I was trying to refresh my memory of what Jill Gough has showed me about leveled assessments, and so I was searching her blog

Experiments in Learning by Doing. In that process, I came across a link she had to

this post from Function of Time, blogged by Kate Nowak. I was intrigued by the idea, and decided to try to adapt it to my classroom.

I teach three sections of Geometry this year, one freshmen and two sophomore. I chose to write an activity for Distance Formula using this self-check routine. With the help of my awesome student teacher, this year I've managed to make meaningful groupwork the norm in my classroom. So the students are used to a lot of the typical classroom rules of groupwork (ask each other before asking teacher, work with your own group rather than others, etc). I wouldn't recommend trying this on the first day of groups.

We've spent a few days applying Pythagorean theorem to triangle problems. The next task in our pacing calendar is to draw the tie to distance formula. I introduced the idea with a brief explanation showing we can calculate distance between points not on the same vertical or horizontal line by making those points endpoints of a segment corresponding to the hypotenuse of a right triangle whose legs are horizontal and vertical. I try to emphasize that the distance formula, littered with subscripts and pesky subtractions and additions and exponents and radicals, is really just the Pythagorean theorem, which my students all knew before they ever met me.

So, we worked a few problems together. Then I let them loose with their worksheets.

As Ms. Nowak describes, I had groupings of four students, four worksheets of graduated difficulty on differently colored paper, the colors posted in order on the board, with the checksum folded inside.

I gave the verbal instructions, as this task is a little different than other group tasks we've done. Each student is to do one problem per sheet. I asked them to write their name next to the problem they worked. When all four problems are finished, add the numerical answers and check it against the checksum on the whiteboard. My classroom calculators were made available to students who don't carry their own.

The orange and blue sheets had straightforward distance problems; orange with integers and blue with radicals. The green sheet gave distances and three of four coordinates, asking for the missing coordinate. The yellow sheet gave vertices of polygons and asked things about the underlying polygons.

Things didn't go so well for the first class. I noticed almost all groups started with the yellow (most difficult) sheet, and didn't make any progress. My suggestion they start with the orange (easier) met few results. When the period bell rang, no group had completed any entire single sheet.

For the second class, I began by only distributing the orange and blue sheets. As groups made progress, I gave them the green, and then the yellow. The second class is my freshmen (ninth grade) who typically have difficulty focusing on work. Even so, they made much better progress than the first group. I used the same distribution pattern for the third class, and they did the most work of all. Almost all the groups at least began work on the last sheet.

I really like the self-reliance aspect of this idea, and will use it again for future lessons. (My paper is Wausau Astrobrights, which I love.)

*** edit 6 April 2014 ***

a link to the

worksheets I used