when we buy a double double we aren’t paying for all of that other stuff, like lettuce and tomato and everything.” The boys chimed in: “Yeah.” I asked them how they would figure it out. Angel: “I think we could subtract the double-double and the regular cheeseburger. The boys, chimed in again: “Yeah, because all you get extra for the double double is 1 cheese and 1 beef.” “Well done, Angel!” You helped yourself and your group make sense of the problem and you helped create a strategy to solve this problem! Angel: (Proud Smile)!
We had to stop, since class time was over. Other groups were also just making sense of the idea that they couldn’t just multiply the cost of a cheeseburger by 100, since they didn’t think they should have to pay for all of the lettuce, tomato, onion, etc.
They came back on Friday ready to go. They picked up their white boards and markers and after a quick review of the previous day’s events and ah-ha moments, they got to work. Here is a sample after about 15 minutes:
Many groups had a similar answer, but followed different solution pathways. I wanted them to share, but I also wanted them to see the value in looking at other students’ work to learn from it. So I showed this group’s work (below-it didn’t have the post-its on it then. That’s next.). I asked them to discuss what they like about the group’s work and what might make it clearer to understand for anyone who just walked in the classroom.
Here’s what they said:
- I like how they have everything one way (top to bottom).
- I like how they have some labels.
- I’m not sure where the 99 came from. Maybe they could label that.
- Where’s the answer…
During this discussion, many groups did just what @approx_normal saw her administrators do when she did this lesson with them. They began to make the improvements they were suggesting for the work at the front of the room. It was beautiful. Students began to recognize that they could make their work better. After about 5 minutes, I asked the class to please take some post-its on the table and do a gallery walk to take a close look at other groups’ work. They were to look at the work and give the groups feedback on their final drafts of the work using these sentence starters (again, from @approx_normal – I’m a relentless thief!):
- I like how you. . .
- It would help me if you. . .
- Can you explain how you. . .
Some of the feedback (because the picture clarity doesn’t show the student feedback well):
- I like how you showed your work and labeled everything.
- I like how you broke it down into broke it down into separate parts.
- It would help me if you spaced it out better.
- I like how you explained your answer.
- It would help me if it was neater.
- I like how you explain your prices.
- I like how you wrote your plan.
- I like how you explain your plan.
- I like how you told what you were going to do.
- Can you explain how you got your numbers.
- I like how you wrote it in different colors.
- It would help me if you wrote a little larger.
Some samples with student feedback:
Not only was the feedback helpful to groups as they returned to their seats, it was positive. Students were excited to see what their peers wrote about their work.
Now for the best part! Remember Angel? As she was packing up to leave, I asked her if her brain hurt. She said, “No.” After a short pause she added, “I actually feel smart!” As she turned the corner to head to class, there was a faint, proud smile on her face. Score one for meaningful math lessons that empower students.
Please check out the websites I mentioned in this post. These are smart people sharing smart teaching practices that are best for students. We can all learn from them.