Some students wanted to try the much harder designs right away, but I told them to keep working on the simpler ones for a bit. One girl tried a hard one, anyway, and got stuck about halfway through. The halfway point was pretty by itself, though, so she was satisfied.
It was interesting to me to see the various ways the students tackled different designs once they understood the concept. Some students seemed to need the numbering system (1, 3, 5, 7, 9, 11, 13, 15 on the x-axis; 2, 4, 6, 8, 10, 12, 14, 16, starting at the TOP of the y-axis in this drawing). Others seemed to not need the numbers at all - just the idea that they needed the same number of points on each line; and they needed to connect points sequentially, starting at the beginning of one line and the end of the other line that was closest to the end of the first line.
The teacher also left some sample of line designs that students had done with yarn on cardboard. That was also inspiring for the kids.
It was a fun lesson.