I had my students create a tower with a suspended 3 oz. cup that needed to be at least 3 inches above the bottom of the tower. We tested the tower's strength with pennies. I modified the worksheets from the boat activity to fit the tower activity. My students were given 20 non-bendable straws, 36" of masking tape, 36" of string, and a 3 oz. cup with holes punched in opposite sides. They could use scissors and rulers. No supplies were replenished. They loved the activity, although a few said they had done something like this previously.
Like others mentioned, I did debate working through the Problem Design Process first, however I used it as a discussion to walk my students through each step and we identified each part of the building tower lesson.