Just finished up with one class making their own quads to find area.  I want to jot down some thoughts while I still have them!

This is what I assigned them:

Task #1:
1.  Cut one your first half-sheet of paper into a convex quadrilateral with only one right angle.
2.  Measure three sides of the quadrilateral and one angle (in addition to the right angle).
(Plan first - which sides/angle do you want to know?)
3.  On the back of your quadrilateral, list the measurements that you made.
4.  Find the area of the quadrilateral.

Task #2:
1.  Cut your second half-sheet into a convex quadrilateral with no right angles.
2.  Measure three sides and two angles.
(Plan first - which sides/angles do you want to know?)
3.  On the back of your quadrilateral, list the measurements that you made.
4.  Find the area of the quadrilateral.


My observations:
1.  Kids struggled with this more than I thought they would.  But it was a good struggle - I was watching them just sit and stare at their shapes and (hopefully) think about what measurements they needed.  They needed the moment to plan and didn't just jump in.
2.  A couple of kids finished up and I was able to spot some mistakes....
           1.  One girl used the Area = 1/2 absinC formula and thought it was the area of her whole quadrilateral.          (I couldn't figure out how she'd finished both tasks so quickly until I spotted her mistake.)
           2.  Another girl drew a diagonal through her quadrilateral and made two (incorrect) assumptions:
                 First, because one of the triangles had a right angle in it, it was automatically a 30-60-90.    Second, the angle that was intersected by the diagonal was automatically bisected.
           3.  The first boy who was done didn't find the area of the quadrilateral.  He found all sides/angles, but didn't do the area.  Then when he went back to compute the area he used Heron's formula instead of the one I mentioned earlier (which probably would've been easier).

I'm hoping that the kids having to do this planning and visualize how they're going to solve the problem of finding the area will help tomorrow when I give them the application problems.  Nevermind that hopefully we'll avoid making some of these silly mistakes, too!

After just this one class I'll consider this a success!  Thanks, Mimi!