## Ratios of Areas Performance Tasks

21 Jun

On the performance task day for our unit on Geometric Measure and Dimension, we worked on Circles and Squares most of the block. With about 20 minutes remaining, we moved to Dan Meyer’s Three-Act Math Task Some Really Obscure Geometry Problem.

Students watched the first act and responded to a Quick Poll with their guesses about the percents.

Then they began to work.

I loved watching students use appropriate tools strategically. I purposefully had not given them a pre-made diagram. Some students chose to build the diagram to help make sense of the relationships between the regions, but not every student. Some students used their handheld as a calculating device for work they were doing on paper, but not every student.

I loved watching students look for and make use of structure.

The bell rang before we finished. I told students they could continue their work on the task for Problem Solving Points. No one did.

There was a comment on my post about Circles and Squares suggesting that the scaffolding provided by the questions from the Mathematics Assessment Project “shoehorned” students into one solution. It made me wonder whether I should have structured the class period differently.

If we had removed the questions from Circles and Squares, it would have taken longer. Some students might have gotten to the obscure geometry problem, but not all of them would have, and we would not have had the class time together looking at student estimates; the task would have played out differently had students just gone straight to calculating the ratios of the areas.

Last year, the reverse happened. We started with the obscure geometry problem, and that took the majority of the period, so we spent only a little time on the Circles and Squares task.

So what’s best in this situation? Providing a little guidance so that students can see both tasks? Or providing less guidance on one task? Or introducing both tasks at the beginning and giving teams a choice in which task they pursue first, culminating in class discussion about solutions to both? Or even discussing solutions to both the next day so that students have the option to spend some time on the tasks outside of class.

I don’t have answers … only questions. But maybe next year as the journey continues I’ll try introducing both tasks and giving students a choice …

### 2 responses to “Ratios of Areas Performance Tasks”

1. June 24, 2014 at 2:09 pm

I like the idea of letting them choose which one they want to work on first. Choice is important (I often give tests with a ‘7 choose A or B.’)
Then proceed with the 5 Practices. The Connect portion will make more sense to one group, but will tantalize the other group. Homework would be to work the other problem.
Since we can’t do it all, all of the time, this would be a hybrid where students worked synchronously/socialized in class and then individually at home. The next day could be a few randomly chosen presentations (more Select than Sequence) that are different from what has been presented. Conclude with a Connection ‘what strategies have we used yet again?’ ‘what concepts popped up yet again?’
[tech, grid paper, auxiliary] [symmetry, shearing, formulas]
I vacillate with giving them a blank sheet and a sheet with 6 diagrams. In this case, since the diagram is so simple, I lean towards the blank sheet.
Sadly, I will not be teaching Geometry next year, but hopefully the year after, so I need to keep this problem in my back pocket.

• June 24, 2014 at 6:16 pm

Yes – I love your sheet with 6 diagrams idea. I’m going to think about which tasks we use for which that might be helpful. Thanks for helping me think through this!