If it were structured, we'd have daily tasks such as:
- Determine the area needed to be painted.
- Determine how much paint will be needed.
- How much will it cost?
From there, I can branch out and give them alternate scenarios and link to other, similar problems (making a patio, etc.).
If it were student-driven, it would basically be:
You are being considered as a contractor for Sabine Parish School Board for the job of painting Mr. Morris's classroom walls. Please submit a completed bid, no later than Friday, that includes the following information: cost of materials (including calculations), estimated hours to completion, number and name of workers, hourly rate, and total amount you will charge.From there, I would let them loose to work at their own pace. After they have completed this and made any necessary corrections, I can give them other problems relating to these skills and buy the paint of their choosing. Once they start painting, I can have them re-estimate time to completion and relate that to linear equations, including graphing. At any point, I can jump in and help, or jump in and enrich, giving harder scenarios (paint the outside of the school, etc.). I would interrupt them and make them solve the same thing different ways or apply what they have learned to other applications. I can have them predict (and validate their predictions) who is going to finish first between the groups and at what point one group will overtake another (systems). Through all of this, they will get percents; ratios; proportions; unit rates; unit conversion; writing expressions; writing, graphing, and solving linear equations and inequalities; writing, graphing, and solving systems of linear equations and inequalities; various aspects of measurement; and statistics.
I'm sure you can tell toward which way I am leaning.
One of the problems with letting them run amok is that they are severely lacking. I attempted to do Dan Meyer's three-act about time it takes light to get to the moon with them last month. It took two weeks. I kept having to backtrack to add scaffolding, which is fine and enjoyable, but I'm worried about how that will go here. For example, two students didn't know how many minutes there were in an hour. That was a smack in the face. I was asking kids to "go for it" and figure out how long it takes light to travel to the moon and they didn't even know how many minutes there were in an hour. I don't want to group by ability level and have the weaker group get discouraged by falling behind, though I could arrange it to where their group has the easiest portion to figure out. But I also don't want to have mixed groups where the lost stay lost and the ones who pick it up do all of the work.
Ideas?
Thanks for reading my rant about algebra. I've been sitting on it for a while. I actually also became an accidental math minor. I was a history and Japanese major, but kept taking math on the side because it was fun. I looked up senior year and realized I had enough credits for a major! I didn't want to take the comprehensive exams though so went for a minor.
ReplyDeleteFor your wall project, I would suggest that you break it down into mini-skills. Introduce the whole exploratory project to get them excited about it, but then conquer a skill each day (or each two days) as a whole class. Do a traditional lesson on, say, calculating the area of irregular shapes, give them some practice problems that they're used to (kids know how to fill out worksheets! and as much as we may hate them as teachers, kids find the structure comforting) then give them the second half of class or the next day to explore how to apply their new knowledge to the wall task. Once they've figured out that chunk, give them a new mini-lesson on the next skill (say taking an area and determining what fraction of a gallon of paint they'll need). Chunking it like this may help the kids feel like they have structure and they understand what's being asked of them and how to do it, while still giving them creative reign over the project as a whole.
This is just a suggestion though- it all depends on your students. Some groups of kids I've taught would LOVE the open ended plan you suggest above, but my weaker students prefer structure and tasks in formats they're used to. I'm also not great at managing a classroom, so the only way I can do it is by instilling a lot of structure in my tasks and you may not have this difficulty or this need.
Those are some good ideas to ponder. It's definitely going to take some more thinking. I might work on it until through Christmas break and begin it after...
ReplyDeleteI will have 4 teams of 4 and could always let some groups go open ended while others were taught. I was kind of hoping to use the open-ended, student-driven learning to create the basis and hook needed to relate the ideas to "math on paper".